TSTP Solution File: SYN475-1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SYN475-1 : TPTP v8.1.0. Released v2.1.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n025.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 29 23:55:45 EDT 2022
% Result : Unsatisfiable 0.86s 0.78s
% Output : Proof 1.02s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.11 % Problem : SYN475-1 : TPTP v8.1.0. Released v2.1.0.
% 0.02/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33 % Computer : n025.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Mon Sep 5 04:24:04 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.33 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.33 Usage: tptp [options] [-file:]file
% 0.12/0.33 -h, -? prints this message.
% 0.12/0.33 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.33 -m, -model generate model.
% 0.12/0.33 -p, -proof generate proof.
% 0.12/0.33 -c, -core generate unsat core of named formulas.
% 0.12/0.33 -st, -statistics display statistics.
% 0.12/0.33 -t:timeout set timeout (in second).
% 0.12/0.33 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.33 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.33 -<param>:<value> configuration parameter and value.
% 0.12/0.33 -o:<output-file> file to place output in.
% 0.86/0.78 % SZS status Unsatisfiable
% 0.86/0.78 % SZS output start Proof
% 0.86/0.78 tff(c1_1_type, type, (
% 0.86/0.78 c1_1: $i > $o)).
% 0.86/0.78 tff(a1037_type, type, (
% 0.86/0.78 a1037: $i)).
% 0.86/0.78 tff(hskp19_type, type, (
% 0.86/0.78 hskp19: $o)).
% 0.86/0.78 tff(c0_1_type, type, (
% 0.86/0.78 c0_1: $i > $o)).
% 0.86/0.78 tff(a1008_type, type, (
% 0.86/0.78 a1008: $i)).
% 0.86/0.78 tff(c2_1_type, type, (
% 0.86/0.78 c2_1: $i > $o)).
% 0.86/0.78 tff(a1044_type, type, (
% 0.86/0.78 a1044: $i)).
% 0.86/0.78 tff(a1032_type, type, (
% 0.86/0.78 a1032: $i)).
% 0.86/0.78 tff(hskp17_type, type, (
% 0.86/0.78 hskp17: $o)).
% 0.86/0.78 tff(c3_1_type, type, (
% 0.86/0.78 c3_1: $i > $o)).
% 0.86/0.78 tff(ndr1_0_type, type, (
% 0.86/0.78 ndr1_0: $o)).
% 0.86/0.78 tff(hskp23_type, type, (
% 0.86/0.78 hskp23: $o)).
% 0.86/0.78 tff(hskp8_type, type, (
% 0.86/0.78 hskp8: $o)).
% 0.86/0.78 tff(a1003_type, type, (
% 0.86/0.78 a1003: $i)).
% 0.86/0.78 tff(hskp3_type, type, (
% 0.86/0.78 hskp3: $o)).
% 0.86/0.78 tff(a1040_type, type, (
% 0.86/0.78 a1040: $i)).
% 0.86/0.78 tff(hskp5_type, type, (
% 0.86/0.78 hskp5: $o)).
% 0.86/0.78 tff(hskp2_type, type, (
% 0.86/0.78 hskp2: $o)).
% 0.86/0.78 tff(a1002_type, type, (
% 0.86/0.78 a1002: $i)).
% 0.86/0.78 tff(hskp13_type, type, (
% 0.86/0.78 hskp13: $o)).
% 0.86/0.78 tff(hskp29_type, type, (
% 0.86/0.78 hskp29: $o)).
% 0.86/0.78 tff(a1001_type, type, (
% 0.86/0.78 a1001: $i)).
% 0.86/0.78 tff(hskp1_type, type, (
% 0.86/0.78 hskp1: $o)).
% 0.86/0.78 tff(hskp0_type, type, (
% 0.86/0.78 hskp0: $o)).
% 0.86/0.78 tff(a1023_type, type, (
% 0.86/0.78 a1023: $i)).
% 0.86/0.78 tff(a1000_type, type, (
% 0.86/0.78 a1000: $i)).
% 0.86/0.78 tff(hskp7_type, type, (
% 0.86/0.78 hskp7: $o)).
% 0.86/0.78 tff(a1045_type, type, (
% 0.86/0.78 a1045: $i)).
% 0.86/0.78 tff(hskp24_type, type, (
% 0.86/0.78 hskp24: $o)).
% 0.86/0.78 tff(a1010_type, type, (
% 0.86/0.78 a1010: $i)).
% 0.86/0.78 tff(a1005_type, type, (
% 0.86/0.78 a1005: $i)).
% 0.86/0.78 tff(a1006_type, type, (
% 0.86/0.78 a1006: $i)).
% 0.86/0.78 tff(hskp6_type, type, (
% 0.86/0.78 hskp6: $o)).
% 0.86/0.78 tff(a1041_type, type, (
% 0.86/0.78 a1041: $i)).
% 0.86/0.78 tff(hskp21_type, type, (
% 0.86/0.78 hskp21: $o)).
% 0.86/0.78 tff(hskp4_type, type, (
% 0.86/0.78 hskp4: $o)).
% 0.86/0.78 tff(a1004_type, type, (
% 0.86/0.78 a1004: $i)).
% 0.86/0.78 tff(a1043_type, type, (
% 0.86/0.78 a1043: $i)).
% 0.86/0.78 tff(a1052_type, type, (
% 0.86/0.78 a1052: $i)).
% 0.86/0.78 tff(hskp26_type, type, (
% 0.86/0.78 hskp26: $o)).
% 0.86/0.78 tff(a1048_type, type, (
% 0.86/0.78 a1048: $i)).
% 0.86/0.78 tff(hskp25_type, type, (
% 0.86/0.78 hskp25: $o)).
% 0.86/0.78 tff(a1026_type, type, (
% 0.86/0.78 a1026: $i)).
% 0.86/0.78 tff(hskp15_type, type, (
% 0.86/0.78 hskp15: $o)).
% 0.86/0.78 tff(hskp22_type, type, (
% 0.86/0.78 hskp22: $o)).
% 0.86/0.78 tff(hskp28_type, type, (
% 0.86/0.78 hskp28: $o)).
% 0.86/0.78 tff(a1033_type, type, (
% 0.86/0.78 a1033: $i)).
% 0.86/0.78 tff(1,assumption,(c2_1(a1044)), introduced(assumption)).
% 0.86/0.78 tff(2,plain,
% 0.86/0.78 (^[V: $i, U: $i] : refl((hskp17 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V))) <=> (hskp17 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V))))),
% 0.86/0.78 inference(bind,[status(th)],[])).
% 0.86/0.78 tff(3,plain,
% 0.86/0.78 (![V: $i, U: $i] : (hskp17 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp17 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 0.86/0.78 inference(quant_intro,[status(thm)],[2])).
% 0.86/0.78 tff(4,plain,
% 0.86/0.78 (![V: $i, U: $i] : (hskp17 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp17 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 0.86/0.78 inference(rewrite,[status(thm)],[])).
% 0.86/0.78 tff(5,plain,
% 0.86/0.78 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) <=> ((~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) <=> (((~c1_1(U)) | (~c2_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c1_1(U)) | (~c2_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c3_1(V)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V))) | c3_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c3_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c3_1(V)) | hskp17) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V))) | hskp17))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V))) | hskp17) <=> (hskp17 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c3_1(V)) | hskp17) <=> (hskp17 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))))),
% 0.86/0.78 inference(bind,[status(th)],[])).
% 0.86/0.78 tff(6,plain,
% 0.86/0.78 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c3_1(V)) | hskp17) <=> ![V: $i, U: $i] : (hskp17 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 0.86/0.78 inference(quant_intro,[status(thm)],[5])).
% 0.86/0.78 tff(7,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c3_1(V)) | hskp17)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause182')).
% 0.86/0.78 tff(8,plain,
% 0.86/0.78 (![V: $i, U: $i] : (hskp17 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 0.86/0.78 inference(modus_ponens,[status(thm)],[7, 6])).
% 0.86/0.78 tff(9,plain,
% 0.86/0.78 (![V: $i, U: $i] : (hskp17 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 0.86/0.78 inference(modus_ponens,[status(thm)],[8, 4])).
% 0.86/0.78 tff(10,plain,(
% 0.86/0.78 ![V: $i, U: $i] : (hskp17 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 0.86/0.78 inference(skolemize,[status(sab)],[9])).
% 0.86/0.78 tff(11,plain,
% 0.86/0.78 (![V: $i, U: $i] : (hskp17 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 0.86/0.78 inference(modus_ponens,[status(thm)],[10, 3])).
% 0.86/0.78 tff(12,plain,
% 0.86/0.78 (^[V: $i, U: $i] : refl((hskp8 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V))) <=> (hskp8 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V))))),
% 0.86/0.78 inference(bind,[status(th)],[])).
% 0.86/0.78 tff(13,plain,
% 0.86/0.78 (![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))),
% 0.86/0.78 inference(quant_intro,[status(thm)],[12])).
% 0.86/0.78 tff(14,plain,
% 0.86/0.78 (![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))),
% 0.86/0.78 inference(rewrite,[status(thm)],[])).
% 0.86/0.78 tff(15,plain,
% 0.86/0.78 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c2_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)))), ((((~c2_1(U)) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c2_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(V)))), ((((~c2_1(U)) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(V))))), (((((~c2_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c1_1(V)))), (((((~c2_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c1_1(V))))), ((((((~c2_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c1_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c1_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | (~c1_1(V)))), ((((((~c2_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | (~c1_1(V))))), (((((((~c2_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | (~c1_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | (~c1_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)))), (((((((~c2_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V))))), ((((((((~c2_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V))) | c2_1(V)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))), ((((((((~c2_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V))))), (((((((((~c2_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | hskp8) <=> (((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V))) | hskp8))), rewrite((((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V))) | hskp8) <=> (hskp8 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))), (((((((((~c2_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | hskp8) <=> (hskp8 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))))),
% 0.86/0.78 inference(bind,[status(th)],[])).
% 0.86/0.78 tff(16,plain,
% 0.86/0.78 (![V: $i, U: $i] : ((((((((~c2_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | hskp8) <=> ![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))),
% 0.86/0.78 inference(quant_intro,[status(thm)],[15])).
% 0.86/0.78 tff(17,axiom,(![V: $i, U: $i] : ((((((((~c2_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | hskp8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause158')).
% 0.86/0.78 tff(18,plain,
% 0.86/0.78 (![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))),
% 0.86/0.78 inference(modus_ponens,[status(thm)],[17, 16])).
% 0.86/0.78 tff(19,plain,
% 0.86/0.78 (![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))),
% 0.86/0.78 inference(modus_ponens,[status(thm)],[18, 14])).
% 0.86/0.78 tff(20,plain,(
% 0.86/0.78 ![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))),
% 0.86/0.78 inference(skolemize,[status(sab)],[19])).
% 0.86/0.78 tff(21,plain,
% 0.86/0.78 (![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))),
% 0.86/0.78 inference(modus_ponens,[status(thm)],[20, 13])).
% 0.86/0.78 tff(22,assumption,(~hskp23), introduced(assumption)).
% 0.86/0.78 tff(23,plain,
% 0.86/0.78 (^[U: $i] : refl((hskp23 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) <=> (hskp23 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))))),
% 0.86/0.78 inference(bind,[status(th)],[])).
% 0.86/0.78 tff(24,plain,
% 0.86/0.78 (![U: $i] : (hskp23 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp23 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 0.86/0.78 inference(quant_intro,[status(thm)],[23])).
% 0.86/0.78 tff(25,plain,
% 0.86/0.78 (![U: $i] : (hskp23 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp23 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 0.86/0.78 inference(rewrite,[status(thm)],[])).
% 0.86/0.78 tff(26,plain,
% 0.86/0.78 (^[U: $i] : trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp23) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp23))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp23) <=> (hskp23 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp23) <=> (hskp23 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))))),
% 0.86/0.78 inference(bind,[status(th)],[])).
% 0.86/0.78 tff(27,plain,
% 0.86/0.78 (![U: $i] : (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp23) <=> ![U: $i] : (hskp23 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 0.86/0.78 inference(quant_intro,[status(thm)],[26])).
% 0.86/0.78 tff(28,axiom,(![U: $i] : (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp23)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause138')).
% 0.86/0.78 tff(29,plain,
% 0.86/0.78 (![U: $i] : (hskp23 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 0.86/0.78 inference(modus_ponens,[status(thm)],[28, 27])).
% 0.86/0.78 tff(30,plain,
% 0.86/0.78 (![U: $i] : (hskp23 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 0.86/0.78 inference(modus_ponens,[status(thm)],[29, 25])).
% 0.86/0.78 tff(31,plain,(
% 0.86/0.78 ![U: $i] : (hskp23 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 0.86/0.78 inference(skolemize,[status(sab)],[30])).
% 0.86/0.78 tff(32,plain,
% 0.86/0.78 (![U: $i] : (hskp23 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 0.86/0.78 inference(modus_ponens,[status(thm)],[31, 24])).
% 0.86/0.78 tff(33,assumption,(hskp2), introduced(assumption)).
% 0.86/0.78 tff(34,plain,
% 0.86/0.78 (((~hskp2) | (~c1_1(a1002))) <=> ((~hskp2) | (~c1_1(a1002)))),
% 0.86/0.78 inference(rewrite,[status(thm)],[])).
% 0.86/0.78 tff(35,plain,
% 0.86/0.78 (((~c1_1(a1002)) | (~hskp2)) <=> ((~hskp2) | (~c1_1(a1002)))),
% 0.86/0.78 inference(rewrite,[status(thm)],[])).
% 0.86/0.78 tff(36,axiom,((~c1_1(a1002)) | (~hskp2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause127')).
% 0.86/0.78 tff(37,plain,
% 0.86/0.78 ((~hskp2) | (~c1_1(a1002))),
% 0.86/0.78 inference(modus_ponens,[status(thm)],[36, 35])).
% 0.86/0.78 tff(38,plain,
% 0.86/0.78 ((~hskp2) | (~c1_1(a1002))),
% 0.86/0.78 inference(modus_ponens,[status(thm)],[37, 34])).
% 0.86/0.78 tff(39,plain,
% 0.86/0.78 (~c1_1(a1002)),
% 0.86/0.78 inference(unit_resolution,[status(thm)],[38, 33])).
% 0.86/0.78 tff(40,plain,
% 0.86/0.78 (((~hskp2) | c0_1(a1002)) <=> ((~hskp2) | c0_1(a1002))),
% 0.86/0.78 inference(rewrite,[status(thm)],[])).
% 0.86/0.78 tff(41,axiom,((~hskp2) | c0_1(a1002)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause79')).
% 0.86/0.78 tff(42,plain,
% 0.86/0.78 ((~hskp2) | c0_1(a1002)),
% 0.86/0.78 inference(modus_ponens,[status(thm)],[41, 40])).
% 0.86/0.78 tff(43,plain,
% 0.86/0.78 ((~hskp2) | c0_1(a1002)),
% 0.86/0.78 inference(modus_ponens,[status(thm)],[42, 40])).
% 0.86/0.78 tff(44,plain,
% 0.86/0.78 ((~hskp2) | c0_1(a1002)),
% 0.86/0.78 inference(modus_ponens,[status(thm)],[43, 40])).
% 0.86/0.78 tff(45,plain,
% 0.86/0.78 ((~hskp2) | c0_1(a1002)),
% 0.86/0.78 inference(modus_ponens,[status(thm)],[44, 40])).
% 0.86/0.78 tff(46,plain,
% 0.86/0.78 ((~hskp2) | c0_1(a1002)),
% 0.86/0.78 inference(modus_ponens,[status(thm)],[45, 40])).
% 0.86/0.78 tff(47,plain,
% 0.86/0.78 ((~hskp2) | c0_1(a1002)),
% 0.86/0.78 inference(modus_ponens,[status(thm)],[46, 40])).
% 0.86/0.78 tff(48,plain,
% 0.86/0.78 ((~hskp2) | c0_1(a1002)),
% 0.86/0.78 inference(modus_ponens,[status(thm)],[47, 40])).
% 0.86/0.78 tff(49,plain,
% 0.86/0.78 ((~hskp2) | c0_1(a1002)),
% 0.86/0.78 inference(modus_ponens,[status(thm)],[48, 40])).
% 0.86/0.78 tff(50,plain,
% 0.86/0.78 (c0_1(a1002)),
% 0.86/0.78 inference(unit_resolution,[status(thm)],[49, 33])).
% 0.86/0.78 tff(51,assumption,(~ndr1_0), introduced(assumption)).
% 0.86/0.78 tff(52,plain,
% 0.86/0.78 ((ndr1_0 | (~hskp13)) <=> (ndr1_0 | (~hskp13))),
% 0.86/0.78 inference(rewrite,[status(thm)],[])).
% 0.86/0.78 tff(53,plain,
% 0.86/0.78 (((~hskp13) | ndr1_0) <=> (ndr1_0 | (~hskp13))),
% 0.86/0.78 inference(rewrite,[status(thm)],[])).
% 0.86/0.78 tff(54,axiom,((~hskp13) | ndr1_0), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause17')).
% 0.86/0.78 tff(55,plain,
% 0.86/0.78 (ndr1_0 | (~hskp13)),
% 0.86/0.78 inference(modus_ponens,[status(thm)],[54, 53])).
% 0.86/0.78 tff(56,plain,
% 0.86/0.78 (ndr1_0 | (~hskp13)),
% 0.86/0.78 inference(modus_ponens,[status(thm)],[55, 52])).
% 0.86/0.78 tff(57,plain,
% 0.86/0.78 (~hskp13),
% 0.86/0.78 inference(unit_resolution,[status(thm)],[56, 51])).
% 0.86/0.78 tff(58,plain,
% 0.86/0.78 (((~hskp29) | ndr1_0) <=> ((~hskp29) | ndr1_0)),
% 0.86/0.78 inference(rewrite,[status(thm)],[])).
% 0.86/0.78 tff(59,axiom,((~hskp29) | ndr1_0), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause1')).
% 0.86/0.78 tff(60,plain,
% 0.86/0.78 ((~hskp29) | ndr1_0),
% 0.86/0.78 inference(modus_ponens,[status(thm)],[59, 58])).
% 0.86/0.78 tff(61,plain,
% 0.86/0.78 ((~hskp29) | ndr1_0),
% 0.86/0.78 inference(modus_ponens,[status(thm)],[60, 58])).
% 0.86/0.78 tff(62,plain,
% 0.86/0.78 ((~hskp29) | ndr1_0),
% 0.86/0.78 inference(modus_ponens,[status(thm)],[61, 58])).
% 0.86/0.78 tff(63,plain,
% 0.86/0.78 ((~hskp29) | ndr1_0),
% 0.86/0.78 inference(modus_ponens,[status(thm)],[62, 58])).
% 0.86/0.78 tff(64,plain,
% 0.86/0.78 ((~hskp29) | ndr1_0),
% 0.86/0.78 inference(modus_ponens,[status(thm)],[63, 58])).
% 0.86/0.78 tff(65,plain,
% 0.86/0.78 ((~hskp29) | ndr1_0),
% 0.86/0.78 inference(modus_ponens,[status(thm)],[64, 58])).
% 0.86/0.78 tff(66,plain,
% 0.86/0.78 ((~hskp29) | ndr1_0),
% 0.86/0.78 inference(modus_ponens,[status(thm)],[65, 58])).
% 0.86/0.78 tff(67,plain,
% 0.86/0.78 ((~hskp29) | ndr1_0),
% 0.86/0.78 inference(modus_ponens,[status(thm)],[66, 58])).
% 0.86/0.78 tff(68,plain,
% 0.86/0.78 (~hskp29),
% 0.86/0.78 inference(unit_resolution,[status(thm)],[67, 51])).
% 0.86/0.78 tff(69,plain,
% 0.86/0.78 ((ndr1_0 | (~hskp23)) <=> (ndr1_0 | (~hskp23))),
% 0.86/0.78 inference(rewrite,[status(thm)],[])).
% 0.86/0.78 tff(70,plain,
% 0.86/0.78 (((~hskp23) | ndr1_0) <=> (ndr1_0 | (~hskp23))),
% 0.86/0.78 inference(rewrite,[status(thm)],[])).
% 0.86/0.78 tff(71,axiom,((~hskp23) | ndr1_0), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause7')).
% 0.86/0.78 tff(72,plain,
% 0.86/0.78 (ndr1_0 | (~hskp23)),
% 0.86/0.78 inference(modus_ponens,[status(thm)],[71, 70])).
% 0.86/0.78 tff(73,plain,
% 0.86/0.78 (ndr1_0 | (~hskp23)),
% 0.86/0.78 inference(modus_ponens,[status(thm)],[72, 69])).
% 0.86/0.78 tff(74,plain,
% 0.86/0.78 (~hskp23),
% 0.86/0.78 inference(unit_resolution,[status(thm)],[73, 51])).
% 0.86/0.78 tff(75,plain,
% 0.86/0.78 ((hskp29 | hskp23 | hskp13) <=> (hskp29 | hskp23 | hskp13)),
% 0.86/0.78 inference(rewrite,[status(thm)],[])).
% 0.86/0.78 tff(76,plain,
% 0.86/0.78 (((hskp29 | hskp23) | hskp13) <=> (hskp29 | hskp23 | hskp13)),
% 0.86/0.78 inference(rewrite,[status(thm)],[])).
% 0.86/0.78 tff(77,plain,
% 0.86/0.78 ((hskp29 | hskp23) <=> (hskp29 | hskp23)),
% 0.86/0.78 inference(rewrite,[status(thm)],[])).
% 0.86/0.78 tff(78,plain,
% 0.86/0.78 (((hskp29 | hskp23) | hskp13) <=> ((hskp29 | hskp23) | hskp13)),
% 0.86/0.78 inference(monotonicity,[status(thm)],[77])).
% 0.86/0.78 tff(79,plain,
% 0.86/0.78 (((hskp29 | hskp23) | hskp13) <=> (hskp29 | hskp23 | hskp13)),
% 0.86/0.78 inference(transitivity,[status(thm)],[78, 76])).
% 0.86/0.78 tff(80,axiom,((hskp29 | hskp23) | hskp13), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause31')).
% 0.86/0.78 tff(81,plain,
% 0.86/0.78 (hskp29 | hskp23 | hskp13),
% 0.86/0.78 inference(modus_ponens,[status(thm)],[80, 79])).
% 0.86/0.78 tff(82,plain,
% 0.86/0.78 (hskp29 | hskp23 | hskp13),
% 0.86/0.78 inference(modus_ponens,[status(thm)],[81, 75])).
% 0.86/0.78 tff(83,plain,
% 0.86/0.78 (hskp29 | hskp23 | hskp13),
% 0.86/0.78 inference(modus_ponens,[status(thm)],[82, 75])).
% 0.86/0.78 tff(84,plain,
% 0.86/0.78 (hskp29 | hskp23 | hskp13),
% 0.86/0.78 inference(modus_ponens,[status(thm)],[83, 75])).
% 0.86/0.78 tff(85,plain,
% 0.86/0.78 (hskp29 | hskp23 | hskp13),
% 0.86/0.78 inference(modus_ponens,[status(thm)],[84, 75])).
% 0.86/0.78 tff(86,plain,
% 0.86/0.78 (hskp29 | hskp23 | hskp13),
% 0.86/0.78 inference(modus_ponens,[status(thm)],[85, 75])).
% 0.86/0.78 tff(87,plain,
% 0.86/0.78 (hskp29 | hskp23 | hskp13),
% 0.86/0.78 inference(modus_ponens,[status(thm)],[86, 75])).
% 0.86/0.78 tff(88,plain,
% 0.86/0.78 (hskp29 | hskp23 | hskp13),
% 0.86/0.78 inference(modus_ponens,[status(thm)],[87, 75])).
% 0.86/0.78 tff(89,plain,
% 0.86/0.78 ($false),
% 0.86/0.78 inference(unit_resolution,[status(thm)],[88, 74, 68, 57])).
% 0.86/0.78 tff(90,plain,(ndr1_0), inference(lemma,lemma(discharge,[]))).
% 0.86/0.78 tff(91,plain,
% 0.86/0.78 (((~![U: $i] : (hskp23 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp23 | c1_1(a1002) | (~ndr1_0) | (~c0_1(a1002)) | (~c3_1(a1002)))) <=> ((~![U: $i] : (hskp23 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp23 | c1_1(a1002) | (~ndr1_0) | (~c0_1(a1002)) | (~c3_1(a1002)))),
% 0.86/0.78 inference(rewrite,[status(thm)],[])).
% 0.86/0.78 tff(92,plain,
% 0.86/0.78 ((hskp23 | (~ndr1_0) | c1_1(a1002) | (~c3_1(a1002)) | (~c0_1(a1002))) <=> (hskp23 | c1_1(a1002) | (~ndr1_0) | (~c0_1(a1002)) | (~c3_1(a1002)))),
% 0.86/0.78 inference(rewrite,[status(thm)],[])).
% 0.86/0.78 tff(93,plain,
% 0.86/0.78 (((~![U: $i] : (hskp23 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp23 | (~ndr1_0) | c1_1(a1002) | (~c3_1(a1002)) | (~c0_1(a1002)))) <=> ((~![U: $i] : (hskp23 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp23 | c1_1(a1002) | (~ndr1_0) | (~c0_1(a1002)) | (~c3_1(a1002))))),
% 0.86/0.78 inference(monotonicity,[status(thm)],[92])).
% 0.86/0.78 tff(94,plain,
% 0.86/0.78 (((~![U: $i] : (hskp23 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp23 | (~ndr1_0) | c1_1(a1002) | (~c3_1(a1002)) | (~c0_1(a1002)))) <=> ((~![U: $i] : (hskp23 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp23 | c1_1(a1002) | (~ndr1_0) | (~c0_1(a1002)) | (~c3_1(a1002)))),
% 0.86/0.78 inference(transitivity,[status(thm)],[93, 91])).
% 0.86/0.78 tff(95,plain,
% 0.86/0.78 ((~![U: $i] : (hskp23 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp23 | (~ndr1_0) | c1_1(a1002) | (~c3_1(a1002)) | (~c0_1(a1002)))),
% 0.86/0.78 inference(quant_inst,[status(thm)],[])).
% 0.86/0.78 tff(96,plain,
% 0.86/0.78 ((~![U: $i] : (hskp23 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp23 | c1_1(a1002) | (~ndr1_0) | (~c0_1(a1002)) | (~c3_1(a1002))),
% 0.86/0.78 inference(modus_ponens,[status(thm)],[95, 94])).
% 0.86/0.78 tff(97,plain,
% 0.86/0.78 (~c3_1(a1002)),
% 0.86/0.78 inference(unit_resolution,[status(thm)],[96, 90, 22, 50, 39, 32])).
% 0.86/0.78 tff(98,plain,
% 0.86/0.78 (^[V: $i, U: $i] : refl((hskp13 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V)) <=> (hskp13 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V)))),
% 0.86/0.78 inference(bind,[status(th)],[])).
% 0.86/0.78 tff(99,plain,
% 0.86/0.78 (![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V)) <=> ![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))),
% 0.86/0.78 inference(quant_intro,[status(thm)],[98])).
% 0.86/0.78 tff(100,plain,
% 0.86/0.78 (![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V)) <=> ![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))),
% 0.86/0.78 inference(rewrite,[status(thm)],[])).
% 0.86/0.78 tff(101,plain,
% 0.86/0.78 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c0_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) <=> (((~ndr1_0) | (~c0_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U))))), (((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c0_1(U))) | c3_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c0_1(U))) | c3_1(U)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))), (((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U))))), ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U))) | c1_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U))) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V))), ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V)))), (((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V)) | c2_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V))), (((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V)))), ((((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V)) | c3_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))), ((((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V)))), (((((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) | hskp13) <=> (((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V)) | hskp13))), rewrite((((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V)) | hskp13) <=> (hskp13 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))), (((((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) | hskp13) <=> (hskp13 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))))),
% 0.86/0.78 inference(bind,[status(th)],[])).
% 0.86/0.78 tff(102,plain,
% 0.86/0.78 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) | hskp13) <=> ![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))),
% 0.86/0.78 inference(quant_intro,[status(thm)],[101])).
% 0.86/0.78 tff(103,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) | hskp13)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause152')).
% 0.86/0.78 tff(104,plain,
% 0.86/0.78 (![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))),
% 0.86/0.78 inference(modus_ponens,[status(thm)],[103, 102])).
% 0.86/0.78 tff(105,plain,
% 0.86/0.78 (![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))),
% 0.86/0.78 inference(modus_ponens,[status(thm)],[104, 100])).
% 0.86/0.78 tff(106,plain,(
% 0.86/0.78 ![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))),
% 0.86/0.78 inference(skolemize,[status(sab)],[105])).
% 0.86/0.78 tff(107,plain,
% 0.86/0.78 (![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))),
% 0.86/0.78 inference(modus_ponens,[status(thm)],[106, 99])).
% 0.86/0.78 tff(108,plain,
% 0.86/0.78 (^[V: $i, U: $i] : refl((hskp19 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V))) <=> (hskp19 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V))))),
% 0.86/0.78 inference(bind,[status(th)],[])).
% 0.86/0.78 tff(109,plain,
% 0.86/0.78 (![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))),
% 0.86/0.78 inference(quant_intro,[status(thm)],[108])).
% 0.86/0.78 tff(110,plain,
% 0.86/0.78 (![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))),
% 0.86/0.78 inference(rewrite,[status(thm)],[])).
% 0.86/0.78 tff(111,plain,
% 0.86/0.78 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V))))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) | c1_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V))) | c3_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) | c1_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V))))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) | c1_1(V)) | c3_1(V)) | hskp19) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V))) | hskp19))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V))) | hskp19) <=> (hskp19 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) | c1_1(V)) | c3_1(V)) | hskp19) <=> (hskp19 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))))),
% 0.86/0.78 inference(bind,[status(th)],[])).
% 0.86/0.78 tff(112,plain,
% 0.86/0.78 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) | c1_1(V)) | c3_1(V)) | hskp19) <=> ![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))),
% 0.86/0.78 inference(quant_intro,[status(thm)],[111])).
% 0.86/0.78 tff(113,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) | c1_1(V)) | c3_1(V)) | hskp19)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause170')).
% 0.86/0.78 tff(114,plain,
% 0.86/0.78 (![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))),
% 0.86/0.78 inference(modus_ponens,[status(thm)],[113, 112])).
% 0.86/0.78 tff(115,plain,
% 0.86/0.78 (![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))),
% 0.86/0.78 inference(modus_ponens,[status(thm)],[114, 110])).
% 0.86/0.78 tff(116,plain,(
% 0.86/0.78 ![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))),
% 0.86/0.78 inference(skolemize,[status(sab)],[115])).
% 0.86/0.78 tff(117,plain,
% 0.86/0.78 (![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))),
% 0.86/0.78 inference(modus_ponens,[status(thm)],[116, 109])).
% 0.86/0.78 tff(118,plain,
% 0.86/0.78 (((~hskp2) | c2_1(a1002)) <=> ((~hskp2) | c2_1(a1002))),
% 0.86/0.78 inference(rewrite,[status(thm)],[])).
% 0.86/0.78 tff(119,axiom,((~hskp2) | c2_1(a1002)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause80')).
% 0.86/0.78 tff(120,plain,
% 0.86/0.78 ((~hskp2) | c2_1(a1002)),
% 0.86/0.78 inference(modus_ponens,[status(thm)],[119, 118])).
% 0.86/0.78 tff(121,plain,
% 0.86/0.78 ((~hskp2) | c2_1(a1002)),
% 0.86/0.78 inference(modus_ponens,[status(thm)],[120, 118])).
% 0.86/0.78 tff(122,plain,
% 0.86/0.78 ((~hskp2) | c2_1(a1002)),
% 0.86/0.78 inference(modus_ponens,[status(thm)],[121, 118])).
% 0.86/0.79 tff(123,plain,
% 0.86/0.79 ((~hskp2) | c2_1(a1002)),
% 0.86/0.79 inference(modus_ponens,[status(thm)],[122, 118])).
% 0.86/0.79 tff(124,plain,
% 0.86/0.79 ((~hskp2) | c2_1(a1002)),
% 0.86/0.79 inference(modus_ponens,[status(thm)],[123, 118])).
% 0.86/0.79 tff(125,plain,
% 0.86/0.79 ((~hskp2) | c2_1(a1002)),
% 0.86/0.79 inference(modus_ponens,[status(thm)],[124, 118])).
% 0.86/0.79 tff(126,plain,
% 0.86/0.79 ((~hskp2) | c2_1(a1002)),
% 0.86/0.79 inference(modus_ponens,[status(thm)],[125, 118])).
% 0.86/0.79 tff(127,plain,
% 0.86/0.79 ((~hskp2) | c2_1(a1002)),
% 0.86/0.79 inference(modus_ponens,[status(thm)],[126, 118])).
% 0.86/0.79 tff(128,plain,
% 0.86/0.79 (c2_1(a1002)),
% 0.86/0.79 inference(unit_resolution,[status(thm)],[127, 33])).
% 0.86/0.79 tff(129,plain,
% 0.86/0.79 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp19 | c1_1(a1002) | (~ndr1_0) | (~c0_1(a1002)) | c3_1(a1002) | (~c2_1(a1002)))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | hskp19 | c1_1(a1002) | (~ndr1_0) | (~c0_1(a1002)) | c3_1(a1002) | (~c2_1(a1002)))),
% 0.86/0.79 inference(rewrite,[status(thm)],[])).
% 0.86/0.79 tff(130,plain,
% 0.86/0.79 ((hskp19 | (~ndr1_0) | c1_1(a1002) | (~c2_1(a1002)) | (~c0_1(a1002)) | c3_1(a1002) | c1_1(a1002) | (~c0_1(a1002))) <=> (hskp19 | c1_1(a1002) | (~ndr1_0) | (~c0_1(a1002)) | c3_1(a1002) | (~c2_1(a1002)))),
% 0.86/0.79 inference(rewrite,[status(thm)],[])).
% 0.86/0.79 tff(131,plain,
% 0.86/0.79 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp19 | (~ndr1_0) | c1_1(a1002) | (~c2_1(a1002)) | (~c0_1(a1002)) | c3_1(a1002) | c1_1(a1002) | (~c0_1(a1002)))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp19 | c1_1(a1002) | (~ndr1_0) | (~c0_1(a1002)) | c3_1(a1002) | (~c2_1(a1002))))),
% 0.86/0.79 inference(monotonicity,[status(thm)],[130])).
% 0.86/0.79 tff(132,plain,
% 0.86/0.79 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp19 | (~ndr1_0) | c1_1(a1002) | (~c2_1(a1002)) | (~c0_1(a1002)) | c3_1(a1002) | c1_1(a1002) | (~c0_1(a1002)))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | hskp19 | c1_1(a1002) | (~ndr1_0) | (~c0_1(a1002)) | c3_1(a1002) | (~c2_1(a1002)))),
% 0.86/0.79 inference(transitivity,[status(thm)],[131, 129])).
% 0.86/0.79 tff(133,plain,
% 0.86/0.79 ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp19 | (~ndr1_0) | c1_1(a1002) | (~c2_1(a1002)) | (~c0_1(a1002)) | c3_1(a1002) | c1_1(a1002) | (~c0_1(a1002)))),
% 0.86/0.79 inference(quant_inst,[status(thm)],[])).
% 0.86/0.79 tff(134,plain,
% 0.86/0.79 ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | hskp19 | c1_1(a1002) | (~ndr1_0) | (~c0_1(a1002)) | c3_1(a1002) | (~c2_1(a1002))),
% 0.86/0.79 inference(modus_ponens,[status(thm)],[133, 132])).
% 0.86/0.79 tff(135,plain,
% 0.86/0.79 (hskp19),
% 0.86/0.79 inference(unit_resolution,[status(thm)],[134, 90, 50, 128, 39, 117, 97])).
% 0.86/0.79 tff(136,plain,
% 0.86/0.79 (((~hskp19) | (~c3_1(a1037))) <=> ((~hskp19) | (~c3_1(a1037)))),
% 0.86/0.79 inference(rewrite,[status(thm)],[])).
% 0.86/0.79 tff(137,plain,
% 0.86/0.79 (((~c3_1(a1037)) | (~hskp19)) <=> ((~hskp19) | (~c3_1(a1037)))),
% 0.86/0.79 inference(rewrite,[status(thm)],[])).
% 0.86/0.79 tff(138,axiom,((~c3_1(a1037)) | (~hskp19)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause100')).
% 0.86/0.79 tff(139,plain,
% 0.86/0.79 ((~hskp19) | (~c3_1(a1037))),
% 0.86/0.79 inference(modus_ponens,[status(thm)],[138, 137])).
% 0.86/0.79 tff(140,plain,
% 0.86/0.79 ((~hskp19) | (~c3_1(a1037))),
% 0.86/0.79 inference(modus_ponens,[status(thm)],[139, 136])).
% 0.86/0.79 tff(141,plain,
% 0.86/0.79 (~c3_1(a1037)),
% 0.86/0.79 inference(unit_resolution,[status(thm)],[140, 135])).
% 0.86/0.79 tff(142,plain,
% 0.86/0.79 (((~hskp19) | (~c1_1(a1037))) <=> ((~hskp19) | (~c1_1(a1037)))),
% 0.86/0.79 inference(rewrite,[status(thm)],[])).
% 0.86/0.79 tff(143,plain,
% 0.86/0.79 (((~c1_1(a1037)) | (~hskp19)) <=> ((~hskp19) | (~c1_1(a1037)))),
% 0.86/0.79 inference(rewrite,[status(thm)],[])).
% 0.86/0.79 tff(144,axiom,((~c1_1(a1037)) | (~hskp19)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause99')).
% 0.86/0.79 tff(145,plain,
% 0.86/0.79 ((~hskp19) | (~c1_1(a1037))),
% 0.86/0.79 inference(modus_ponens,[status(thm)],[144, 143])).
% 0.86/0.79 tff(146,plain,
% 0.86/0.79 ((~hskp19) | (~c1_1(a1037))),
% 0.86/0.79 inference(modus_ponens,[status(thm)],[145, 142])).
% 0.86/0.79 tff(147,plain,
% 0.86/0.79 (~c1_1(a1037)),
% 0.86/0.79 inference(unit_resolution,[status(thm)],[146, 135])).
% 0.86/0.79 tff(148,assumption,(hskp13), introduced(assumption)).
% 0.86/0.79 tff(149,plain,
% 0.86/0.79 (((~hskp13) | (~c1_1(a1023))) <=> ((~hskp13) | (~c1_1(a1023)))),
% 0.86/0.79 inference(rewrite,[status(thm)],[])).
% 0.86/0.79 tff(150,plain,
% 0.86/0.79 (((~c1_1(a1023)) | (~hskp13)) <=> ((~hskp13) | (~c1_1(a1023)))),
% 0.86/0.79 inference(rewrite,[status(thm)],[])).
% 0.86/0.79 tff(151,axiom,((~c1_1(a1023)) | (~hskp13)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause109')).
% 0.86/0.79 tff(152,plain,
% 0.86/0.79 ((~hskp13) | (~c1_1(a1023))),
% 0.86/0.79 inference(modus_ponens,[status(thm)],[151, 150])).
% 0.86/0.79 tff(153,plain,
% 0.86/0.79 ((~hskp13) | (~c1_1(a1023))),
% 0.86/0.79 inference(modus_ponens,[status(thm)],[152, 149])).
% 0.86/0.79 tff(154,plain,
% 0.86/0.79 (~c1_1(a1023)),
% 0.86/0.79 inference(unit_resolution,[status(thm)],[153, 148])).
% 0.86/0.79 tff(155,plain,
% 0.86/0.79 (((~hskp13) | c3_1(a1023)) <=> ((~hskp13) | c3_1(a1023))),
% 0.86/0.79 inference(rewrite,[status(thm)],[])).
% 0.86/0.79 tff(156,axiom,((~hskp13) | c3_1(a1023)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause64')).
% 0.86/0.79 tff(157,plain,
% 0.86/0.79 ((~hskp13) | c3_1(a1023)),
% 0.86/0.79 inference(modus_ponens,[status(thm)],[156, 155])).
% 0.86/0.79 tff(158,plain,
% 0.86/0.79 ((~hskp13) | c3_1(a1023)),
% 0.86/0.79 inference(modus_ponens,[status(thm)],[157, 155])).
% 0.86/0.79 tff(159,plain,
% 0.86/0.79 ((~hskp13) | c3_1(a1023)),
% 0.86/0.79 inference(modus_ponens,[status(thm)],[158, 155])).
% 0.86/0.79 tff(160,plain,
% 0.86/0.79 ((~hskp13) | c3_1(a1023)),
% 0.86/0.79 inference(modus_ponens,[status(thm)],[159, 155])).
% 0.86/0.79 tff(161,plain,
% 0.86/0.79 ((~hskp13) | c3_1(a1023)),
% 0.86/0.79 inference(modus_ponens,[status(thm)],[160, 155])).
% 0.86/0.79 tff(162,plain,
% 0.86/0.79 ((~hskp13) | c3_1(a1023)),
% 0.86/0.79 inference(modus_ponens,[status(thm)],[161, 155])).
% 0.86/0.79 tff(163,plain,
% 0.86/0.79 ((~hskp13) | c3_1(a1023)),
% 0.86/0.79 inference(modus_ponens,[status(thm)],[162, 155])).
% 0.86/0.79 tff(164,plain,
% 0.86/0.79 ((~hskp13) | c3_1(a1023)),
% 0.86/0.79 inference(modus_ponens,[status(thm)],[163, 155])).
% 0.86/0.79 tff(165,plain,
% 0.86/0.79 (c3_1(a1023)),
% 0.86/0.79 inference(unit_resolution,[status(thm)],[164, 148])).
% 0.86/0.79 tff(166,plain,
% 0.86/0.79 (((~![U: $i] : (hskp23 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp23 | c1_1(a1023) | (~ndr1_0) | (~c0_1(a1023)) | (~c3_1(a1023)))) <=> ((~![U: $i] : (hskp23 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp23 | c1_1(a1023) | (~ndr1_0) | (~c0_1(a1023)) | (~c3_1(a1023)))),
% 0.86/0.79 inference(rewrite,[status(thm)],[])).
% 0.86/0.79 tff(167,plain,
% 0.86/0.79 ((hskp23 | (~ndr1_0) | c1_1(a1023) | (~c3_1(a1023)) | (~c0_1(a1023))) <=> (hskp23 | c1_1(a1023) | (~ndr1_0) | (~c0_1(a1023)) | (~c3_1(a1023)))),
% 0.86/0.79 inference(rewrite,[status(thm)],[])).
% 0.86/0.79 tff(168,plain,
% 0.86/0.79 (((~![U: $i] : (hskp23 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp23 | (~ndr1_0) | c1_1(a1023) | (~c3_1(a1023)) | (~c0_1(a1023)))) <=> ((~![U: $i] : (hskp23 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp23 | c1_1(a1023) | (~ndr1_0) | (~c0_1(a1023)) | (~c3_1(a1023))))),
% 0.86/0.79 inference(monotonicity,[status(thm)],[167])).
% 0.86/0.79 tff(169,plain,
% 0.86/0.79 (((~![U: $i] : (hskp23 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp23 | (~ndr1_0) | c1_1(a1023) | (~c3_1(a1023)) | (~c0_1(a1023)))) <=> ((~![U: $i] : (hskp23 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp23 | c1_1(a1023) | (~ndr1_0) | (~c0_1(a1023)) | (~c3_1(a1023)))),
% 0.86/0.79 inference(transitivity,[status(thm)],[168, 166])).
% 0.86/0.79 tff(170,plain,
% 0.86/0.79 ((~![U: $i] : (hskp23 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp23 | (~ndr1_0) | c1_1(a1023) | (~c3_1(a1023)) | (~c0_1(a1023)))),
% 0.86/0.79 inference(quant_inst,[status(thm)],[])).
% 0.86/0.79 tff(171,plain,
% 0.86/0.79 ((~![U: $i] : (hskp23 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp23 | c1_1(a1023) | (~ndr1_0) | (~c0_1(a1023)) | (~c3_1(a1023))),
% 0.86/0.79 inference(modus_ponens,[status(thm)],[170, 169])).
% 0.86/0.79 tff(172,plain,
% 0.86/0.79 (~c0_1(a1023)),
% 0.86/0.79 inference(unit_resolution,[status(thm)],[171, 90, 22, 165, 154, 32])).
% 0.86/0.79 tff(173,plain,
% 0.86/0.79 (((~hskp13) | (~c2_1(a1023))) <=> ((~hskp13) | (~c2_1(a1023)))),
% 0.86/0.79 inference(rewrite,[status(thm)],[])).
% 0.86/0.79 tff(174,plain,
% 0.86/0.79 (((~c2_1(a1023)) | (~hskp13)) <=> ((~hskp13) | (~c2_1(a1023)))),
% 0.86/0.79 inference(rewrite,[status(thm)],[])).
% 0.86/0.79 tff(175,axiom,((~c2_1(a1023)) | (~hskp13)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause110')).
% 0.86/0.79 tff(176,plain,
% 0.86/0.79 ((~hskp13) | (~c2_1(a1023))),
% 0.86/0.79 inference(modus_ponens,[status(thm)],[175, 174])).
% 0.86/0.79 tff(177,plain,
% 0.86/0.79 ((~hskp13) | (~c2_1(a1023))),
% 0.86/0.79 inference(modus_ponens,[status(thm)],[176, 173])).
% 0.86/0.79 tff(178,plain,
% 0.86/0.79 (~c2_1(a1023)),
% 0.86/0.79 inference(unit_resolution,[status(thm)],[177, 148])).
% 0.86/0.79 tff(179,plain,
% 0.86/0.79 (^[U: $i] : refl((hskp7 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U))) <=> (hskp7 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U))))),
% 0.86/0.79 inference(bind,[status(th)],[])).
% 0.86/0.79 tff(180,plain,
% 0.86/0.79 (![U: $i] : (hskp7 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp7 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)))),
% 0.86/0.79 inference(quant_intro,[status(thm)],[179])).
% 0.86/0.79 tff(181,plain,
% 0.86/0.79 (![U: $i] : (hskp7 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp7 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)))),
% 0.86/0.79 inference(rewrite,[status(thm)],[])).
% 0.86/0.79 tff(182,plain,
% 0.86/0.79 (^[U: $i] : trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) <=> ((~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) <=> (((~c1_1(U)) | (~c2_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c1_1(U)) | (~c2_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | hskp7) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U))) | hskp7))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U))) | hskp7) <=> (hskp7 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | hskp7) <=> (hskp7 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)))))),
% 0.86/0.79 inference(bind,[status(th)],[])).
% 0.86/0.79 tff(183,plain,
% 0.86/0.79 (![U: $i] : (((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | hskp7) <=> ![U: $i] : (hskp7 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)))),
% 0.86/0.79 inference(quant_intro,[status(thm)],[182])).
% 0.86/0.79 tff(184,axiom,(![U: $i] : (((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | hskp7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause147')).
% 0.86/0.79 tff(185,plain,
% 0.86/0.79 (![U: $i] : (hskp7 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)))),
% 0.86/0.79 inference(modus_ponens,[status(thm)],[184, 183])).
% 0.86/0.79 tff(186,plain,
% 0.86/0.79 (![U: $i] : (hskp7 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)))),
% 0.86/0.79 inference(modus_ponens,[status(thm)],[185, 181])).
% 0.86/0.79 tff(187,plain,(
% 0.86/0.79 ![U: $i] : (hskp7 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)))),
% 0.86/0.79 inference(skolemize,[status(sab)],[186])).
% 0.86/0.79 tff(188,plain,
% 0.86/0.79 (![U: $i] : (hskp7 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)))),
% 0.86/0.79 inference(modus_ponens,[status(thm)],[187, 180])).
% 0.86/0.79 tff(189,assumption,(hskp0), introduced(assumption)).
% 0.86/0.79 tff(190,plain,
% 0.86/0.79 (((~hskp0) | c2_1(a1000)) <=> ((~hskp0) | c2_1(a1000))),
% 0.86/0.79 inference(rewrite,[status(thm)],[])).
% 0.86/0.79 tff(191,axiom,((~hskp0) | c2_1(a1000)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause84')).
% 0.86/0.79 tff(192,plain,
% 0.86/0.79 ((~hskp0) | c2_1(a1000)),
% 0.86/0.79 inference(modus_ponens,[status(thm)],[191, 190])).
% 0.86/0.79 tff(193,plain,
% 0.86/0.79 ((~hskp0) | c2_1(a1000)),
% 0.86/0.79 inference(modus_ponens,[status(thm)],[192, 190])).
% 0.86/0.79 tff(194,plain,
% 0.86/0.79 ((~hskp0) | c2_1(a1000)),
% 0.86/0.79 inference(modus_ponens,[status(thm)],[193, 190])).
% 0.86/0.79 tff(195,plain,
% 0.86/0.79 ((~hskp0) | c2_1(a1000)),
% 0.86/0.79 inference(modus_ponens,[status(thm)],[194, 190])).
% 0.86/0.79 tff(196,plain,
% 0.86/0.79 ((~hskp0) | c2_1(a1000)),
% 0.86/0.79 inference(modus_ponens,[status(thm)],[195, 190])).
% 0.86/0.79 tff(197,plain,
% 0.86/0.79 ((~hskp0) | c2_1(a1000)),
% 0.86/0.79 inference(modus_ponens,[status(thm)],[196, 190])).
% 0.86/0.79 tff(198,plain,
% 0.86/0.79 ((~hskp0) | c2_1(a1000)),
% 0.86/0.79 inference(modus_ponens,[status(thm)],[197, 190])).
% 0.86/0.79 tff(199,plain,
% 0.86/0.79 ((~hskp0) | c2_1(a1000)),
% 0.86/0.79 inference(modus_ponens,[status(thm)],[198, 190])).
% 0.86/0.79 tff(200,plain,
% 0.86/0.79 (c2_1(a1000)),
% 0.86/0.79 inference(unit_resolution,[status(thm)],[199, 189])).
% 0.86/0.79 tff(201,plain,
% 0.86/0.79 (((~hskp0) | c0_1(a1000)) <=> ((~hskp0) | c0_1(a1000))),
% 0.86/0.79 inference(rewrite,[status(thm)],[])).
% 0.86/0.79 tff(202,axiom,((~hskp0) | c0_1(a1000)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause83')).
% 0.86/0.79 tff(203,plain,
% 0.86/0.79 ((~hskp0) | c0_1(a1000)),
% 0.86/0.79 inference(modus_ponens,[status(thm)],[202, 201])).
% 0.86/0.79 tff(204,plain,
% 0.86/0.79 ((~hskp0) | c0_1(a1000)),
% 0.86/0.79 inference(modus_ponens,[status(thm)],[203, 201])).
% 0.86/0.79 tff(205,plain,
% 0.86/0.79 ((~hskp0) | c0_1(a1000)),
% 0.86/0.79 inference(modus_ponens,[status(thm)],[204, 201])).
% 0.86/0.79 tff(206,plain,
% 0.86/0.79 ((~hskp0) | c0_1(a1000)),
% 0.86/0.79 inference(modus_ponens,[status(thm)],[205, 201])).
% 0.86/0.79 tff(207,plain,
% 0.86/0.79 ((~hskp0) | c0_1(a1000)),
% 0.86/0.79 inference(modus_ponens,[status(thm)],[206, 201])).
% 0.86/0.79 tff(208,plain,
% 0.86/0.79 ((~hskp0) | c0_1(a1000)),
% 0.86/0.79 inference(modus_ponens,[status(thm)],[207, 201])).
% 0.86/0.79 tff(209,plain,
% 0.86/0.79 ((~hskp0) | c0_1(a1000)),
% 0.86/0.79 inference(modus_ponens,[status(thm)],[208, 201])).
% 0.86/0.79 tff(210,plain,
% 0.86/0.79 ((~hskp0) | c0_1(a1000)),
% 0.86/0.79 inference(modus_ponens,[status(thm)],[209, 201])).
% 0.86/0.79 tff(211,plain,
% 0.86/0.79 (c0_1(a1000)),
% 0.86/0.79 inference(unit_resolution,[status(thm)],[210, 189])).
% 0.86/0.79 tff(212,assumption,(~c0_1(a1023)), introduced(assumption)).
% 0.86/0.79 tff(213,assumption,(~c2_1(a1023)), introduced(assumption)).
% 0.86/0.79 tff(214,assumption,(~c1_1(a1023)), introduced(assumption)).
% 0.86/0.79 tff(215,assumption,(c3_1(a1023)), introduced(assumption)).
% 0.86/0.79 tff(216,plain,
% 0.86/0.79 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W))) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W))))),
% 0.86/0.79 inference(bind,[status(th)],[])).
% 0.86/0.79 tff(217,plain,
% 0.86/0.79 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))),
% 0.86/0.79 inference(quant_intro,[status(thm)],[216])).
% 0.86/0.79 tff(218,plain,
% 0.86/0.79 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))),
% 0.86/0.79 inference(rewrite,[status(thm)],[])).
% 0.86/0.79 tff(219,plain,
% 0.86/0.79 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c2_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)))), ((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) <=> (((~ndr1_0) | (~c2_1(U))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(V)))), ((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(V))))), (((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c3_1(W))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(V))) | (~c3_1(W))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(V))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(V)) | (~c3_1(W)))), (((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(V)) | (~c3_1(W))))), ((((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c3_1(W))) | c1_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(V)) | (~c3_1(W))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(V)) | (~c3_1(W))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(V)) | (~c3_1(W)))), ((((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c3_1(W))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(V)) | (~c3_1(W))))), (((((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c3_1(W))) | c1_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(V)) | (~c3_1(W))) | c3_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(V)) | (~c3_1(W))) | c3_1(U)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | (~c3_1(V)) | (~c3_1(W)))), (((((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c3_1(W))) | c1_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | (~c3_1(V)) | (~c3_1(W))))), ((((((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c3_1(W))) | c1_1(U)) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | (~c3_1(V)) | (~c3_1(W))) | c0_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | (~c3_1(V)) | (~c3_1(W))) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c3_1(W)))), ((((((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c3_1(W))) | c1_1(U)) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c3_1(W))))), (((((((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c3_1(W))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c3_1(W))) | c2_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c3_1(W))) | c2_1(V)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | (~c3_1(W)))), (((((((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c3_1(W))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | (~c3_1(W))))), ((((((((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c3_1(W))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | (~c3_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | (~c3_1(W))) | c0_1(W)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)))), ((((((((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c3_1(W))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c3_1(W))))), (((((((((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c3_1(W))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | c0_1(W)) | c1_1(W)) <=> (((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c3_1(W))) | c1_1(W)))), rewrite((((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c3_1(W))) | c1_1(W)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))), (((((((((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c3_1(W))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))))),
% 0.86/0.79 inference(bind,[status(th)],[])).
% 0.86/0.79 tff(220,plain,
% 0.86/0.79 (![W: $i, V: $i, U: $i] : ((((((((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c3_1(W))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | c0_1(W)) | c1_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))),
% 0.86/0.79 inference(quant_intro,[status(thm)],[219])).
% 0.86/0.79 tff(221,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c3_1(W))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | c0_1(W)) | c1_1(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause185')).
% 0.86/0.79 tff(222,plain,
% 0.86/0.79 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))),
% 0.86/0.79 inference(modus_ponens,[status(thm)],[221, 220])).
% 0.86/0.79 tff(223,plain,
% 0.86/0.79 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))),
% 0.86/0.79 inference(modus_ponens,[status(thm)],[222, 218])).
% 0.86/0.79 tff(224,plain,(
% 0.86/0.79 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))),
% 0.86/0.79 inference(skolemize,[status(sab)],[223])).
% 0.86/0.79 tff(225,plain,
% 0.86/0.79 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))),
% 0.86/0.79 inference(modus_ponens,[status(thm)],[224, 217])).
% 0.86/0.79 tff(226,assumption,(hskp7), introduced(assumption)).
% 0.86/0.79 tff(227,plain,
% 0.86/0.79 (((~hskp7) | (~c3_1(a1008))) <=> ((~hskp7) | (~c3_1(a1008)))),
% 0.86/0.79 inference(rewrite,[status(thm)],[])).
% 0.86/0.79 tff(228,plain,
% 0.86/0.79 (((~c3_1(a1008)) | (~hskp7)) <=> ((~hskp7) | (~c3_1(a1008)))),
% 0.86/0.79 inference(rewrite,[status(thm)],[])).
% 0.86/0.79 tff(229,axiom,((~c3_1(a1008)) | (~hskp7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause119')).
% 0.86/0.79 tff(230,plain,
% 0.86/0.79 ((~hskp7) | (~c3_1(a1008))),
% 0.86/0.79 inference(modus_ponens,[status(thm)],[229, 228])).
% 0.86/0.79 tff(231,plain,
% 0.86/0.79 ((~hskp7) | (~c3_1(a1008))),
% 0.86/0.79 inference(modus_ponens,[status(thm)],[230, 227])).
% 0.86/0.79 tff(232,plain,
% 0.86/0.79 (~c3_1(a1008)),
% 0.86/0.79 inference(unit_resolution,[status(thm)],[231, 226])).
% 0.86/0.79 tff(233,plain,
% 0.86/0.79 (((~hskp7) | (~c1_1(a1008))) <=> ((~hskp7) | (~c1_1(a1008)))),
% 0.86/0.79 inference(rewrite,[status(thm)],[])).
% 0.86/0.79 tff(234,plain,
% 0.86/0.79 (((~c1_1(a1008)) | (~hskp7)) <=> ((~hskp7) | (~c1_1(a1008)))),
% 0.86/0.79 inference(rewrite,[status(thm)],[])).
% 0.86/0.79 tff(235,axiom,((~c1_1(a1008)) | (~hskp7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause118')).
% 0.86/0.79 tff(236,plain,
% 0.86/0.79 ((~hskp7) | (~c1_1(a1008))),
% 0.86/0.79 inference(modus_ponens,[status(thm)],[235, 234])).
% 0.86/0.79 tff(237,plain,
% 0.86/0.79 ((~hskp7) | (~c1_1(a1008))),
% 0.86/0.79 inference(modus_ponens,[status(thm)],[236, 233])).
% 0.86/0.79 tff(238,plain,
% 0.86/0.79 (~c1_1(a1008)),
% 0.86/0.79 inference(unit_resolution,[status(thm)],[237, 226])).
% 0.86/0.79 tff(239,plain,
% 0.86/0.79 (((~hskp7) | c2_1(a1008)) <=> ((~hskp7) | c2_1(a1008))),
% 0.86/0.79 inference(rewrite,[status(thm)],[])).
% 0.86/0.79 tff(240,axiom,((~hskp7) | c2_1(a1008)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause73')).
% 0.86/0.79 tff(241,plain,
% 0.86/0.79 ((~hskp7) | c2_1(a1008)),
% 0.86/0.79 inference(modus_ponens,[status(thm)],[240, 239])).
% 0.86/0.79 tff(242,plain,
% 0.86/0.79 ((~hskp7) | c2_1(a1008)),
% 0.86/0.79 inference(modus_ponens,[status(thm)],[241, 239])).
% 0.86/0.79 tff(243,plain,
% 0.86/0.79 ((~hskp7) | c2_1(a1008)),
% 0.86/0.79 inference(modus_ponens,[status(thm)],[242, 239])).
% 0.86/0.79 tff(244,plain,
% 0.86/0.79 ((~hskp7) | c2_1(a1008)),
% 0.86/0.79 inference(modus_ponens,[status(thm)],[243, 239])).
% 0.86/0.79 tff(245,plain,
% 0.86/0.79 ((~hskp7) | c2_1(a1008)),
% 0.86/0.79 inference(modus_ponens,[status(thm)],[244, 239])).
% 0.86/0.79 tff(246,plain,
% 0.86/0.79 ((~hskp7) | c2_1(a1008)),
% 0.86/0.79 inference(modus_ponens,[status(thm)],[245, 239])).
% 0.86/0.79 tff(247,plain,
% 0.86/0.79 ((~hskp7) | c2_1(a1008)),
% 0.86/0.79 inference(modus_ponens,[status(thm)],[246, 239])).
% 0.86/0.79 tff(248,plain,
% 0.86/0.79 ((~hskp7) | c2_1(a1008)),
% 0.86/0.79 inference(modus_ponens,[status(thm)],[247, 239])).
% 0.86/0.79 tff(249,plain,
% 0.86/0.79 (c2_1(a1008)),
% 0.86/0.79 inference(unit_resolution,[status(thm)],[248, 226])).
% 0.86/0.79 tff(250,plain,
% 0.86/0.79 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))) | (c1_1(a1023) | c2_1(a1023) | c1_1(a1008) | c3_1(a1008) | (~ndr1_0) | (~c2_1(a1008)) | c0_1(a1023) | (~c3_1(a1023)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))) | c1_1(a1023) | c2_1(a1023) | c1_1(a1008) | c3_1(a1008) | (~ndr1_0) | (~c2_1(a1008)) | c0_1(a1023) | (~c3_1(a1023)))),
% 0.86/0.79 inference(rewrite,[status(thm)],[])).
% 0.86/0.79 tff(251,plain,
% 0.86/0.79 (((~ndr1_0) | c1_1(a1008) | c3_1(a1008) | (~c2_1(a1008)) | c0_1(a1023) | c2_1(a1023) | (~c3_1(a1023)) | c0_1(a1023) | c1_1(a1023) | (~c3_1(a1023))) <=> (c1_1(a1023) | c2_1(a1023) | c1_1(a1008) | c3_1(a1008) | (~ndr1_0) | (~c2_1(a1008)) | c0_1(a1023) | (~c3_1(a1023)))),
% 0.86/0.79 inference(rewrite,[status(thm)],[])).
% 0.86/0.79 tff(252,plain,
% 0.86/0.79 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a1008) | c3_1(a1008) | (~c2_1(a1008)) | c0_1(a1023) | c2_1(a1023) | (~c3_1(a1023)) | c0_1(a1023) | c1_1(a1023) | (~c3_1(a1023)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))) | (c1_1(a1023) | c2_1(a1023) | c1_1(a1008) | c3_1(a1008) | (~ndr1_0) | (~c2_1(a1008)) | c0_1(a1023) | (~c3_1(a1023))))),
% 0.86/0.79 inference(monotonicity,[status(thm)],[251])).
% 0.86/0.79 tff(253,plain,
% 0.86/0.79 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a1008) | c3_1(a1008) | (~c2_1(a1008)) | c0_1(a1023) | c2_1(a1023) | (~c3_1(a1023)) | c0_1(a1023) | c1_1(a1023) | (~c3_1(a1023)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))) | c1_1(a1023) | c2_1(a1023) | c1_1(a1008) | c3_1(a1008) | (~ndr1_0) | (~c2_1(a1008)) | c0_1(a1023) | (~c3_1(a1023)))),
% 0.86/0.79 inference(transitivity,[status(thm)],[252, 250])).
% 0.86/0.79 tff(254,plain,
% 0.86/0.79 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a1008) | c3_1(a1008) | (~c2_1(a1008)) | c0_1(a1023) | c2_1(a1023) | (~c3_1(a1023)) | c0_1(a1023) | c1_1(a1023) | (~c3_1(a1023)))),
% 0.86/0.79 inference(quant_inst,[status(thm)],[])).
% 0.86/0.80 tff(255,plain,
% 0.86/0.80 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))) | c1_1(a1023) | c2_1(a1023) | c1_1(a1008) | c3_1(a1008) | (~ndr1_0) | (~c2_1(a1008)) | c0_1(a1023) | (~c3_1(a1023))),
% 0.86/0.80 inference(modus_ponens,[status(thm)],[254, 253])).
% 0.86/0.80 tff(256,plain,
% 0.86/0.80 ($false),
% 0.86/0.80 inference(unit_resolution,[status(thm)],[255, 90, 215, 249, 214, 213, 238, 232, 225, 212])).
% 0.86/0.80 tff(257,plain,((~hskp7) | (~c3_1(a1023)) | c1_1(a1023) | c2_1(a1023) | c0_1(a1023)), inference(lemma,lemma(discharge,[]))).
% 0.86/0.80 tff(258,plain,
% 0.86/0.80 (~hskp7),
% 0.86/0.80 inference(unit_resolution,[status(thm)],[257, 215, 214, 213, 212])).
% 0.86/0.80 tff(259,plain,
% 0.86/0.80 (((~![U: $i] : (hskp7 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)))) | (hskp7 | (~ndr1_0) | (~c2_1(a1000)) | (~c0_1(a1000)) | (~c1_1(a1000)))) <=> ((~![U: $i] : (hskp7 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)))) | hskp7 | (~ndr1_0) | (~c2_1(a1000)) | (~c0_1(a1000)) | (~c1_1(a1000)))),
% 0.86/0.80 inference(rewrite,[status(thm)],[])).
% 0.86/0.80 tff(260,plain,
% 0.86/0.80 ((hskp7 | (~ndr1_0) | (~c1_1(a1000)) | (~c2_1(a1000)) | (~c0_1(a1000))) <=> (hskp7 | (~ndr1_0) | (~c2_1(a1000)) | (~c0_1(a1000)) | (~c1_1(a1000)))),
% 0.86/0.80 inference(rewrite,[status(thm)],[])).
% 0.86/0.80 tff(261,plain,
% 0.86/0.80 (((~![U: $i] : (hskp7 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)))) | (hskp7 | (~ndr1_0) | (~c1_1(a1000)) | (~c2_1(a1000)) | (~c0_1(a1000)))) <=> ((~![U: $i] : (hskp7 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)))) | (hskp7 | (~ndr1_0) | (~c2_1(a1000)) | (~c0_1(a1000)) | (~c1_1(a1000))))),
% 0.86/0.80 inference(monotonicity,[status(thm)],[260])).
% 0.86/0.80 tff(262,plain,
% 0.86/0.80 (((~![U: $i] : (hskp7 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)))) | (hskp7 | (~ndr1_0) | (~c1_1(a1000)) | (~c2_1(a1000)) | (~c0_1(a1000)))) <=> ((~![U: $i] : (hskp7 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)))) | hskp7 | (~ndr1_0) | (~c2_1(a1000)) | (~c0_1(a1000)) | (~c1_1(a1000)))),
% 0.86/0.80 inference(transitivity,[status(thm)],[261, 259])).
% 0.86/0.80 tff(263,plain,
% 0.86/0.80 ((~![U: $i] : (hskp7 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)))) | (hskp7 | (~ndr1_0) | (~c1_1(a1000)) | (~c2_1(a1000)) | (~c0_1(a1000)))),
% 0.86/0.80 inference(quant_inst,[status(thm)],[])).
% 0.86/0.80 tff(264,plain,
% 0.86/0.80 ((~![U: $i] : (hskp7 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)))) | hskp7 | (~ndr1_0) | (~c2_1(a1000)) | (~c0_1(a1000)) | (~c1_1(a1000))),
% 0.86/0.80 inference(modus_ponens,[status(thm)],[263, 262])).
% 0.86/0.80 tff(265,plain,
% 0.86/0.80 (~c1_1(a1000)),
% 0.86/0.80 inference(unit_resolution,[status(thm)],[264, 90, 258, 211, 200, 188])).
% 0.86/0.80 tff(266,plain,
% 0.86/0.80 (((~hskp0) | (~c3_1(a1000))) <=> ((~hskp0) | (~c3_1(a1000)))),
% 0.86/0.80 inference(rewrite,[status(thm)],[])).
% 0.86/0.80 tff(267,plain,
% 0.86/0.80 (((~c3_1(a1000)) | (~hskp0)) <=> ((~hskp0) | (~c3_1(a1000)))),
% 0.86/0.80 inference(rewrite,[status(thm)],[])).
% 0.86/0.80 tff(268,axiom,((~c3_1(a1000)) | (~hskp0)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause129')).
% 0.86/0.80 tff(269,plain,
% 0.86/0.80 ((~hskp0) | (~c3_1(a1000))),
% 0.86/0.80 inference(modus_ponens,[status(thm)],[268, 267])).
% 0.86/0.80 tff(270,plain,
% 0.86/0.80 ((~hskp0) | (~c3_1(a1000))),
% 0.86/0.80 inference(modus_ponens,[status(thm)],[269, 266])).
% 0.86/0.80 tff(271,plain,
% 0.86/0.80 (~c3_1(a1000)),
% 0.86/0.80 inference(unit_resolution,[status(thm)],[270, 189])).
% 0.86/0.80 tff(272,plain,
% 0.86/0.80 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))) | (c1_1(a1023) | c2_1(a1023) | c3_1(a1000) | (~ndr1_0) | (~c2_1(a1000)) | c1_1(a1000) | c0_1(a1023) | (~c3_1(a1023)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))) | c1_1(a1023) | c2_1(a1023) | c3_1(a1000) | (~ndr1_0) | (~c2_1(a1000)) | c1_1(a1000) | c0_1(a1023) | (~c3_1(a1023)))),
% 0.86/0.80 inference(rewrite,[status(thm)],[])).
% 0.86/0.80 tff(273,plain,
% 0.86/0.80 (((~ndr1_0) | c1_1(a1000) | c3_1(a1000) | (~c2_1(a1000)) | c0_1(a1023) | c2_1(a1023) | (~c3_1(a1023)) | c0_1(a1023) | c1_1(a1023) | (~c3_1(a1023))) <=> (c1_1(a1023) | c2_1(a1023) | c3_1(a1000) | (~ndr1_0) | (~c2_1(a1000)) | c1_1(a1000) | c0_1(a1023) | (~c3_1(a1023)))),
% 0.86/0.80 inference(rewrite,[status(thm)],[])).
% 0.86/0.80 tff(274,plain,
% 0.86/0.80 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a1000) | c3_1(a1000) | (~c2_1(a1000)) | c0_1(a1023) | c2_1(a1023) | (~c3_1(a1023)) | c0_1(a1023) | c1_1(a1023) | (~c3_1(a1023)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))) | (c1_1(a1023) | c2_1(a1023) | c3_1(a1000) | (~ndr1_0) | (~c2_1(a1000)) | c1_1(a1000) | c0_1(a1023) | (~c3_1(a1023))))),
% 0.86/0.80 inference(monotonicity,[status(thm)],[273])).
% 0.86/0.80 tff(275,plain,
% 0.86/0.80 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a1000) | c3_1(a1000) | (~c2_1(a1000)) | c0_1(a1023) | c2_1(a1023) | (~c3_1(a1023)) | c0_1(a1023) | c1_1(a1023) | (~c3_1(a1023)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))) | c1_1(a1023) | c2_1(a1023) | c3_1(a1000) | (~ndr1_0) | (~c2_1(a1000)) | c1_1(a1000) | c0_1(a1023) | (~c3_1(a1023)))),
% 0.86/0.80 inference(transitivity,[status(thm)],[274, 272])).
% 0.86/0.80 tff(276,plain,
% 0.86/0.80 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a1000) | c3_1(a1000) | (~c2_1(a1000)) | c0_1(a1023) | c2_1(a1023) | (~c3_1(a1023)) | c0_1(a1023) | c1_1(a1023) | (~c3_1(a1023)))),
% 0.86/0.80 inference(quant_inst,[status(thm)],[])).
% 0.86/0.80 tff(277,plain,
% 0.86/0.80 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))) | c1_1(a1023) | c2_1(a1023) | c3_1(a1000) | (~ndr1_0) | (~c2_1(a1000)) | c1_1(a1000) | c0_1(a1023) | (~c3_1(a1023))),
% 0.86/0.80 inference(modus_ponens,[status(thm)],[276, 275])).
% 0.86/0.80 tff(278,plain,
% 0.86/0.80 ($false),
% 0.86/0.80 inference(unit_resolution,[status(thm)],[277, 90, 215, 200, 214, 213, 271, 225, 212, 265])).
% 0.86/0.80 tff(279,plain,((~hskp0) | (~c3_1(a1023)) | c1_1(a1023) | c2_1(a1023) | c0_1(a1023)), inference(lemma,lemma(discharge,[]))).
% 0.86/0.80 tff(280,plain,
% 0.86/0.80 (~hskp0),
% 0.86/0.80 inference(unit_resolution,[status(thm)],[279, 165, 154, 178, 172])).
% 0.86/0.80 tff(281,plain,
% 0.86/0.80 (^[U: $i] : refl((hskp1 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)) <=> (hskp1 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)))),
% 0.86/0.80 inference(bind,[status(th)],[])).
% 0.86/0.80 tff(282,plain,
% 0.86/0.80 (![U: $i] : (hskp1 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)) <=> ![U: $i] : (hskp1 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))),
% 0.86/0.80 inference(quant_intro,[status(thm)],[281])).
% 0.86/0.80 tff(283,plain,
% 0.86/0.80 (![U: $i] : (hskp1 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)) <=> ![U: $i] : (hskp1 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))),
% 0.86/0.80 inference(rewrite,[status(thm)],[])).
% 0.86/0.80 tff(284,plain,
% 0.86/0.80 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~ndr1_0) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U))), ((((~ndr1_0) | c0_1(U)) | c1_1(U)) <=> (((~ndr1_0) | c0_1(U)) | c1_1(U)))), rewrite((((~ndr1_0) | c0_1(U)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U))), ((((~ndr1_0) | c0_1(U)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U)))), (((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c1_1(U) | c0_1(U)) | c2_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | c0_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))), (((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)))), ((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c2_1(U)) | hskp0) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)) | hskp0))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)) | hskp0) <=> (hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))), ((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c2_1(U)) | hskp0) <=> (hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)))), (((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c2_1(U)) | hskp0) | hskp1) <=> ((hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)) | hskp1))), rewrite(((hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)) | hskp1) <=> (hskp1 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))), (((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c2_1(U)) | hskp0) | hskp1) <=> (hskp1 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))))),
% 0.86/0.80 inference(bind,[status(th)],[])).
% 0.86/0.80 tff(285,plain,
% 0.86/0.80 (![U: $i] : ((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c2_1(U)) | hskp0) | hskp1) <=> ![U: $i] : (hskp1 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))),
% 0.86/0.80 inference(quant_intro,[status(thm)],[284])).
% 0.86/0.80 tff(286,axiom,(![U: $i] : ((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c2_1(U)) | hskp0) | hskp1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause130')).
% 0.86/0.80 tff(287,plain,
% 0.86/0.80 (![U: $i] : (hskp1 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))),
% 0.86/0.80 inference(modus_ponens,[status(thm)],[286, 285])).
% 0.86/0.80 tff(288,plain,
% 0.86/0.80 (![U: $i] : (hskp1 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))),
% 0.86/0.80 inference(modus_ponens,[status(thm)],[287, 283])).
% 0.86/0.80 tff(289,plain,(
% 0.86/0.80 ![U: $i] : (hskp1 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))),
% 0.86/0.80 inference(skolemize,[status(sab)],[288])).
% 0.86/0.80 tff(290,plain,
% 0.86/0.80 (![U: $i] : (hskp1 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))),
% 0.86/0.80 inference(modus_ponens,[status(thm)],[289, 282])).
% 0.86/0.80 tff(291,plain,
% 0.86/0.80 (((~![U: $i] : (hskp1 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp1 | hskp0 | c1_1(a1023) | c2_1(a1023) | (~ndr1_0) | c0_1(a1023))) <=> ((~![U: $i] : (hskp1 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | hskp1 | hskp0 | c1_1(a1023) | c2_1(a1023) | (~ndr1_0) | c0_1(a1023))),
% 0.86/0.80 inference(rewrite,[status(thm)],[])).
% 0.86/0.80 tff(292,plain,
% 0.86/0.80 ((hskp1 | hskp0 | (~ndr1_0) | c2_1(a1023) | c1_1(a1023) | c0_1(a1023)) <=> (hskp1 | hskp0 | c1_1(a1023) | c2_1(a1023) | (~ndr1_0) | c0_1(a1023))),
% 0.86/0.80 inference(rewrite,[status(thm)],[])).
% 0.86/0.80 tff(293,plain,
% 0.86/0.80 (((~![U: $i] : (hskp1 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp1 | hskp0 | (~ndr1_0) | c2_1(a1023) | c1_1(a1023) | c0_1(a1023))) <=> ((~![U: $i] : (hskp1 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp1 | hskp0 | c1_1(a1023) | c2_1(a1023) | (~ndr1_0) | c0_1(a1023)))),
% 0.86/0.80 inference(monotonicity,[status(thm)],[292])).
% 0.86/0.80 tff(294,plain,
% 0.86/0.80 (((~![U: $i] : (hskp1 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp1 | hskp0 | (~ndr1_0) | c2_1(a1023) | c1_1(a1023) | c0_1(a1023))) <=> ((~![U: $i] : (hskp1 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | hskp1 | hskp0 | c1_1(a1023) | c2_1(a1023) | (~ndr1_0) | c0_1(a1023))),
% 0.86/0.80 inference(transitivity,[status(thm)],[293, 291])).
% 0.86/0.80 tff(295,plain,
% 0.86/0.80 ((~![U: $i] : (hskp1 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp1 | hskp0 | (~ndr1_0) | c2_1(a1023) | c1_1(a1023) | c0_1(a1023))),
% 0.86/0.80 inference(quant_inst,[status(thm)],[])).
% 0.86/0.80 tff(296,plain,
% 0.86/0.80 ((~![U: $i] : (hskp1 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | hskp1 | hskp0 | c1_1(a1023) | c2_1(a1023) | (~ndr1_0) | c0_1(a1023)),
% 0.86/0.80 inference(modus_ponens,[status(thm)],[295, 294])).
% 0.86/0.80 tff(297,plain,
% 0.86/0.80 (hskp1 | hskp0),
% 0.86/0.80 inference(unit_resolution,[status(thm)],[296, 90, 154, 178, 290, 172])).
% 0.86/0.80 tff(298,plain,
% 0.86/0.80 (hskp1),
% 0.86/0.80 inference(unit_resolution,[status(thm)],[297, 280])).
% 0.86/0.80 tff(299,plain,
% 0.86/0.80 (((~hskp1) | (~c1_1(a1001))) <=> ((~hskp1) | (~c1_1(a1001)))),
% 0.86/0.80 inference(rewrite,[status(thm)],[])).
% 0.86/0.80 tff(300,plain,
% 0.86/0.80 (((~c1_1(a1001)) | (~hskp1)) <=> ((~hskp1) | (~c1_1(a1001)))),
% 0.86/0.80 inference(rewrite,[status(thm)],[])).
% 0.86/0.80 tff(301,axiom,((~c1_1(a1001)) | (~hskp1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause128')).
% 0.86/0.80 tff(302,plain,
% 0.86/0.80 ((~hskp1) | (~c1_1(a1001))),
% 0.86/0.80 inference(modus_ponens,[status(thm)],[301, 300])).
% 0.86/0.80 tff(303,plain,
% 0.86/0.80 ((~hskp1) | (~c1_1(a1001))),
% 0.86/0.80 inference(modus_ponens,[status(thm)],[302, 299])).
% 0.86/0.80 tff(304,plain,
% 0.86/0.80 (~c1_1(a1001)),
% 0.86/0.80 inference(unit_resolution,[status(thm)],[303, 298])).
% 0.86/0.80 tff(305,plain,
% 0.86/0.80 (((~hskp1) | c3_1(a1001)) <=> ((~hskp1) | c3_1(a1001))),
% 0.86/0.80 inference(rewrite,[status(thm)],[])).
% 0.86/0.80 tff(306,axiom,((~hskp1) | c3_1(a1001)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause82')).
% 0.86/0.80 tff(307,plain,
% 0.86/0.80 ((~hskp1) | c3_1(a1001)),
% 0.86/0.80 inference(modus_ponens,[status(thm)],[306, 305])).
% 0.86/0.80 tff(308,plain,
% 0.86/0.80 ((~hskp1) | c3_1(a1001)),
% 0.86/0.80 inference(modus_ponens,[status(thm)],[307, 305])).
% 0.86/0.80 tff(309,plain,
% 0.86/0.80 ((~hskp1) | c3_1(a1001)),
% 0.86/0.80 inference(modus_ponens,[status(thm)],[308, 305])).
% 0.86/0.80 tff(310,plain,
% 0.86/0.80 ((~hskp1) | c3_1(a1001)),
% 0.86/0.80 inference(modus_ponens,[status(thm)],[309, 305])).
% 0.86/0.80 tff(311,plain,
% 0.86/0.80 ((~hskp1) | c3_1(a1001)),
% 0.86/0.80 inference(modus_ponens,[status(thm)],[310, 305])).
% 0.86/0.80 tff(312,plain,
% 0.86/0.80 ((~hskp1) | c3_1(a1001)),
% 0.86/0.80 inference(modus_ponens,[status(thm)],[311, 305])).
% 0.86/0.80 tff(313,plain,
% 0.86/0.80 ((~hskp1) | c3_1(a1001)),
% 0.86/0.80 inference(modus_ponens,[status(thm)],[312, 305])).
% 0.86/0.80 tff(314,plain,
% 0.86/0.80 ((~hskp1) | c3_1(a1001)),
% 0.86/0.80 inference(modus_ponens,[status(thm)],[313, 305])).
% 0.86/0.80 tff(315,plain,
% 0.86/0.80 (c3_1(a1001)),
% 0.86/0.80 inference(unit_resolution,[status(thm)],[314, 298])).
% 0.86/0.80 tff(316,plain,
% 0.86/0.80 (((~![U: $i] : (hskp23 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp23 | c1_1(a1001) | (~ndr1_0) | (~c0_1(a1001)) | (~c3_1(a1001)))) <=> ((~![U: $i] : (hskp23 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp23 | c1_1(a1001) | (~ndr1_0) | (~c0_1(a1001)) | (~c3_1(a1001)))),
% 0.86/0.80 inference(rewrite,[status(thm)],[])).
% 0.86/0.80 tff(317,plain,
% 0.86/0.80 ((hskp23 | (~ndr1_0) | c1_1(a1001) | (~c3_1(a1001)) | (~c0_1(a1001))) <=> (hskp23 | c1_1(a1001) | (~ndr1_0) | (~c0_1(a1001)) | (~c3_1(a1001)))),
% 0.86/0.80 inference(rewrite,[status(thm)],[])).
% 0.86/0.80 tff(318,plain,
% 0.86/0.80 (((~![U: $i] : (hskp23 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp23 | (~ndr1_0) | c1_1(a1001) | (~c3_1(a1001)) | (~c0_1(a1001)))) <=> ((~![U: $i] : (hskp23 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp23 | c1_1(a1001) | (~ndr1_0) | (~c0_1(a1001)) | (~c3_1(a1001))))),
% 0.86/0.80 inference(monotonicity,[status(thm)],[317])).
% 0.86/0.80 tff(319,plain,
% 0.86/0.80 (((~![U: $i] : (hskp23 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp23 | (~ndr1_0) | c1_1(a1001) | (~c3_1(a1001)) | (~c0_1(a1001)))) <=> ((~![U: $i] : (hskp23 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp23 | c1_1(a1001) | (~ndr1_0) | (~c0_1(a1001)) | (~c3_1(a1001)))),
% 0.86/0.80 inference(transitivity,[status(thm)],[318, 316])).
% 0.86/0.80 tff(320,plain,
% 0.86/0.80 ((~![U: $i] : (hskp23 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp23 | (~ndr1_0) | c1_1(a1001) | (~c3_1(a1001)) | (~c0_1(a1001)))),
% 0.86/0.80 inference(quant_inst,[status(thm)],[])).
% 0.86/0.80 tff(321,plain,
% 0.86/0.80 ((~![U: $i] : (hskp23 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp23 | c1_1(a1001) | (~ndr1_0) | (~c0_1(a1001)) | (~c3_1(a1001))),
% 0.86/0.80 inference(modus_ponens,[status(thm)],[320, 319])).
% 0.86/0.80 tff(322,plain,
% 0.86/0.80 (~c0_1(a1001)),
% 0.86/0.80 inference(unit_resolution,[status(thm)],[321, 90, 22, 315, 304, 32])).
% 0.86/0.80 tff(323,plain,
% 0.86/0.80 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c1_1(W)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c1_1(W)))),
% 0.86/0.80 inference(bind,[status(th)],[])).
% 0.86/0.80 tff(324,plain,
% 0.86/0.80 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c1_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c1_1(W))),
% 0.86/0.80 inference(quant_intro,[status(thm)],[323])).
% 0.86/0.80 tff(325,plain,
% 0.86/0.80 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c1_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c1_1(W))),
% 0.86/0.80 inference(rewrite,[status(thm)],[])).
% 0.86/0.80 tff(326,plain,
% 0.86/0.80 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c3_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)))), ((((~c3_1(U)) | (~ndr1_0)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c3_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(V)))), ((((~c3_1(U)) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(V))))), (((((~c3_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(V))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(V))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(V)))), (((((~c3_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(V))))), ((((((~c3_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | (~c2_1(V)))), ((((((~c3_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | (~c2_1(V))))), (((((((~c3_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c2_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | (~c2_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | (~c2_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)))), (((((((~c3_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c2_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c0_1(V) | (~c2_1(V))))), ((((((((~c3_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c2_1(U)) | c0_1(V)) | c1_1(V)) <=> (((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c0_1(V) | (~c2_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c0_1(V) | (~c2_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))), ((((((((~c3_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c2_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))))), (((((((((~c3_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))) | c0_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c0_1(W))), (((((((((~c3_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c0_1(W)))), ((((((((((~c3_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | c0_1(W)) | c1_1(W)) <=> (((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c0_1(W)) | c1_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c0_1(W) | c1_1(W))), ((((((((((~c3_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c0_1(W) | c1_1(W)))), (((((((((((~c3_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | c0_1(W)) | c1_1(W)) | c2_1(W)) <=> (((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c0_1(W) | c1_1(W)) | c2_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c0_1(W) | c1_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c1_1(W))), (((((((((((~c3_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | c0_1(W)) | c1_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c1_1(W))))),
% 0.86/0.80 inference(bind,[status(th)],[])).
% 0.86/0.80 tff(327,plain,
% 0.86/0.80 (![W: $i, V: $i, U: $i] : ((((((((((~c3_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | c0_1(W)) | c1_1(W)) | c2_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c1_1(W))),
% 0.86/0.80 inference(quant_intro,[status(thm)],[326])).
% 0.86/0.80 tff(328,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c3_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | c0_1(W)) | c1_1(W)) | c2_1(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause183')).
% 0.86/0.80 tff(329,plain,
% 0.86/0.80 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c1_1(W))),
% 0.86/0.80 inference(modus_ponens,[status(thm)],[328, 327])).
% 0.86/0.80 tff(330,plain,
% 0.86/0.80 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c1_1(W))),
% 0.86/0.80 inference(modus_ponens,[status(thm)],[329, 325])).
% 0.86/0.80 tff(331,plain,(
% 0.86/0.80 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c1_1(W))),
% 0.86/0.80 inference(skolemize,[status(sab)],[330])).
% 0.86/0.80 tff(332,plain,
% 0.86/0.80 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c1_1(W))),
% 0.86/0.80 inference(modus_ponens,[status(thm)],[331, 324])).
% 0.86/0.80 tff(333,plain,
% 0.86/0.80 (((~hskp1) | c2_1(a1001)) <=> ((~hskp1) | c2_1(a1001))),
% 0.86/0.80 inference(rewrite,[status(thm)],[])).
% 0.86/0.80 tff(334,axiom,((~hskp1) | c2_1(a1001)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause81')).
% 0.86/0.80 tff(335,plain,
% 0.86/0.80 ((~hskp1) | c2_1(a1001)),
% 0.86/0.80 inference(modus_ponens,[status(thm)],[334, 333])).
% 0.86/0.80 tff(336,plain,
% 0.86/0.80 ((~hskp1) | c2_1(a1001)),
% 0.86/0.80 inference(modus_ponens,[status(thm)],[335, 333])).
% 0.86/0.80 tff(337,plain,
% 0.86/0.80 ((~hskp1) | c2_1(a1001)),
% 0.86/0.80 inference(modus_ponens,[status(thm)],[336, 333])).
% 0.86/0.80 tff(338,plain,
% 0.86/0.80 ((~hskp1) | c2_1(a1001)),
% 0.86/0.80 inference(modus_ponens,[status(thm)],[337, 333])).
% 0.86/0.80 tff(339,plain,
% 0.86/0.80 ((~hskp1) | c2_1(a1001)),
% 0.86/0.80 inference(modus_ponens,[status(thm)],[338, 333])).
% 0.86/0.80 tff(340,plain,
% 0.86/0.80 ((~hskp1) | c2_1(a1001)),
% 0.86/0.80 inference(modus_ponens,[status(thm)],[339, 333])).
% 0.86/0.80 tff(341,plain,
% 0.86/0.80 ((~hskp1) | c2_1(a1001)),
% 0.86/0.80 inference(modus_ponens,[status(thm)],[340, 333])).
% 0.86/0.80 tff(342,plain,
% 0.86/0.80 ((~hskp1) | c2_1(a1001)),
% 0.86/0.80 inference(modus_ponens,[status(thm)],[341, 333])).
% 0.86/0.80 tff(343,plain,
% 0.86/0.80 (c2_1(a1001)),
% 0.86/0.80 inference(unit_resolution,[status(thm)],[342, 298])).
% 0.86/0.80 tff(344,plain,
% 0.86/0.80 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c1_1(W))) | (c1_1(a1023) | c2_1(a1023) | c1_1(a1001) | (~ndr1_0) | c0_1(a1001) | (~c2_1(a1001)) | c0_1(a1023) | (~c3_1(a1023)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c1_1(W))) | c1_1(a1023) | c2_1(a1023) | c1_1(a1001) | (~ndr1_0) | c0_1(a1001) | (~c2_1(a1001)) | c0_1(a1023) | (~c3_1(a1023)))),
% 0.86/0.80 inference(rewrite,[status(thm)],[])).
% 0.86/0.80 tff(345,plain,
% 0.86/0.80 (((~ndr1_0) | c2_1(a1023) | c0_1(a1023) | (~c3_1(a1023)) | c1_1(a1001) | c0_1(a1001) | (~c2_1(a1001)) | c2_1(a1023) | c0_1(a1023) | c1_1(a1023)) <=> (c1_1(a1023) | c2_1(a1023) | c1_1(a1001) | (~ndr1_0) | c0_1(a1001) | (~c2_1(a1001)) | c0_1(a1023) | (~c3_1(a1023)))),
% 0.86/0.80 inference(rewrite,[status(thm)],[])).
% 0.86/0.80 tff(346,plain,
% 0.86/0.80 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c1_1(W))) | ((~ndr1_0) | c2_1(a1023) | c0_1(a1023) | (~c3_1(a1023)) | c1_1(a1001) | c0_1(a1001) | (~c2_1(a1001)) | c2_1(a1023) | c0_1(a1023) | c1_1(a1023))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c1_1(W))) | (c1_1(a1023) | c2_1(a1023) | c1_1(a1001) | (~ndr1_0) | c0_1(a1001) | (~c2_1(a1001)) | c0_1(a1023) | (~c3_1(a1023))))),
% 0.86/0.80 inference(monotonicity,[status(thm)],[345])).
% 0.86/0.80 tff(347,plain,
% 0.86/0.80 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c1_1(W))) | ((~ndr1_0) | c2_1(a1023) | c0_1(a1023) | (~c3_1(a1023)) | c1_1(a1001) | c0_1(a1001) | (~c2_1(a1001)) | c2_1(a1023) | c0_1(a1023) | c1_1(a1023))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c1_1(W))) | c1_1(a1023) | c2_1(a1023) | c1_1(a1001) | (~ndr1_0) | c0_1(a1001) | (~c2_1(a1001)) | c0_1(a1023) | (~c3_1(a1023)))),
% 0.86/0.81 inference(transitivity,[status(thm)],[346, 344])).
% 0.86/0.81 tff(348,plain,
% 0.86/0.81 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c1_1(W))) | ((~ndr1_0) | c2_1(a1023) | c0_1(a1023) | (~c3_1(a1023)) | c1_1(a1001) | c0_1(a1001) | (~c2_1(a1001)) | c2_1(a1023) | c0_1(a1023) | c1_1(a1023))),
% 0.86/0.81 inference(quant_inst,[status(thm)],[])).
% 0.86/0.81 tff(349,plain,
% 0.86/0.81 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c1_1(W))) | c1_1(a1023) | c2_1(a1023) | c1_1(a1001) | (~ndr1_0) | c0_1(a1001) | (~c2_1(a1001)) | c0_1(a1023) | (~c3_1(a1023))),
% 0.86/0.81 inference(modus_ponens,[status(thm)],[348, 347])).
% 0.86/0.81 tff(350,plain,
% 0.86/0.81 ($false),
% 0.86/0.81 inference(unit_resolution,[status(thm)],[349, 90, 165, 343, 154, 178, 304, 332, 172, 322])).
% 0.86/0.81 tff(351,plain,((~hskp13) | hskp23), inference(lemma,lemma(discharge,[]))).
% 0.86/0.81 tff(352,plain,
% 0.86/0.81 (~hskp13),
% 0.86/0.81 inference(unit_resolution,[status(thm)],[351, 22])).
% 0.86/0.81 tff(353,plain,
% 0.86/0.81 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp13 | c1_1(a1037) | c3_1(a1037) | c1_1(a1002) | (~ndr1_0) | (~c0_1(a1002)) | c3_1(a1002) | c2_1(a1037))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp13 | c1_1(a1037) | c3_1(a1037) | c1_1(a1002) | (~ndr1_0) | (~c0_1(a1002)) | c3_1(a1002) | c2_1(a1037))),
% 0.86/0.81 inference(rewrite,[status(thm)],[])).
% 0.86/0.81 tff(354,plain,
% 0.86/0.81 ((hskp13 | (~ndr1_0) | c1_1(a1002) | c3_1(a1002) | (~c0_1(a1002)) | c3_1(a1037) | c1_1(a1037) | c2_1(a1037)) <=> (hskp13 | c1_1(a1037) | c3_1(a1037) | c1_1(a1002) | (~ndr1_0) | (~c0_1(a1002)) | c3_1(a1002) | c2_1(a1037))),
% 0.86/0.81 inference(rewrite,[status(thm)],[])).
% 0.86/0.81 tff(355,plain,
% 0.86/0.81 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp13 | (~ndr1_0) | c1_1(a1002) | c3_1(a1002) | (~c0_1(a1002)) | c3_1(a1037) | c1_1(a1037) | c2_1(a1037))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp13 | c1_1(a1037) | c3_1(a1037) | c1_1(a1002) | (~ndr1_0) | (~c0_1(a1002)) | c3_1(a1002) | c2_1(a1037)))),
% 0.86/0.81 inference(monotonicity,[status(thm)],[354])).
% 0.86/0.81 tff(356,plain,
% 0.86/0.81 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp13 | (~ndr1_0) | c1_1(a1002) | c3_1(a1002) | (~c0_1(a1002)) | c3_1(a1037) | c1_1(a1037) | c2_1(a1037))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp13 | c1_1(a1037) | c3_1(a1037) | c1_1(a1002) | (~ndr1_0) | (~c0_1(a1002)) | c3_1(a1002) | c2_1(a1037))),
% 0.86/0.81 inference(transitivity,[status(thm)],[355, 353])).
% 0.86/0.81 tff(357,plain,
% 0.86/0.81 ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp13 | (~ndr1_0) | c1_1(a1002) | c3_1(a1002) | (~c0_1(a1002)) | c3_1(a1037) | c1_1(a1037) | c2_1(a1037))),
% 0.86/0.81 inference(quant_inst,[status(thm)],[])).
% 0.86/0.81 tff(358,plain,
% 0.86/0.81 ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp13 | c1_1(a1037) | c3_1(a1037) | c1_1(a1002) | (~ndr1_0) | (~c0_1(a1002)) | c3_1(a1002) | c2_1(a1037)),
% 0.86/0.81 inference(modus_ponens,[status(thm)],[357, 356])).
% 0.86/0.81 tff(359,plain,
% 0.86/0.81 (c2_1(a1037)),
% 0.86/0.81 inference(unit_resolution,[status(thm)],[358, 90, 352, 50, 147, 141, 39, 107, 97])).
% 0.86/0.81 tff(360,assumption,(~hskp3), introduced(assumption)).
% 0.86/0.81 tff(361,plain,
% 0.86/0.81 (^[U: $i] : refl((hskp23 | hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))) <=> (hskp23 | hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))))),
% 0.86/0.81 inference(bind,[status(th)],[])).
% 0.86/0.81 tff(362,plain,
% 0.86/0.81 (![U: $i] : (hskp23 | hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp23 | hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 0.86/0.81 inference(quant_intro,[status(thm)],[361])).
% 0.86/0.81 tff(363,plain,
% 0.86/0.81 (![U: $i] : (hskp23 | hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp23 | hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 0.86/0.81 inference(rewrite,[status(thm)],[])).
% 0.86/0.81 tff(364,plain,
% 0.86/0.81 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp23) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp23))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp23) <=> (hskp23 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp23) <=> (hskp23 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp23) | hskp3) <=> ((hskp23 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp3))), rewrite(((hskp23 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp3) <=> (hskp23 | hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp23) | hskp3) <=> (hskp23 | hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))))),
% 0.86/0.81 inference(bind,[status(th)],[])).
% 0.86/0.81 tff(365,plain,
% 0.86/0.81 (![U: $i] : ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp23) | hskp3) <=> ![U: $i] : (hskp23 | hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 0.86/0.81 inference(quant_intro,[status(thm)],[364])).
% 0.86/0.81 tff(366,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp23) | hskp3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause143')).
% 0.86/0.81 tff(367,plain,
% 0.86/0.81 (![U: $i] : (hskp23 | hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 0.86/0.81 inference(modus_ponens,[status(thm)],[366, 365])).
% 0.86/0.81 tff(368,plain,
% 0.86/0.81 (![U: $i] : (hskp23 | hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 0.86/0.81 inference(modus_ponens,[status(thm)],[367, 363])).
% 0.86/0.81 tff(369,plain,(
% 0.86/0.81 ![U: $i] : (hskp23 | hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 0.86/0.81 inference(skolemize,[status(sab)],[368])).
% 0.86/0.81 tff(370,plain,
% 0.86/0.81 (![U: $i] : (hskp23 | hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 0.86/0.81 inference(modus_ponens,[status(thm)],[369, 362])).
% 0.86/0.81 tff(371,plain,
% 0.86/0.81 (hskp29),
% 0.86/0.81 inference(unit_resolution,[status(thm)],[88, 352, 22])).
% 0.86/0.81 tff(372,plain,
% 0.86/0.81 (((~hskp29) | c3_1(a1040)) <=> ((~hskp29) | c3_1(a1040))),
% 0.86/0.81 inference(rewrite,[status(thm)],[])).
% 0.86/0.81 tff(373,axiom,((~hskp29) | c3_1(a1040)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause42')).
% 0.86/0.81 tff(374,plain,
% 0.86/0.81 ((~hskp29) | c3_1(a1040)),
% 0.86/0.81 inference(modus_ponens,[status(thm)],[373, 372])).
% 0.86/0.81 tff(375,plain,
% 0.86/0.81 ((~hskp29) | c3_1(a1040)),
% 0.86/0.81 inference(modus_ponens,[status(thm)],[374, 372])).
% 0.86/0.81 tff(376,plain,
% 0.86/0.81 ((~hskp29) | c3_1(a1040)),
% 0.86/0.81 inference(modus_ponens,[status(thm)],[375, 372])).
% 0.86/0.81 tff(377,plain,
% 0.86/0.81 ((~hskp29) | c3_1(a1040)),
% 0.86/0.81 inference(modus_ponens,[status(thm)],[376, 372])).
% 0.86/0.81 tff(378,plain,
% 0.86/0.81 ((~hskp29) | c3_1(a1040)),
% 0.86/0.81 inference(modus_ponens,[status(thm)],[377, 372])).
% 0.86/0.81 tff(379,plain,
% 0.86/0.81 ((~hskp29) | c3_1(a1040)),
% 0.86/0.81 inference(modus_ponens,[status(thm)],[378, 372])).
% 0.86/0.81 tff(380,plain,
% 0.86/0.81 ((~hskp29) | c3_1(a1040)),
% 0.86/0.81 inference(modus_ponens,[status(thm)],[379, 372])).
% 0.86/0.81 tff(381,plain,
% 0.86/0.81 ((~hskp29) | c3_1(a1040)),
% 0.86/0.81 inference(modus_ponens,[status(thm)],[380, 372])).
% 0.86/0.81 tff(382,plain,
% 0.86/0.81 (c3_1(a1040)),
% 0.86/0.81 inference(unit_resolution,[status(thm)],[381, 371])).
% 0.86/0.81 tff(383,plain,
% 0.86/0.81 (((~hskp29) | c0_1(a1040)) <=> ((~hskp29) | c0_1(a1040))),
% 0.86/0.81 inference(rewrite,[status(thm)],[])).
% 0.86/0.81 tff(384,axiom,((~hskp29) | c0_1(a1040)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause40')).
% 0.86/0.81 tff(385,plain,
% 0.86/0.81 ((~hskp29) | c0_1(a1040)),
% 0.86/0.81 inference(modus_ponens,[status(thm)],[384, 383])).
% 0.86/0.81 tff(386,plain,
% 0.86/0.81 ((~hskp29) | c0_1(a1040)),
% 0.86/0.81 inference(modus_ponens,[status(thm)],[385, 383])).
% 0.86/0.81 tff(387,plain,
% 0.86/0.81 ((~hskp29) | c0_1(a1040)),
% 0.86/0.81 inference(modus_ponens,[status(thm)],[386, 383])).
% 0.86/0.81 tff(388,plain,
% 0.86/0.81 ((~hskp29) | c0_1(a1040)),
% 0.86/0.81 inference(modus_ponens,[status(thm)],[387, 383])).
% 0.86/0.81 tff(389,plain,
% 0.86/0.81 ((~hskp29) | c0_1(a1040)),
% 0.86/0.81 inference(modus_ponens,[status(thm)],[388, 383])).
% 0.86/0.81 tff(390,plain,
% 0.86/0.81 ((~hskp29) | c0_1(a1040)),
% 0.86/0.81 inference(modus_ponens,[status(thm)],[389, 383])).
% 0.86/0.81 tff(391,plain,
% 0.86/0.81 ((~hskp29) | c0_1(a1040)),
% 0.86/0.81 inference(modus_ponens,[status(thm)],[390, 383])).
% 0.86/0.81 tff(392,plain,
% 0.86/0.81 ((~hskp29) | c0_1(a1040)),
% 0.86/0.81 inference(modus_ponens,[status(thm)],[391, 383])).
% 0.86/0.81 tff(393,plain,
% 0.86/0.81 (c0_1(a1040)),
% 0.86/0.81 inference(unit_resolution,[status(thm)],[392, 371])).
% 0.86/0.81 tff(394,plain,
% 0.86/0.81 (((~![U: $i] : (hskp23 | hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp23 | hskp3 | (~ndr1_0) | c2_1(a1040) | (~c0_1(a1040)) | (~c3_1(a1040)))) <=> ((~![U: $i] : (hskp23 | hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp23 | hskp3 | (~ndr1_0) | c2_1(a1040) | (~c0_1(a1040)) | (~c3_1(a1040)))),
% 0.86/0.81 inference(rewrite,[status(thm)],[])).
% 0.86/0.81 tff(395,plain,
% 0.86/0.81 ((hskp23 | hskp3 | (~ndr1_0) | c2_1(a1040) | (~c3_1(a1040)) | (~c0_1(a1040))) <=> (hskp23 | hskp3 | (~ndr1_0) | c2_1(a1040) | (~c0_1(a1040)) | (~c3_1(a1040)))),
% 0.86/0.81 inference(rewrite,[status(thm)],[])).
% 0.86/0.81 tff(396,plain,
% 0.86/0.81 (((~![U: $i] : (hskp23 | hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp23 | hskp3 | (~ndr1_0) | c2_1(a1040) | (~c3_1(a1040)) | (~c0_1(a1040)))) <=> ((~![U: $i] : (hskp23 | hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp23 | hskp3 | (~ndr1_0) | c2_1(a1040) | (~c0_1(a1040)) | (~c3_1(a1040))))),
% 0.86/0.81 inference(monotonicity,[status(thm)],[395])).
% 0.86/0.81 tff(397,plain,
% 0.86/0.81 (((~![U: $i] : (hskp23 | hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp23 | hskp3 | (~ndr1_0) | c2_1(a1040) | (~c3_1(a1040)) | (~c0_1(a1040)))) <=> ((~![U: $i] : (hskp23 | hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp23 | hskp3 | (~ndr1_0) | c2_1(a1040) | (~c0_1(a1040)) | (~c3_1(a1040)))),
% 0.86/0.81 inference(transitivity,[status(thm)],[396, 394])).
% 0.86/0.81 tff(398,plain,
% 0.86/0.81 ((~![U: $i] : (hskp23 | hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp23 | hskp3 | (~ndr1_0) | c2_1(a1040) | (~c3_1(a1040)) | (~c0_1(a1040)))),
% 0.86/0.81 inference(quant_inst,[status(thm)],[])).
% 0.86/0.81 tff(399,plain,
% 0.86/0.81 ((~![U: $i] : (hskp23 | hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp23 | hskp3 | (~ndr1_0) | c2_1(a1040) | (~c0_1(a1040)) | (~c3_1(a1040))),
% 0.86/0.81 inference(modus_ponens,[status(thm)],[398, 397])).
% 0.86/0.81 tff(400,plain,
% 0.86/0.81 (hskp3 | c2_1(a1040)),
% 0.86/0.81 inference(unit_resolution,[status(thm)],[399, 90, 22, 393, 382, 370])).
% 0.86/0.81 tff(401,plain,
% 0.86/0.81 (c2_1(a1040)),
% 0.86/0.81 inference(unit_resolution,[status(thm)],[400, 360])).
% 0.86/0.81 tff(402,plain,
% 0.86/0.81 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W))))),
% 0.86/0.81 inference(bind,[status(th)],[])).
% 0.86/0.81 tff(403,plain,
% 0.86/0.81 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))),
% 0.86/0.81 inference(quant_intro,[status(thm)],[402])).
% 0.86/0.81 tff(404,plain,
% 0.86/0.81 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))),
% 0.86/0.81 inference(rewrite,[status(thm)],[])).
% 0.86/0.81 tff(405,plain,
% 0.86/0.81 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c1_1(U)) | (~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)))), rewrite((((~c1_1(U)) | (~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | (~c2_1(V)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | (~c2_1(V))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | (~c2_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c3_1(V)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c3_1(V))))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c1_1(W))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c3_1(V))) | (~c1_1(W))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c3_1(V))) | (~c1_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c1_1(W)))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c1_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c1_1(W))))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c1_1(W))) | (~c3_1(W))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c1_1(W))) | (~c3_1(W))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c1_1(W))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c3_1(W)) | (~c1_1(W)))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c1_1(W))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c3_1(W)) | (~c1_1(W))))), ((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c1_1(W))) | (~c3_1(W))) | c0_1(V)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c3_1(W)) | (~c1_1(W))) | c0_1(V)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c3_1(W)) | (~c1_1(W))) | c0_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | (~c3_1(W)) | (~c1_1(W)))), ((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c1_1(W))) | (~c3_1(W))) | c0_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | (~c3_1(W)) | (~c1_1(W))))), (((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c1_1(W))) | (~c3_1(W))) | c0_1(V)) | c0_1(W)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | (~c3_1(W)) | (~c1_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | (~c3_1(W)) | (~c1_1(W))) | c0_1(W)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))), (((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c1_1(W))) | (~c3_1(W))) | c0_1(V)) | c0_1(W)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))))),
% 0.86/0.81 inference(bind,[status(th)],[])).
% 0.86/0.81 tff(406,plain,
% 0.86/0.81 (![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c1_1(W))) | (~c3_1(W))) | c0_1(V)) | c0_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))),
% 0.86/0.81 inference(quant_intro,[status(thm)],[405])).
% 0.86/0.81 tff(407,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c1_1(W))) | (~c3_1(W))) | c0_1(V)) | c0_1(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause191')).
% 0.86/0.81 tff(408,plain,
% 0.86/0.81 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))),
% 0.86/0.81 inference(modus_ponens,[status(thm)],[407, 406])).
% 0.86/0.81 tff(409,plain,
% 0.86/0.81 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))),
% 0.86/0.81 inference(modus_ponens,[status(thm)],[408, 404])).
% 0.86/0.81 tff(410,plain,(
% 0.86/0.81 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))),
% 0.86/0.81 inference(skolemize,[status(sab)],[409])).
% 0.86/0.81 tff(411,plain,
% 0.86/0.81 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))),
% 0.86/0.81 inference(modus_ponens,[status(thm)],[410, 403])).
% 0.86/0.81 tff(412,assumption,(~c3_1(a1002)), introduced(assumption)).
% 0.86/0.81 tff(413,assumption,(c2_1(a1002)), introduced(assumption)).
% 0.86/0.81 tff(414,assumption,(c0_1(a1002)), introduced(assumption)).
% 0.86/0.81 tff(415,plain,
% 0.86/0.81 (((~hskp29) | c1_1(a1040)) <=> ((~hskp29) | c1_1(a1040))),
% 0.86/0.81 inference(rewrite,[status(thm)],[])).
% 0.86/0.81 tff(416,axiom,((~hskp29) | c1_1(a1040)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause41')).
% 0.86/0.81 tff(417,plain,
% 0.86/0.81 ((~hskp29) | c1_1(a1040)),
% 0.86/0.81 inference(modus_ponens,[status(thm)],[416, 415])).
% 0.86/0.81 tff(418,plain,
% 0.86/0.81 ((~hskp29) | c1_1(a1040)),
% 0.86/0.81 inference(modus_ponens,[status(thm)],[417, 415])).
% 0.86/0.81 tff(419,plain,
% 0.86/0.81 ((~hskp29) | c1_1(a1040)),
% 0.86/0.81 inference(modus_ponens,[status(thm)],[418, 415])).
% 0.86/0.81 tff(420,plain,
% 0.86/0.81 ((~hskp29) | c1_1(a1040)),
% 0.86/0.81 inference(modus_ponens,[status(thm)],[419, 415])).
% 0.86/0.81 tff(421,plain,
% 0.86/0.81 ((~hskp29) | c1_1(a1040)),
% 0.86/0.81 inference(modus_ponens,[status(thm)],[420, 415])).
% 0.86/0.81 tff(422,plain,
% 0.86/0.81 ((~hskp29) | c1_1(a1040)),
% 0.86/0.81 inference(modus_ponens,[status(thm)],[421, 415])).
% 0.86/0.81 tff(423,plain,
% 0.86/0.81 ((~hskp29) | c1_1(a1040)),
% 0.86/0.81 inference(modus_ponens,[status(thm)],[422, 415])).
% 0.86/0.81 tff(424,plain,
% 0.86/0.81 ((~hskp29) | c1_1(a1040)),
% 0.86/0.81 inference(modus_ponens,[status(thm)],[423, 415])).
% 0.86/0.81 tff(425,plain,
% 0.86/0.81 (c1_1(a1040)),
% 0.86/0.81 inference(unit_resolution,[status(thm)],[424, 371])).
% 0.86/0.81 tff(426,plain,
% 0.86/0.81 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp17 | (~ndr1_0) | (~c2_1(a1040)) | (~c0_1(a1040)) | (~c1_1(a1040)) | (~c0_1(a1002)) | c3_1(a1002) | (~c2_1(a1002)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp17 | (~ndr1_0) | (~c2_1(a1040)) | (~c0_1(a1040)) | (~c1_1(a1040)) | (~c0_1(a1002)) | c3_1(a1002) | (~c2_1(a1002)))),
% 0.86/0.81 inference(rewrite,[status(thm)],[])).
% 0.86/0.81 tff(427,plain,
% 0.86/0.81 ((hskp17 | (~ndr1_0) | (~c1_1(a1040)) | (~c2_1(a1040)) | (~c0_1(a1040)) | c3_1(a1002) | (~c2_1(a1002)) | (~c0_1(a1002))) <=> (hskp17 | (~ndr1_0) | (~c2_1(a1040)) | (~c0_1(a1040)) | (~c1_1(a1040)) | (~c0_1(a1002)) | c3_1(a1002) | (~c2_1(a1002)))),
% 0.86/0.81 inference(rewrite,[status(thm)],[])).
% 0.86/0.81 tff(428,plain,
% 0.86/0.81 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp17 | (~ndr1_0) | (~c1_1(a1040)) | (~c2_1(a1040)) | (~c0_1(a1040)) | c3_1(a1002) | (~c2_1(a1002)) | (~c0_1(a1002)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp17 | (~ndr1_0) | (~c2_1(a1040)) | (~c0_1(a1040)) | (~c1_1(a1040)) | (~c0_1(a1002)) | c3_1(a1002) | (~c2_1(a1002))))),
% 0.86/0.81 inference(monotonicity,[status(thm)],[427])).
% 0.86/0.81 tff(429,plain,
% 0.86/0.81 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp17 | (~ndr1_0) | (~c1_1(a1040)) | (~c2_1(a1040)) | (~c0_1(a1040)) | c3_1(a1002) | (~c2_1(a1002)) | (~c0_1(a1002)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp17 | (~ndr1_0) | (~c2_1(a1040)) | (~c0_1(a1040)) | (~c1_1(a1040)) | (~c0_1(a1002)) | c3_1(a1002) | (~c2_1(a1002)))),
% 0.86/0.81 inference(transitivity,[status(thm)],[428, 426])).
% 0.86/0.81 tff(430,plain,
% 0.86/0.81 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp17 | (~ndr1_0) | (~c1_1(a1040)) | (~c2_1(a1040)) | (~c0_1(a1040)) | c3_1(a1002) | (~c2_1(a1002)) | (~c0_1(a1002)))),
% 0.86/0.81 inference(quant_inst,[status(thm)],[])).
% 0.86/0.81 tff(431,plain,
% 0.86/0.81 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp17 | (~ndr1_0) | (~c2_1(a1040)) | (~c0_1(a1040)) | (~c1_1(a1040)) | (~c0_1(a1002)) | c3_1(a1002) | (~c2_1(a1002))),
% 0.86/0.81 inference(modus_ponens,[status(thm)],[430, 429])).
% 0.86/0.81 tff(432,plain,
% 0.86/0.81 (hskp17 | (~c2_1(a1040))),
% 0.86/0.81 inference(unit_resolution,[status(thm)],[431, 90, 393, 425, 414, 413, 11, 412])).
% 0.86/0.81 tff(433,plain,
% 0.86/0.81 (hskp17),
% 0.86/0.81 inference(unit_resolution,[status(thm)],[432, 401])).
% 0.86/0.81 tff(434,plain,
% 0.86/0.81 (((~hskp17) | (~c0_1(a1032))) <=> ((~hskp17) | (~c0_1(a1032)))),
% 0.86/0.81 inference(rewrite,[status(thm)],[])).
% 0.86/0.81 tff(435,plain,
% 0.86/0.81 (((~c0_1(a1032)) | (~hskp17)) <=> ((~hskp17) | (~c0_1(a1032)))),
% 0.86/0.81 inference(rewrite,[status(thm)],[])).
% 0.86/0.81 tff(436,axiom,((~c0_1(a1032)) | (~hskp17)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause102')).
% 0.86/0.81 tff(437,plain,
% 0.86/0.81 ((~hskp17) | (~c0_1(a1032))),
% 0.86/0.81 inference(modus_ponens,[status(thm)],[436, 435])).
% 0.86/0.81 tff(438,plain,
% 0.86/0.81 ((~hskp17) | (~c0_1(a1032))),
% 0.86/0.81 inference(modus_ponens,[status(thm)],[437, 434])).
% 0.86/0.81 tff(439,plain,
% 0.86/0.81 (~c0_1(a1032)),
% 0.86/0.81 inference(unit_resolution,[status(thm)],[438, 433])).
% 0.86/0.81 tff(440,plain,
% 0.86/0.81 (^[U: $i] : refl((hskp24 | hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) <=> (hskp24 | hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))))),
% 0.86/0.81 inference(bind,[status(th)],[])).
% 0.86/0.81 tff(441,plain,
% 0.86/0.81 (![U: $i] : (hskp24 | hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp24 | hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))),
% 0.86/0.81 inference(quant_intro,[status(thm)],[440])).
% 0.86/0.81 tff(442,plain,
% 0.86/0.81 (![U: $i] : (hskp24 | hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp24 | hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))),
% 0.86/0.81 inference(rewrite,[status(thm)],[])).
% 0.86/0.81 tff(443,plain,
% 0.86/0.81 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp24) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | hskp24))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | hskp24) <=> (hskp24 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp24) <=> (hskp24 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp24) | hskp3) <=> ((hskp24 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | hskp3))), rewrite(((hskp24 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | hskp3) <=> (hskp24 | hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp24) | hskp3) <=> (hskp24 | hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))))),
% 0.86/0.81 inference(bind,[status(th)],[])).
% 0.86/0.81 tff(444,plain,
% 0.86/0.81 (![U: $i] : ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp24) | hskp3) <=> ![U: $i] : (hskp24 | hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))),
% 0.86/0.81 inference(quant_intro,[status(thm)],[443])).
% 0.86/0.81 tff(445,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp24) | hskp3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause149')).
% 0.86/0.81 tff(446,plain,
% 0.86/0.81 (![U: $i] : (hskp24 | hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))),
% 0.86/0.81 inference(modus_ponens,[status(thm)],[445, 444])).
% 0.86/0.81 tff(447,plain,
% 0.86/0.81 (![U: $i] : (hskp24 | hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))),
% 0.86/0.81 inference(modus_ponens,[status(thm)],[446, 442])).
% 0.86/0.81 tff(448,plain,(
% 0.86/0.81 ![U: $i] : (hskp24 | hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))),
% 0.86/0.81 inference(skolemize,[status(sab)],[447])).
% 0.86/0.81 tff(449,plain,
% 0.86/0.81 (![U: $i] : (hskp24 | hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))),
% 0.86/0.81 inference(modus_ponens,[status(thm)],[448, 441])).
% 0.86/0.81 tff(450,plain,
% 0.86/0.81 (((~![U: $i] : (hskp24 | hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))) | (hskp24 | hskp3 | (~ndr1_0) | (~c2_1(a1040)) | (~c0_1(a1040)) | (~c3_1(a1040)))) <=> ((~![U: $i] : (hskp24 | hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))) | hskp24 | hskp3 | (~ndr1_0) | (~c2_1(a1040)) | (~c0_1(a1040)) | (~c3_1(a1040)))),
% 0.86/0.81 inference(rewrite,[status(thm)],[])).
% 0.86/0.81 tff(451,plain,
% 0.86/0.81 ((hskp24 | hskp3 | (~ndr1_0) | (~c2_1(a1040)) | (~c3_1(a1040)) | (~c0_1(a1040))) <=> (hskp24 | hskp3 | (~ndr1_0) | (~c2_1(a1040)) | (~c0_1(a1040)) | (~c3_1(a1040)))),
% 0.86/0.81 inference(rewrite,[status(thm)],[])).
% 0.86/0.81 tff(452,plain,
% 0.86/0.81 (((~![U: $i] : (hskp24 | hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))) | (hskp24 | hskp3 | (~ndr1_0) | (~c2_1(a1040)) | (~c3_1(a1040)) | (~c0_1(a1040)))) <=> ((~![U: $i] : (hskp24 | hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))) | (hskp24 | hskp3 | (~ndr1_0) | (~c2_1(a1040)) | (~c0_1(a1040)) | (~c3_1(a1040))))),
% 0.86/0.81 inference(monotonicity,[status(thm)],[451])).
% 0.86/0.81 tff(453,plain,
% 0.86/0.81 (((~![U: $i] : (hskp24 | hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))) | (hskp24 | hskp3 | (~ndr1_0) | (~c2_1(a1040)) | (~c3_1(a1040)) | (~c0_1(a1040)))) <=> ((~![U: $i] : (hskp24 | hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))) | hskp24 | hskp3 | (~ndr1_0) | (~c2_1(a1040)) | (~c0_1(a1040)) | (~c3_1(a1040)))),
% 0.86/0.81 inference(transitivity,[status(thm)],[452, 450])).
% 0.86/0.81 tff(454,plain,
% 0.86/0.81 ((~![U: $i] : (hskp24 | hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))) | (hskp24 | hskp3 | (~ndr1_0) | (~c2_1(a1040)) | (~c3_1(a1040)) | (~c0_1(a1040)))),
% 0.86/0.81 inference(quant_inst,[status(thm)],[])).
% 0.86/0.81 tff(455,plain,
% 0.86/0.81 ((~![U: $i] : (hskp24 | hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))) | hskp24 | hskp3 | (~ndr1_0) | (~c2_1(a1040)) | (~c0_1(a1040)) | (~c3_1(a1040))),
% 0.86/0.81 inference(modus_ponens,[status(thm)],[454, 453])).
% 0.86/0.81 tff(456,plain,
% 0.86/0.81 (hskp24 | hskp3 | (~c2_1(a1040))),
% 0.86/0.81 inference(unit_resolution,[status(thm)],[455, 90, 393, 382, 449])).
% 0.86/0.81 tff(457,plain,
% 0.86/0.81 (hskp24),
% 0.86/0.81 inference(unit_resolution,[status(thm)],[456, 401, 360])).
% 0.86/0.81 tff(458,plain,
% 0.86/0.81 (((~hskp24) | (~c0_1(a1045))) <=> ((~hskp24) | (~c0_1(a1045)))),
% 0.86/0.81 inference(rewrite,[status(thm)],[])).
% 0.86/0.81 tff(459,plain,
% 0.86/0.81 (((~c0_1(a1045)) | (~hskp24)) <=> ((~hskp24) | (~c0_1(a1045)))),
% 0.86/0.82 inference(rewrite,[status(thm)],[])).
% 0.86/0.82 tff(460,axiom,((~c0_1(a1045)) | (~hskp24)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause89')).
% 0.86/0.82 tff(461,plain,
% 0.86/0.82 ((~hskp24) | (~c0_1(a1045))),
% 0.86/0.82 inference(modus_ponens,[status(thm)],[460, 459])).
% 0.86/0.82 tff(462,plain,
% 0.86/0.82 ((~hskp24) | (~c0_1(a1045))),
% 0.86/0.82 inference(modus_ponens,[status(thm)],[461, 458])).
% 0.86/0.82 tff(463,plain,
% 0.86/0.82 (~c0_1(a1045)),
% 0.86/0.82 inference(unit_resolution,[status(thm)],[462, 457])).
% 0.86/0.82 tff(464,plain,
% 0.86/0.82 (((~hskp17) | c3_1(a1032)) <=> ((~hskp17) | c3_1(a1032))),
% 0.86/0.82 inference(rewrite,[status(thm)],[])).
% 0.86/0.82 tff(465,axiom,((~hskp17) | c3_1(a1032)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause60')).
% 0.86/0.82 tff(466,plain,
% 0.86/0.82 ((~hskp17) | c3_1(a1032)),
% 0.86/0.82 inference(modus_ponens,[status(thm)],[465, 464])).
% 0.86/0.82 tff(467,plain,
% 0.86/0.82 ((~hskp17) | c3_1(a1032)),
% 0.86/0.82 inference(modus_ponens,[status(thm)],[466, 464])).
% 0.86/0.82 tff(468,plain,
% 0.86/0.82 ((~hskp17) | c3_1(a1032)),
% 0.86/0.82 inference(modus_ponens,[status(thm)],[467, 464])).
% 0.86/0.82 tff(469,plain,
% 0.86/0.82 ((~hskp17) | c3_1(a1032)),
% 0.86/0.82 inference(modus_ponens,[status(thm)],[468, 464])).
% 0.86/0.82 tff(470,plain,
% 0.86/0.82 ((~hskp17) | c3_1(a1032)),
% 0.86/0.82 inference(modus_ponens,[status(thm)],[469, 464])).
% 0.86/0.82 tff(471,plain,
% 0.86/0.82 ((~hskp17) | c3_1(a1032)),
% 0.86/0.82 inference(modus_ponens,[status(thm)],[470, 464])).
% 0.86/0.82 tff(472,plain,
% 0.86/0.82 ((~hskp17) | c3_1(a1032)),
% 0.86/0.82 inference(modus_ponens,[status(thm)],[471, 464])).
% 0.86/0.82 tff(473,plain,
% 0.86/0.82 ((~hskp17) | c3_1(a1032)),
% 0.86/0.82 inference(modus_ponens,[status(thm)],[472, 464])).
% 0.86/0.82 tff(474,plain,
% 0.86/0.82 (c3_1(a1032)),
% 0.86/0.82 inference(unit_resolution,[status(thm)],[473, 433])).
% 0.86/0.82 tff(475,plain,
% 0.86/0.82 (((~hskp17) | c2_1(a1032)) <=> ((~hskp17) | c2_1(a1032))),
% 0.86/0.82 inference(rewrite,[status(thm)],[])).
% 0.86/0.82 tff(476,axiom,((~hskp17) | c2_1(a1032)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause59')).
% 0.86/0.82 tff(477,plain,
% 0.86/0.82 ((~hskp17) | c2_1(a1032)),
% 0.86/0.82 inference(modus_ponens,[status(thm)],[476, 475])).
% 0.86/0.82 tff(478,plain,
% 0.86/0.82 ((~hskp17) | c2_1(a1032)),
% 0.86/0.82 inference(modus_ponens,[status(thm)],[477, 475])).
% 0.86/0.82 tff(479,plain,
% 0.86/0.82 ((~hskp17) | c2_1(a1032)),
% 0.86/0.82 inference(modus_ponens,[status(thm)],[478, 475])).
% 0.86/0.82 tff(480,plain,
% 0.86/0.82 ((~hskp17) | c2_1(a1032)),
% 0.86/0.82 inference(modus_ponens,[status(thm)],[479, 475])).
% 0.86/0.82 tff(481,plain,
% 0.86/0.82 ((~hskp17) | c2_1(a1032)),
% 0.86/0.82 inference(modus_ponens,[status(thm)],[480, 475])).
% 0.86/0.82 tff(482,plain,
% 0.86/0.82 ((~hskp17) | c2_1(a1032)),
% 0.86/0.82 inference(modus_ponens,[status(thm)],[481, 475])).
% 0.86/0.82 tff(483,plain,
% 0.86/0.82 ((~hskp17) | c2_1(a1032)),
% 0.86/0.82 inference(modus_ponens,[status(thm)],[482, 475])).
% 0.86/0.82 tff(484,plain,
% 0.86/0.82 ((~hskp17) | c2_1(a1032)),
% 0.86/0.82 inference(modus_ponens,[status(thm)],[483, 475])).
% 0.86/0.82 tff(485,plain,
% 0.86/0.82 (c2_1(a1032)),
% 0.86/0.82 inference(unit_resolution,[status(thm)],[484, 433])).
% 0.86/0.82 tff(486,plain,
% 0.86/0.82 (((~hskp24) | c3_1(a1045)) <=> ((~hskp24) | c3_1(a1045))),
% 0.86/0.82 inference(rewrite,[status(thm)],[])).
% 0.86/0.82 tff(487,axiom,((~hskp24) | c3_1(a1045)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause52')).
% 0.86/0.82 tff(488,plain,
% 0.86/0.82 ((~hskp24) | c3_1(a1045)),
% 0.86/0.82 inference(modus_ponens,[status(thm)],[487, 486])).
% 0.86/0.82 tff(489,plain,
% 0.86/0.82 ((~hskp24) | c3_1(a1045)),
% 0.86/0.82 inference(modus_ponens,[status(thm)],[488, 486])).
% 0.86/0.82 tff(490,plain,
% 0.86/0.82 ((~hskp24) | c3_1(a1045)),
% 0.86/0.82 inference(modus_ponens,[status(thm)],[489, 486])).
% 0.86/0.82 tff(491,plain,
% 0.86/0.82 ((~hskp24) | c3_1(a1045)),
% 0.86/0.82 inference(modus_ponens,[status(thm)],[490, 486])).
% 0.86/0.82 tff(492,plain,
% 0.86/0.82 ((~hskp24) | c3_1(a1045)),
% 0.86/0.82 inference(modus_ponens,[status(thm)],[491, 486])).
% 0.86/0.82 tff(493,plain,
% 0.86/0.82 ((~hskp24) | c3_1(a1045)),
% 0.86/0.82 inference(modus_ponens,[status(thm)],[492, 486])).
% 0.86/0.82 tff(494,plain,
% 0.86/0.82 ((~hskp24) | c3_1(a1045)),
% 0.86/0.82 inference(modus_ponens,[status(thm)],[493, 486])).
% 0.86/0.82 tff(495,plain,
% 0.86/0.82 ((~hskp24) | c3_1(a1045)),
% 0.86/0.82 inference(modus_ponens,[status(thm)],[494, 486])).
% 0.86/0.82 tff(496,plain,
% 0.86/0.82 (c3_1(a1045)),
% 0.86/0.82 inference(unit_resolution,[status(thm)],[495, 457])).
% 0.86/0.82 tff(497,plain,
% 0.86/0.82 (((~hskp24) | c1_1(a1045)) <=> ((~hskp24) | c1_1(a1045))),
% 0.86/0.82 inference(rewrite,[status(thm)],[])).
% 0.86/0.82 tff(498,axiom,((~hskp24) | c1_1(a1045)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause51')).
% 0.86/0.82 tff(499,plain,
% 0.86/0.82 ((~hskp24) | c1_1(a1045)),
% 0.86/0.82 inference(modus_ponens,[status(thm)],[498, 497])).
% 0.86/0.82 tff(500,plain,
% 0.86/0.82 ((~hskp24) | c1_1(a1045)),
% 0.86/0.82 inference(modus_ponens,[status(thm)],[499, 497])).
% 0.86/0.82 tff(501,plain,
% 0.86/0.82 ((~hskp24) | c1_1(a1045)),
% 0.86/0.82 inference(modus_ponens,[status(thm)],[500, 497])).
% 0.86/0.82 tff(502,plain,
% 0.86/0.82 ((~hskp24) | c1_1(a1045)),
% 0.86/0.82 inference(modus_ponens,[status(thm)],[501, 497])).
% 0.86/0.82 tff(503,plain,
% 0.86/0.82 ((~hskp24) | c1_1(a1045)),
% 0.86/0.82 inference(modus_ponens,[status(thm)],[502, 497])).
% 0.86/0.82 tff(504,plain,
% 0.86/0.82 ((~hskp24) | c1_1(a1045)),
% 0.86/0.82 inference(modus_ponens,[status(thm)],[503, 497])).
% 0.86/0.82 tff(505,plain,
% 0.86/0.82 ((~hskp24) | c1_1(a1045)),
% 0.86/0.82 inference(modus_ponens,[status(thm)],[504, 497])).
% 0.86/0.82 tff(506,plain,
% 0.86/0.82 ((~hskp24) | c1_1(a1045)),
% 0.86/0.82 inference(modus_ponens,[status(thm)],[505, 497])).
% 0.86/0.82 tff(507,plain,
% 0.86/0.82 (c1_1(a1045)),
% 0.86/0.82 inference(unit_resolution,[status(thm)],[506, 457])).
% 0.86/0.82 tff(508,plain,
% 0.86/0.82 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | (c0_1(a1045) | c0_1(a1032) | (~ndr1_0) | (~c2_1(a1040)) | (~c3_1(a1040)) | (~c1_1(a1040)) | (~c2_1(a1032)) | (~c3_1(a1032)) | (~c3_1(a1045)) | (~c1_1(a1045)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | c0_1(a1045) | c0_1(a1032) | (~ndr1_0) | (~c2_1(a1040)) | (~c3_1(a1040)) | (~c1_1(a1040)) | (~c2_1(a1032)) | (~c3_1(a1032)) | (~c3_1(a1045)) | (~c1_1(a1045)))),
% 0.86/0.82 inference(rewrite,[status(thm)],[])).
% 0.86/0.82 tff(509,plain,
% 0.86/0.82 (((~ndr1_0) | (~c1_1(a1040)) | (~c2_1(a1040)) | (~c3_1(a1040)) | c0_1(a1032) | (~c2_1(a1032)) | (~c3_1(a1032)) | c0_1(a1045) | (~c3_1(a1045)) | (~c1_1(a1045))) <=> (c0_1(a1045) | c0_1(a1032) | (~ndr1_0) | (~c2_1(a1040)) | (~c3_1(a1040)) | (~c1_1(a1040)) | (~c2_1(a1032)) | (~c3_1(a1032)) | (~c3_1(a1045)) | (~c1_1(a1045)))),
% 0.86/0.82 inference(rewrite,[status(thm)],[])).
% 0.86/0.82 tff(510,plain,
% 0.86/0.82 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | (~c1_1(a1040)) | (~c2_1(a1040)) | (~c3_1(a1040)) | c0_1(a1032) | (~c2_1(a1032)) | (~c3_1(a1032)) | c0_1(a1045) | (~c3_1(a1045)) | (~c1_1(a1045)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | (c0_1(a1045) | c0_1(a1032) | (~ndr1_0) | (~c2_1(a1040)) | (~c3_1(a1040)) | (~c1_1(a1040)) | (~c2_1(a1032)) | (~c3_1(a1032)) | (~c3_1(a1045)) | (~c1_1(a1045))))),
% 0.86/0.82 inference(monotonicity,[status(thm)],[509])).
% 0.86/0.82 tff(511,plain,
% 0.86/0.82 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | (~c1_1(a1040)) | (~c2_1(a1040)) | (~c3_1(a1040)) | c0_1(a1032) | (~c2_1(a1032)) | (~c3_1(a1032)) | c0_1(a1045) | (~c3_1(a1045)) | (~c1_1(a1045)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | c0_1(a1045) | c0_1(a1032) | (~ndr1_0) | (~c2_1(a1040)) | (~c3_1(a1040)) | (~c1_1(a1040)) | (~c2_1(a1032)) | (~c3_1(a1032)) | (~c3_1(a1045)) | (~c1_1(a1045)))),
% 0.86/0.82 inference(transitivity,[status(thm)],[510, 508])).
% 0.86/0.82 tff(512,plain,
% 0.86/0.82 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | (~c1_1(a1040)) | (~c2_1(a1040)) | (~c3_1(a1040)) | c0_1(a1032) | (~c2_1(a1032)) | (~c3_1(a1032)) | c0_1(a1045) | (~c3_1(a1045)) | (~c1_1(a1045)))),
% 0.86/0.82 inference(quant_inst,[status(thm)],[])).
% 0.86/0.82 tff(513,plain,
% 0.86/0.82 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | c0_1(a1045) | c0_1(a1032) | (~ndr1_0) | (~c2_1(a1040)) | (~c3_1(a1040)) | (~c1_1(a1040)) | (~c2_1(a1032)) | (~c3_1(a1032)) | (~c3_1(a1045)) | (~c1_1(a1045))),
% 0.86/0.82 inference(modus_ponens,[status(thm)],[512, 511])).
% 0.86/0.82 tff(514,plain,
% 0.86/0.82 ($false),
% 0.86/0.82 inference(unit_resolution,[status(thm)],[513, 90, 425, 382, 507, 496, 485, 474, 463, 439, 411, 401])).
% 0.86/0.82 tff(515,plain,(hskp3 | (~c0_1(a1002)) | (~c2_1(a1002)) | c3_1(a1002) | hskp23), inference(lemma,lemma(discharge,[]))).
% 0.86/0.82 tff(516,plain,
% 0.86/0.82 (hskp3),
% 0.86/0.82 inference(unit_resolution,[status(thm)],[515, 50, 128, 97, 22])).
% 0.86/0.82 tff(517,plain,
% 0.86/0.82 (((~hskp3) | (~c2_1(a1003))) <=> ((~hskp3) | (~c2_1(a1003)))),
% 0.86/0.82 inference(rewrite,[status(thm)],[])).
% 0.86/0.82 tff(518,plain,
% 0.86/0.82 (((~c2_1(a1003)) | (~hskp3)) <=> ((~hskp3) | (~c2_1(a1003)))),
% 0.86/0.82 inference(rewrite,[status(thm)],[])).
% 0.86/0.82 tff(519,axiom,((~c2_1(a1003)) | (~hskp3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause126')).
% 0.86/0.82 tff(520,plain,
% 0.86/0.82 ((~hskp3) | (~c2_1(a1003))),
% 0.86/0.82 inference(modus_ponens,[status(thm)],[519, 518])).
% 0.86/0.82 tff(521,plain,
% 0.86/0.82 ((~hskp3) | (~c2_1(a1003))),
% 0.86/0.82 inference(modus_ponens,[status(thm)],[520, 517])).
% 0.86/0.82 tff(522,plain,
% 0.86/0.82 (~c2_1(a1003)),
% 0.86/0.82 inference(unit_resolution,[status(thm)],[521, 516])).
% 0.86/0.82 tff(523,plain,
% 0.86/0.82 (((~hskp3) | (~c0_1(a1003))) <=> ((~hskp3) | (~c0_1(a1003)))),
% 0.86/0.82 inference(rewrite,[status(thm)],[])).
% 0.86/0.82 tff(524,plain,
% 0.86/0.82 (((~c0_1(a1003)) | (~hskp3)) <=> ((~hskp3) | (~c0_1(a1003)))),
% 0.86/0.82 inference(rewrite,[status(thm)],[])).
% 0.86/0.82 tff(525,axiom,((~c0_1(a1003)) | (~hskp3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause125')).
% 0.86/0.82 tff(526,plain,
% 0.86/0.82 ((~hskp3) | (~c0_1(a1003))),
% 0.86/0.82 inference(modus_ponens,[status(thm)],[525, 524])).
% 0.86/0.82 tff(527,plain,
% 0.86/0.82 ((~hskp3) | (~c0_1(a1003))),
% 0.86/0.82 inference(modus_ponens,[status(thm)],[526, 523])).
% 0.86/0.82 tff(528,plain,
% 0.86/0.82 (~c0_1(a1003)),
% 0.86/0.82 inference(unit_resolution,[status(thm)],[527, 516])).
% 0.86/0.82 tff(529,plain,
% 0.86/0.82 (((~hskp3) | c1_1(a1003)) <=> ((~hskp3) | c1_1(a1003))),
% 0.86/0.82 inference(rewrite,[status(thm)],[])).
% 0.86/0.82 tff(530,axiom,((~hskp3) | c1_1(a1003)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause78')).
% 0.86/0.82 tff(531,plain,
% 0.86/0.82 ((~hskp3) | c1_1(a1003)),
% 0.86/0.82 inference(modus_ponens,[status(thm)],[530, 529])).
% 0.86/0.82 tff(532,plain,
% 0.86/0.82 ((~hskp3) | c1_1(a1003)),
% 0.86/0.82 inference(modus_ponens,[status(thm)],[531, 529])).
% 0.86/0.82 tff(533,plain,
% 0.86/0.82 ((~hskp3) | c1_1(a1003)),
% 0.86/0.82 inference(modus_ponens,[status(thm)],[532, 529])).
% 0.86/0.82 tff(534,plain,
% 0.86/0.82 ((~hskp3) | c1_1(a1003)),
% 0.86/0.82 inference(modus_ponens,[status(thm)],[533, 529])).
% 0.86/0.82 tff(535,plain,
% 0.86/0.82 ((~hskp3) | c1_1(a1003)),
% 0.86/0.82 inference(modus_ponens,[status(thm)],[534, 529])).
% 0.86/0.82 tff(536,plain,
% 0.86/0.82 ((~hskp3) | c1_1(a1003)),
% 0.86/0.82 inference(modus_ponens,[status(thm)],[535, 529])).
% 0.86/0.82 tff(537,plain,
% 0.86/0.82 ((~hskp3) | c1_1(a1003)),
% 0.86/0.82 inference(modus_ponens,[status(thm)],[536, 529])).
% 0.86/0.82 tff(538,plain,
% 0.86/0.82 ((~hskp3) | c1_1(a1003)),
% 0.86/0.82 inference(modus_ponens,[status(thm)],[537, 529])).
% 0.86/0.82 tff(539,plain,
% 0.86/0.82 (c1_1(a1003)),
% 0.86/0.82 inference(unit_resolution,[status(thm)],[538, 516])).
% 0.86/0.82 tff(540,assumption,(hskp8), introduced(assumption)).
% 0.86/0.82 tff(541,plain,
% 0.86/0.82 (((~hskp8) | (~c1_1(a1010))) <=> ((~hskp8) | (~c1_1(a1010)))),
% 0.86/0.82 inference(rewrite,[status(thm)],[])).
% 0.86/0.82 tff(542,plain,
% 0.86/0.82 (((~c1_1(a1010)) | (~hskp8)) <=> ((~hskp8) | (~c1_1(a1010)))),
% 0.86/0.82 inference(rewrite,[status(thm)],[])).
% 0.86/0.82 tff(543,axiom,((~c1_1(a1010)) | (~hskp8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause117')).
% 0.86/0.82 tff(544,plain,
% 0.86/0.82 ((~hskp8) | (~c1_1(a1010))),
% 0.86/0.82 inference(modus_ponens,[status(thm)],[543, 542])).
% 0.86/0.82 tff(545,plain,
% 0.86/0.82 ((~hskp8) | (~c1_1(a1010))),
% 0.86/0.82 inference(modus_ponens,[status(thm)],[544, 541])).
% 0.86/0.82 tff(546,plain,
% 0.86/0.82 (~c1_1(a1010)),
% 0.86/0.82 inference(unit_resolution,[status(thm)],[545, 540])).
% 0.86/0.82 tff(547,plain,
% 0.86/0.82 (((~hskp8) | c3_1(a1010)) <=> ((~hskp8) | c3_1(a1010))),
% 0.86/0.82 inference(rewrite,[status(thm)],[])).
% 0.86/0.82 tff(548,axiom,((~hskp8) | c3_1(a1010)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause72')).
% 0.86/0.82 tff(549,plain,
% 0.86/0.82 ((~hskp8) | c3_1(a1010)),
% 0.86/0.82 inference(modus_ponens,[status(thm)],[548, 547])).
% 0.86/0.82 tff(550,plain,
% 0.86/0.82 ((~hskp8) | c3_1(a1010)),
% 0.86/0.82 inference(modus_ponens,[status(thm)],[549, 547])).
% 0.86/0.82 tff(551,plain,
% 0.86/0.82 ((~hskp8) | c3_1(a1010)),
% 0.86/0.82 inference(modus_ponens,[status(thm)],[550, 547])).
% 0.86/0.82 tff(552,plain,
% 0.86/0.82 ((~hskp8) | c3_1(a1010)),
% 0.86/0.82 inference(modus_ponens,[status(thm)],[551, 547])).
% 0.86/0.82 tff(553,plain,
% 0.86/0.82 ((~hskp8) | c3_1(a1010)),
% 0.86/0.82 inference(modus_ponens,[status(thm)],[552, 547])).
% 0.86/0.82 tff(554,plain,
% 0.86/0.82 ((~hskp8) | c3_1(a1010)),
% 0.86/0.82 inference(modus_ponens,[status(thm)],[553, 547])).
% 0.86/0.82 tff(555,plain,
% 0.86/0.82 ((~hskp8) | c3_1(a1010)),
% 0.86/0.82 inference(modus_ponens,[status(thm)],[554, 547])).
% 0.86/0.82 tff(556,plain,
% 0.86/0.82 ((~hskp8) | c3_1(a1010)),
% 0.86/0.82 inference(modus_ponens,[status(thm)],[555, 547])).
% 0.86/0.82 tff(557,plain,
% 0.86/0.82 (c3_1(a1010)),
% 0.86/0.82 inference(unit_resolution,[status(thm)],[556, 540])).
% 0.86/0.82 tff(558,plain,
% 0.86/0.82 (((~hskp8) | c0_1(a1010)) <=> ((~hskp8) | c0_1(a1010))),
% 0.86/0.82 inference(rewrite,[status(thm)],[])).
% 0.86/0.82 tff(559,axiom,((~hskp8) | c0_1(a1010)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause71')).
% 0.86/0.82 tff(560,plain,
% 0.86/0.82 ((~hskp8) | c0_1(a1010)),
% 0.86/0.82 inference(modus_ponens,[status(thm)],[559, 558])).
% 0.86/0.82 tff(561,plain,
% 0.86/0.82 ((~hskp8) | c0_1(a1010)),
% 0.86/0.82 inference(modus_ponens,[status(thm)],[560, 558])).
% 0.86/0.82 tff(562,plain,
% 0.86/0.82 ((~hskp8) | c0_1(a1010)),
% 0.86/0.82 inference(modus_ponens,[status(thm)],[561, 558])).
% 0.86/0.82 tff(563,plain,
% 0.86/0.82 ((~hskp8) | c0_1(a1010)),
% 0.86/0.82 inference(modus_ponens,[status(thm)],[562, 558])).
% 0.86/0.82 tff(564,plain,
% 0.86/0.82 ((~hskp8) | c0_1(a1010)),
% 0.86/0.82 inference(modus_ponens,[status(thm)],[563, 558])).
% 0.86/0.82 tff(565,plain,
% 0.86/0.82 ((~hskp8) | c0_1(a1010)),
% 0.86/0.82 inference(modus_ponens,[status(thm)],[564, 558])).
% 0.86/0.82 tff(566,plain,
% 0.86/0.82 ((~hskp8) | c0_1(a1010)),
% 0.86/0.82 inference(modus_ponens,[status(thm)],[565, 558])).
% 0.86/0.82 tff(567,plain,
% 0.86/0.82 ((~hskp8) | c0_1(a1010)),
% 0.86/0.82 inference(modus_ponens,[status(thm)],[566, 558])).
% 0.86/0.82 tff(568,plain,
% 0.86/0.82 (c0_1(a1010)),
% 0.86/0.82 inference(unit_resolution,[status(thm)],[567, 540])).
% 0.86/0.82 tff(569,plain,
% 0.86/0.82 (((~![U: $i] : (hskp23 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp23 | c1_1(a1010) | (~ndr1_0) | (~c0_1(a1010)) | (~c3_1(a1010)))) <=> ((~![U: $i] : (hskp23 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp23 | c1_1(a1010) | (~ndr1_0) | (~c0_1(a1010)) | (~c3_1(a1010)))),
% 0.86/0.82 inference(rewrite,[status(thm)],[])).
% 0.86/0.82 tff(570,plain,
% 0.86/0.82 ((hskp23 | (~ndr1_0) | c1_1(a1010) | (~c3_1(a1010)) | (~c0_1(a1010))) <=> (hskp23 | c1_1(a1010) | (~ndr1_0) | (~c0_1(a1010)) | (~c3_1(a1010)))),
% 0.86/0.82 inference(rewrite,[status(thm)],[])).
% 0.86/0.82 tff(571,plain,
% 0.86/0.82 (((~![U: $i] : (hskp23 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp23 | (~ndr1_0) | c1_1(a1010) | (~c3_1(a1010)) | (~c0_1(a1010)))) <=> ((~![U: $i] : (hskp23 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp23 | c1_1(a1010) | (~ndr1_0) | (~c0_1(a1010)) | (~c3_1(a1010))))),
% 0.86/0.82 inference(monotonicity,[status(thm)],[570])).
% 0.86/0.82 tff(572,plain,
% 0.86/0.82 (((~![U: $i] : (hskp23 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp23 | (~ndr1_0) | c1_1(a1010) | (~c3_1(a1010)) | (~c0_1(a1010)))) <=> ((~![U: $i] : (hskp23 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp23 | c1_1(a1010) | (~ndr1_0) | (~c0_1(a1010)) | (~c3_1(a1010)))),
% 0.86/0.82 inference(transitivity,[status(thm)],[571, 569])).
% 0.86/0.82 tff(573,plain,
% 0.86/0.82 ((~![U: $i] : (hskp23 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp23 | (~ndr1_0) | c1_1(a1010) | (~c3_1(a1010)) | (~c0_1(a1010)))),
% 0.86/0.82 inference(quant_inst,[status(thm)],[])).
% 0.86/0.82 tff(574,plain,
% 0.86/0.82 ((~![U: $i] : (hskp23 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp23 | c1_1(a1010) | (~ndr1_0) | (~c0_1(a1010)) | (~c3_1(a1010))),
% 0.86/0.82 inference(modus_ponens,[status(thm)],[573, 572])).
% 0.86/0.82 tff(575,plain,
% 0.86/0.82 ($false),
% 0.86/0.82 inference(unit_resolution,[status(thm)],[574, 90, 22, 568, 557, 546, 32])).
% 0.86/0.82 tff(576,plain,((~hskp8) | hskp23), inference(lemma,lemma(discharge,[]))).
% 0.86/0.82 tff(577,plain,
% 0.86/0.82 (~hskp8),
% 0.86/0.82 inference(unit_resolution,[status(thm)],[576, 22])).
% 0.86/0.82 tff(578,plain,
% 0.86/0.82 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp8 | c1_1(a1037) | c3_1(a1037) | c0_1(a1003) | c2_1(a1003) | (~ndr1_0) | (~c1_1(a1003)) | (~c2_1(a1037)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp8 | c1_1(a1037) | c3_1(a1037) | c0_1(a1003) | c2_1(a1003) | (~ndr1_0) | (~c1_1(a1003)) | (~c2_1(a1037)))),
% 0.86/0.82 inference(rewrite,[status(thm)],[])).
% 0.86/0.82 tff(579,plain,
% 0.86/0.82 ((hskp8 | (~ndr1_0) | c1_1(a1037) | c3_1(a1037) | (~c2_1(a1037)) | c0_1(a1003) | c2_1(a1003) | (~c1_1(a1003))) <=> (hskp8 | c1_1(a1037) | c3_1(a1037) | c0_1(a1003) | c2_1(a1003) | (~ndr1_0) | (~c1_1(a1003)) | (~c2_1(a1037)))),
% 0.86/0.82 inference(rewrite,[status(thm)],[])).
% 0.86/0.82 tff(580,plain,
% 0.86/0.82 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp8 | (~ndr1_0) | c1_1(a1037) | c3_1(a1037) | (~c2_1(a1037)) | c0_1(a1003) | c2_1(a1003) | (~c1_1(a1003)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp8 | c1_1(a1037) | c3_1(a1037) | c0_1(a1003) | c2_1(a1003) | (~ndr1_0) | (~c1_1(a1003)) | (~c2_1(a1037))))),
% 0.86/0.82 inference(monotonicity,[status(thm)],[579])).
% 0.86/0.82 tff(581,plain,
% 0.86/0.82 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp8 | (~ndr1_0) | c1_1(a1037) | c3_1(a1037) | (~c2_1(a1037)) | c0_1(a1003) | c2_1(a1003) | (~c1_1(a1003)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp8 | c1_1(a1037) | c3_1(a1037) | c0_1(a1003) | c2_1(a1003) | (~ndr1_0) | (~c1_1(a1003)) | (~c2_1(a1037)))),
% 0.86/0.82 inference(transitivity,[status(thm)],[580, 578])).
% 0.86/0.82 tff(582,plain,
% 0.86/0.82 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp8 | (~ndr1_0) | c1_1(a1037) | c3_1(a1037) | (~c2_1(a1037)) | c0_1(a1003) | c2_1(a1003) | (~c1_1(a1003)))),
% 0.86/0.82 inference(quant_inst,[status(thm)],[])).
% 0.86/0.82 tff(583,plain,
% 0.86/0.82 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp8 | c1_1(a1037) | c3_1(a1037) | c0_1(a1003) | c2_1(a1003) | (~ndr1_0) | (~c1_1(a1003)) | (~c2_1(a1037))),
% 0.86/0.82 inference(modus_ponens,[status(thm)],[582, 581])).
% 0.86/0.82 tff(584,plain,
% 0.86/0.82 ($false),
% 0.86/0.82 inference(unit_resolution,[status(thm)],[583, 90, 577, 539, 147, 141, 528, 522, 21, 359])).
% 0.86/0.82 tff(585,plain,((~hskp2) | hskp23), inference(lemma,lemma(discharge,[]))).
% 0.86/0.82 tff(586,plain,
% 0.86/0.82 (~hskp2),
% 0.86/0.82 inference(unit_resolution,[status(thm)],[585, 22])).
% 0.86/0.82 tff(587,plain,
% 0.86/0.82 (^[V: $i, U: $i] : refl((hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c1_1(V) | c0_1(V)) <=> (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c1_1(V) | c0_1(V)))),
% 0.86/0.82 inference(bind,[status(th)],[])).
% 0.86/0.82 tff(588,plain,
% 0.86/0.82 (![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c1_1(V) | c0_1(V)) <=> ![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c1_1(V) | c0_1(V))),
% 0.86/0.82 inference(quant_intro,[status(thm)],[587])).
% 0.86/0.82 tff(589,plain,
% 0.86/0.82 (![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c1_1(V) | c0_1(V)) <=> ![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c1_1(V) | c0_1(V))),
% 0.86/0.82 inference(rewrite,[status(thm)],[])).
% 0.86/0.82 tff(590,plain,
% 0.86/0.82 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~ndr1_0) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U))), ((((~ndr1_0) | c1_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c1_1(U)) | c2_1(U)))), rewrite((((~ndr1_0) | c1_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U))), ((((~ndr1_0) | c1_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U)))), (((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c2_1(U) | c1_1(U)) | c3_1(U)))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))), (((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U)))), ((((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U)) | c0_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c0_1(V))), ((((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c0_1(V)))), (((((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c0_1(V)) | c1_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c1_1(V) | c0_1(V))), (((((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c1_1(V) | c0_1(V)))), ((((((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c1_1(V) | c0_1(V)) | c3_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c1_1(V) | c0_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c1_1(V) | c0_1(V))), ((((((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c1_1(V) | c0_1(V)))), (((((((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | hskp2) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c1_1(V) | c0_1(V)) | hskp2))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c1_1(V) | c0_1(V)) | hskp2) <=> (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c1_1(V) | c0_1(V))), (((((((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | hskp2) <=> (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c1_1(V) | c0_1(V))))),
% 0.86/0.82 inference(bind,[status(th)],[])).
% 0.86/0.82 tff(591,plain,
% 0.86/0.82 (![V: $i, U: $i] : ((((((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | hskp2) <=> ![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c1_1(V) | c0_1(V))),
% 0.86/0.82 inference(quant_intro,[status(thm)],[590])).
% 0.86/0.82 tff(592,axiom,(![V: $i, U: $i] : ((((((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | hskp2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause151')).
% 0.86/0.82 tff(593,plain,
% 0.86/0.82 (![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c1_1(V) | c0_1(V))),
% 0.86/0.82 inference(modus_ponens,[status(thm)],[592, 591])).
% 0.86/0.82 tff(594,plain,
% 0.86/0.82 (![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c1_1(V) | c0_1(V))),
% 0.86/0.82 inference(modus_ponens,[status(thm)],[593, 589])).
% 0.86/0.82 tff(595,plain,(
% 0.86/0.82 ![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c1_1(V) | c0_1(V))),
% 0.86/0.82 inference(skolemize,[status(sab)],[594])).
% 0.86/0.82 tff(596,plain,
% 0.86/0.82 (![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c1_1(V) | c0_1(V))),
% 0.86/0.82 inference(modus_ponens,[status(thm)],[595, 588])).
% 0.86/0.82 tff(597,assumption,(hskp5), introduced(assumption)).
% 0.86/0.82 tff(598,plain,
% 0.86/0.82 (((~hskp5) | (~c3_1(a1005))) <=> ((~hskp5) | (~c3_1(a1005)))),
% 0.86/0.82 inference(rewrite,[status(thm)],[])).
% 0.86/0.82 tff(599,plain,
% 0.86/0.82 (((~c3_1(a1005)) | (~hskp5)) <=> ((~hskp5) | (~c3_1(a1005)))),
% 0.86/0.82 inference(rewrite,[status(thm)],[])).
% 0.86/0.82 tff(600,axiom,((~c3_1(a1005)) | (~hskp5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause123')).
% 0.86/0.82 tff(601,plain,
% 0.86/0.82 ((~hskp5) | (~c3_1(a1005))),
% 0.86/0.82 inference(modus_ponens,[status(thm)],[600, 599])).
% 0.86/0.82 tff(602,plain,
% 0.86/0.82 ((~hskp5) | (~c3_1(a1005))),
% 0.86/0.82 inference(modus_ponens,[status(thm)],[601, 598])).
% 0.86/0.82 tff(603,plain,
% 0.86/0.82 (~c3_1(a1005)),
% 0.86/0.82 inference(unit_resolution,[status(thm)],[602, 597])).
% 0.86/0.82 tff(604,plain,
% 0.86/0.82 (((~hskp5) | (~c2_1(a1005))) <=> ((~hskp5) | (~c2_1(a1005)))),
% 0.86/0.82 inference(rewrite,[status(thm)],[])).
% 0.86/0.82 tff(605,plain,
% 0.86/0.82 (((~c2_1(a1005)) | (~hskp5)) <=> ((~hskp5) | (~c2_1(a1005)))),
% 0.86/0.82 inference(rewrite,[status(thm)],[])).
% 0.86/0.82 tff(606,axiom,((~c2_1(a1005)) | (~hskp5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause122')).
% 0.86/0.82 tff(607,plain,
% 0.86/0.82 ((~hskp5) | (~c2_1(a1005))),
% 0.86/0.82 inference(modus_ponens,[status(thm)],[606, 605])).
% 0.86/0.82 tff(608,plain,
% 0.86/0.82 ((~hskp5) | (~c2_1(a1005))),
% 0.86/0.82 inference(modus_ponens,[status(thm)],[607, 604])).
% 0.86/0.82 tff(609,plain,
% 0.86/0.82 (~c2_1(a1005)),
% 0.86/0.82 inference(unit_resolution,[status(thm)],[608, 597])).
% 0.86/0.83 tff(610,plain,
% 0.86/0.83 (((~hskp5) | (~c1_1(a1005))) <=> ((~hskp5) | (~c1_1(a1005)))),
% 0.86/0.83 inference(rewrite,[status(thm)],[])).
% 0.86/0.83 tff(611,plain,
% 0.86/0.83 (((~c1_1(a1005)) | (~hskp5)) <=> ((~hskp5) | (~c1_1(a1005)))),
% 0.86/0.83 inference(rewrite,[status(thm)],[])).
% 0.86/0.83 tff(612,axiom,((~c1_1(a1005)) | (~hskp5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause121')).
% 0.86/0.83 tff(613,plain,
% 0.86/0.83 ((~hskp5) | (~c1_1(a1005))),
% 0.86/0.83 inference(modus_ponens,[status(thm)],[612, 611])).
% 0.86/0.83 tff(614,plain,
% 0.86/0.83 ((~hskp5) | (~c1_1(a1005))),
% 0.86/0.83 inference(modus_ponens,[status(thm)],[613, 610])).
% 0.86/0.83 tff(615,plain,
% 0.86/0.83 (~c1_1(a1005)),
% 0.86/0.83 inference(unit_resolution,[status(thm)],[614, 597])).
% 0.86/0.83 tff(616,assumption,(~hskp2), introduced(assumption)).
% 0.86/0.83 tff(617,plain,
% 0.86/0.83 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | c1_1(a1005) | c2_1(a1005) | c3_1(a1005) | (~ndr1_0) | c0_1(a1005))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp2 | c1_1(a1005) | c2_1(a1005) | c3_1(a1005) | (~ndr1_0) | c0_1(a1005))),
% 0.86/0.83 inference(rewrite,[status(thm)],[])).
% 0.86/0.83 tff(618,plain,
% 0.86/0.83 ((hskp2 | (~ndr1_0) | c2_1(a1005) | c1_1(a1005) | c3_1(a1005) | c3_1(a1005) | c1_1(a1005) | c0_1(a1005)) <=> (hskp2 | c1_1(a1005) | c2_1(a1005) | c3_1(a1005) | (~ndr1_0) | c0_1(a1005))),
% 0.86/0.83 inference(rewrite,[status(thm)],[])).
% 0.86/0.83 tff(619,plain,
% 0.86/0.83 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | (~ndr1_0) | c2_1(a1005) | c1_1(a1005) | c3_1(a1005) | c3_1(a1005) | c1_1(a1005) | c0_1(a1005))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | c1_1(a1005) | c2_1(a1005) | c3_1(a1005) | (~ndr1_0) | c0_1(a1005)))),
% 0.86/0.83 inference(monotonicity,[status(thm)],[618])).
% 0.86/0.83 tff(620,plain,
% 0.86/0.83 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | (~ndr1_0) | c2_1(a1005) | c1_1(a1005) | c3_1(a1005) | c3_1(a1005) | c1_1(a1005) | c0_1(a1005))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp2 | c1_1(a1005) | c2_1(a1005) | c3_1(a1005) | (~ndr1_0) | c0_1(a1005))),
% 0.86/0.83 inference(transitivity,[status(thm)],[619, 617])).
% 0.86/0.83 tff(621,plain,
% 0.86/0.83 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | (~ndr1_0) | c2_1(a1005) | c1_1(a1005) | c3_1(a1005) | c3_1(a1005) | c1_1(a1005) | c0_1(a1005))),
% 0.86/0.83 inference(quant_inst,[status(thm)],[])).
% 0.86/0.83 tff(622,plain,
% 0.86/0.83 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp2 | c1_1(a1005) | c2_1(a1005) | c3_1(a1005) | (~ndr1_0) | c0_1(a1005)),
% 0.86/0.83 inference(modus_ponens,[status(thm)],[621, 620])).
% 0.86/0.83 tff(623,plain,
% 0.86/0.83 (c0_1(a1005)),
% 0.86/0.83 inference(unit_resolution,[status(thm)],[622, 90, 616, 615, 609, 603, 596])).
% 0.86/0.83 tff(624,assumption,(~hskp13), introduced(assumption)).
% 0.86/0.83 tff(625,plain,
% 0.86/0.83 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp13 | c1_1(a1005) | c2_1(a1005) | c3_1(a1005) | (~ndr1_0) | (~c0_1(a1005)))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp13 | c1_1(a1005) | c2_1(a1005) | c3_1(a1005) | (~ndr1_0) | (~c0_1(a1005)))),
% 0.86/0.83 inference(rewrite,[status(thm)],[])).
% 0.86/0.83 tff(626,plain,
% 0.86/0.83 ((hskp13 | (~ndr1_0) | c1_1(a1005) | c3_1(a1005) | (~c0_1(a1005)) | c3_1(a1005) | c1_1(a1005) | c2_1(a1005)) <=> (hskp13 | c1_1(a1005) | c2_1(a1005) | c3_1(a1005) | (~ndr1_0) | (~c0_1(a1005)))),
% 0.86/0.83 inference(rewrite,[status(thm)],[])).
% 0.86/0.83 tff(627,plain,
% 0.86/0.83 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp13 | (~ndr1_0) | c1_1(a1005) | c3_1(a1005) | (~c0_1(a1005)) | c3_1(a1005) | c1_1(a1005) | c2_1(a1005))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp13 | c1_1(a1005) | c2_1(a1005) | c3_1(a1005) | (~ndr1_0) | (~c0_1(a1005))))),
% 0.86/0.83 inference(monotonicity,[status(thm)],[626])).
% 0.86/0.83 tff(628,plain,
% 0.86/0.83 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp13 | (~ndr1_0) | c1_1(a1005) | c3_1(a1005) | (~c0_1(a1005)) | c3_1(a1005) | c1_1(a1005) | c2_1(a1005))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp13 | c1_1(a1005) | c2_1(a1005) | c3_1(a1005) | (~ndr1_0) | (~c0_1(a1005)))),
% 0.86/0.83 inference(transitivity,[status(thm)],[627, 625])).
% 0.86/0.83 tff(629,plain,
% 0.86/0.83 ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp13 | (~ndr1_0) | c1_1(a1005) | c3_1(a1005) | (~c0_1(a1005)) | c3_1(a1005) | c1_1(a1005) | c2_1(a1005))),
% 0.86/0.83 inference(quant_inst,[status(thm)],[])).
% 0.86/0.83 tff(630,plain,
% 0.86/0.83 ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp13 | c1_1(a1005) | c2_1(a1005) | c3_1(a1005) | (~ndr1_0) | (~c0_1(a1005))),
% 0.86/0.83 inference(modus_ponens,[status(thm)],[629, 628])).
% 0.86/0.83 tff(631,plain,
% 0.86/0.83 ($false),
% 0.86/0.83 inference(unit_resolution,[status(thm)],[630, 90, 624, 615, 609, 603, 107, 623])).
% 0.86/0.83 tff(632,plain,((~hskp5) | hskp13 | hskp2), inference(lemma,lemma(discharge,[]))).
% 0.86/0.83 tff(633,plain,
% 0.86/0.83 (~hskp5),
% 0.86/0.83 inference(unit_resolution,[status(thm)],[632, 352, 586])).
% 0.86/0.83 tff(634,plain,
% 0.86/0.83 (^[U: $i] : refl((hskp8 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U))) <=> (hskp8 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U))))),
% 0.86/0.83 inference(bind,[status(th)],[])).
% 0.86/0.83 tff(635,plain,
% 0.86/0.83 (![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U))) <=> ![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))),
% 0.86/0.83 inference(quant_intro,[status(thm)],[634])).
% 0.86/0.83 tff(636,plain,
% 0.86/0.83 (![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U))) <=> ![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))),
% 0.86/0.83 inference(rewrite,[status(thm)],[])).
% 0.86/0.83 tff(637,plain,
% 0.86/0.83 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c1_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)))), ((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) <=> (((~ndr1_0) | (~c1_1(U))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)))), ((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U))))), (((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c0_1(U) | (~c1_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | c0_1(U) | (~c1_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))), (((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U))))), ((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp8) <=> (((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U))) | hskp8))), rewrite((((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U))) | hskp8) <=> (hskp8 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))), ((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp8) <=> (hskp8 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U))))), (((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp8) | hskp7) <=> ((hskp8 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U))) | hskp7))), rewrite(((hskp8 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U))) | hskp7) <=> (hskp8 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))), (((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp8) | hskp7) <=> (hskp8 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))))),
% 0.86/0.83 inference(bind,[status(th)],[])).
% 0.86/0.83 tff(638,plain,
% 0.86/0.83 (![U: $i] : ((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp8) | hskp7) <=> ![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))),
% 0.86/0.83 inference(quant_intro,[status(thm)],[637])).
% 0.86/0.83 tff(639,axiom,(![U: $i] : ((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp8) | hskp7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause132')).
% 0.86/0.83 tff(640,plain,
% 0.86/0.83 (![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))),
% 0.86/0.83 inference(modus_ponens,[status(thm)],[639, 638])).
% 0.86/0.83 tff(641,plain,
% 0.86/0.83 (![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))),
% 0.86/0.83 inference(modus_ponens,[status(thm)],[640, 636])).
% 0.86/0.83 tff(642,plain,(
% 0.86/0.83 ![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))),
% 0.86/0.83 inference(skolemize,[status(sab)],[641])).
% 0.86/0.83 tff(643,plain,
% 0.86/0.83 (![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))),
% 0.86/0.83 inference(modus_ponens,[status(thm)],[642, 635])).
% 0.86/0.83 tff(644,assumption,(~hskp7), introduced(assumption)).
% 0.86/0.83 tff(645,plain,
% 0.86/0.83 (((~![U: $i] : (hskp7 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)))) | (hskp7 | (~ndr1_0) | (~c2_1(a1040)) | (~c0_1(a1040)) | (~c1_1(a1040)))) <=> ((~![U: $i] : (hskp7 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)))) | hskp7 | (~ndr1_0) | (~c2_1(a1040)) | (~c0_1(a1040)) | (~c1_1(a1040)))),
% 0.86/0.83 inference(rewrite,[status(thm)],[])).
% 0.86/0.83 tff(646,plain,
% 0.86/0.83 ((hskp7 | (~ndr1_0) | (~c1_1(a1040)) | (~c2_1(a1040)) | (~c0_1(a1040))) <=> (hskp7 | (~ndr1_0) | (~c2_1(a1040)) | (~c0_1(a1040)) | (~c1_1(a1040)))),
% 0.86/0.83 inference(rewrite,[status(thm)],[])).
% 0.86/0.83 tff(647,plain,
% 0.86/0.83 (((~![U: $i] : (hskp7 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)))) | (hskp7 | (~ndr1_0) | (~c1_1(a1040)) | (~c2_1(a1040)) | (~c0_1(a1040)))) <=> ((~![U: $i] : (hskp7 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)))) | (hskp7 | (~ndr1_0) | (~c2_1(a1040)) | (~c0_1(a1040)) | (~c1_1(a1040))))),
% 0.86/0.83 inference(monotonicity,[status(thm)],[646])).
% 0.86/0.83 tff(648,plain,
% 0.86/0.83 (((~![U: $i] : (hskp7 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)))) | (hskp7 | (~ndr1_0) | (~c1_1(a1040)) | (~c2_1(a1040)) | (~c0_1(a1040)))) <=> ((~![U: $i] : (hskp7 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)))) | hskp7 | (~ndr1_0) | (~c2_1(a1040)) | (~c0_1(a1040)) | (~c1_1(a1040)))),
% 0.86/0.83 inference(transitivity,[status(thm)],[647, 645])).
% 0.86/0.83 tff(649,plain,
% 0.86/0.83 ((~![U: $i] : (hskp7 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)))) | (hskp7 | (~ndr1_0) | (~c1_1(a1040)) | (~c2_1(a1040)) | (~c0_1(a1040)))),
% 0.86/0.83 inference(quant_inst,[status(thm)],[])).
% 0.86/0.83 tff(650,plain,
% 0.86/0.83 ((~![U: $i] : (hskp7 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)))) | hskp7 | (~ndr1_0) | (~c2_1(a1040)) | (~c0_1(a1040)) | (~c1_1(a1040))),
% 0.86/0.83 inference(modus_ponens,[status(thm)],[649, 648])).
% 0.86/0.83 tff(651,plain,
% 0.86/0.83 (hskp7 | (~c2_1(a1040))),
% 0.86/0.83 inference(unit_resolution,[status(thm)],[650, 90, 393, 425, 188])).
% 0.86/0.83 tff(652,plain,
% 0.86/0.83 (~c2_1(a1040)),
% 0.86/0.83 inference(unit_resolution,[status(thm)],[651, 644])).
% 0.86/0.83 tff(653,plain,
% 0.86/0.83 (hskp3),
% 0.86/0.83 inference(unit_resolution,[status(thm)],[400, 652])).
% 0.86/0.83 tff(654,plain,
% 0.86/0.83 (~c2_1(a1003)),
% 0.86/0.83 inference(unit_resolution,[status(thm)],[521, 653])).
% 0.86/0.83 tff(655,plain,
% 0.86/0.83 (~c0_1(a1003)),
% 0.86/0.83 inference(unit_resolution,[status(thm)],[527, 653])).
% 0.86/0.83 tff(656,plain,
% 0.86/0.83 (c1_1(a1003)),
% 0.86/0.83 inference(unit_resolution,[status(thm)],[538, 653])).
% 0.86/0.83 tff(657,plain,
% 0.86/0.83 (((~![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))) | (hskp8 | hskp7 | c0_1(a1003) | c2_1(a1003) | (~ndr1_0) | (~c1_1(a1003)))) <=> ((~![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))) | hskp8 | hskp7 | c0_1(a1003) | c2_1(a1003) | (~ndr1_0) | (~c1_1(a1003)))),
% 0.86/0.83 inference(rewrite,[status(thm)],[])).
% 0.86/0.83 tff(658,plain,
% 0.86/0.83 ((hskp8 | hskp7 | (~ndr1_0) | c2_1(a1003) | c0_1(a1003) | (~c1_1(a1003))) <=> (hskp8 | hskp7 | c0_1(a1003) | c2_1(a1003) | (~ndr1_0) | (~c1_1(a1003)))),
% 0.86/0.83 inference(rewrite,[status(thm)],[])).
% 0.86/0.83 tff(659,plain,
% 0.86/0.83 (((~![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))) | (hskp8 | hskp7 | (~ndr1_0) | c2_1(a1003) | c0_1(a1003) | (~c1_1(a1003)))) <=> ((~![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))) | (hskp8 | hskp7 | c0_1(a1003) | c2_1(a1003) | (~ndr1_0) | (~c1_1(a1003))))),
% 0.86/0.83 inference(monotonicity,[status(thm)],[658])).
% 0.86/0.83 tff(660,plain,
% 0.86/0.83 (((~![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))) | (hskp8 | hskp7 | (~ndr1_0) | c2_1(a1003) | c0_1(a1003) | (~c1_1(a1003)))) <=> ((~![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))) | hskp8 | hskp7 | c0_1(a1003) | c2_1(a1003) | (~ndr1_0) | (~c1_1(a1003)))),
% 0.86/0.83 inference(transitivity,[status(thm)],[659, 657])).
% 0.86/0.83 tff(661,plain,
% 0.86/0.83 ((~![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))) | (hskp8 | hskp7 | (~ndr1_0) | c2_1(a1003) | c0_1(a1003) | (~c1_1(a1003)))),
% 0.86/0.83 inference(quant_inst,[status(thm)],[])).
% 0.86/0.83 tff(662,plain,
% 0.86/0.83 ((~![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))) | hskp8 | hskp7 | c0_1(a1003) | c2_1(a1003) | (~ndr1_0) | (~c1_1(a1003))),
% 0.86/0.83 inference(modus_ponens,[status(thm)],[661, 660])).
% 0.86/0.83 tff(663,plain,
% 0.86/0.83 ($false),
% 0.86/0.83 inference(unit_resolution,[status(thm)],[662, 90, 577, 644, 656, 655, 654, 643])).
% 0.86/0.83 tff(664,plain,(hskp7 | hskp23), inference(lemma,lemma(discharge,[]))).
% 0.86/0.83 tff(665,plain,
% 0.86/0.83 (hskp7),
% 0.86/0.83 inference(unit_resolution,[status(thm)],[664, 22])).
% 0.86/0.83 tff(666,plain,
% 0.86/0.83 (c2_1(a1008)),
% 0.86/0.83 inference(unit_resolution,[status(thm)],[248, 665])).
% 0.86/0.83 tff(667,plain,
% 0.86/0.83 (~c3_1(a1008)),
% 0.86/0.83 inference(unit_resolution,[status(thm)],[231, 665])).
% 0.86/0.83 tff(668,plain,
% 0.86/0.83 (~c1_1(a1008)),
% 0.86/0.83 inference(unit_resolution,[status(thm)],[237, 665])).
% 0.86/0.83 tff(669,plain,
% 0.86/0.83 (^[U: $i] : refl((hskp2 | hskp1 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U))) <=> (hskp2 | hskp1 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U))))),
% 0.86/0.83 inference(bind,[status(th)],[])).
% 0.86/0.83 tff(670,plain,
% 0.86/0.83 (![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U))) <=> ![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))),
% 0.86/0.83 inference(quant_intro,[status(thm)],[669])).
% 0.86/0.83 tff(671,plain,
% 0.86/0.83 (![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U))) <=> ![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))),
% 0.86/0.83 inference(rewrite,[status(thm)],[])).
% 0.86/0.83 tff(672,plain,
% 0.86/0.83 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c2_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)))), ((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) <=> (((~ndr1_0) | (~c2_1(U))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)))), ((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U))))), (((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c0_1(U) | (~c2_1(U))) | c3_1(U)))), rewrite((((~ndr1_0) | c0_1(U) | (~c2_1(U))) | c3_1(U)) <=> ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))), (((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U))))), ((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp2) <=> (((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U))) | hskp2))), rewrite((((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U))) | hskp2) <=> (hskp2 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))), ((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp2) <=> (hskp2 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U))))), (((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp2) | hskp1) <=> ((hskp2 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U))) | hskp1))), rewrite(((hskp2 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U))) | hskp1) <=> (hskp2 | hskp1 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))), (((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp2) | hskp1) <=> (hskp2 | hskp1 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))))),
% 0.86/0.83 inference(bind,[status(th)],[])).
% 0.86/0.83 tff(673,plain,
% 0.86/0.83 (![U: $i] : ((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp2) | hskp1) <=> ![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))),
% 0.86/0.83 inference(quant_intro,[status(thm)],[672])).
% 0.86/0.83 tff(674,axiom,(![U: $i] : ((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp2) | hskp1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause134')).
% 0.86/0.83 tff(675,plain,
% 0.86/0.83 (![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))),
% 0.86/0.83 inference(modus_ponens,[status(thm)],[674, 673])).
% 0.86/0.83 tff(676,plain,
% 0.86/0.83 (![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))),
% 0.86/0.83 inference(modus_ponens,[status(thm)],[675, 671])).
% 0.86/0.83 tff(677,plain,(
% 0.86/0.83 ![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))),
% 0.86/0.83 inference(skolemize,[status(sab)],[676])).
% 0.86/0.83 tff(678,plain,
% 0.86/0.83 (![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))),
% 0.86/0.83 inference(modus_ponens,[status(thm)],[677, 670])).
% 0.86/0.83 tff(679,assumption,(~hskp1), introduced(assumption)).
% 0.86/0.83 tff(680,assumption,(~c3_1(a1008)), introduced(assumption)).
% 0.86/0.83 tff(681,assumption,(c2_1(a1008)), introduced(assumption)).
% 0.86/0.83 tff(682,plain,
% 0.86/0.83 (((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp2 | hskp1 | c3_1(a1008) | (~ndr1_0) | (~c2_1(a1008)) | c0_1(a1008))) <=> ((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | hskp2 | hskp1 | c3_1(a1008) | (~ndr1_0) | (~c2_1(a1008)) | c0_1(a1008))),
% 0.86/0.83 inference(rewrite,[status(thm)],[])).
% 0.86/0.83 tff(683,plain,
% 0.86/0.83 ((hskp2 | hskp1 | (~ndr1_0) | c0_1(a1008) | c3_1(a1008) | (~c2_1(a1008))) <=> (hskp2 | hskp1 | c3_1(a1008) | (~ndr1_0) | (~c2_1(a1008)) | c0_1(a1008))),
% 0.86/0.83 inference(rewrite,[status(thm)],[])).
% 0.86/0.83 tff(684,plain,
% 0.86/0.83 (((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp2 | hskp1 | (~ndr1_0) | c0_1(a1008) | c3_1(a1008) | (~c2_1(a1008)))) <=> ((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp2 | hskp1 | c3_1(a1008) | (~ndr1_0) | (~c2_1(a1008)) | c0_1(a1008)))),
% 0.86/0.83 inference(monotonicity,[status(thm)],[683])).
% 0.86/0.83 tff(685,plain,
% 0.86/0.83 (((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp2 | hskp1 | (~ndr1_0) | c0_1(a1008) | c3_1(a1008) | (~c2_1(a1008)))) <=> ((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | hskp2 | hskp1 | c3_1(a1008) | (~ndr1_0) | (~c2_1(a1008)) | c0_1(a1008))),
% 0.86/0.83 inference(transitivity,[status(thm)],[684, 682])).
% 0.86/0.83 tff(686,plain,
% 0.86/0.83 ((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp2 | hskp1 | (~ndr1_0) | c0_1(a1008) | c3_1(a1008) | (~c2_1(a1008)))),
% 0.86/0.83 inference(quant_inst,[status(thm)],[])).
% 0.86/0.83 tff(687,plain,
% 0.86/0.83 ((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | hskp2 | hskp1 | c3_1(a1008) | (~ndr1_0) | (~c2_1(a1008)) | c0_1(a1008)),
% 0.86/0.83 inference(modus_ponens,[status(thm)],[686, 685])).
% 0.86/0.83 tff(688,plain,
% 0.86/0.83 (hskp2 | hskp1 | c0_1(a1008)),
% 0.86/0.83 inference(unit_resolution,[status(thm)],[687, 90, 681, 680, 678])).
% 0.86/0.83 tff(689,plain,
% 0.86/0.83 (c0_1(a1008)),
% 0.86/0.83 inference(unit_resolution,[status(thm)],[688, 616, 679])).
% 0.86/0.83 tff(690,assumption,(~c1_1(a1008)), introduced(assumption)).
% 0.86/0.83 tff(691,plain,
% 0.86/0.83 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp19 | c1_1(a1008) | c3_1(a1008) | (~ndr1_0) | (~c2_1(a1008)) | (~c0_1(a1008)))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | hskp19 | c1_1(a1008) | c3_1(a1008) | (~ndr1_0) | (~c2_1(a1008)) | (~c0_1(a1008)))),
% 0.86/0.83 inference(rewrite,[status(thm)],[])).
% 0.86/0.83 tff(692,plain,
% 0.86/0.83 ((hskp19 | (~ndr1_0) | c1_1(a1008) | (~c2_1(a1008)) | (~c0_1(a1008)) | c3_1(a1008) | c1_1(a1008) | (~c0_1(a1008))) <=> (hskp19 | c1_1(a1008) | c3_1(a1008) | (~ndr1_0) | (~c2_1(a1008)) | (~c0_1(a1008)))),
% 0.86/0.83 inference(rewrite,[status(thm)],[])).
% 0.86/0.83 tff(693,plain,
% 0.86/0.83 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp19 | (~ndr1_0) | c1_1(a1008) | (~c2_1(a1008)) | (~c0_1(a1008)) | c3_1(a1008) | c1_1(a1008) | (~c0_1(a1008)))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp19 | c1_1(a1008) | c3_1(a1008) | (~ndr1_0) | (~c2_1(a1008)) | (~c0_1(a1008))))),
% 0.86/0.83 inference(monotonicity,[status(thm)],[692])).
% 0.86/0.83 tff(694,plain,
% 0.86/0.83 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp19 | (~ndr1_0) | c1_1(a1008) | (~c2_1(a1008)) | (~c0_1(a1008)) | c3_1(a1008) | c1_1(a1008) | (~c0_1(a1008)))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | hskp19 | c1_1(a1008) | c3_1(a1008) | (~ndr1_0) | (~c2_1(a1008)) | (~c0_1(a1008)))),
% 0.86/0.83 inference(transitivity,[status(thm)],[693, 691])).
% 0.86/0.83 tff(695,plain,
% 0.86/0.83 ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp19 | (~ndr1_0) | c1_1(a1008) | (~c2_1(a1008)) | (~c0_1(a1008)) | c3_1(a1008) | c1_1(a1008) | (~c0_1(a1008)))),
% 0.86/0.83 inference(quant_inst,[status(thm)],[])).
% 0.86/0.83 tff(696,plain,
% 0.86/0.83 ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | hskp19 | c1_1(a1008) | c3_1(a1008) | (~ndr1_0) | (~c2_1(a1008)) | (~c0_1(a1008))),
% 0.86/0.83 inference(modus_ponens,[status(thm)],[695, 694])).
% 0.86/0.83 tff(697,plain,
% 0.86/0.83 (hskp19 | (~c0_1(a1008))),
% 0.86/0.83 inference(unit_resolution,[status(thm)],[696, 90, 681, 690, 680, 117])).
% 0.86/0.83 tff(698,plain,
% 0.86/0.83 (hskp19),
% 0.86/0.83 inference(unit_resolution,[status(thm)],[697, 689])).
% 0.86/0.83 tff(699,plain,
% 0.86/0.83 (~c3_1(a1037)),
% 0.86/0.83 inference(unit_resolution,[status(thm)],[140, 698])).
% 0.86/0.83 tff(700,plain,
% 0.86/0.83 (((~hskp19) | (~c0_1(a1037))) <=> ((~hskp19) | (~c0_1(a1037)))),
% 0.86/0.83 inference(rewrite,[status(thm)],[])).
% 0.86/0.83 tff(701,plain,
% 0.86/0.83 (((~c0_1(a1037)) | (~hskp19)) <=> ((~hskp19) | (~c0_1(a1037)))),
% 0.86/0.83 inference(rewrite,[status(thm)],[])).
% 0.86/0.83 tff(702,axiom,((~c0_1(a1037)) | (~hskp19)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause98')).
% 0.86/0.83 tff(703,plain,
% 0.86/0.83 ((~hskp19) | (~c0_1(a1037))),
% 0.86/0.83 inference(modus_ponens,[status(thm)],[702, 701])).
% 0.86/0.83 tff(704,plain,
% 0.86/0.83 ((~hskp19) | (~c0_1(a1037))),
% 0.86/0.83 inference(modus_ponens,[status(thm)],[703, 700])).
% 0.86/0.83 tff(705,plain,
% 0.86/0.83 (~c0_1(a1037)),
% 0.86/0.83 inference(unit_resolution,[status(thm)],[704, 698])).
% 0.86/0.83 tff(706,plain,
% 0.86/0.83 (((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp2 | hskp1 | c0_1(a1037) | c3_1(a1037) | (~ndr1_0) | (~c2_1(a1037)))) <=> ((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | hskp2 | hskp1 | c0_1(a1037) | c3_1(a1037) | (~ndr1_0) | (~c2_1(a1037)))),
% 0.86/0.83 inference(rewrite,[status(thm)],[])).
% 0.86/0.83 tff(707,plain,
% 0.86/0.83 ((hskp2 | hskp1 | (~ndr1_0) | c0_1(a1037) | c3_1(a1037) | (~c2_1(a1037))) <=> (hskp2 | hskp1 | c0_1(a1037) | c3_1(a1037) | (~ndr1_0) | (~c2_1(a1037)))),
% 0.86/0.83 inference(rewrite,[status(thm)],[])).
% 0.86/0.83 tff(708,plain,
% 0.86/0.83 (((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp2 | hskp1 | (~ndr1_0) | c0_1(a1037) | c3_1(a1037) | (~c2_1(a1037)))) <=> ((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp2 | hskp1 | c0_1(a1037) | c3_1(a1037) | (~ndr1_0) | (~c2_1(a1037))))),
% 0.86/0.83 inference(monotonicity,[status(thm)],[707])).
% 0.86/0.83 tff(709,plain,
% 0.86/0.83 (((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp2 | hskp1 | (~ndr1_0) | c0_1(a1037) | c3_1(a1037) | (~c2_1(a1037)))) <=> ((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | hskp2 | hskp1 | c0_1(a1037) | c3_1(a1037) | (~ndr1_0) | (~c2_1(a1037)))),
% 0.86/0.83 inference(transitivity,[status(thm)],[708, 706])).
% 0.86/0.83 tff(710,plain,
% 0.86/0.83 ((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp2 | hskp1 | (~ndr1_0) | c0_1(a1037) | c3_1(a1037) | (~c2_1(a1037)))),
% 0.86/0.83 inference(quant_inst,[status(thm)],[])).
% 0.86/0.83 tff(711,plain,
% 0.86/0.83 ((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | hskp2 | hskp1 | c0_1(a1037) | c3_1(a1037) | (~ndr1_0) | (~c2_1(a1037))),
% 0.86/0.83 inference(modus_ponens,[status(thm)],[710, 709])).
% 0.86/0.83 tff(712,plain,
% 0.86/0.83 (~c2_1(a1037)),
% 0.86/0.83 inference(unit_resolution,[status(thm)],[711, 90, 616, 679, 705, 699, 678])).
% 0.86/0.83 tff(713,plain,
% 0.86/0.83 (~c1_1(a1037)),
% 0.86/0.83 inference(unit_resolution,[status(thm)],[146, 698])).
% 0.86/0.83 tff(714,plain,
% 0.86/0.83 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp13 | c1_1(a1037) | c3_1(a1037) | c1_1(a1008) | c3_1(a1008) | (~ndr1_0) | (~c0_1(a1008)) | c2_1(a1037))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp13 | c1_1(a1037) | c3_1(a1037) | c1_1(a1008) | c3_1(a1008) | (~ndr1_0) | (~c0_1(a1008)) | c2_1(a1037))),
% 0.86/0.84 inference(rewrite,[status(thm)],[])).
% 0.86/0.84 tff(715,plain,
% 0.86/0.84 ((hskp13 | (~ndr1_0) | c1_1(a1008) | c3_1(a1008) | (~c0_1(a1008)) | c3_1(a1037) | c1_1(a1037) | c2_1(a1037)) <=> (hskp13 | c1_1(a1037) | c3_1(a1037) | c1_1(a1008) | c3_1(a1008) | (~ndr1_0) | (~c0_1(a1008)) | c2_1(a1037))),
% 0.86/0.84 inference(rewrite,[status(thm)],[])).
% 0.86/0.84 tff(716,plain,
% 0.86/0.84 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp13 | (~ndr1_0) | c1_1(a1008) | c3_1(a1008) | (~c0_1(a1008)) | c3_1(a1037) | c1_1(a1037) | c2_1(a1037))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp13 | c1_1(a1037) | c3_1(a1037) | c1_1(a1008) | c3_1(a1008) | (~ndr1_0) | (~c0_1(a1008)) | c2_1(a1037)))),
% 0.86/0.84 inference(monotonicity,[status(thm)],[715])).
% 0.86/0.84 tff(717,plain,
% 0.86/0.84 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp13 | (~ndr1_0) | c1_1(a1008) | c3_1(a1008) | (~c0_1(a1008)) | c3_1(a1037) | c1_1(a1037) | c2_1(a1037))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp13 | c1_1(a1037) | c3_1(a1037) | c1_1(a1008) | c3_1(a1008) | (~ndr1_0) | (~c0_1(a1008)) | c2_1(a1037))),
% 0.86/0.84 inference(transitivity,[status(thm)],[716, 714])).
% 0.86/0.84 tff(718,plain,
% 0.86/0.84 ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp13 | (~ndr1_0) | c1_1(a1008) | c3_1(a1008) | (~c0_1(a1008)) | c3_1(a1037) | c1_1(a1037) | c2_1(a1037))),
% 0.86/0.84 inference(quant_inst,[status(thm)],[])).
% 0.86/0.84 tff(719,plain,
% 0.86/0.84 ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp13 | c1_1(a1037) | c3_1(a1037) | c1_1(a1008) | c3_1(a1008) | (~ndr1_0) | (~c0_1(a1008)) | c2_1(a1037)),
% 0.86/0.84 inference(modus_ponens,[status(thm)],[718, 717])).
% 0.86/0.84 tff(720,plain,
% 0.86/0.84 ($false),
% 0.86/0.84 inference(unit_resolution,[status(thm)],[719, 90, 624, 713, 699, 690, 680, 107, 689, 712])).
% 0.86/0.84 tff(721,plain,(hskp2 | hskp13 | c1_1(a1008) | c3_1(a1008) | hskp1 | (~c2_1(a1008))), inference(lemma,lemma(discharge,[]))).
% 0.86/0.84 tff(722,plain,
% 0.86/0.84 (hskp1),
% 0.86/0.84 inference(unit_resolution,[status(thm)],[721, 586, 668, 667, 352, 666])).
% 0.86/0.84 tff(723,plain,
% 0.86/0.84 (~c1_1(a1001)),
% 0.86/0.84 inference(unit_resolution,[status(thm)],[303, 722])).
% 0.86/0.84 tff(724,plain,
% 0.86/0.84 (c3_1(a1001)),
% 0.86/0.84 inference(unit_resolution,[status(thm)],[314, 722])).
% 0.86/0.84 tff(725,plain,
% 0.86/0.84 (~c0_1(a1001)),
% 0.86/0.84 inference(unit_resolution,[status(thm)],[321, 90, 22, 724, 723, 32])).
% 0.86/0.84 tff(726,plain,
% 0.86/0.84 (^[V: $i, U: $i] : refl((hskp5 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) <=> (hskp5 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))))),
% 0.86/0.84 inference(bind,[status(th)],[])).
% 0.86/0.84 tff(727,plain,
% 0.86/0.84 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 0.86/0.84 inference(quant_intro,[status(thm)],[726])).
% 0.86/0.84 tff(728,plain,
% 0.86/0.84 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 0.86/0.84 inference(rewrite,[status(thm)],[])).
% 0.86/0.84 tff(729,plain,
% 0.86/0.84 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) <=> ((~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) <=> (((~c1_1(U)) | (~c2_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c1_1(U)) | (~c2_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(V)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V))) | c0_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(V)) | c1_1(V)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V))) | c1_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(V)) | c1_1(V)) | hskp5) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) | hskp5))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) | hskp5) <=> (hskp5 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(V)) | c1_1(V)) | hskp5) <=> (hskp5 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))))),
% 0.86/0.84 inference(bind,[status(th)],[])).
% 0.86/0.84 tff(730,plain,
% 0.86/0.84 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(V)) | c1_1(V)) | hskp5) <=> ![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 0.86/0.84 inference(quant_intro,[status(thm)],[729])).
% 0.86/0.84 tff(731,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(V)) | c1_1(V)) | hskp5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause174')).
% 0.86/0.84 tff(732,plain,
% 0.86/0.84 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 0.86/0.84 inference(modus_ponens,[status(thm)],[731, 730])).
% 0.86/0.84 tff(733,plain,
% 0.86/0.84 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 0.86/0.84 inference(modus_ponens,[status(thm)],[732, 728])).
% 0.86/0.84 tff(734,plain,(
% 0.86/0.84 ![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 0.86/0.84 inference(skolemize,[status(sab)],[733])).
% 0.86/0.84 tff(735,plain,
% 0.86/0.84 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 0.86/0.84 inference(modus_ponens,[status(thm)],[734, 727])).
% 0.86/0.84 tff(736,plain,
% 0.86/0.84 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp5 | c1_1(a1001) | (~ndr1_0) | (~c2_1(a1040)) | (~c0_1(a1040)) | (~c1_1(a1040)) | c0_1(a1001) | (~c3_1(a1001)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp5 | c1_1(a1001) | (~ndr1_0) | (~c2_1(a1040)) | (~c0_1(a1040)) | (~c1_1(a1040)) | c0_1(a1001) | (~c3_1(a1001)))),
% 0.86/0.84 inference(rewrite,[status(thm)],[])).
% 0.86/0.84 tff(737,plain,
% 0.86/0.84 ((hskp5 | (~ndr1_0) | (~c1_1(a1040)) | (~c2_1(a1040)) | (~c0_1(a1040)) | c1_1(a1001) | c0_1(a1001) | (~c3_1(a1001))) <=> (hskp5 | c1_1(a1001) | (~ndr1_0) | (~c2_1(a1040)) | (~c0_1(a1040)) | (~c1_1(a1040)) | c0_1(a1001) | (~c3_1(a1001)))),
% 0.86/0.84 inference(rewrite,[status(thm)],[])).
% 0.86/0.84 tff(738,plain,
% 0.86/0.84 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp5 | (~ndr1_0) | (~c1_1(a1040)) | (~c2_1(a1040)) | (~c0_1(a1040)) | c1_1(a1001) | c0_1(a1001) | (~c3_1(a1001)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp5 | c1_1(a1001) | (~ndr1_0) | (~c2_1(a1040)) | (~c0_1(a1040)) | (~c1_1(a1040)) | c0_1(a1001) | (~c3_1(a1001))))),
% 0.86/0.84 inference(monotonicity,[status(thm)],[737])).
% 0.86/0.84 tff(739,plain,
% 0.86/0.84 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp5 | (~ndr1_0) | (~c1_1(a1040)) | (~c2_1(a1040)) | (~c0_1(a1040)) | c1_1(a1001) | c0_1(a1001) | (~c3_1(a1001)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp5 | c1_1(a1001) | (~ndr1_0) | (~c2_1(a1040)) | (~c0_1(a1040)) | (~c1_1(a1040)) | c0_1(a1001) | (~c3_1(a1001)))),
% 0.86/0.84 inference(transitivity,[status(thm)],[738, 736])).
% 0.86/0.84 tff(740,plain,
% 0.86/0.84 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp5 | (~ndr1_0) | (~c1_1(a1040)) | (~c2_1(a1040)) | (~c0_1(a1040)) | c1_1(a1001) | c0_1(a1001) | (~c3_1(a1001)))),
% 0.86/0.84 inference(quant_inst,[status(thm)],[])).
% 0.86/0.84 tff(741,plain,
% 0.86/0.84 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp5 | c1_1(a1001) | (~ndr1_0) | (~c2_1(a1040)) | (~c0_1(a1040)) | (~c1_1(a1040)) | c0_1(a1001) | (~c3_1(a1001))),
% 0.86/0.84 inference(modus_ponens,[status(thm)],[740, 739])).
% 0.86/0.84 tff(742,plain,
% 0.86/0.84 (hskp5 | (~c2_1(a1040))),
% 0.86/0.84 inference(unit_resolution,[status(thm)],[741, 90, 393, 425, 724, 723, 735, 725])).
% 0.86/0.84 tff(743,plain,
% 0.86/0.84 (~c2_1(a1040)),
% 0.86/0.84 inference(unit_resolution,[status(thm)],[742, 633])).
% 0.86/0.84 tff(744,plain,
% 0.86/0.84 (hskp3),
% 0.86/0.84 inference(unit_resolution,[status(thm)],[400, 743])).
% 0.86/0.84 tff(745,plain,
% 0.86/0.84 (~c2_1(a1003)),
% 0.86/0.84 inference(unit_resolution,[status(thm)],[521, 744])).
% 0.86/0.84 tff(746,plain,
% 0.86/0.84 (~c0_1(a1003)),
% 0.86/0.84 inference(unit_resolution,[status(thm)],[527, 744])).
% 0.86/0.84 tff(747,plain,
% 0.86/0.84 (c1_1(a1003)),
% 0.86/0.84 inference(unit_resolution,[status(thm)],[538, 744])).
% 0.86/0.84 tff(748,plain,
% 0.86/0.84 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp8 | c1_1(a1008) | c3_1(a1008) | c0_1(a1003) | c2_1(a1003) | (~ndr1_0) | (~c1_1(a1003)) | (~c2_1(a1008)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp8 | c1_1(a1008) | c3_1(a1008) | c0_1(a1003) | c2_1(a1003) | (~ndr1_0) | (~c1_1(a1003)) | (~c2_1(a1008)))),
% 0.86/0.84 inference(rewrite,[status(thm)],[])).
% 0.86/0.84 tff(749,plain,
% 0.86/0.84 ((hskp8 | (~ndr1_0) | c1_1(a1008) | c3_1(a1008) | (~c2_1(a1008)) | c0_1(a1003) | c2_1(a1003) | (~c1_1(a1003))) <=> (hskp8 | c1_1(a1008) | c3_1(a1008) | c0_1(a1003) | c2_1(a1003) | (~ndr1_0) | (~c1_1(a1003)) | (~c2_1(a1008)))),
% 0.86/0.84 inference(rewrite,[status(thm)],[])).
% 0.86/0.84 tff(750,plain,
% 0.86/0.84 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp8 | (~ndr1_0) | c1_1(a1008) | c3_1(a1008) | (~c2_1(a1008)) | c0_1(a1003) | c2_1(a1003) | (~c1_1(a1003)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp8 | c1_1(a1008) | c3_1(a1008) | c0_1(a1003) | c2_1(a1003) | (~ndr1_0) | (~c1_1(a1003)) | (~c2_1(a1008))))),
% 0.86/0.84 inference(monotonicity,[status(thm)],[749])).
% 0.86/0.84 tff(751,plain,
% 0.86/0.84 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp8 | (~ndr1_0) | c1_1(a1008) | c3_1(a1008) | (~c2_1(a1008)) | c0_1(a1003) | c2_1(a1003) | (~c1_1(a1003)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp8 | c1_1(a1008) | c3_1(a1008) | c0_1(a1003) | c2_1(a1003) | (~ndr1_0) | (~c1_1(a1003)) | (~c2_1(a1008)))),
% 0.93/0.84 inference(transitivity,[status(thm)],[750, 748])).
% 0.93/0.84 tff(752,plain,
% 0.93/0.84 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp8 | (~ndr1_0) | c1_1(a1008) | c3_1(a1008) | (~c2_1(a1008)) | c0_1(a1003) | c2_1(a1003) | (~c1_1(a1003)))),
% 0.93/0.84 inference(quant_inst,[status(thm)],[])).
% 0.93/0.84 tff(753,plain,
% 0.93/0.84 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp8 | c1_1(a1008) | c3_1(a1008) | c0_1(a1003) | c2_1(a1003) | (~ndr1_0) | (~c1_1(a1003)) | (~c2_1(a1008))),
% 0.93/0.84 inference(modus_ponens,[status(thm)],[752, 751])).
% 0.93/0.84 tff(754,plain,
% 0.93/0.84 ($false),
% 0.93/0.84 inference(unit_resolution,[status(thm)],[753, 90, 577, 666, 747, 668, 667, 746, 745, 21])).
% 0.93/0.84 tff(755,plain,(hskp23), inference(lemma,lemma(discharge,[]))).
% 0.93/0.84 tff(756,plain,
% 0.93/0.84 (((~hskp23) | (~c3_1(a1044))) <=> ((~hskp23) | (~c3_1(a1044)))),
% 0.93/0.84 inference(rewrite,[status(thm)],[])).
% 0.93/0.84 tff(757,plain,
% 0.93/0.84 (((~c3_1(a1044)) | (~hskp23)) <=> ((~hskp23) | (~c3_1(a1044)))),
% 0.93/0.84 inference(rewrite,[status(thm)],[])).
% 0.93/0.84 tff(758,axiom,((~c3_1(a1044)) | (~hskp23)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause90')).
% 0.93/0.84 tff(759,plain,
% 0.93/0.84 ((~hskp23) | (~c3_1(a1044))),
% 0.93/0.84 inference(modus_ponens,[status(thm)],[758, 757])).
% 0.93/0.84 tff(760,plain,
% 0.93/0.84 ((~hskp23) | (~c3_1(a1044))),
% 0.93/0.84 inference(modus_ponens,[status(thm)],[759, 756])).
% 0.93/0.84 tff(761,plain,
% 0.93/0.84 (~c3_1(a1044)),
% 0.93/0.84 inference(unit_resolution,[status(thm)],[760, 755])).
% 0.93/0.84 tff(762,plain,
% 0.93/0.84 (((~hskp23) | c1_1(a1044)) <=> ((~hskp23) | c1_1(a1044))),
% 0.93/0.84 inference(rewrite,[status(thm)],[])).
% 0.93/0.84 tff(763,axiom,((~hskp23) | c1_1(a1044)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause54')).
% 0.93/0.84 tff(764,plain,
% 0.93/0.84 ((~hskp23) | c1_1(a1044)),
% 0.93/0.84 inference(modus_ponens,[status(thm)],[763, 762])).
% 0.93/0.84 tff(765,plain,
% 0.93/0.84 ((~hskp23) | c1_1(a1044)),
% 0.93/0.84 inference(modus_ponens,[status(thm)],[764, 762])).
% 0.93/0.84 tff(766,plain,
% 0.93/0.84 ((~hskp23) | c1_1(a1044)),
% 0.93/0.84 inference(modus_ponens,[status(thm)],[765, 762])).
% 0.93/0.84 tff(767,plain,
% 0.93/0.84 ((~hskp23) | c1_1(a1044)),
% 0.93/0.84 inference(modus_ponens,[status(thm)],[766, 762])).
% 0.93/0.84 tff(768,plain,
% 0.93/0.84 ((~hskp23) | c1_1(a1044)),
% 0.93/0.84 inference(modus_ponens,[status(thm)],[767, 762])).
% 0.93/0.84 tff(769,plain,
% 0.93/0.84 ((~hskp23) | c1_1(a1044)),
% 0.93/0.84 inference(modus_ponens,[status(thm)],[768, 762])).
% 0.93/0.84 tff(770,plain,
% 0.93/0.84 ((~hskp23) | c1_1(a1044)),
% 0.93/0.84 inference(modus_ponens,[status(thm)],[769, 762])).
% 0.93/0.84 tff(771,plain,
% 0.93/0.84 ((~hskp23) | c1_1(a1044)),
% 0.93/0.84 inference(modus_ponens,[status(thm)],[770, 762])).
% 0.93/0.84 tff(772,plain,
% 0.93/0.84 (c1_1(a1044)),
% 0.93/0.84 inference(unit_resolution,[status(thm)],[771, 755])).
% 0.93/0.84 tff(773,plain,
% 0.93/0.84 (((~hskp23) | c0_1(a1044)) <=> ((~hskp23) | c0_1(a1044))),
% 0.93/0.84 inference(rewrite,[status(thm)],[])).
% 0.93/0.84 tff(774,axiom,((~hskp23) | c0_1(a1044)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause53')).
% 0.93/0.84 tff(775,plain,
% 0.93/0.84 ((~hskp23) | c0_1(a1044)),
% 0.93/0.84 inference(modus_ponens,[status(thm)],[774, 773])).
% 0.93/0.84 tff(776,plain,
% 0.93/0.84 ((~hskp23) | c0_1(a1044)),
% 0.93/0.84 inference(modus_ponens,[status(thm)],[775, 773])).
% 0.93/0.84 tff(777,plain,
% 0.93/0.84 ((~hskp23) | c0_1(a1044)),
% 0.93/0.84 inference(modus_ponens,[status(thm)],[776, 773])).
% 0.93/0.84 tff(778,plain,
% 0.93/0.84 ((~hskp23) | c0_1(a1044)),
% 0.93/0.84 inference(modus_ponens,[status(thm)],[777, 773])).
% 0.93/0.84 tff(779,plain,
% 0.93/0.84 ((~hskp23) | c0_1(a1044)),
% 0.93/0.84 inference(modus_ponens,[status(thm)],[778, 773])).
% 0.93/0.84 tff(780,plain,
% 0.93/0.84 ((~hskp23) | c0_1(a1044)),
% 0.93/0.84 inference(modus_ponens,[status(thm)],[779, 773])).
% 0.93/0.84 tff(781,plain,
% 0.93/0.84 ((~hskp23) | c0_1(a1044)),
% 0.93/0.84 inference(modus_ponens,[status(thm)],[780, 773])).
% 0.93/0.84 tff(782,plain,
% 0.93/0.84 ((~hskp23) | c0_1(a1044)),
% 0.93/0.84 inference(modus_ponens,[status(thm)],[781, 773])).
% 0.93/0.84 tff(783,plain,
% 0.93/0.84 (c0_1(a1044)),
% 0.93/0.84 inference(unit_resolution,[status(thm)],[782, 755])).
% 0.93/0.84 tff(784,plain,
% 0.93/0.84 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp17 | c3_1(a1044) | (~ndr1_0) | (~c2_1(a1044)) | (~c0_1(a1044)) | (~c1_1(a1044)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp17 | c3_1(a1044) | (~ndr1_0) | (~c2_1(a1044)) | (~c0_1(a1044)) | (~c1_1(a1044)))),
% 0.93/0.84 inference(rewrite,[status(thm)],[])).
% 0.93/0.84 tff(785,plain,
% 0.93/0.84 ((hskp17 | (~ndr1_0) | (~c1_1(a1044)) | (~c2_1(a1044)) | (~c0_1(a1044)) | c3_1(a1044) | (~c2_1(a1044)) | (~c0_1(a1044))) <=> (hskp17 | c3_1(a1044) | (~ndr1_0) | (~c2_1(a1044)) | (~c0_1(a1044)) | (~c1_1(a1044)))),
% 0.93/0.84 inference(rewrite,[status(thm)],[])).
% 0.93/0.84 tff(786,plain,
% 0.93/0.84 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp17 | (~ndr1_0) | (~c1_1(a1044)) | (~c2_1(a1044)) | (~c0_1(a1044)) | c3_1(a1044) | (~c2_1(a1044)) | (~c0_1(a1044)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp17 | c3_1(a1044) | (~ndr1_0) | (~c2_1(a1044)) | (~c0_1(a1044)) | (~c1_1(a1044))))),
% 0.93/0.84 inference(monotonicity,[status(thm)],[785])).
% 0.93/0.84 tff(787,plain,
% 0.93/0.84 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp17 | (~ndr1_0) | (~c1_1(a1044)) | (~c2_1(a1044)) | (~c0_1(a1044)) | c3_1(a1044) | (~c2_1(a1044)) | (~c0_1(a1044)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp17 | c3_1(a1044) | (~ndr1_0) | (~c2_1(a1044)) | (~c0_1(a1044)) | (~c1_1(a1044)))),
% 0.93/0.84 inference(transitivity,[status(thm)],[786, 784])).
% 0.93/0.84 tff(788,plain,
% 0.93/0.84 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp17 | (~ndr1_0) | (~c1_1(a1044)) | (~c2_1(a1044)) | (~c0_1(a1044)) | c3_1(a1044) | (~c2_1(a1044)) | (~c0_1(a1044)))),
% 0.93/0.84 inference(quant_inst,[status(thm)],[])).
% 0.93/0.84 tff(789,plain,
% 0.93/0.84 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp17 | c3_1(a1044) | (~ndr1_0) | (~c2_1(a1044)) | (~c0_1(a1044)) | (~c1_1(a1044))),
% 0.93/0.84 inference(modus_ponens,[status(thm)],[788, 787])).
% 0.93/0.84 tff(790,plain,
% 0.93/0.84 (hskp17 | (~c2_1(a1044))),
% 0.93/0.84 inference(unit_resolution,[status(thm)],[789, 90, 783, 772, 761, 11])).
% 0.93/0.84 tff(791,plain,
% 0.93/0.84 (hskp17),
% 0.93/0.84 inference(unit_resolution,[status(thm)],[790, 1])).
% 0.93/0.84 tff(792,plain,
% 0.93/0.84 (~c0_1(a1032)),
% 0.93/0.84 inference(unit_resolution,[status(thm)],[438, 791])).
% 0.93/0.84 tff(793,plain,
% 0.93/0.84 (c3_1(a1032)),
% 0.93/0.84 inference(unit_resolution,[status(thm)],[473, 791])).
% 0.93/0.84 tff(794,plain,
% 0.93/0.84 (c2_1(a1032)),
% 0.93/0.84 inference(unit_resolution,[status(thm)],[484, 791])).
% 0.93/0.84 tff(795,assumption,(c1_1(a1032)), introduced(assumption)).
% 0.93/0.84 tff(796,assumption,(~c0_1(a1032)), introduced(assumption)).
% 0.93/0.84 tff(797,assumption,(c3_1(a1032)), introduced(assumption)).
% 0.93/0.84 tff(798,assumption,(c2_1(a1032)), introduced(assumption)).
% 0.93/0.84 tff(799,plain,
% 0.93/0.84 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | (c0_1(a1032) | (~ndr1_0) | (~c2_1(a1032)) | (~c3_1(a1032)) | (~c1_1(a1032)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | c0_1(a1032) | (~ndr1_0) | (~c2_1(a1032)) | (~c3_1(a1032)) | (~c1_1(a1032)))),
% 0.93/0.84 inference(rewrite,[status(thm)],[])).
% 0.93/0.84 tff(800,plain,
% 0.93/0.84 (((~ndr1_0) | (~c1_1(a1032)) | (~c2_1(a1032)) | (~c3_1(a1032)) | c0_1(a1032) | (~c2_1(a1032)) | (~c3_1(a1032)) | c0_1(a1032) | (~c3_1(a1032)) | (~c1_1(a1032))) <=> (c0_1(a1032) | (~ndr1_0) | (~c2_1(a1032)) | (~c3_1(a1032)) | (~c1_1(a1032)))),
% 0.93/0.84 inference(rewrite,[status(thm)],[])).
% 0.93/0.84 tff(801,plain,
% 0.93/0.84 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | (~c1_1(a1032)) | (~c2_1(a1032)) | (~c3_1(a1032)) | c0_1(a1032) | (~c2_1(a1032)) | (~c3_1(a1032)) | c0_1(a1032) | (~c3_1(a1032)) | (~c1_1(a1032)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | (c0_1(a1032) | (~ndr1_0) | (~c2_1(a1032)) | (~c3_1(a1032)) | (~c1_1(a1032))))),
% 0.93/0.84 inference(monotonicity,[status(thm)],[800])).
% 0.93/0.84 tff(802,plain,
% 0.93/0.84 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | (~c1_1(a1032)) | (~c2_1(a1032)) | (~c3_1(a1032)) | c0_1(a1032) | (~c2_1(a1032)) | (~c3_1(a1032)) | c0_1(a1032) | (~c3_1(a1032)) | (~c1_1(a1032)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | c0_1(a1032) | (~ndr1_0) | (~c2_1(a1032)) | (~c3_1(a1032)) | (~c1_1(a1032)))),
% 0.93/0.84 inference(transitivity,[status(thm)],[801, 799])).
% 0.93/0.84 tff(803,plain,
% 0.93/0.84 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | (~c1_1(a1032)) | (~c2_1(a1032)) | (~c3_1(a1032)) | c0_1(a1032) | (~c2_1(a1032)) | (~c3_1(a1032)) | c0_1(a1032) | (~c3_1(a1032)) | (~c1_1(a1032)))),
% 0.93/0.84 inference(quant_inst,[status(thm)],[])).
% 0.93/0.84 tff(804,plain,
% 0.93/0.84 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | c0_1(a1032) | (~ndr1_0) | (~c2_1(a1032)) | (~c3_1(a1032)) | (~c1_1(a1032))),
% 0.93/0.84 inference(modus_ponens,[status(thm)],[803, 802])).
% 0.93/0.84 tff(805,plain,
% 0.93/0.84 ($false),
% 0.93/0.84 inference(unit_resolution,[status(thm)],[804, 90, 798, 797, 796, 411, 795])).
% 0.93/0.84 tff(806,plain,((~c1_1(a1032)) | (~c2_1(a1032)) | (~c3_1(a1032)) | c0_1(a1032)), inference(lemma,lemma(discharge,[]))).
% 0.93/0.84 tff(807,plain,
% 0.93/0.84 (~c1_1(a1032)),
% 0.93/0.84 inference(unit_resolution,[status(thm)],[806, 794, 793, 792])).
% 0.93/0.84 tff(808,plain,
% 0.93/0.84 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c1_1(W) | (~c3_1(W)) | (~c2_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c1_1(W) | (~c3_1(W)) | (~c2_1(W))))),
% 0.93/0.84 inference(bind,[status(th)],[])).
% 0.93/0.84 tff(809,plain,
% 0.93/0.84 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c1_1(W) | (~c3_1(W)) | (~c2_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c1_1(W) | (~c3_1(W)) | (~c2_1(W)))),
% 0.93/0.84 inference(quant_intro,[status(thm)],[808])).
% 0.93/0.84 tff(810,plain,
% 0.93/0.84 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c1_1(W) | (~c3_1(W)) | (~c2_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c1_1(W) | (~c3_1(W)) | (~c2_1(W)))),
% 0.93/0.84 inference(rewrite,[status(thm)],[])).
% 0.93/0.84 tff(811,plain,
% 0.93/0.84 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(V)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(V))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(V)) | (~c3_1(V)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(V)) | (~c3_1(V))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c2_1(W))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(V)) | (~c3_1(V))) | (~c2_1(W))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(V)) | (~c3_1(V))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(V)) | (~c3_1(V)) | (~c2_1(W)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(V)) | (~c3_1(V)) | (~c2_1(W))))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c2_1(W))) | (~c3_1(W))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(V)) | (~c3_1(V)) | (~c2_1(W))) | (~c3_1(W))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(V)) | (~c3_1(V)) | (~c2_1(W))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(V)) | (~c3_1(V)) | (~c3_1(W)) | (~c2_1(W)))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c2_1(W))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(V)) | (~c3_1(V)) | (~c3_1(W)) | (~c2_1(W))))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c2_1(W))) | (~c3_1(W))) | c3_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(V)) | (~c3_1(V)) | (~c3_1(W)) | (~c2_1(W))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(V)) | (~c3_1(V)) | (~c3_1(W)) | (~c2_1(W))) | c3_1(U)) <=> ((~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c2_1(U)) | (~c0_1(V)) | (~c3_1(V)) | (~c3_1(W)) | (~c2_1(W)))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c2_1(W))) | (~c3_1(W))) | c3_1(U)) <=> ((~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c2_1(U)) | (~c0_1(V)) | (~c3_1(V)) | (~c3_1(W)) | (~c2_1(W))))), ((((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c2_1(W))) | (~c3_1(W))) | c3_1(U)) | c2_1(V)) <=> (((~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c2_1(U)) | (~c0_1(V)) | (~c3_1(V)) | (~c3_1(W)) | (~c2_1(W))) | c2_1(V)))), rewrite((((~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c2_1(U)) | (~c0_1(V)) | (~c3_1(V)) | (~c3_1(W)) | (~c2_1(W))) | c2_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | (~c3_1(W)) | (~c2_1(W)))), ((((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c2_1(W))) | (~c3_1(W))) | c3_1(U)) | c2_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | (~c3_1(W)) | (~c2_1(W))))), (((((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c2_1(W))) | (~c3_1(W))) | c3_1(U)) | c2_1(V)) | c1_1(W)) <=> (((~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | (~c3_1(W)) | (~c2_1(W))) | c1_1(W)))), rewrite((((~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | (~c3_1(W)) | (~c2_1(W))) | c1_1(W)) <=> ((~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c1_1(W) | (~c3_1(W)) | (~c2_1(W)))), (((((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c2_1(W))) | (~c3_1(W))) | c3_1(U)) | c2_1(V)) | c1_1(W)) <=> ((~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c1_1(W) | (~c3_1(W)) | (~c2_1(W)))))),
% 0.93/0.84 inference(bind,[status(th)],[])).
% 0.93/0.84 tff(812,plain,
% 0.93/0.84 (![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c2_1(W))) | (~c3_1(W))) | c3_1(U)) | c2_1(V)) | c1_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c1_1(W) | (~c3_1(W)) | (~c2_1(W)))),
% 0.93/0.84 inference(quant_intro,[status(thm)],[811])).
% 0.93/0.84 tff(813,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c2_1(W))) | (~c3_1(W))) | c3_1(U)) | c2_1(V)) | c1_1(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause190')).
% 0.93/0.84 tff(814,plain,
% 0.93/0.84 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c1_1(W) | (~c3_1(W)) | (~c2_1(W)))),
% 0.93/0.84 inference(modus_ponens,[status(thm)],[813, 812])).
% 0.93/0.84 tff(815,plain,
% 0.93/0.84 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c1_1(W) | (~c3_1(W)) | (~c2_1(W)))),
% 0.93/0.84 inference(modus_ponens,[status(thm)],[814, 810])).
% 0.93/0.84 tff(816,plain,(
% 0.93/0.84 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c1_1(W) | (~c3_1(W)) | (~c2_1(W)))),
% 0.93/0.84 inference(skolemize,[status(sab)],[815])).
% 0.93/0.84 tff(817,plain,
% 0.93/0.84 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c1_1(W) | (~c3_1(W)) | (~c2_1(W)))),
% 0.93/0.84 inference(modus_ponens,[status(thm)],[816, 809])).
% 0.93/0.84 tff(818,plain,
% 0.93/0.84 (^[V: $i, U: $i] : refl((hskp6 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V))) <=> (hskp6 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V))))),
% 0.93/0.84 inference(bind,[status(th)],[])).
% 0.93/0.84 tff(819,plain,
% 0.93/0.84 (![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 0.93/0.84 inference(quant_intro,[status(thm)],[818])).
% 0.93/0.84 tff(820,plain,
% 0.93/0.84 (![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 0.93/0.84 inference(rewrite,[status(thm)],[])).
% 0.93/0.84 tff(821,plain,
% 0.93/0.84 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(V)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(V))))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(V))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c0_1(V)))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c0_1(V))))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c1_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c0_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c0_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c0_1(V)))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c0_1(V))))), ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c1_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c0_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c0_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))), ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c1_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V))))), (((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c1_1(U)) | c1_1(V)) | hskp6) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V))) | hskp6))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V))) | hskp6) <=> (hskp6 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))), (((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c1_1(U)) | c1_1(V)) | hskp6) <=> (hskp6 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))))),
% 0.93/0.84 inference(bind,[status(th)],[])).
% 0.93/0.84 tff(822,plain,
% 0.93/0.84 (![V: $i, U: $i] : ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c1_1(U)) | c1_1(V)) | hskp6) <=> ![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 0.93/0.84 inference(quant_intro,[status(thm)],[821])).
% 0.93/0.84 tff(823,axiom,(![V: $i, U: $i] : ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c1_1(U)) | c1_1(V)) | hskp6)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause179')).
% 0.93/0.84 tff(824,plain,
% 0.93/0.84 (![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 0.93/0.84 inference(modus_ponens,[status(thm)],[823, 822])).
% 0.93/0.84 tff(825,plain,
% 0.93/0.84 (![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 0.93/0.84 inference(modus_ponens,[status(thm)],[824, 820])).
% 0.93/0.84 tff(826,plain,(
% 0.93/0.84 ![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 0.93/0.84 inference(skolemize,[status(sab)],[825])).
% 0.93/0.84 tff(827,plain,
% 0.93/0.84 (![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 0.93/0.84 inference(modus_ponens,[status(thm)],[826, 819])).
% 0.93/0.84 tff(828,plain,
% 0.93/0.84 ($false),
% 0.93/0.84 inference(unit_resolution,[status(thm)],[721, 232, 238, 616, 679, 624, 249])).
% 0.93/0.84 tff(829,plain,((~hskp7) | hskp2 | hskp1 | hskp13), inference(lemma,lemma(discharge,[]))).
% 0.93/0.84 tff(830,plain,
% 0.93/0.84 (~hskp7),
% 0.93/0.84 inference(unit_resolution,[status(thm)],[829, 679, 616, 624])).
% 0.93/0.84 tff(831,assumption,(hskp4), introduced(assumption)).
% 0.93/0.84 tff(832,plain,
% 0.93/0.84 (((~hskp4) | c2_1(a1004)) <=> ((~hskp4) | c2_1(a1004))),
% 0.93/0.84 inference(rewrite,[status(thm)],[])).
% 0.93/0.84 tff(833,axiom,((~hskp4) | c2_1(a1004)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause77')).
% 0.93/0.84 tff(834,plain,
% 0.93/0.84 ((~hskp4) | c2_1(a1004)),
% 0.93/0.84 inference(modus_ponens,[status(thm)],[833, 832])).
% 0.93/0.84 tff(835,plain,
% 0.93/0.84 ((~hskp4) | c2_1(a1004)),
% 0.93/0.84 inference(modus_ponens,[status(thm)],[834, 832])).
% 0.93/0.84 tff(836,plain,
% 0.93/0.84 ((~hskp4) | c2_1(a1004)),
% 0.93/0.84 inference(modus_ponens,[status(thm)],[835, 832])).
% 0.93/0.84 tff(837,plain,
% 0.93/0.84 ((~hskp4) | c2_1(a1004)),
% 0.93/0.84 inference(modus_ponens,[status(thm)],[836, 832])).
% 0.93/0.84 tff(838,plain,
% 0.93/0.84 ((~hskp4) | c2_1(a1004)),
% 0.93/0.84 inference(modus_ponens,[status(thm)],[837, 832])).
% 0.93/0.84 tff(839,plain,
% 0.93/0.84 ((~hskp4) | c2_1(a1004)),
% 0.93/0.84 inference(modus_ponens,[status(thm)],[838, 832])).
% 0.93/0.84 tff(840,plain,
% 0.93/0.84 ((~hskp4) | c2_1(a1004)),
% 0.93/0.84 inference(modus_ponens,[status(thm)],[839, 832])).
% 0.93/0.84 tff(841,plain,
% 0.93/0.84 ((~hskp4) | c2_1(a1004)),
% 0.93/0.84 inference(modus_ponens,[status(thm)],[840, 832])).
% 0.93/0.84 tff(842,plain,
% 0.93/0.84 (c2_1(a1004)),
% 0.93/0.84 inference(unit_resolution,[status(thm)],[841, 831])).
% 0.93/0.84 tff(843,plain,
% 0.93/0.84 (((~hskp4) | c1_1(a1004)) <=> ((~hskp4) | c1_1(a1004))),
% 0.93/0.84 inference(rewrite,[status(thm)],[])).
% 0.93/0.84 tff(844,axiom,((~hskp4) | c1_1(a1004)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause76')).
% 0.93/0.84 tff(845,plain,
% 0.93/0.84 ((~hskp4) | c1_1(a1004)),
% 0.93/0.84 inference(modus_ponens,[status(thm)],[844, 843])).
% 0.93/0.84 tff(846,plain,
% 0.93/0.84 ((~hskp4) | c1_1(a1004)),
% 0.93/0.84 inference(modus_ponens,[status(thm)],[845, 843])).
% 0.93/0.84 tff(847,plain,
% 0.93/0.84 ((~hskp4) | c1_1(a1004)),
% 0.93/0.84 inference(modus_ponens,[status(thm)],[846, 843])).
% 0.93/0.84 tff(848,plain,
% 0.93/0.84 ((~hskp4) | c1_1(a1004)),
% 0.93/0.84 inference(modus_ponens,[status(thm)],[847, 843])).
% 0.93/0.84 tff(849,plain,
% 0.93/0.84 ((~hskp4) | c1_1(a1004)),
% 0.93/0.84 inference(modus_ponens,[status(thm)],[848, 843])).
% 0.93/0.84 tff(850,plain,
% 0.93/0.84 ((~hskp4) | c1_1(a1004)),
% 0.93/0.84 inference(modus_ponens,[status(thm)],[849, 843])).
% 0.93/0.84 tff(851,plain,
% 0.93/0.84 ((~hskp4) | c1_1(a1004)),
% 0.93/0.84 inference(modus_ponens,[status(thm)],[850, 843])).
% 0.93/0.84 tff(852,plain,
% 0.93/0.84 ((~hskp4) | c1_1(a1004)),
% 0.93/0.84 inference(modus_ponens,[status(thm)],[851, 843])).
% 0.93/0.84 tff(853,plain,
% 0.93/0.84 (c1_1(a1004)),
% 0.93/0.84 inference(unit_resolution,[status(thm)],[852, 831])).
% 0.93/0.84 tff(854,plain,
% 0.93/0.84 (((~![U: $i] : (hskp7 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)))) | (hskp7 | (~ndr1_0) | (~c2_1(a1004)) | (~c0_1(a1004)) | (~c1_1(a1004)))) <=> ((~![U: $i] : (hskp7 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)))) | hskp7 | (~ndr1_0) | (~c2_1(a1004)) | (~c0_1(a1004)) | (~c1_1(a1004)))),
% 0.93/0.85 inference(rewrite,[status(thm)],[])).
% 0.93/0.85 tff(855,plain,
% 0.93/0.85 ((hskp7 | (~ndr1_0) | (~c1_1(a1004)) | (~c2_1(a1004)) | (~c0_1(a1004))) <=> (hskp7 | (~ndr1_0) | (~c2_1(a1004)) | (~c0_1(a1004)) | (~c1_1(a1004)))),
% 0.93/0.85 inference(rewrite,[status(thm)],[])).
% 0.93/0.85 tff(856,plain,
% 0.93/0.85 (((~![U: $i] : (hskp7 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)))) | (hskp7 | (~ndr1_0) | (~c1_1(a1004)) | (~c2_1(a1004)) | (~c0_1(a1004)))) <=> ((~![U: $i] : (hskp7 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)))) | (hskp7 | (~ndr1_0) | (~c2_1(a1004)) | (~c0_1(a1004)) | (~c1_1(a1004))))),
% 0.93/0.85 inference(monotonicity,[status(thm)],[855])).
% 0.93/0.85 tff(857,plain,
% 0.93/0.85 (((~![U: $i] : (hskp7 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)))) | (hskp7 | (~ndr1_0) | (~c1_1(a1004)) | (~c2_1(a1004)) | (~c0_1(a1004)))) <=> ((~![U: $i] : (hskp7 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)))) | hskp7 | (~ndr1_0) | (~c2_1(a1004)) | (~c0_1(a1004)) | (~c1_1(a1004)))),
% 0.93/0.85 inference(transitivity,[status(thm)],[856, 854])).
% 0.93/0.85 tff(858,plain,
% 0.93/0.85 ((~![U: $i] : (hskp7 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)))) | (hskp7 | (~ndr1_0) | (~c1_1(a1004)) | (~c2_1(a1004)) | (~c0_1(a1004)))),
% 0.93/0.85 inference(quant_inst,[status(thm)],[])).
% 0.93/0.85 tff(859,plain,
% 0.93/0.85 ((~![U: $i] : (hskp7 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)))) | hskp7 | (~ndr1_0) | (~c2_1(a1004)) | (~c0_1(a1004)) | (~c1_1(a1004))),
% 0.93/0.85 inference(modus_ponens,[status(thm)],[858, 857])).
% 0.93/0.85 tff(860,plain,
% 0.93/0.85 (~c0_1(a1004)),
% 0.93/0.85 inference(unit_resolution,[status(thm)],[859, 90, 644, 853, 842, 188])).
% 0.93/0.85 tff(861,plain,
% 0.93/0.85 (((~hskp4) | (~c3_1(a1004))) <=> ((~hskp4) | (~c3_1(a1004)))),
% 0.93/0.85 inference(rewrite,[status(thm)],[])).
% 0.93/0.85 tff(862,plain,
% 0.93/0.85 (((~c3_1(a1004)) | (~hskp4)) <=> ((~hskp4) | (~c3_1(a1004)))),
% 0.93/0.85 inference(rewrite,[status(thm)],[])).
% 0.93/0.85 tff(863,axiom,((~c3_1(a1004)) | (~hskp4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause124')).
% 0.93/0.85 tff(864,plain,
% 0.93/0.85 ((~hskp4) | (~c3_1(a1004))),
% 0.93/0.85 inference(modus_ponens,[status(thm)],[863, 862])).
% 0.93/0.85 tff(865,plain,
% 0.93/0.85 ((~hskp4) | (~c3_1(a1004))),
% 0.93/0.85 inference(modus_ponens,[status(thm)],[864, 861])).
% 0.93/0.85 tff(866,plain,
% 0.93/0.85 (~c3_1(a1004)),
% 0.93/0.85 inference(unit_resolution,[status(thm)],[865, 831])).
% 0.93/0.85 tff(867,plain,
% 0.93/0.85 (((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp2 | hskp1 | c3_1(a1004) | (~ndr1_0) | (~c2_1(a1004)) | c0_1(a1004))) <=> ((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | hskp2 | hskp1 | c3_1(a1004) | (~ndr1_0) | (~c2_1(a1004)) | c0_1(a1004))),
% 0.93/0.85 inference(rewrite,[status(thm)],[])).
% 0.93/0.85 tff(868,plain,
% 0.93/0.85 ((hskp2 | hskp1 | (~ndr1_0) | c0_1(a1004) | c3_1(a1004) | (~c2_1(a1004))) <=> (hskp2 | hskp1 | c3_1(a1004) | (~ndr1_0) | (~c2_1(a1004)) | c0_1(a1004))),
% 0.93/0.85 inference(rewrite,[status(thm)],[])).
% 0.93/0.85 tff(869,plain,
% 0.93/0.85 (((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp2 | hskp1 | (~ndr1_0) | c0_1(a1004) | c3_1(a1004) | (~c2_1(a1004)))) <=> ((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp2 | hskp1 | c3_1(a1004) | (~ndr1_0) | (~c2_1(a1004)) | c0_1(a1004)))),
% 0.93/0.85 inference(monotonicity,[status(thm)],[868])).
% 0.93/0.85 tff(870,plain,
% 0.93/0.85 (((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp2 | hskp1 | (~ndr1_0) | c0_1(a1004) | c3_1(a1004) | (~c2_1(a1004)))) <=> ((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | hskp2 | hskp1 | c3_1(a1004) | (~ndr1_0) | (~c2_1(a1004)) | c0_1(a1004))),
% 0.93/0.85 inference(transitivity,[status(thm)],[869, 867])).
% 0.93/0.85 tff(871,plain,
% 0.93/0.85 ((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp2 | hskp1 | (~ndr1_0) | c0_1(a1004) | c3_1(a1004) | (~c2_1(a1004)))),
% 0.93/0.85 inference(quant_inst,[status(thm)],[])).
% 0.93/0.85 tff(872,plain,
% 0.93/0.85 ((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | hskp2 | hskp1 | c3_1(a1004) | (~ndr1_0) | (~c2_1(a1004)) | c0_1(a1004)),
% 0.93/0.85 inference(modus_ponens,[status(thm)],[871, 870])).
% 0.93/0.85 tff(873,plain,
% 0.93/0.85 ($false),
% 0.93/0.85 inference(unit_resolution,[status(thm)],[872, 90, 616, 679, 842, 866, 678, 860])).
% 0.93/0.85 tff(874,plain,((~hskp4) | hskp2 | hskp1 | hskp7), inference(lemma,lemma(discharge,[]))).
% 0.93/0.85 tff(875,plain,
% 0.93/0.85 (~hskp4),
% 0.93/0.85 inference(unit_resolution,[status(thm)],[874, 679, 616, 830])).
% 0.93/0.85 tff(876,plain,
% 0.93/0.85 ((hskp21 | hskp7 | hskp4) <=> (hskp21 | hskp7 | hskp4)),
% 0.93/0.85 inference(rewrite,[status(thm)],[])).
% 0.93/0.85 tff(877,plain,
% 0.93/0.85 (((hskp21 | hskp4) | hskp7) <=> (hskp21 | hskp7 | hskp4)),
% 0.93/0.85 inference(rewrite,[status(thm)],[])).
% 0.93/0.85 tff(878,plain,
% 0.93/0.85 ((hskp4 | hskp21) <=> (hskp21 | hskp4)),
% 0.93/0.85 inference(rewrite,[status(thm)],[])).
% 0.93/0.85 tff(879,plain,
% 0.93/0.85 (((hskp4 | hskp21) | hskp7) <=> ((hskp21 | hskp4) | hskp7)),
% 0.93/0.85 inference(monotonicity,[status(thm)],[878])).
% 0.93/0.85 tff(880,plain,
% 0.93/0.85 (((hskp4 | hskp21) | hskp7) <=> (hskp21 | hskp7 | hskp4)),
% 0.93/0.85 inference(transitivity,[status(thm)],[879, 877])).
% 0.93/0.85 tff(881,axiom,((hskp4 | hskp21) | hskp7), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause38')).
% 0.93/0.85 tff(882,plain,
% 0.93/0.85 (hskp21 | hskp7 | hskp4),
% 0.93/0.85 inference(modus_ponens,[status(thm)],[881, 880])).
% 0.93/0.85 tff(883,plain,
% 0.93/0.85 (hskp21 | hskp7 | hskp4),
% 0.93/0.85 inference(modus_ponens,[status(thm)],[882, 876])).
% 0.93/0.85 tff(884,plain,
% 0.93/0.85 (hskp21 | hskp7 | hskp4),
% 0.93/0.85 inference(modus_ponens,[status(thm)],[883, 876])).
% 0.93/0.85 tff(885,plain,
% 0.93/0.85 (hskp21 | hskp7 | hskp4),
% 0.93/0.85 inference(modus_ponens,[status(thm)],[884, 876])).
% 0.93/0.85 tff(886,plain,
% 0.93/0.85 (hskp21 | hskp7 | hskp4),
% 0.93/0.85 inference(modus_ponens,[status(thm)],[885, 876])).
% 0.93/0.85 tff(887,plain,
% 0.93/0.85 (hskp21 | hskp7 | hskp4),
% 0.93/0.85 inference(modus_ponens,[status(thm)],[886, 876])).
% 0.93/0.85 tff(888,plain,
% 0.93/0.85 (hskp21 | hskp7 | hskp4),
% 0.93/0.85 inference(modus_ponens,[status(thm)],[887, 876])).
% 0.93/0.85 tff(889,plain,
% 0.93/0.85 (hskp21 | hskp7 | hskp4),
% 0.93/0.85 inference(modus_ponens,[status(thm)],[888, 876])).
% 0.93/0.85 tff(890,plain,
% 0.93/0.85 (hskp21),
% 0.93/0.85 inference(unit_resolution,[status(thm)],[889, 875, 830])).
% 0.93/0.85 tff(891,plain,
% 0.93/0.85 (((~hskp21) | (~c3_1(a1041))) <=> ((~hskp21) | (~c3_1(a1041)))),
% 0.93/0.85 inference(rewrite,[status(thm)],[])).
% 0.93/0.85 tff(892,plain,
% 0.93/0.85 (((~c3_1(a1041)) | (~hskp21)) <=> ((~hskp21) | (~c3_1(a1041)))),
% 0.93/0.85 inference(rewrite,[status(thm)],[])).
% 0.93/0.85 tff(893,axiom,((~c3_1(a1041)) | (~hskp21)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause94')).
% 0.93/0.85 tff(894,plain,
% 0.93/0.85 ((~hskp21) | (~c3_1(a1041))),
% 0.93/0.85 inference(modus_ponens,[status(thm)],[893, 892])).
% 0.93/0.85 tff(895,plain,
% 0.93/0.85 ((~hskp21) | (~c3_1(a1041))),
% 0.93/0.85 inference(modus_ponens,[status(thm)],[894, 891])).
% 0.93/0.85 tff(896,plain,
% 0.93/0.85 (~c3_1(a1041)),
% 0.93/0.85 inference(unit_resolution,[status(thm)],[895, 890])).
% 0.93/0.85 tff(897,plain,
% 0.93/0.85 (((~hskp21) | (~c0_1(a1041))) <=> ((~hskp21) | (~c0_1(a1041)))),
% 0.93/0.85 inference(rewrite,[status(thm)],[])).
% 0.93/0.85 tff(898,plain,
% 0.93/0.85 (((~c0_1(a1041)) | (~hskp21)) <=> ((~hskp21) | (~c0_1(a1041)))),
% 0.93/0.85 inference(rewrite,[status(thm)],[])).
% 0.93/0.85 tff(899,axiom,((~c0_1(a1041)) | (~hskp21)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause93')).
% 0.93/0.85 tff(900,plain,
% 0.93/0.85 ((~hskp21) | (~c0_1(a1041))),
% 0.93/0.85 inference(modus_ponens,[status(thm)],[899, 898])).
% 0.93/0.85 tff(901,plain,
% 0.93/0.85 ((~hskp21) | (~c0_1(a1041))),
% 0.93/0.85 inference(modus_ponens,[status(thm)],[900, 897])).
% 0.93/0.85 tff(902,plain,
% 0.93/0.85 (~c0_1(a1041)),
% 0.93/0.85 inference(unit_resolution,[status(thm)],[901, 890])).
% 0.93/0.85 tff(903,plain,
% 0.93/0.85 (((~hskp21) | c2_1(a1041)) <=> ((~hskp21) | c2_1(a1041))),
% 0.93/0.85 inference(rewrite,[status(thm)],[])).
% 0.93/0.85 tff(904,axiom,((~hskp21) | c2_1(a1041)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause56')).
% 0.93/0.85 tff(905,plain,
% 0.93/0.85 ((~hskp21) | c2_1(a1041)),
% 0.93/0.85 inference(modus_ponens,[status(thm)],[904, 903])).
% 0.93/0.85 tff(906,plain,
% 0.93/0.85 ((~hskp21) | c2_1(a1041)),
% 0.93/0.85 inference(modus_ponens,[status(thm)],[905, 903])).
% 0.93/0.85 tff(907,plain,
% 0.93/0.85 ((~hskp21) | c2_1(a1041)),
% 0.93/0.85 inference(modus_ponens,[status(thm)],[906, 903])).
% 0.93/0.85 tff(908,plain,
% 0.93/0.85 ((~hskp21) | c2_1(a1041)),
% 0.93/0.85 inference(modus_ponens,[status(thm)],[907, 903])).
% 0.93/0.85 tff(909,plain,
% 0.93/0.85 ((~hskp21) | c2_1(a1041)),
% 0.93/0.85 inference(modus_ponens,[status(thm)],[908, 903])).
% 0.93/0.85 tff(910,plain,
% 0.93/0.85 ((~hskp21) | c2_1(a1041)),
% 0.93/0.85 inference(modus_ponens,[status(thm)],[909, 903])).
% 0.93/0.85 tff(911,plain,
% 0.93/0.85 ((~hskp21) | c2_1(a1041)),
% 0.93/0.85 inference(modus_ponens,[status(thm)],[910, 903])).
% 0.93/0.85 tff(912,plain,
% 0.93/0.85 ((~hskp21) | c2_1(a1041)),
% 0.93/0.85 inference(modus_ponens,[status(thm)],[911, 903])).
% 0.93/0.85 tff(913,plain,
% 0.93/0.85 (c2_1(a1041)),
% 0.93/0.85 inference(unit_resolution,[status(thm)],[912, 890])).
% 0.93/0.85 tff(914,plain,
% 0.93/0.85 (((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp2 | hskp1 | c0_1(a1041) | c3_1(a1041) | (~ndr1_0) | (~c2_1(a1041)))) <=> ((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | hskp2 | hskp1 | c0_1(a1041) | c3_1(a1041) | (~ndr1_0) | (~c2_1(a1041)))),
% 0.93/0.85 inference(rewrite,[status(thm)],[])).
% 0.93/0.85 tff(915,plain,
% 0.93/0.85 ((hskp2 | hskp1 | (~ndr1_0) | c0_1(a1041) | c3_1(a1041) | (~c2_1(a1041))) <=> (hskp2 | hskp1 | c0_1(a1041) | c3_1(a1041) | (~ndr1_0) | (~c2_1(a1041)))),
% 0.93/0.85 inference(rewrite,[status(thm)],[])).
% 0.93/0.85 tff(916,plain,
% 0.93/0.85 (((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp2 | hskp1 | (~ndr1_0) | c0_1(a1041) | c3_1(a1041) | (~c2_1(a1041)))) <=> ((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp2 | hskp1 | c0_1(a1041) | c3_1(a1041) | (~ndr1_0) | (~c2_1(a1041))))),
% 0.93/0.85 inference(monotonicity,[status(thm)],[915])).
% 0.93/0.85 tff(917,plain,
% 0.93/0.85 (((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp2 | hskp1 | (~ndr1_0) | c0_1(a1041) | c3_1(a1041) | (~c2_1(a1041)))) <=> ((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | hskp2 | hskp1 | c0_1(a1041) | c3_1(a1041) | (~ndr1_0) | (~c2_1(a1041)))),
% 0.93/0.85 inference(transitivity,[status(thm)],[916, 914])).
% 0.93/0.85 tff(918,plain,
% 0.93/0.85 ((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp2 | hskp1 | (~ndr1_0) | c0_1(a1041) | c3_1(a1041) | (~c2_1(a1041)))),
% 0.93/0.85 inference(quant_inst,[status(thm)],[])).
% 0.93/0.85 tff(919,plain,
% 0.93/0.85 ((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | hskp2 | hskp1 | c0_1(a1041) | c3_1(a1041) | (~ndr1_0) | (~c2_1(a1041))),
% 0.93/0.85 inference(modus_ponens,[status(thm)],[918, 917])).
% 0.93/0.85 tff(920,plain,
% 0.93/0.85 ($false),
% 0.93/0.85 inference(unit_resolution,[status(thm)],[919, 90, 616, 679, 913, 902, 896, 678])).
% 0.93/0.85 tff(921,plain,(hskp1 | hskp2 | hskp13), inference(lemma,lemma(discharge,[]))).
% 0.93/0.85 tff(922,plain,
% 0.93/0.85 (hskp1),
% 0.93/0.85 inference(unit_resolution,[status(thm)],[921, 624, 616])).
% 0.93/0.85 tff(923,plain,
% 0.93/0.85 (~c1_1(a1001)),
% 0.93/0.85 inference(unit_resolution,[status(thm)],[303, 922])).
% 0.93/0.85 tff(924,plain,
% 0.93/0.85 (~hskp5),
% 0.93/0.85 inference(unit_resolution,[status(thm)],[632, 624, 616])).
% 0.93/0.85 tff(925,plain,
% 0.93/0.85 (c3_1(a1001)),
% 0.93/0.85 inference(unit_resolution,[status(thm)],[314, 922])).
% 0.93/0.85 tff(926,plain,
% 0.93/0.85 (c2_1(a1001)),
% 0.93/0.85 inference(unit_resolution,[status(thm)],[342, 922])).
% 0.93/0.85 tff(927,assumption,(~c1_1(a1001)), introduced(assumption)).
% 0.93/0.85 tff(928,assumption,(c3_1(a1001)), introduced(assumption)).
% 0.93/0.85 tff(929,assumption,(~hskp5), introduced(assumption)).
% 0.93/0.85 tff(930,plain,
% 0.93/0.85 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp5 | c1_1(a1001) | (~ndr1_0) | c0_1(a1001) | (~c3_1(a1001)) | (~c2_1(a1044)) | (~c0_1(a1044)) | (~c1_1(a1044)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp5 | c1_1(a1001) | (~ndr1_0) | c0_1(a1001) | (~c3_1(a1001)) | (~c2_1(a1044)) | (~c0_1(a1044)) | (~c1_1(a1044)))),
% 0.93/0.85 inference(rewrite,[status(thm)],[])).
% 0.93/0.85 tff(931,plain,
% 0.93/0.85 ((hskp5 | (~ndr1_0) | (~c1_1(a1044)) | (~c2_1(a1044)) | (~c0_1(a1044)) | c1_1(a1001) | c0_1(a1001) | (~c3_1(a1001))) <=> (hskp5 | c1_1(a1001) | (~ndr1_0) | c0_1(a1001) | (~c3_1(a1001)) | (~c2_1(a1044)) | (~c0_1(a1044)) | (~c1_1(a1044)))),
% 0.93/0.85 inference(rewrite,[status(thm)],[])).
% 0.93/0.85 tff(932,plain,
% 0.93/0.85 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp5 | (~ndr1_0) | (~c1_1(a1044)) | (~c2_1(a1044)) | (~c0_1(a1044)) | c1_1(a1001) | c0_1(a1001) | (~c3_1(a1001)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp5 | c1_1(a1001) | (~ndr1_0) | c0_1(a1001) | (~c3_1(a1001)) | (~c2_1(a1044)) | (~c0_1(a1044)) | (~c1_1(a1044))))),
% 0.93/0.85 inference(monotonicity,[status(thm)],[931])).
% 0.93/0.85 tff(933,plain,
% 0.93/0.85 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp5 | (~ndr1_0) | (~c1_1(a1044)) | (~c2_1(a1044)) | (~c0_1(a1044)) | c1_1(a1001) | c0_1(a1001) | (~c3_1(a1001)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp5 | c1_1(a1001) | (~ndr1_0) | c0_1(a1001) | (~c3_1(a1001)) | (~c2_1(a1044)) | (~c0_1(a1044)) | (~c1_1(a1044)))),
% 0.93/0.85 inference(transitivity,[status(thm)],[932, 930])).
% 0.93/0.85 tff(934,plain,
% 0.93/0.85 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp5 | (~ndr1_0) | (~c1_1(a1044)) | (~c2_1(a1044)) | (~c0_1(a1044)) | c1_1(a1001) | c0_1(a1001) | (~c3_1(a1001)))),
% 0.93/0.85 inference(quant_inst,[status(thm)],[])).
% 0.93/0.85 tff(935,plain,
% 0.93/0.85 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp5 | c1_1(a1001) | (~ndr1_0) | c0_1(a1001) | (~c3_1(a1001)) | (~c2_1(a1044)) | (~c0_1(a1044)) | (~c1_1(a1044))),
% 0.93/0.85 inference(modus_ponens,[status(thm)],[934, 933])).
% 0.93/0.85 tff(936,plain,
% 0.93/0.85 (c0_1(a1001) | (~c2_1(a1044))),
% 0.93/0.85 inference(unit_resolution,[status(thm)],[935, 90, 929, 783, 772, 928, 927, 735])).
% 0.93/0.85 tff(937,plain,
% 0.93/0.85 (c0_1(a1001)),
% 0.93/0.85 inference(unit_resolution,[status(thm)],[936, 1])).
% 0.93/0.85 tff(938,assumption,(c2_1(a1001)), introduced(assumption)).
% 0.93/0.85 tff(939,plain,
% 0.93/0.85 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp6 | c1_1(a1001) | (~ndr1_0) | (~c0_1(a1001)) | (~c3_1(a1001)) | (~c2_1(a1001)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp6 | c1_1(a1001) | (~ndr1_0) | (~c0_1(a1001)) | (~c3_1(a1001)) | (~c2_1(a1001)))),
% 0.93/0.85 inference(rewrite,[status(thm)],[])).
% 0.93/0.85 tff(940,plain,
% 0.93/0.85 ((hskp6 | (~ndr1_0) | c1_1(a1001) | (~c2_1(a1001)) | (~c3_1(a1001)) | c1_1(a1001) | (~c2_1(a1001)) | (~c0_1(a1001))) <=> (hskp6 | c1_1(a1001) | (~ndr1_0) | (~c0_1(a1001)) | (~c3_1(a1001)) | (~c2_1(a1001)))),
% 0.93/0.85 inference(rewrite,[status(thm)],[])).
% 0.93/0.85 tff(941,plain,
% 0.93/0.85 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp6 | (~ndr1_0) | c1_1(a1001) | (~c2_1(a1001)) | (~c3_1(a1001)) | c1_1(a1001) | (~c2_1(a1001)) | (~c0_1(a1001)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp6 | c1_1(a1001) | (~ndr1_0) | (~c0_1(a1001)) | (~c3_1(a1001)) | (~c2_1(a1001))))),
% 0.93/0.85 inference(monotonicity,[status(thm)],[940])).
% 0.93/0.85 tff(942,plain,
% 0.93/0.85 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp6 | (~ndr1_0) | c1_1(a1001) | (~c2_1(a1001)) | (~c3_1(a1001)) | c1_1(a1001) | (~c2_1(a1001)) | (~c0_1(a1001)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp6 | c1_1(a1001) | (~ndr1_0) | (~c0_1(a1001)) | (~c3_1(a1001)) | (~c2_1(a1001)))),
% 0.93/0.85 inference(transitivity,[status(thm)],[941, 939])).
% 0.93/0.85 tff(943,plain,
% 0.93/0.85 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp6 | (~ndr1_0) | c1_1(a1001) | (~c2_1(a1001)) | (~c3_1(a1001)) | c1_1(a1001) | (~c2_1(a1001)) | (~c0_1(a1001)))),
% 0.93/0.85 inference(quant_inst,[status(thm)],[])).
% 0.93/0.85 tff(944,plain,
% 0.93/0.85 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp6 | c1_1(a1001) | (~ndr1_0) | (~c0_1(a1001)) | (~c3_1(a1001)) | (~c2_1(a1001))),
% 0.93/0.85 inference(modus_ponens,[status(thm)],[943, 942])).
% 0.93/0.85 tff(945,plain,
% 0.93/0.85 (hskp6 | (~c0_1(a1001))),
% 0.93/0.85 inference(unit_resolution,[status(thm)],[944, 90, 938, 928, 927, 827])).
% 0.93/0.85 tff(946,plain,
% 0.93/0.85 (hskp6),
% 0.93/0.85 inference(unit_resolution,[status(thm)],[945, 937])).
% 0.93/0.85 tff(947,plain,
% 0.93/0.85 (((~hskp6) | (~c2_1(a1006))) <=> ((~hskp6) | (~c2_1(a1006)))),
% 0.93/0.85 inference(rewrite,[status(thm)],[])).
% 0.93/0.85 tff(948,plain,
% 0.93/0.85 (((~c2_1(a1006)) | (~hskp6)) <=> ((~hskp6) | (~c2_1(a1006)))),
% 0.93/0.85 inference(rewrite,[status(thm)],[])).
% 0.93/0.85 tff(949,axiom,((~c2_1(a1006)) | (~hskp6)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause120')).
% 0.93/0.85 tff(950,plain,
% 0.93/0.85 ((~hskp6) | (~c2_1(a1006))),
% 0.93/0.85 inference(modus_ponens,[status(thm)],[949, 948])).
% 0.93/0.85 tff(951,plain,
% 0.93/0.85 ((~hskp6) | (~c2_1(a1006))),
% 0.93/0.85 inference(modus_ponens,[status(thm)],[950, 947])).
% 0.93/0.85 tff(952,plain,
% 0.93/0.85 (~c2_1(a1006)),
% 0.93/0.85 inference(unit_resolution,[status(thm)],[951, 946])).
% 0.93/0.85 tff(953,plain,
% 0.93/0.85 (((~hskp6) | c3_1(a1006)) <=> ((~hskp6) | c3_1(a1006))),
% 0.93/0.85 inference(rewrite,[status(thm)],[])).
% 0.93/0.85 tff(954,axiom,((~hskp6) | c3_1(a1006)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause75')).
% 0.93/0.85 tff(955,plain,
% 0.93/0.85 ((~hskp6) | c3_1(a1006)),
% 0.93/0.85 inference(modus_ponens,[status(thm)],[954, 953])).
% 0.93/0.85 tff(956,plain,
% 0.93/0.85 ((~hskp6) | c3_1(a1006)),
% 0.93/0.85 inference(modus_ponens,[status(thm)],[955, 953])).
% 0.93/0.85 tff(957,plain,
% 0.93/0.85 ((~hskp6) | c3_1(a1006)),
% 0.93/0.85 inference(modus_ponens,[status(thm)],[956, 953])).
% 0.93/0.85 tff(958,plain,
% 0.93/0.85 ((~hskp6) | c3_1(a1006)),
% 0.93/0.85 inference(modus_ponens,[status(thm)],[957, 953])).
% 0.93/0.85 tff(959,plain,
% 0.93/0.85 ((~hskp6) | c3_1(a1006)),
% 0.93/0.85 inference(modus_ponens,[status(thm)],[958, 953])).
% 0.93/0.85 tff(960,plain,
% 0.93/0.85 ((~hskp6) | c3_1(a1006)),
% 0.93/0.85 inference(modus_ponens,[status(thm)],[959, 953])).
% 0.93/0.85 tff(961,plain,
% 0.93/0.85 ((~hskp6) | c3_1(a1006)),
% 0.93/0.85 inference(modus_ponens,[status(thm)],[960, 953])).
% 0.93/0.85 tff(962,plain,
% 0.93/0.85 ((~hskp6) | c3_1(a1006)),
% 0.93/0.85 inference(modus_ponens,[status(thm)],[961, 953])).
% 0.93/0.85 tff(963,plain,
% 0.93/0.85 (c3_1(a1006)),
% 0.93/0.85 inference(unit_resolution,[status(thm)],[962, 946])).
% 0.93/0.85 tff(964,plain,
% 0.93/0.85 (((~hskp6) | c0_1(a1006)) <=> ((~hskp6) | c0_1(a1006))),
% 0.93/0.85 inference(rewrite,[status(thm)],[])).
% 0.93/0.85 tff(965,axiom,((~hskp6) | c0_1(a1006)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause74')).
% 0.93/0.85 tff(966,plain,
% 0.93/0.85 ((~hskp6) | c0_1(a1006)),
% 0.93/0.85 inference(modus_ponens,[status(thm)],[965, 964])).
% 0.93/0.85 tff(967,plain,
% 0.93/0.85 ((~hskp6) | c0_1(a1006)),
% 0.93/0.85 inference(modus_ponens,[status(thm)],[966, 964])).
% 0.93/0.85 tff(968,plain,
% 0.93/0.85 ((~hskp6) | c0_1(a1006)),
% 0.93/0.85 inference(modus_ponens,[status(thm)],[967, 964])).
% 0.93/0.85 tff(969,plain,
% 0.93/0.85 ((~hskp6) | c0_1(a1006)),
% 0.93/0.85 inference(modus_ponens,[status(thm)],[968, 964])).
% 0.93/0.85 tff(970,plain,
% 0.93/0.85 ((~hskp6) | c0_1(a1006)),
% 0.93/0.85 inference(modus_ponens,[status(thm)],[969, 964])).
% 0.93/0.85 tff(971,plain,
% 0.93/0.85 ((~hskp6) | c0_1(a1006)),
% 0.93/0.85 inference(modus_ponens,[status(thm)],[970, 964])).
% 0.93/0.85 tff(972,plain,
% 0.93/0.85 ((~hskp6) | c0_1(a1006)),
% 0.93/0.85 inference(modus_ponens,[status(thm)],[971, 964])).
% 0.93/0.85 tff(973,plain,
% 0.93/0.85 ((~hskp6) | c0_1(a1006)),
% 0.93/0.85 inference(modus_ponens,[status(thm)],[972, 964])).
% 0.93/0.85 tff(974,plain,
% 0.93/0.85 (c0_1(a1006)),
% 0.93/0.85 inference(unit_resolution,[status(thm)],[973, 946])).
% 0.93/0.85 tff(975,plain,
% 0.93/0.85 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c1_1(W) | (~c3_1(W)) | (~c2_1(W)))) | (c3_1(a1044) | c2_1(a1006) | c1_1(a1001) | (~ndr1_0) | (~c3_1(a1001)) | (~c2_1(a1001)) | (~c0_1(a1006)) | (~c3_1(a1006)) | (~c2_1(a1044)) | (~c1_1(a1044)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c1_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c3_1(a1044) | c2_1(a1006) | c1_1(a1001) | (~ndr1_0) | (~c3_1(a1001)) | (~c2_1(a1001)) | (~c0_1(a1006)) | (~c3_1(a1006)) | (~c2_1(a1044)) | (~c1_1(a1044)))),
% 0.93/0.85 inference(rewrite,[status(thm)],[])).
% 0.93/0.85 tff(976,plain,
% 0.93/0.85 (((~ndr1_0) | (~c1_1(a1044)) | c3_1(a1044) | (~c2_1(a1044)) | c2_1(a1006) | (~c0_1(a1006)) | (~c3_1(a1006)) | c1_1(a1001) | (~c3_1(a1001)) | (~c2_1(a1001))) <=> (c3_1(a1044) | c2_1(a1006) | c1_1(a1001) | (~ndr1_0) | (~c3_1(a1001)) | (~c2_1(a1001)) | (~c0_1(a1006)) | (~c3_1(a1006)) | (~c2_1(a1044)) | (~c1_1(a1044)))),
% 0.93/0.85 inference(rewrite,[status(thm)],[])).
% 0.93/0.85 tff(977,plain,
% 0.93/0.85 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c1_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c1_1(a1044)) | c3_1(a1044) | (~c2_1(a1044)) | c2_1(a1006) | (~c0_1(a1006)) | (~c3_1(a1006)) | c1_1(a1001) | (~c3_1(a1001)) | (~c2_1(a1001)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c1_1(W) | (~c3_1(W)) | (~c2_1(W)))) | (c3_1(a1044) | c2_1(a1006) | c1_1(a1001) | (~ndr1_0) | (~c3_1(a1001)) | (~c2_1(a1001)) | (~c0_1(a1006)) | (~c3_1(a1006)) | (~c2_1(a1044)) | (~c1_1(a1044))))),
% 0.93/0.85 inference(monotonicity,[status(thm)],[976])).
% 0.93/0.85 tff(978,plain,
% 0.93/0.85 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c1_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c1_1(a1044)) | c3_1(a1044) | (~c2_1(a1044)) | c2_1(a1006) | (~c0_1(a1006)) | (~c3_1(a1006)) | c1_1(a1001) | (~c3_1(a1001)) | (~c2_1(a1001)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c1_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c3_1(a1044) | c2_1(a1006) | c1_1(a1001) | (~ndr1_0) | (~c3_1(a1001)) | (~c2_1(a1001)) | (~c0_1(a1006)) | (~c3_1(a1006)) | (~c2_1(a1044)) | (~c1_1(a1044)))),
% 0.93/0.85 inference(transitivity,[status(thm)],[977, 975])).
% 0.93/0.85 tff(979,plain,
% 0.93/0.85 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c1_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c1_1(a1044)) | c3_1(a1044) | (~c2_1(a1044)) | c2_1(a1006) | (~c0_1(a1006)) | (~c3_1(a1006)) | c1_1(a1001) | (~c3_1(a1001)) | (~c2_1(a1001)))),
% 0.93/0.85 inference(quant_inst,[status(thm)],[])).
% 0.93/0.85 tff(980,plain,
% 0.93/0.85 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c1_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c3_1(a1044) | c2_1(a1006) | c1_1(a1001) | (~ndr1_0) | (~c3_1(a1001)) | (~c2_1(a1001)) | (~c0_1(a1006)) | (~c3_1(a1006)) | (~c2_1(a1044)) | (~c1_1(a1044))),
% 0.93/0.85 inference(modus_ponens,[status(thm)],[979, 978])).
% 0.93/0.85 tff(981,plain,
% 0.93/0.85 ($false),
% 0.93/0.85 inference(unit_resolution,[status(thm)],[980, 90, 772, 974, 963, 938, 928, 761, 952, 927, 817, 1])).
% 0.93/0.85 tff(982,plain,((~c2_1(a1044)) | (~c2_1(a1001)) | (~c3_1(a1001)) | c1_1(a1001) | hskp5), inference(lemma,lemma(discharge,[]))).
% 0.93/0.85 tff(983,plain,
% 0.93/0.85 (~c2_1(a1044)),
% 0.93/0.85 inference(unit_resolution,[status(thm)],[982, 926, 925, 923, 924])).
% 0.93/0.85 tff(984,plain,
% 0.93/0.85 (^[U: $i] : refl((hskp13 | hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))) <=> (hskp13 | hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))))),
% 0.93/0.85 inference(bind,[status(th)],[])).
% 0.93/0.85 tff(985,plain,
% 0.93/0.85 (![U: $i] : (hskp13 | hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp13 | hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 0.93/0.85 inference(quant_intro,[status(thm)],[984])).
% 0.93/0.85 tff(986,plain,
% 0.93/0.85 (![U: $i] : (hskp13 | hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp13 | hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 0.93/0.85 inference(rewrite,[status(thm)],[])).
% 0.93/0.85 tff(987,plain,
% 0.93/0.85 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp6) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))) | hskp6))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))) | hskp6) <=> (hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp6) <=> (hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp6) | hskp13) <=> ((hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))) | hskp13))), rewrite(((hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))) | hskp13) <=> (hskp13 | hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp6) | hskp13) <=> (hskp13 | hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))))),
% 0.93/0.85 inference(bind,[status(th)],[])).
% 0.93/0.85 tff(988,plain,
% 0.93/0.85 (![U: $i] : ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp6) | hskp13) <=> ![U: $i] : (hskp13 | hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 0.93/0.85 inference(quant_intro,[status(thm)],[987])).
% 0.93/0.85 tff(989,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp6) | hskp13)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause142')).
% 0.93/0.85 tff(990,plain,
% 0.93/0.85 (![U: $i] : (hskp13 | hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 0.93/0.85 inference(modus_ponens,[status(thm)],[989, 988])).
% 0.93/0.85 tff(991,plain,
% 0.93/0.85 (![U: $i] : (hskp13 | hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 0.93/0.85 inference(modus_ponens,[status(thm)],[990, 986])).
% 0.93/0.85 tff(992,plain,(
% 0.93/0.85 ![U: $i] : (hskp13 | hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 0.93/0.85 inference(skolemize,[status(sab)],[991])).
% 0.93/0.85 tff(993,plain,
% 0.93/0.85 (![U: $i] : (hskp13 | hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 0.93/0.85 inference(modus_ponens,[status(thm)],[992, 985])).
% 0.93/0.85 tff(994,plain,
% 0.93/0.85 (((~![U: $i] : (hskp13 | hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp13 | hskp6 | (~ndr1_0) | c2_1(a1044) | (~c0_1(a1044)) | (~c1_1(a1044)))) <=> ((~![U: $i] : (hskp13 | hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp13 | hskp6 | (~ndr1_0) | c2_1(a1044) | (~c0_1(a1044)) | (~c1_1(a1044)))),
% 0.93/0.85 inference(rewrite,[status(thm)],[])).
% 0.93/0.85 tff(995,plain,
% 0.93/0.85 ((hskp13 | hskp6 | (~ndr1_0) | c2_1(a1044) | (~c1_1(a1044)) | (~c0_1(a1044))) <=> (hskp13 | hskp6 | (~ndr1_0) | c2_1(a1044) | (~c0_1(a1044)) | (~c1_1(a1044)))),
% 0.93/0.85 inference(rewrite,[status(thm)],[])).
% 0.93/0.85 tff(996,plain,
% 0.93/0.85 (((~![U: $i] : (hskp13 | hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp13 | hskp6 | (~ndr1_0) | c2_1(a1044) | (~c1_1(a1044)) | (~c0_1(a1044)))) <=> ((~![U: $i] : (hskp13 | hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp13 | hskp6 | (~ndr1_0) | c2_1(a1044) | (~c0_1(a1044)) | (~c1_1(a1044))))),
% 0.93/0.85 inference(monotonicity,[status(thm)],[995])).
% 0.93/0.85 tff(997,plain,
% 0.93/0.85 (((~![U: $i] : (hskp13 | hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp13 | hskp6 | (~ndr1_0) | c2_1(a1044) | (~c1_1(a1044)) | (~c0_1(a1044)))) <=> ((~![U: $i] : (hskp13 | hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp13 | hskp6 | (~ndr1_0) | c2_1(a1044) | (~c0_1(a1044)) | (~c1_1(a1044)))),
% 0.93/0.85 inference(transitivity,[status(thm)],[996, 994])).
% 0.93/0.85 tff(998,plain,
% 0.93/0.85 ((~![U: $i] : (hskp13 | hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp13 | hskp6 | (~ndr1_0) | c2_1(a1044) | (~c1_1(a1044)) | (~c0_1(a1044)))),
% 0.93/0.85 inference(quant_inst,[status(thm)],[])).
% 0.93/0.85 tff(999,plain,
% 0.93/0.85 ((~![U: $i] : (hskp13 | hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp13 | hskp6 | (~ndr1_0) | c2_1(a1044) | (~c0_1(a1044)) | (~c1_1(a1044))),
% 0.93/0.85 inference(modus_ponens,[status(thm)],[998, 997])).
% 0.93/0.85 tff(1000,plain,
% 0.93/0.85 (hskp13 | hskp6 | c2_1(a1044)),
% 0.93/0.85 inference(unit_resolution,[status(thm)],[999, 90, 783, 772, 993])).
% 0.93/0.85 tff(1001,plain,
% 0.93/0.85 (hskp6),
% 0.93/0.85 inference(unit_resolution,[status(thm)],[1000, 983, 624])).
% 0.93/0.85 tff(1002,plain,
% 0.93/0.85 (~c2_1(a1006)),
% 0.93/0.85 inference(unit_resolution,[status(thm)],[951, 1001])).
% 0.93/0.85 tff(1003,plain,
% 0.93/0.85 (c3_1(a1006)),
% 0.93/0.85 inference(unit_resolution,[status(thm)],[962, 1001])).
% 0.93/0.85 tff(1004,plain,
% 0.93/0.85 (c0_1(a1006)),
% 0.93/0.85 inference(unit_resolution,[status(thm)],[973, 1001])).
% 0.93/0.85 tff(1005,plain,
% 0.93/0.85 (^[V: $i, U: $i] : refl((hskp7 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V))) <=> (hskp7 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V))))),
% 0.93/0.85 inference(bind,[status(th)],[])).
% 0.93/0.85 tff(1006,plain,
% 0.93/0.85 (![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))),
% 0.93/0.86 inference(quant_intro,[status(thm)],[1005])).
% 0.93/0.86 tff(1007,plain,
% 0.93/0.86 (![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))),
% 0.93/0.86 inference(rewrite,[status(thm)],[])).
% 0.93/0.86 tff(1008,plain,
% 0.93/0.86 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c3_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)))), ((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c3_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(V)))), ((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(V))))), (((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c1_1(V)))), (((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c1_1(V))))), ((((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c1_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c1_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | (~c1_1(V)))), ((((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | (~c1_1(V))))), (((((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | (~c1_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | (~c1_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)))), (((((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c1_1(V))))), ((((((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c1_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c1_1(V))) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))), ((((((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V))))), (((((((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c2_1(V)) | hskp7) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V))) | hskp7))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V))) | hskp7) <=> (hskp7 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))), (((((((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c2_1(V)) | hskp7) <=> (hskp7 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))))),
% 0.93/0.86 inference(bind,[status(th)],[])).
% 0.93/0.86 tff(1009,plain,
% 0.93/0.86 (![V: $i, U: $i] : ((((((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c2_1(V)) | hskp7) <=> ![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))),
% 0.93/0.86 inference(quant_intro,[status(thm)],[1008])).
% 0.93/0.86 tff(1010,axiom,(![V: $i, U: $i] : ((((((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c2_1(V)) | hskp7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause156')).
% 0.93/0.86 tff(1011,plain,
% 0.93/0.86 (![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))),
% 0.93/0.86 inference(modus_ponens,[status(thm)],[1010, 1009])).
% 0.93/0.86 tff(1012,plain,
% 0.93/0.86 (![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))),
% 0.93/0.86 inference(modus_ponens,[status(thm)],[1011, 1007])).
% 0.93/0.86 tff(1013,plain,(
% 0.93/0.86 ![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))),
% 0.93/0.86 inference(skolemize,[status(sab)],[1012])).
% 0.93/0.86 tff(1014,plain,
% 0.93/0.86 (![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))),
% 0.93/0.86 inference(modus_ponens,[status(thm)],[1013, 1006])).
% 0.93/0.86 tff(1015,plain,
% 0.93/0.86 (((~![U: $i] : (hskp7 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)))) | (hskp7 | (~ndr1_0) | (~c2_1(a1044)) | (~c0_1(a1044)) | (~c1_1(a1044)))) <=> ((~![U: $i] : (hskp7 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)))) | hskp7 | (~ndr1_0) | (~c2_1(a1044)) | (~c0_1(a1044)) | (~c1_1(a1044)))),
% 0.93/0.86 inference(rewrite,[status(thm)],[])).
% 0.93/0.86 tff(1016,plain,
% 0.93/0.86 ((hskp7 | (~ndr1_0) | (~c1_1(a1044)) | (~c2_1(a1044)) | (~c0_1(a1044))) <=> (hskp7 | (~ndr1_0) | (~c2_1(a1044)) | (~c0_1(a1044)) | (~c1_1(a1044)))),
% 0.93/0.86 inference(rewrite,[status(thm)],[])).
% 0.93/0.86 tff(1017,plain,
% 0.93/0.86 (((~![U: $i] : (hskp7 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)))) | (hskp7 | (~ndr1_0) | (~c1_1(a1044)) | (~c2_1(a1044)) | (~c0_1(a1044)))) <=> ((~![U: $i] : (hskp7 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)))) | (hskp7 | (~ndr1_0) | (~c2_1(a1044)) | (~c0_1(a1044)) | (~c1_1(a1044))))),
% 0.93/0.86 inference(monotonicity,[status(thm)],[1016])).
% 0.93/0.86 tff(1018,plain,
% 0.93/0.86 (((~![U: $i] : (hskp7 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)))) | (hskp7 | (~ndr1_0) | (~c1_1(a1044)) | (~c2_1(a1044)) | (~c0_1(a1044)))) <=> ((~![U: $i] : (hskp7 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)))) | hskp7 | (~ndr1_0) | (~c2_1(a1044)) | (~c0_1(a1044)) | (~c1_1(a1044)))),
% 0.93/0.86 inference(transitivity,[status(thm)],[1017, 1015])).
% 0.93/0.86 tff(1019,plain,
% 0.93/0.86 ((~![U: $i] : (hskp7 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)))) | (hskp7 | (~ndr1_0) | (~c1_1(a1044)) | (~c2_1(a1044)) | (~c0_1(a1044)))),
% 0.93/0.86 inference(quant_inst,[status(thm)],[])).
% 0.93/0.86 tff(1020,plain,
% 0.93/0.86 ((~![U: $i] : (hskp7 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)))) | hskp7 | (~ndr1_0) | (~c2_1(a1044)) | (~c0_1(a1044)) | (~c1_1(a1044))),
% 0.93/0.86 inference(modus_ponens,[status(thm)],[1019, 1018])).
% 0.93/0.86 tff(1021,plain,
% 0.93/0.86 (hskp7 | (~c2_1(a1044))),
% 0.93/0.86 inference(unit_resolution,[status(thm)],[1020, 90, 783, 772, 188])).
% 0.93/0.86 tff(1022,plain,
% 0.93/0.86 (~c2_1(a1044)),
% 0.93/0.86 inference(unit_resolution,[status(thm)],[1021, 644])).
% 0.93/0.86 tff(1023,assumption,(~hskp8), introduced(assumption)).
% 0.93/0.86 tff(1024,plain,
% 0.93/0.86 (^[U: $i] : refl((hskp26 | hskp8 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))) <=> (hskp26 | hskp8 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))))),
% 0.93/0.86 inference(bind,[status(th)],[])).
% 0.93/0.86 tff(1025,plain,
% 0.93/0.86 (![U: $i] : (hskp26 | hskp8 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp26 | hskp8 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 0.93/0.86 inference(quant_intro,[status(thm)],[1024])).
% 0.93/0.86 tff(1026,plain,
% 0.93/0.86 (![U: $i] : (hskp26 | hskp8 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp26 | hskp8 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 0.93/0.86 inference(rewrite,[status(thm)],[])).
% 0.93/0.86 tff(1027,plain,
% 0.93/0.86 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp8) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))) | hskp8))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))) | hskp8) <=> (hskp8 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp8) <=> (hskp8 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp8) | hskp26) <=> ((hskp8 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))) | hskp26))), rewrite(((hskp8 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))) | hskp26) <=> (hskp26 | hskp8 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp8) | hskp26) <=> (hskp26 | hskp8 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))))),
% 0.93/0.86 inference(bind,[status(th)],[])).
% 0.93/0.86 tff(1028,plain,
% 0.93/0.86 (![U: $i] : ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp8) | hskp26) <=> ![U: $i] : (hskp26 | hskp8 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 0.93/0.86 inference(quant_intro,[status(thm)],[1027])).
% 0.93/0.86 tff(1029,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp8) | hskp26)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause141')).
% 0.93/0.86 tff(1030,plain,
% 0.93/0.86 (![U: $i] : (hskp26 | hskp8 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 0.93/0.86 inference(modus_ponens,[status(thm)],[1029, 1028])).
% 0.93/0.86 tff(1031,plain,
% 0.93/0.86 (![U: $i] : (hskp26 | hskp8 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 0.93/0.86 inference(modus_ponens,[status(thm)],[1030, 1026])).
% 0.93/0.86 tff(1032,plain,(
% 0.93/0.86 ![U: $i] : (hskp26 | hskp8 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 0.93/0.86 inference(skolemize,[status(sab)],[1031])).
% 0.93/0.86 tff(1033,plain,
% 0.93/0.86 (![U: $i] : (hskp26 | hskp8 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 0.93/0.86 inference(modus_ponens,[status(thm)],[1032, 1025])).
% 0.93/0.86 tff(1034,plain,
% 0.93/0.86 (((~![U: $i] : (hskp26 | hskp8 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp26 | hskp8 | (~ndr1_0) | c2_1(a1044) | (~c0_1(a1044)) | (~c1_1(a1044)))) <=> ((~![U: $i] : (hskp26 | hskp8 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp26 | hskp8 | (~ndr1_0) | c2_1(a1044) | (~c0_1(a1044)) | (~c1_1(a1044)))),
% 0.93/0.86 inference(rewrite,[status(thm)],[])).
% 0.93/0.86 tff(1035,plain,
% 0.93/0.86 ((hskp26 | hskp8 | (~ndr1_0) | c2_1(a1044) | (~c1_1(a1044)) | (~c0_1(a1044))) <=> (hskp26 | hskp8 | (~ndr1_0) | c2_1(a1044) | (~c0_1(a1044)) | (~c1_1(a1044)))),
% 0.93/0.86 inference(rewrite,[status(thm)],[])).
% 0.93/0.86 tff(1036,plain,
% 0.93/0.86 (((~![U: $i] : (hskp26 | hskp8 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp26 | hskp8 | (~ndr1_0) | c2_1(a1044) | (~c1_1(a1044)) | (~c0_1(a1044)))) <=> ((~![U: $i] : (hskp26 | hskp8 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp26 | hskp8 | (~ndr1_0) | c2_1(a1044) | (~c0_1(a1044)) | (~c1_1(a1044))))),
% 0.93/0.86 inference(monotonicity,[status(thm)],[1035])).
% 0.93/0.86 tff(1037,plain,
% 0.93/0.86 (((~![U: $i] : (hskp26 | hskp8 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp26 | hskp8 | (~ndr1_0) | c2_1(a1044) | (~c1_1(a1044)) | (~c0_1(a1044)))) <=> ((~![U: $i] : (hskp26 | hskp8 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp26 | hskp8 | (~ndr1_0) | c2_1(a1044) | (~c0_1(a1044)) | (~c1_1(a1044)))),
% 0.93/0.86 inference(transitivity,[status(thm)],[1036, 1034])).
% 0.93/0.86 tff(1038,plain,
% 0.93/0.86 ((~![U: $i] : (hskp26 | hskp8 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp26 | hskp8 | (~ndr1_0) | c2_1(a1044) | (~c1_1(a1044)) | (~c0_1(a1044)))),
% 0.93/0.86 inference(quant_inst,[status(thm)],[])).
% 0.93/0.86 tff(1039,plain,
% 0.93/0.86 ((~![U: $i] : (hskp26 | hskp8 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp26 | hskp8 | (~ndr1_0) | c2_1(a1044) | (~c0_1(a1044)) | (~c1_1(a1044))),
% 0.93/0.86 inference(modus_ponens,[status(thm)],[1038, 1037])).
% 0.93/0.86 tff(1040,plain,
% 0.93/0.86 (hskp26 | hskp8 | c2_1(a1044)),
% 0.93/0.86 inference(unit_resolution,[status(thm)],[1039, 90, 783, 772, 1033])).
% 0.93/0.86 tff(1041,plain,
% 0.93/0.86 (hskp26),
% 0.93/0.86 inference(unit_resolution,[status(thm)],[1040, 1022, 1023])).
% 0.93/0.86 tff(1042,plain,
% 0.93/0.86 (((~hskp26) | (~c2_1(a1052))) <=> ((~hskp26) | (~c2_1(a1052)))),
% 0.93/0.86 inference(rewrite,[status(thm)],[])).
% 0.93/0.86 tff(1043,plain,
% 0.93/0.86 (((~c2_1(a1052)) | (~hskp26)) <=> ((~hskp26) | (~c2_1(a1052)))),
% 0.93/0.86 inference(rewrite,[status(thm)],[])).
% 0.93/0.86 tff(1044,axiom,((~c2_1(a1052)) | (~hskp26)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause86')).
% 0.93/0.86 tff(1045,plain,
% 0.93/0.86 ((~hskp26) | (~c2_1(a1052))),
% 0.93/0.86 inference(modus_ponens,[status(thm)],[1044, 1043])).
% 0.93/0.86 tff(1046,plain,
% 0.93/0.86 ((~hskp26) | (~c2_1(a1052))),
% 0.93/0.86 inference(modus_ponens,[status(thm)],[1045, 1042])).
% 0.93/0.86 tff(1047,plain,
% 0.93/0.86 (~c2_1(a1052)),
% 0.93/0.86 inference(unit_resolution,[status(thm)],[1046, 1041])).
% 0.93/0.86 tff(1048,plain,
% 0.93/0.86 (((~hskp26) | (~c0_1(a1052))) <=> ((~hskp26) | (~c0_1(a1052)))),
% 0.93/0.86 inference(rewrite,[status(thm)],[])).
% 0.93/0.86 tff(1049,plain,
% 0.93/0.86 (((~c0_1(a1052)) | (~hskp26)) <=> ((~hskp26) | (~c0_1(a1052)))),
% 0.93/0.86 inference(rewrite,[status(thm)],[])).
% 0.93/0.86 tff(1050,axiom,((~c0_1(a1052)) | (~hskp26)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause85')).
% 0.93/0.86 tff(1051,plain,
% 0.93/0.86 ((~hskp26) | (~c0_1(a1052))),
% 0.93/0.86 inference(modus_ponens,[status(thm)],[1050, 1049])).
% 0.93/0.86 tff(1052,plain,
% 0.93/0.86 ((~hskp26) | (~c0_1(a1052))),
% 0.93/0.86 inference(modus_ponens,[status(thm)],[1051, 1048])).
% 0.93/0.86 tff(1053,plain,
% 0.93/0.86 (~c0_1(a1052)),
% 0.93/0.86 inference(unit_resolution,[status(thm)],[1052, 1041])).
% 0.93/0.86 tff(1054,plain,
% 0.93/0.86 (((~![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))) | (hskp8 | hskp7 | c0_1(a1052) | c2_1(a1052) | (~ndr1_0) | (~c1_1(a1052)))) <=> ((~![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))) | hskp8 | hskp7 | c0_1(a1052) | c2_1(a1052) | (~ndr1_0) | (~c1_1(a1052)))),
% 0.93/0.86 inference(rewrite,[status(thm)],[])).
% 0.93/0.86 tff(1055,plain,
% 0.93/0.86 ((hskp8 | hskp7 | (~ndr1_0) | c2_1(a1052) | c0_1(a1052) | (~c1_1(a1052))) <=> (hskp8 | hskp7 | c0_1(a1052) | c2_1(a1052) | (~ndr1_0) | (~c1_1(a1052)))),
% 0.93/0.86 inference(rewrite,[status(thm)],[])).
% 0.93/0.86 tff(1056,plain,
% 0.93/0.86 (((~![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))) | (hskp8 | hskp7 | (~ndr1_0) | c2_1(a1052) | c0_1(a1052) | (~c1_1(a1052)))) <=> ((~![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))) | (hskp8 | hskp7 | c0_1(a1052) | c2_1(a1052) | (~ndr1_0) | (~c1_1(a1052))))),
% 0.93/0.86 inference(monotonicity,[status(thm)],[1055])).
% 0.93/0.86 tff(1057,plain,
% 0.93/0.86 (((~![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))) | (hskp8 | hskp7 | (~ndr1_0) | c2_1(a1052) | c0_1(a1052) | (~c1_1(a1052)))) <=> ((~![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))) | hskp8 | hskp7 | c0_1(a1052) | c2_1(a1052) | (~ndr1_0) | (~c1_1(a1052)))),
% 0.93/0.86 inference(transitivity,[status(thm)],[1056, 1054])).
% 0.93/0.86 tff(1058,plain,
% 0.93/0.86 ((~![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))) | (hskp8 | hskp7 | (~ndr1_0) | c2_1(a1052) | c0_1(a1052) | (~c1_1(a1052)))),
% 0.93/0.86 inference(quant_inst,[status(thm)],[])).
% 0.93/0.86 tff(1059,plain,
% 0.93/0.86 ((~![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))) | hskp8 | hskp7 | c0_1(a1052) | c2_1(a1052) | (~ndr1_0) | (~c1_1(a1052))),
% 0.93/0.86 inference(modus_ponens,[status(thm)],[1058, 1057])).
% 0.93/0.86 tff(1060,plain,
% 0.93/0.86 (~c1_1(a1052)),
% 0.93/0.86 inference(unit_resolution,[status(thm)],[1059, 90, 1023, 644, 1053, 1047, 643])).
% 0.93/0.86 tff(1061,plain,
% 0.93/0.86 (^[V: $i, U: $i] : refl((hskp13 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V))) <=> (hskp13 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V))))),
% 0.93/0.86 inference(bind,[status(th)],[])).
% 0.93/0.86 tff(1062,plain,
% 0.93/0.86 (![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))),
% 0.93/0.86 inference(quant_intro,[status(thm)],[1061])).
% 0.93/0.86 tff(1063,plain,
% 0.93/0.86 (![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))),
% 0.93/0.86 inference(rewrite,[status(thm)],[])).
% 0.93/0.86 tff(1064,plain,
% 0.93/0.86 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c3_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)))), ((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c3_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(V)))), ((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(V))))), (((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(V))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(V)) | (~c1_1(V)))), (((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(V)) | (~c1_1(V))))), ((((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c1_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(V)) | (~c1_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(V)) | (~c1_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(V)) | (~c1_1(V)))), ((((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(V)) | (~c1_1(V))))), (((((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c1_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(V)) | (~c1_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(V)) | (~c1_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | (~c2_1(V)) | (~c1_1(V)))), (((((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c1_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | (~c2_1(V)) | (~c1_1(V))))), ((((((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | (~c2_1(V)) | (~c1_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | (~c2_1(V)) | (~c1_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))), ((((((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V))))), (((((((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | hskp13) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V))) | hskp13))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V))) | hskp13) <=> (hskp13 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))), (((((((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | hskp13) <=> (hskp13 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))))),
% 0.93/0.86 inference(bind,[status(th)],[])).
% 0.93/0.86 tff(1065,plain,
% 0.93/0.86 (![V: $i, U: $i] : ((((((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | hskp13) <=> ![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))),
% 0.93/0.86 inference(quant_intro,[status(thm)],[1064])).
% 0.93/0.86 tff(1066,axiom,(![V: $i, U: $i] : ((((((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | hskp13)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause168')).
% 0.93/0.86 tff(1067,plain,
% 0.93/0.86 (![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))),
% 0.93/0.86 inference(modus_ponens,[status(thm)],[1066, 1065])).
% 0.93/0.86 tff(1068,plain,
% 0.93/0.86 (![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))),
% 0.93/0.86 inference(modus_ponens,[status(thm)],[1067, 1063])).
% 0.93/0.86 tff(1069,plain,(
% 0.93/0.86 ![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))),
% 0.93/0.86 inference(skolemize,[status(sab)],[1068])).
% 0.93/0.86 tff(1070,plain,
% 0.93/0.86 (![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))),
% 0.93/0.86 inference(modus_ponens,[status(thm)],[1069, 1062])).
% 0.93/0.86 tff(1071,plain,
% 0.93/0.86 (^[U: $i] : refl((hskp25 | hskp3 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U))) <=> (hskp25 | hskp3 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U))))),
% 0.93/0.86 inference(bind,[status(th)],[])).
% 0.93/0.86 tff(1072,plain,
% 0.93/0.86 (![U: $i] : (hskp25 | hskp3 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U))) <=> ![U: $i] : (hskp25 | hskp3 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))),
% 0.93/0.86 inference(quant_intro,[status(thm)],[1071])).
% 0.93/0.86 tff(1073,plain,
% 0.93/0.86 (![U: $i] : (hskp25 | hskp3 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U))) <=> ![U: $i] : (hskp25 | hskp3 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))),
% 0.93/0.86 inference(rewrite,[status(thm)],[])).
% 0.93/0.86 tff(1074,plain,
% 0.93/0.86 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c0_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) <=> (((~ndr1_0) | (~c0_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U))))), (((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c2_1(U) | (~c0_1(U))) | c3_1(U)))), rewrite((((~ndr1_0) | c2_1(U) | (~c0_1(U))) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))), (((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U))))), ((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp3) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U))) | hskp3))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U))) | hskp3) <=> (hskp3 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))), ((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp3) <=> (hskp3 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U))))), (((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp3) | hskp25) <=> ((hskp3 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U))) | hskp25))), rewrite(((hskp3 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U))) | hskp25) <=> (hskp25 | hskp3 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))), (((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp3) | hskp25) <=> (hskp25 | hskp3 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))))),
% 0.93/0.86 inference(bind,[status(th)],[])).
% 0.93/0.86 tff(1075,plain,
% 0.93/0.86 (![U: $i] : ((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp3) | hskp25) <=> ![U: $i] : (hskp25 | hskp3 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))),
% 0.93/0.86 inference(quant_intro,[status(thm)],[1074])).
% 0.93/0.86 tff(1076,axiom,(![U: $i] : ((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp3) | hskp25)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause139')).
% 0.93/0.86 tff(1077,plain,
% 0.93/0.86 (![U: $i] : (hskp25 | hskp3 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))),
% 0.93/0.86 inference(modus_ponens,[status(thm)],[1076, 1075])).
% 0.93/0.86 tff(1078,plain,
% 0.93/0.86 (![U: $i] : (hskp25 | hskp3 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))),
% 0.93/0.86 inference(modus_ponens,[status(thm)],[1077, 1073])).
% 0.93/0.86 tff(1079,plain,(
% 0.93/0.86 ![U: $i] : (hskp25 | hskp3 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))),
% 0.93/0.86 inference(skolemize,[status(sab)],[1078])).
% 0.93/0.86 tff(1080,plain,
% 0.93/0.86 (![U: $i] : (hskp25 | hskp3 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))),
% 0.93/0.86 inference(modus_ponens,[status(thm)],[1079, 1072])).
% 0.93/0.86 tff(1081,plain,
% 0.93/0.86 (((~![U: $i] : (hskp25 | hskp3 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp25 | hskp3 | c3_1(a1044) | (~ndr1_0) | c2_1(a1044) | (~c0_1(a1044)))) <=> ((~![U: $i] : (hskp25 | hskp3 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | hskp25 | hskp3 | c3_1(a1044) | (~ndr1_0) | c2_1(a1044) | (~c0_1(a1044)))),
% 0.93/0.86 inference(rewrite,[status(thm)],[])).
% 0.93/0.86 tff(1082,plain,
% 0.93/0.86 ((hskp25 | hskp3 | (~ndr1_0) | c2_1(a1044) | c3_1(a1044) | (~c0_1(a1044))) <=> (hskp25 | hskp3 | c3_1(a1044) | (~ndr1_0) | c2_1(a1044) | (~c0_1(a1044)))),
% 0.93/0.86 inference(rewrite,[status(thm)],[])).
% 0.93/0.86 tff(1083,plain,
% 0.93/0.86 (((~![U: $i] : (hskp25 | hskp3 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp25 | hskp3 | (~ndr1_0) | c2_1(a1044) | c3_1(a1044) | (~c0_1(a1044)))) <=> ((~![U: $i] : (hskp25 | hskp3 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp25 | hskp3 | c3_1(a1044) | (~ndr1_0) | c2_1(a1044) | (~c0_1(a1044))))),
% 0.93/0.86 inference(monotonicity,[status(thm)],[1082])).
% 0.93/0.86 tff(1084,plain,
% 0.93/0.86 (((~![U: $i] : (hskp25 | hskp3 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp25 | hskp3 | (~ndr1_0) | c2_1(a1044) | c3_1(a1044) | (~c0_1(a1044)))) <=> ((~![U: $i] : (hskp25 | hskp3 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | hskp25 | hskp3 | c3_1(a1044) | (~ndr1_0) | c2_1(a1044) | (~c0_1(a1044)))),
% 0.93/0.86 inference(transitivity,[status(thm)],[1083, 1081])).
% 0.93/0.86 tff(1085,plain,
% 0.93/0.86 ((~![U: $i] : (hskp25 | hskp3 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp25 | hskp3 | (~ndr1_0) | c2_1(a1044) | c3_1(a1044) | (~c0_1(a1044)))),
% 0.93/0.86 inference(quant_inst,[status(thm)],[])).
% 0.93/0.86 tff(1086,plain,
% 0.93/0.86 ((~![U: $i] : (hskp25 | hskp3 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | hskp25 | hskp3 | c3_1(a1044) | (~ndr1_0) | c2_1(a1044) | (~c0_1(a1044))),
% 0.93/0.86 inference(modus_ponens,[status(thm)],[1085, 1084])).
% 0.93/0.86 tff(1087,plain,
% 0.93/0.86 (hskp25 | hskp3 | c2_1(a1044)),
% 0.93/0.86 inference(unit_resolution,[status(thm)],[1086, 90, 783, 761, 1080])).
% 0.93/0.86 tff(1088,plain,
% 0.93/0.86 (hskp25),
% 0.93/0.86 inference(unit_resolution,[status(thm)],[1087, 1022, 360])).
% 0.93/0.86 tff(1089,plain,
% 0.93/0.86 (((~hskp25) | (~c0_1(a1048))) <=> ((~hskp25) | (~c0_1(a1048)))),
% 0.93/0.86 inference(rewrite,[status(thm)],[])).
% 0.93/0.86 tff(1090,plain,
% 0.93/0.86 (((~c0_1(a1048)) | (~hskp25)) <=> ((~hskp25) | (~c0_1(a1048)))),
% 0.93/0.86 inference(rewrite,[status(thm)],[])).
% 0.93/0.86 tff(1091,axiom,((~c0_1(a1048)) | (~hskp25)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause87')).
% 0.93/0.86 tff(1092,plain,
% 0.93/0.86 ((~hskp25) | (~c0_1(a1048))),
% 0.93/0.86 inference(modus_ponens,[status(thm)],[1091, 1090])).
% 0.93/0.86 tff(1093,plain,
% 0.93/0.86 ((~hskp25) | (~c0_1(a1048))),
% 0.93/0.86 inference(modus_ponens,[status(thm)],[1092, 1089])).
% 0.93/0.86 tff(1094,plain,
% 0.93/0.86 (~c0_1(a1048)),
% 0.93/0.86 inference(unit_resolution,[status(thm)],[1093, 1088])).
% 0.93/0.86 tff(1095,plain,
% 0.93/0.86 (((~hskp25) | c1_1(a1048)) <=> ((~hskp25) | c1_1(a1048))),
% 0.93/0.86 inference(rewrite,[status(thm)],[])).
% 0.93/0.86 tff(1096,axiom,((~hskp25) | c1_1(a1048)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause50')).
% 0.93/0.86 tff(1097,plain,
% 0.93/0.86 ((~hskp25) | c1_1(a1048)),
% 0.93/0.86 inference(modus_ponens,[status(thm)],[1096, 1095])).
% 0.93/0.86 tff(1098,plain,
% 0.93/0.86 ((~hskp25) | c1_1(a1048)),
% 0.93/0.86 inference(modus_ponens,[status(thm)],[1097, 1095])).
% 0.93/0.86 tff(1099,plain,
% 0.93/0.86 ((~hskp25) | c1_1(a1048)),
% 0.93/0.86 inference(modus_ponens,[status(thm)],[1098, 1095])).
% 0.93/0.86 tff(1100,plain,
% 0.93/0.86 ((~hskp25) | c1_1(a1048)),
% 0.93/0.86 inference(modus_ponens,[status(thm)],[1099, 1095])).
% 0.93/0.86 tff(1101,plain,
% 0.93/0.86 ((~hskp25) | c1_1(a1048)),
% 0.93/0.86 inference(modus_ponens,[status(thm)],[1100, 1095])).
% 0.93/0.86 tff(1102,plain,
% 0.93/0.86 ((~hskp25) | c1_1(a1048)),
% 0.93/0.86 inference(modus_ponens,[status(thm)],[1101, 1095])).
% 0.93/0.86 tff(1103,plain,
% 0.93/0.86 ((~hskp25) | c1_1(a1048)),
% 0.93/0.86 inference(modus_ponens,[status(thm)],[1102, 1095])).
% 0.93/0.86 tff(1104,plain,
% 0.93/0.86 ((~hskp25) | c1_1(a1048)),
% 0.93/0.86 inference(modus_ponens,[status(thm)],[1103, 1095])).
% 0.93/0.86 tff(1105,plain,
% 0.93/0.86 (c1_1(a1048)),
% 0.93/0.86 inference(unit_resolution,[status(thm)],[1104, 1088])).
% 0.93/0.86 tff(1106,plain,
% 0.93/0.86 (((~hskp26) | c3_1(a1052)) <=> ((~hskp26) | c3_1(a1052))),
% 0.93/0.86 inference(rewrite,[status(thm)],[])).
% 0.93/0.86 tff(1107,axiom,((~hskp26) | c3_1(a1052)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause49')).
% 0.93/0.86 tff(1108,plain,
% 0.93/0.86 ((~hskp26) | c3_1(a1052)),
% 0.93/0.86 inference(modus_ponens,[status(thm)],[1107, 1106])).
% 0.93/0.86 tff(1109,plain,
% 0.93/0.86 ((~hskp26) | c3_1(a1052)),
% 0.93/0.86 inference(modus_ponens,[status(thm)],[1108, 1106])).
% 0.93/0.86 tff(1110,plain,
% 0.93/0.86 ((~hskp26) | c3_1(a1052)),
% 0.93/0.86 inference(modus_ponens,[status(thm)],[1109, 1106])).
% 0.93/0.86 tff(1111,plain,
% 0.93/0.86 ((~hskp26) | c3_1(a1052)),
% 0.93/0.86 inference(modus_ponens,[status(thm)],[1110, 1106])).
% 0.93/0.86 tff(1112,plain,
% 0.93/0.86 ((~hskp26) | c3_1(a1052)),
% 0.93/0.86 inference(modus_ponens,[status(thm)],[1111, 1106])).
% 0.93/0.86 tff(1113,plain,
% 0.93/0.86 ((~hskp26) | c3_1(a1052)),
% 0.93/0.86 inference(modus_ponens,[status(thm)],[1112, 1106])).
% 0.93/0.86 tff(1114,plain,
% 0.93/0.86 ((~hskp26) | c3_1(a1052)),
% 0.93/0.86 inference(modus_ponens,[status(thm)],[1113, 1106])).
% 0.93/0.86 tff(1115,plain,
% 0.93/0.86 ((~hskp26) | c3_1(a1052)),
% 0.93/0.86 inference(modus_ponens,[status(thm)],[1114, 1106])).
% 0.93/0.86 tff(1116,plain,
% 0.93/0.86 (c3_1(a1052)),
% 0.93/0.86 inference(unit_resolution,[status(thm)],[1115, 1041])).
% 0.93/0.86 tff(1117,plain,
% 0.93/0.86 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp13 | c2_1(a1052) | c0_1(a1048) | (~ndr1_0) | (~c2_1(a1048)) | (~c1_1(a1048)) | c1_1(a1052) | (~c3_1(a1052)))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | hskp13 | c2_1(a1052) | c0_1(a1048) | (~ndr1_0) | (~c2_1(a1048)) | (~c1_1(a1048)) | c1_1(a1052) | (~c3_1(a1052)))),
% 0.93/0.86 inference(rewrite,[status(thm)],[])).
% 0.93/0.86 tff(1118,plain,
% 0.93/0.86 ((hskp13 | (~ndr1_0) | c2_1(a1052) | c1_1(a1052) | (~c3_1(a1052)) | c0_1(a1048) | (~c2_1(a1048)) | (~c1_1(a1048))) <=> (hskp13 | c2_1(a1052) | c0_1(a1048) | (~ndr1_0) | (~c2_1(a1048)) | (~c1_1(a1048)) | c1_1(a1052) | (~c3_1(a1052)))),
% 0.93/0.86 inference(rewrite,[status(thm)],[])).
% 0.93/0.86 tff(1119,plain,
% 0.93/0.86 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp13 | (~ndr1_0) | c2_1(a1052) | c1_1(a1052) | (~c3_1(a1052)) | c0_1(a1048) | (~c2_1(a1048)) | (~c1_1(a1048)))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp13 | c2_1(a1052) | c0_1(a1048) | (~ndr1_0) | (~c2_1(a1048)) | (~c1_1(a1048)) | c1_1(a1052) | (~c3_1(a1052))))),
% 0.93/0.86 inference(monotonicity,[status(thm)],[1118])).
% 0.93/0.86 tff(1120,plain,
% 0.93/0.86 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp13 | (~ndr1_0) | c2_1(a1052) | c1_1(a1052) | (~c3_1(a1052)) | c0_1(a1048) | (~c2_1(a1048)) | (~c1_1(a1048)))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | hskp13 | c2_1(a1052) | c0_1(a1048) | (~ndr1_0) | (~c2_1(a1048)) | (~c1_1(a1048)) | c1_1(a1052) | (~c3_1(a1052)))),
% 0.93/0.86 inference(transitivity,[status(thm)],[1119, 1117])).
% 0.93/0.86 tff(1121,plain,
% 0.93/0.86 ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp13 | (~ndr1_0) | c2_1(a1052) | c1_1(a1052) | (~c3_1(a1052)) | c0_1(a1048) | (~c2_1(a1048)) | (~c1_1(a1048)))),
% 0.93/0.86 inference(quant_inst,[status(thm)],[])).
% 0.93/0.86 tff(1122,plain,
% 0.93/0.86 ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | hskp13 | c2_1(a1052) | c0_1(a1048) | (~ndr1_0) | (~c2_1(a1048)) | (~c1_1(a1048)) | c1_1(a1052) | (~c3_1(a1052))),
% 0.93/0.86 inference(modus_ponens,[status(thm)],[1121, 1120])).
% 0.93/0.86 tff(1123,plain,
% 0.93/0.86 (~c2_1(a1048)),
% 0.93/0.86 inference(unit_resolution,[status(thm)],[1122, 90, 624, 1116, 1105, 1047, 1094, 1070, 1060])).
% 0.93/0.86 tff(1124,plain,
% 0.93/0.86 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp7 | c2_1(a1052) | c0_1(a1048) | (~ndr1_0) | c2_1(a1048) | (~c1_1(a1048)) | c1_1(a1052) | (~c3_1(a1052)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp7 | c2_1(a1052) | c0_1(a1048) | (~ndr1_0) | c2_1(a1048) | (~c1_1(a1048)) | c1_1(a1052) | (~c3_1(a1052)))),
% 0.93/0.86 inference(rewrite,[status(thm)],[])).
% 0.93/0.86 tff(1125,plain,
% 0.93/0.86 ((hskp7 | (~ndr1_0) | c2_1(a1052) | c1_1(a1052) | (~c3_1(a1052)) | c0_1(a1048) | c2_1(a1048) | (~c1_1(a1048))) <=> (hskp7 | c2_1(a1052) | c0_1(a1048) | (~ndr1_0) | c2_1(a1048) | (~c1_1(a1048)) | c1_1(a1052) | (~c3_1(a1052)))),
% 0.93/0.86 inference(rewrite,[status(thm)],[])).
% 0.93/0.86 tff(1126,plain,
% 0.93/0.86 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp7 | (~ndr1_0) | c2_1(a1052) | c1_1(a1052) | (~c3_1(a1052)) | c0_1(a1048) | c2_1(a1048) | (~c1_1(a1048)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp7 | c2_1(a1052) | c0_1(a1048) | (~ndr1_0) | c2_1(a1048) | (~c1_1(a1048)) | c1_1(a1052) | (~c3_1(a1052))))),
% 0.93/0.86 inference(monotonicity,[status(thm)],[1125])).
% 0.93/0.86 tff(1127,plain,
% 0.93/0.86 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp7 | (~ndr1_0) | c2_1(a1052) | c1_1(a1052) | (~c3_1(a1052)) | c0_1(a1048) | c2_1(a1048) | (~c1_1(a1048)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp7 | c2_1(a1052) | c0_1(a1048) | (~ndr1_0) | c2_1(a1048) | (~c1_1(a1048)) | c1_1(a1052) | (~c3_1(a1052)))),
% 0.93/0.86 inference(transitivity,[status(thm)],[1126, 1124])).
% 0.93/0.86 tff(1128,plain,
% 0.93/0.86 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp7 | (~ndr1_0) | c2_1(a1052) | c1_1(a1052) | (~c3_1(a1052)) | c0_1(a1048) | c2_1(a1048) | (~c1_1(a1048)))),
% 0.93/0.87 inference(quant_inst,[status(thm)],[])).
% 0.93/0.87 tff(1129,plain,
% 0.93/0.87 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp7 | c2_1(a1052) | c0_1(a1048) | (~ndr1_0) | c2_1(a1048) | (~c1_1(a1048)) | c1_1(a1052) | (~c3_1(a1052))),
% 0.93/0.87 inference(modus_ponens,[status(thm)],[1128, 1127])).
% 0.93/0.87 tff(1130,plain,
% 0.93/0.87 ($false),
% 0.93/0.87 inference(unit_resolution,[status(thm)],[1129, 90, 644, 1116, 1105, 1047, 1094, 1014, 1123, 1060])).
% 0.93/0.87 tff(1131,plain,(hskp7 | hskp13 | hskp8 | hskp3), inference(lemma,lemma(discharge,[]))).
% 0.93/0.87 tff(1132,plain,
% 0.93/0.87 (hskp3),
% 0.93/0.87 inference(unit_resolution,[status(thm)],[1131, 1023, 644, 624])).
% 0.93/0.87 tff(1133,plain,
% 0.93/0.87 (~c2_1(a1003)),
% 0.93/0.87 inference(unit_resolution,[status(thm)],[521, 1132])).
% 0.93/0.87 tff(1134,plain,
% 0.93/0.87 (~c0_1(a1003)),
% 0.93/0.87 inference(unit_resolution,[status(thm)],[527, 1132])).
% 0.93/0.87 tff(1135,plain,
% 0.93/0.87 (c1_1(a1003)),
% 0.93/0.87 inference(unit_resolution,[status(thm)],[538, 1132])).
% 0.93/0.87 tff(1136,plain,
% 0.93/0.87 ($false),
% 0.93/0.87 inference(unit_resolution,[status(thm)],[662, 90, 1023, 644, 1135, 1134, 1133, 643])).
% 0.93/0.87 tff(1137,plain,(hskp8 | hskp7 | hskp13), inference(lemma,lemma(discharge,[]))).
% 0.93/0.87 tff(1138,plain,
% 0.93/0.87 (hskp8),
% 0.93/0.87 inference(unit_resolution,[status(thm)],[1137, 644, 624])).
% 0.93/0.87 tff(1139,plain,
% 0.93/0.87 (~c1_1(a1010)),
% 0.93/0.87 inference(unit_resolution,[status(thm)],[545, 1138])).
% 0.93/0.87 tff(1140,plain,
% 0.93/0.87 (c3_1(a1010)),
% 0.93/0.87 inference(unit_resolution,[status(thm)],[556, 1138])).
% 0.93/0.87 tff(1141,plain,
% 0.93/0.87 (c0_1(a1010)),
% 0.93/0.87 inference(unit_resolution,[status(thm)],[567, 1138])).
% 0.93/0.87 tff(1142,plain,
% 0.93/0.87 (hskp6),
% 0.93/0.87 inference(unit_resolution,[status(thm)],[1000, 1022, 624])).
% 0.93/0.87 tff(1143,plain,
% 0.93/0.87 (~c2_1(a1006)),
% 0.93/0.87 inference(unit_resolution,[status(thm)],[951, 1142])).
% 0.93/0.87 tff(1144,plain,
% 0.93/0.87 (c3_1(a1006)),
% 0.93/0.87 inference(unit_resolution,[status(thm)],[962, 1142])).
% 0.93/0.87 tff(1145,plain,
% 0.93/0.87 (c0_1(a1006)),
% 0.93/0.87 inference(unit_resolution,[status(thm)],[973, 1142])).
% 0.93/0.87 tff(1146,assumption,(~c2_1(a1006)), introduced(assumption)).
% 0.93/0.87 tff(1147,assumption,(~c2_1(a1044)), introduced(assumption)).
% 0.93/0.87 tff(1148,plain,
% 0.93/0.87 (hskp25),
% 0.93/0.87 inference(unit_resolution,[status(thm)],[1087, 360, 1147])).
% 0.93/0.87 tff(1149,plain,
% 0.93/0.87 (((~hskp25) | (~c3_1(a1048))) <=> ((~hskp25) | (~c3_1(a1048)))),
% 0.93/0.87 inference(rewrite,[status(thm)],[])).
% 0.93/0.87 tff(1150,plain,
% 0.93/0.87 (((~c3_1(a1048)) | (~hskp25)) <=> ((~hskp25) | (~c3_1(a1048)))),
% 0.93/0.87 inference(rewrite,[status(thm)],[])).
% 0.93/0.87 tff(1151,axiom,((~c3_1(a1048)) | (~hskp25)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause88')).
% 0.93/0.87 tff(1152,plain,
% 0.93/0.87 ((~hskp25) | (~c3_1(a1048))),
% 0.93/0.87 inference(modus_ponens,[status(thm)],[1151, 1150])).
% 0.93/0.87 tff(1153,plain,
% 0.93/0.87 ((~hskp25) | (~c3_1(a1048))),
% 0.93/0.87 inference(modus_ponens,[status(thm)],[1152, 1149])).
% 0.93/0.87 tff(1154,plain,
% 0.93/0.87 (~c3_1(a1048)),
% 0.93/0.87 inference(unit_resolution,[status(thm)],[1153, 1148])).
% 0.93/0.87 tff(1155,assumption,(c3_1(a1006)), introduced(assumption)).
% 0.93/0.87 tff(1156,assumption,(c0_1(a1006)), introduced(assumption)).
% 0.93/0.87 tff(1157,plain,
% 0.93/0.87 (c1_1(a1048)),
% 0.93/0.87 inference(unit_resolution,[status(thm)],[1104, 1148])).
% 0.93/0.87 tff(1158,plain,
% 0.93/0.87 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c1_1(W) | (~c3_1(W)) | (~c2_1(W)))) | (c3_1(a1048) | c2_1(a1006) | c1_1(a1001) | (~ndr1_0) | (~c3_1(a1001)) | (~c2_1(a1001)) | (~c0_1(a1006)) | (~c3_1(a1006)) | (~c2_1(a1048)) | (~c1_1(a1048)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c1_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c3_1(a1048) | c2_1(a1006) | c1_1(a1001) | (~ndr1_0) | (~c3_1(a1001)) | (~c2_1(a1001)) | (~c0_1(a1006)) | (~c3_1(a1006)) | (~c2_1(a1048)) | (~c1_1(a1048)))),
% 0.93/0.87 inference(rewrite,[status(thm)],[])).
% 0.93/0.87 tff(1159,plain,
% 0.93/0.87 (((~ndr1_0) | (~c1_1(a1048)) | c3_1(a1048) | (~c2_1(a1048)) | c2_1(a1006) | (~c0_1(a1006)) | (~c3_1(a1006)) | c1_1(a1001) | (~c3_1(a1001)) | (~c2_1(a1001))) <=> (c3_1(a1048) | c2_1(a1006) | c1_1(a1001) | (~ndr1_0) | (~c3_1(a1001)) | (~c2_1(a1001)) | (~c0_1(a1006)) | (~c3_1(a1006)) | (~c2_1(a1048)) | (~c1_1(a1048)))),
% 0.93/0.87 inference(rewrite,[status(thm)],[])).
% 0.93/0.87 tff(1160,plain,
% 0.93/0.87 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c1_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c1_1(a1048)) | c3_1(a1048) | (~c2_1(a1048)) | c2_1(a1006) | (~c0_1(a1006)) | (~c3_1(a1006)) | c1_1(a1001) | (~c3_1(a1001)) | (~c2_1(a1001)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c1_1(W) | (~c3_1(W)) | (~c2_1(W)))) | (c3_1(a1048) | c2_1(a1006) | c1_1(a1001) | (~ndr1_0) | (~c3_1(a1001)) | (~c2_1(a1001)) | (~c0_1(a1006)) | (~c3_1(a1006)) | (~c2_1(a1048)) | (~c1_1(a1048))))),
% 0.93/0.87 inference(monotonicity,[status(thm)],[1159])).
% 0.93/0.87 tff(1161,plain,
% 0.93/0.87 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c1_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c1_1(a1048)) | c3_1(a1048) | (~c2_1(a1048)) | c2_1(a1006) | (~c0_1(a1006)) | (~c3_1(a1006)) | c1_1(a1001) | (~c3_1(a1001)) | (~c2_1(a1001)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c1_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c3_1(a1048) | c2_1(a1006) | c1_1(a1001) | (~ndr1_0) | (~c3_1(a1001)) | (~c2_1(a1001)) | (~c0_1(a1006)) | (~c3_1(a1006)) | (~c2_1(a1048)) | (~c1_1(a1048)))),
% 0.93/0.87 inference(transitivity,[status(thm)],[1160, 1158])).
% 0.93/0.87 tff(1162,plain,
% 0.93/0.87 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c1_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c1_1(a1048)) | c3_1(a1048) | (~c2_1(a1048)) | c2_1(a1006) | (~c0_1(a1006)) | (~c3_1(a1006)) | c1_1(a1001) | (~c3_1(a1001)) | (~c2_1(a1001)))),
% 0.93/0.87 inference(quant_inst,[status(thm)],[])).
% 0.93/0.87 tff(1163,plain,
% 0.93/0.87 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c1_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c3_1(a1048) | c2_1(a1006) | c1_1(a1001) | (~ndr1_0) | (~c3_1(a1001)) | (~c2_1(a1001)) | (~c0_1(a1006)) | (~c3_1(a1006)) | (~c2_1(a1048)) | (~c1_1(a1048))),
% 0.93/0.87 inference(modus_ponens,[status(thm)],[1162, 1161])).
% 0.93/0.87 tff(1164,plain,
% 0.93/0.87 (~c2_1(a1048)),
% 0.93/0.87 inference(unit_resolution,[status(thm)],[1163, 90, 1157, 1156, 1155, 938, 928, 1154, 1146, 927, 817])).
% 0.93/0.87 tff(1165,plain,
% 0.93/0.87 (^[V: $i, U: $i] : refl((hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | c3_1(U) | c1_1(V) | c0_1(V) | (~c2_1(V))) <=> (hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | c3_1(U) | c1_1(V) | c0_1(V) | (~c2_1(V))))),
% 0.93/0.87 inference(bind,[status(th)],[])).
% 0.93/0.87 tff(1166,plain,
% 0.93/0.87 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | c3_1(U) | c1_1(V) | c0_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | c3_1(U) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 0.93/0.87 inference(quant_intro,[status(thm)],[1165])).
% 0.93/0.87 tff(1167,plain,
% 0.93/0.87 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | c3_1(U) | c1_1(V) | c0_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | c3_1(U) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 0.93/0.87 inference(rewrite,[status(thm)],[])).
% 0.93/0.87 tff(1168,plain,
% 0.93/0.87 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c1_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)))), ((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c1_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(V)))), ((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(V))))), (((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c2_1(V)))), (((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c2_1(V))))), ((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c2_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c2_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | c3_1(U) | (~c2_1(V)))), ((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | c3_1(U) | (~c2_1(V))))), (((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | c3_1(U) | (~c2_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | c3_1(U) | (~c2_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | c3_1(U) | c0_1(V) | (~c2_1(V)))), (((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | c3_1(U) | c0_1(V) | (~c2_1(V))))), ((((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | c3_1(U) | c0_1(V) | (~c2_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | c3_1(U) | c0_1(V) | (~c2_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | c3_1(U) | c1_1(V) | c0_1(V) | (~c2_1(V)))), ((((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | c3_1(U) | c1_1(V) | c0_1(V) | (~c2_1(V))))), (((((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | hskp3) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | c3_1(U) | c1_1(V) | c0_1(V) | (~c2_1(V))) | hskp3))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | c3_1(U) | c1_1(V) | c0_1(V) | (~c2_1(V))) | hskp3) <=> (hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | c3_1(U) | c1_1(V) | c0_1(V) | (~c2_1(V)))), (((((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | hskp3) <=> (hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | c3_1(U) | c1_1(V) | c0_1(V) | (~c2_1(V)))))),
% 0.96/0.87 inference(bind,[status(th)],[])).
% 0.96/0.87 tff(1169,plain,
% 0.96/0.87 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | hskp3) <=> ![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | c3_1(U) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 0.96/0.87 inference(quant_intro,[status(thm)],[1168])).
% 0.96/0.87 tff(1170,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | hskp3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause154')).
% 0.96/0.87 tff(1171,plain,
% 0.96/0.87 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | c3_1(U) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 0.96/0.87 inference(modus_ponens,[status(thm)],[1170, 1169])).
% 0.96/0.87 tff(1172,plain,
% 0.96/0.87 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | c3_1(U) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 0.96/0.87 inference(modus_ponens,[status(thm)],[1171, 1167])).
% 0.96/0.87 tff(1173,plain,(
% 0.96/0.87 ![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | c3_1(U) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 0.96/0.87 inference(skolemize,[status(sab)],[1172])).
% 0.96/0.87 tff(1174,plain,
% 0.96/0.87 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | c3_1(U) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 0.96/0.87 inference(modus_ponens,[status(thm)],[1173, 1166])).
% 0.96/0.87 tff(1175,plain,
% 0.96/0.87 (^[V: $i, U: $i] : refl((hskp15 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V))) <=> (hskp15 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V))))),
% 0.96/0.87 inference(bind,[status(th)],[])).
% 0.96/0.87 tff(1176,plain,
% 0.96/0.87 (![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))),
% 0.96/0.87 inference(quant_intro,[status(thm)],[1175])).
% 0.96/0.87 tff(1177,plain,
% 0.96/0.87 (![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))),
% 0.96/0.87 inference(rewrite,[status(thm)],[])).
% 0.96/0.87 tff(1178,plain,
% 0.96/0.87 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V))))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V)))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V))))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V)))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V))))), ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))), ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V))))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) | c0_1(V)) | hskp15) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V))) | hskp15))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V))) | hskp15) <=> (hskp15 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) | c0_1(V)) | hskp15) <=> (hskp15 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))))),
% 0.96/0.87 inference(bind,[status(th)],[])).
% 0.96/0.87 tff(1179,plain,
% 0.96/0.87 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) | c0_1(V)) | hskp15) <=> ![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))),
% 0.96/0.87 inference(quant_intro,[status(thm)],[1178])).
% 0.96/0.87 tff(1180,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) | c0_1(V)) | hskp15)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause178')).
% 0.96/0.87 tff(1181,plain,
% 0.96/0.87 (![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))),
% 0.96/0.87 inference(modus_ponens,[status(thm)],[1180, 1179])).
% 0.96/0.87 tff(1182,plain,
% 0.96/0.87 (![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))),
% 0.96/0.87 inference(modus_ponens,[status(thm)],[1181, 1177])).
% 0.96/0.87 tff(1183,plain,(
% 0.96/0.87 ![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))),
% 0.96/0.87 inference(skolemize,[status(sab)],[1182])).
% 0.96/0.87 tff(1184,plain,
% 0.96/0.87 (![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))),
% 0.96/0.87 inference(modus_ponens,[status(thm)],[1183, 1176])).
% 0.96/0.87 tff(1185,assumption,(~c1_1(a1010)), introduced(assumption)).
% 0.96/0.87 tff(1186,plain,
% 0.96/0.87 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | c3_1(U) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp3 | c3_1(a1044) | c1_1(a1001) | (~ndr1_0) | c0_1(a1001) | (~c2_1(a1001)) | c2_1(a1044) | (~c1_1(a1044)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | c3_1(U) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp3 | c3_1(a1044) | c1_1(a1001) | (~ndr1_0) | c0_1(a1001) | (~c2_1(a1001)) | c2_1(a1044) | (~c1_1(a1044)))),
% 0.96/0.87 inference(rewrite,[status(thm)],[])).
% 0.96/0.87 tff(1187,plain,
% 0.96/0.87 ((hskp3 | (~ndr1_0) | c2_1(a1044) | (~c1_1(a1044)) | c3_1(a1044) | c1_1(a1001) | c0_1(a1001) | (~c2_1(a1001))) <=> (hskp3 | c3_1(a1044) | c1_1(a1001) | (~ndr1_0) | c0_1(a1001) | (~c2_1(a1001)) | c2_1(a1044) | (~c1_1(a1044)))),
% 0.96/0.87 inference(rewrite,[status(thm)],[])).
% 0.96/0.87 tff(1188,plain,
% 0.96/0.87 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | c3_1(U) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp3 | (~ndr1_0) | c2_1(a1044) | (~c1_1(a1044)) | c3_1(a1044) | c1_1(a1001) | c0_1(a1001) | (~c2_1(a1001)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | c3_1(U) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp3 | c3_1(a1044) | c1_1(a1001) | (~ndr1_0) | c0_1(a1001) | (~c2_1(a1001)) | c2_1(a1044) | (~c1_1(a1044))))),
% 0.96/0.87 inference(monotonicity,[status(thm)],[1187])).
% 0.96/0.87 tff(1189,plain,
% 0.96/0.87 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | c3_1(U) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp3 | (~ndr1_0) | c2_1(a1044) | (~c1_1(a1044)) | c3_1(a1044) | c1_1(a1001) | c0_1(a1001) | (~c2_1(a1001)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | c3_1(U) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp3 | c3_1(a1044) | c1_1(a1001) | (~ndr1_0) | c0_1(a1001) | (~c2_1(a1001)) | c2_1(a1044) | (~c1_1(a1044)))),
% 0.96/0.87 inference(transitivity,[status(thm)],[1188, 1186])).
% 0.96/0.87 tff(1190,plain,
% 0.96/0.87 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | c3_1(U) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp3 | (~ndr1_0) | c2_1(a1044) | (~c1_1(a1044)) | c3_1(a1044) | c1_1(a1001) | c0_1(a1001) | (~c2_1(a1001)))),
% 0.96/0.87 inference(quant_inst,[status(thm)],[])).
% 0.96/0.87 tff(1191,plain,
% 0.96/0.87 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | c3_1(U) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp3 | c3_1(a1044) | c1_1(a1001) | (~ndr1_0) | c0_1(a1001) | (~c2_1(a1001)) | c2_1(a1044) | (~c1_1(a1044))),
% 0.96/0.87 inference(modus_ponens,[status(thm)],[1190, 1189])).
% 0.96/0.87 tff(1192,plain,
% 0.96/0.87 (hskp3 | c0_1(a1001)),
% 0.96/0.87 inference(unit_resolution,[status(thm)],[1191, 90, 772, 938, 761, 927, 1174, 1147])).
% 0.96/0.87 tff(1193,plain,
% 0.96/0.87 (c0_1(a1001)),
% 0.96/0.87 inference(unit_resolution,[status(thm)],[1192, 360])).
% 0.96/0.87 tff(1194,plain,
% 0.96/0.87 (((~![U: $i] : (hskp24 | hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))) | (hskp24 | hskp3 | (~ndr1_0) | (~c0_1(a1001)) | (~c3_1(a1001)) | (~c2_1(a1001)))) <=> ((~![U: $i] : (hskp24 | hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))) | hskp24 | hskp3 | (~ndr1_0) | (~c0_1(a1001)) | (~c3_1(a1001)) | (~c2_1(a1001)))),
% 0.96/0.87 inference(rewrite,[status(thm)],[])).
% 0.96/0.87 tff(1195,plain,
% 0.96/0.87 ((hskp24 | hskp3 | (~ndr1_0) | (~c2_1(a1001)) | (~c3_1(a1001)) | (~c0_1(a1001))) <=> (hskp24 | hskp3 | (~ndr1_0) | (~c0_1(a1001)) | (~c3_1(a1001)) | (~c2_1(a1001)))),
% 0.96/0.87 inference(rewrite,[status(thm)],[])).
% 0.96/0.87 tff(1196,plain,
% 0.96/0.87 (((~![U: $i] : (hskp24 | hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))) | (hskp24 | hskp3 | (~ndr1_0) | (~c2_1(a1001)) | (~c3_1(a1001)) | (~c0_1(a1001)))) <=> ((~![U: $i] : (hskp24 | hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))) | (hskp24 | hskp3 | (~ndr1_0) | (~c0_1(a1001)) | (~c3_1(a1001)) | (~c2_1(a1001))))),
% 0.96/0.87 inference(monotonicity,[status(thm)],[1195])).
% 0.96/0.87 tff(1197,plain,
% 0.96/0.87 (((~![U: $i] : (hskp24 | hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))) | (hskp24 | hskp3 | (~ndr1_0) | (~c2_1(a1001)) | (~c3_1(a1001)) | (~c0_1(a1001)))) <=> ((~![U: $i] : (hskp24 | hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))) | hskp24 | hskp3 | (~ndr1_0) | (~c0_1(a1001)) | (~c3_1(a1001)) | (~c2_1(a1001)))),
% 0.96/0.87 inference(transitivity,[status(thm)],[1196, 1194])).
% 0.96/0.87 tff(1198,plain,
% 0.96/0.87 ((~![U: $i] : (hskp24 | hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))) | (hskp24 | hskp3 | (~ndr1_0) | (~c2_1(a1001)) | (~c3_1(a1001)) | (~c0_1(a1001)))),
% 0.96/0.87 inference(quant_inst,[status(thm)],[])).
% 0.96/0.87 tff(1199,plain,
% 0.96/0.87 ((~![U: $i] : (hskp24 | hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))) | hskp24 | hskp3 | (~ndr1_0) | (~c0_1(a1001)) | (~c3_1(a1001)) | (~c2_1(a1001))),
% 0.96/0.87 inference(modus_ponens,[status(thm)],[1198, 1197])).
% 0.96/0.87 tff(1200,plain,
% 0.96/0.87 (hskp24 | hskp3 | (~c0_1(a1001))),
% 0.96/0.87 inference(unit_resolution,[status(thm)],[1199, 90, 938, 928, 449])).
% 0.96/0.87 tff(1201,plain,
% 0.96/0.87 (hskp24),
% 0.96/0.87 inference(unit_resolution,[status(thm)],[1200, 1193, 360])).
% 0.96/0.87 tff(1202,plain,
% 0.96/0.87 (~c0_1(a1045)),
% 0.96/0.87 inference(unit_resolution,[status(thm)],[462, 1201])).
% 0.96/0.87 tff(1203,assumption,(c3_1(a1010)), introduced(assumption)).
% 0.96/0.87 tff(1204,assumption,(c0_1(a1010)), introduced(assumption)).
% 0.96/0.87 tff(1205,plain,
% 0.96/0.87 (c3_1(a1045)),
% 0.96/0.87 inference(unit_resolution,[status(thm)],[495, 1201])).
% 0.96/0.87 tff(1206,plain,
% 0.96/0.87 (c1_1(a1045)),
% 0.96/0.87 inference(unit_resolution,[status(thm)],[506, 1201])).
% 0.96/0.87 tff(1207,plain,
% 0.96/0.87 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp15 | c0_1(a1045) | c1_1(a1010) | (~ndr1_0) | (~c0_1(a1010)) | (~c3_1(a1010)) | (~c3_1(a1045)) | (~c1_1(a1045)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp15 | c0_1(a1045) | c1_1(a1010) | (~ndr1_0) | (~c0_1(a1010)) | (~c3_1(a1010)) | (~c3_1(a1045)) | (~c1_1(a1045)))),
% 0.96/0.87 inference(rewrite,[status(thm)],[])).
% 0.96/0.87 tff(1208,plain,
% 0.96/0.87 ((hskp15 | (~ndr1_0) | c1_1(a1010) | (~c3_1(a1010)) | (~c0_1(a1010)) | c0_1(a1045) | (~c1_1(a1045)) | (~c3_1(a1045))) <=> (hskp15 | c0_1(a1045) | c1_1(a1010) | (~ndr1_0) | (~c0_1(a1010)) | (~c3_1(a1010)) | (~c3_1(a1045)) | (~c1_1(a1045)))),
% 0.96/0.87 inference(rewrite,[status(thm)],[])).
% 0.96/0.87 tff(1209,plain,
% 0.96/0.87 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp15 | (~ndr1_0) | c1_1(a1010) | (~c3_1(a1010)) | (~c0_1(a1010)) | c0_1(a1045) | (~c1_1(a1045)) | (~c3_1(a1045)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp15 | c0_1(a1045) | c1_1(a1010) | (~ndr1_0) | (~c0_1(a1010)) | (~c3_1(a1010)) | (~c3_1(a1045)) | (~c1_1(a1045))))),
% 0.96/0.87 inference(monotonicity,[status(thm)],[1208])).
% 0.96/0.87 tff(1210,plain,
% 0.96/0.87 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp15 | (~ndr1_0) | c1_1(a1010) | (~c3_1(a1010)) | (~c0_1(a1010)) | c0_1(a1045) | (~c1_1(a1045)) | (~c3_1(a1045)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp15 | c0_1(a1045) | c1_1(a1010) | (~ndr1_0) | (~c0_1(a1010)) | (~c3_1(a1010)) | (~c3_1(a1045)) | (~c1_1(a1045)))),
% 0.96/0.87 inference(transitivity,[status(thm)],[1209, 1207])).
% 0.96/0.87 tff(1211,plain,
% 0.96/0.87 ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp15 | (~ndr1_0) | c1_1(a1010) | (~c3_1(a1010)) | (~c0_1(a1010)) | c0_1(a1045) | (~c1_1(a1045)) | (~c3_1(a1045)))),
% 0.96/0.87 inference(quant_inst,[status(thm)],[])).
% 0.96/0.87 tff(1212,plain,
% 0.96/0.87 ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp15 | c0_1(a1045) | c1_1(a1010) | (~ndr1_0) | (~c0_1(a1010)) | (~c3_1(a1010)) | (~c3_1(a1045)) | (~c1_1(a1045))),
% 0.96/0.87 inference(modus_ponens,[status(thm)],[1211, 1210])).
% 0.96/0.87 tff(1213,plain,
% 0.96/0.87 (hskp15),
% 0.96/0.87 inference(unit_resolution,[status(thm)],[1212, 90, 1206, 1205, 1204, 1203, 1202, 1185, 1184])).
% 0.96/0.87 tff(1214,plain,
% 0.96/0.87 (((~hskp15) | (~c1_1(a1026))) <=> ((~hskp15) | (~c1_1(a1026)))),
% 0.96/0.87 inference(rewrite,[status(thm)],[])).
% 0.96/0.87 tff(1215,plain,
% 0.96/0.87 (((~c1_1(a1026)) | (~hskp15)) <=> ((~hskp15) | (~c1_1(a1026)))),
% 0.96/0.87 inference(rewrite,[status(thm)],[])).
% 0.96/0.87 tff(1216,axiom,((~c1_1(a1026)) | (~hskp15)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause106')).
% 0.96/0.87 tff(1217,plain,
% 0.96/0.87 ((~hskp15) | (~c1_1(a1026))),
% 0.96/0.87 inference(modus_ponens,[status(thm)],[1216, 1215])).
% 0.96/0.87 tff(1218,plain,
% 0.96/0.87 ((~hskp15) | (~c1_1(a1026))),
% 0.96/0.87 inference(modus_ponens,[status(thm)],[1217, 1214])).
% 0.96/0.87 tff(1219,plain,
% 0.96/0.87 (~c1_1(a1026)),
% 0.96/0.87 inference(unit_resolution,[status(thm)],[1218, 1213])).
% 0.96/0.87 tff(1220,plain,
% 0.96/0.87 (((~hskp15) | (~c0_1(a1026))) <=> ((~hskp15) | (~c0_1(a1026)))),
% 0.96/0.87 inference(rewrite,[status(thm)],[])).
% 0.96/0.87 tff(1221,plain,
% 0.96/0.87 (((~c0_1(a1026)) | (~hskp15)) <=> ((~hskp15) | (~c0_1(a1026)))),
% 0.96/0.87 inference(rewrite,[status(thm)],[])).
% 0.96/0.87 tff(1222,axiom,((~c0_1(a1026)) | (~hskp15)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause105')).
% 0.96/0.87 tff(1223,plain,
% 0.96/0.87 ((~hskp15) | (~c0_1(a1026))),
% 0.96/0.87 inference(modus_ponens,[status(thm)],[1222, 1221])).
% 0.96/0.87 tff(1224,plain,
% 0.96/0.87 ((~hskp15) | (~c0_1(a1026))),
% 0.96/0.87 inference(modus_ponens,[status(thm)],[1223, 1220])).
% 0.96/0.87 tff(1225,plain,
% 0.96/0.87 (~c0_1(a1026)),
% 0.96/0.87 inference(unit_resolution,[status(thm)],[1224, 1213])).
% 0.96/0.87 tff(1226,plain,
% 0.96/0.87 (((~hskp15) | c2_1(a1026)) <=> ((~hskp15) | c2_1(a1026))),
% 0.96/0.87 inference(rewrite,[status(thm)],[])).
% 0.96/0.87 tff(1227,axiom,((~hskp15) | c2_1(a1026)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause62')).
% 0.96/0.87 tff(1228,plain,
% 0.96/0.87 ((~hskp15) | c2_1(a1026)),
% 0.96/0.87 inference(modus_ponens,[status(thm)],[1227, 1226])).
% 0.96/0.87 tff(1229,plain,
% 0.96/0.87 ((~hskp15) | c2_1(a1026)),
% 0.96/0.87 inference(modus_ponens,[status(thm)],[1228, 1226])).
% 0.96/0.87 tff(1230,plain,
% 0.96/0.87 ((~hskp15) | c2_1(a1026)),
% 0.96/0.87 inference(modus_ponens,[status(thm)],[1229, 1226])).
% 0.96/0.87 tff(1231,plain,
% 0.96/0.87 ((~hskp15) | c2_1(a1026)),
% 0.96/0.87 inference(modus_ponens,[status(thm)],[1230, 1226])).
% 0.96/0.87 tff(1232,plain,
% 0.96/0.87 ((~hskp15) | c2_1(a1026)),
% 0.96/0.87 inference(modus_ponens,[status(thm)],[1231, 1226])).
% 0.96/0.87 tff(1233,plain,
% 0.96/0.87 ((~hskp15) | c2_1(a1026)),
% 0.96/0.87 inference(modus_ponens,[status(thm)],[1232, 1226])).
% 0.96/0.87 tff(1234,plain,
% 0.96/0.87 ((~hskp15) | c2_1(a1026)),
% 0.96/0.87 inference(modus_ponens,[status(thm)],[1233, 1226])).
% 0.96/0.87 tff(1235,plain,
% 0.96/0.87 ((~hskp15) | c2_1(a1026)),
% 0.96/0.87 inference(modus_ponens,[status(thm)],[1234, 1226])).
% 0.96/0.87 tff(1236,plain,
% 0.96/0.87 (c2_1(a1026)),
% 0.96/0.87 inference(unit_resolution,[status(thm)],[1235, 1213])).
% 0.96/0.87 tff(1237,plain,
% 0.96/0.87 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | c3_1(U) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp3 | c3_1(a1048) | c0_1(a1026) | c1_1(a1026) | (~ndr1_0) | (~c2_1(a1026)) | c2_1(a1048) | (~c1_1(a1048)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | c3_1(U) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp3 | c3_1(a1048) | c0_1(a1026) | c1_1(a1026) | (~ndr1_0) | (~c2_1(a1026)) | c2_1(a1048) | (~c1_1(a1048)))),
% 0.96/0.87 inference(rewrite,[status(thm)],[])).
% 0.96/0.87 tff(1238,plain,
% 0.96/0.87 ((hskp3 | (~ndr1_0) | c2_1(a1048) | (~c1_1(a1048)) | c3_1(a1048) | c1_1(a1026) | c0_1(a1026) | (~c2_1(a1026))) <=> (hskp3 | c3_1(a1048) | c0_1(a1026) | c1_1(a1026) | (~ndr1_0) | (~c2_1(a1026)) | c2_1(a1048) | (~c1_1(a1048)))),
% 0.96/0.87 inference(rewrite,[status(thm)],[])).
% 0.96/0.87 tff(1239,plain,
% 0.96/0.87 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | c3_1(U) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp3 | (~ndr1_0) | c2_1(a1048) | (~c1_1(a1048)) | c3_1(a1048) | c1_1(a1026) | c0_1(a1026) | (~c2_1(a1026)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | c3_1(U) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp3 | c3_1(a1048) | c0_1(a1026) | c1_1(a1026) | (~ndr1_0) | (~c2_1(a1026)) | c2_1(a1048) | (~c1_1(a1048))))),
% 0.96/0.87 inference(monotonicity,[status(thm)],[1238])).
% 0.96/0.87 tff(1240,plain,
% 0.96/0.87 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | c3_1(U) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp3 | (~ndr1_0) | c2_1(a1048) | (~c1_1(a1048)) | c3_1(a1048) | c1_1(a1026) | c0_1(a1026) | (~c2_1(a1026)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | c3_1(U) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp3 | c3_1(a1048) | c0_1(a1026) | c1_1(a1026) | (~ndr1_0) | (~c2_1(a1026)) | c2_1(a1048) | (~c1_1(a1048)))),
% 0.96/0.87 inference(transitivity,[status(thm)],[1239, 1237])).
% 0.96/0.87 tff(1241,plain,
% 0.96/0.87 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | c3_1(U) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp3 | (~ndr1_0) | c2_1(a1048) | (~c1_1(a1048)) | c3_1(a1048) | c1_1(a1026) | c0_1(a1026) | (~c2_1(a1026)))),
% 0.96/0.87 inference(quant_inst,[status(thm)],[])).
% 0.96/0.87 tff(1242,plain,
% 0.96/0.87 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | c3_1(U) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp3 | c3_1(a1048) | c0_1(a1026) | c1_1(a1026) | (~ndr1_0) | (~c2_1(a1026)) | c2_1(a1048) | (~c1_1(a1048))),
% 0.96/0.87 inference(modus_ponens,[status(thm)],[1241, 1240])).
% 0.96/0.87 tff(1243,plain,
% 0.96/0.87 ($false),
% 0.96/0.87 inference(unit_resolution,[status(thm)],[1242, 90, 360, 1157, 1236, 1154, 1225, 1219, 1174, 1164])).
% 0.96/0.87 tff(1244,plain,(hskp3 | (~c0_1(a1006)) | (~c3_1(a1006)) | (~c2_1(a1001)) | (~c3_1(a1001)) | c2_1(a1006) | c1_1(a1001) | (~c0_1(a1010)) | (~c3_1(a1010)) | c1_1(a1010) | c2_1(a1044)), inference(lemma,lemma(discharge,[]))).
% 0.96/0.87 tff(1245,plain,
% 0.96/0.87 (hskp3),
% 0.96/0.87 inference(unit_resolution,[status(thm)],[1244, 1145, 1144, 938, 928, 1143, 927, 1141, 1140, 1139, 1022])).
% 0.96/0.87 tff(1246,plain,
% 0.96/0.87 (~c2_1(a1003)),
% 0.96/0.87 inference(unit_resolution,[status(thm)],[521, 1245])).
% 0.96/0.87 tff(1247,plain,
% 0.96/0.87 (~c0_1(a1003)),
% 0.96/0.87 inference(unit_resolution,[status(thm)],[527, 1245])).
% 0.96/0.87 tff(1248,plain,
% 0.96/0.87 (^[V: $i, U: $i] : refl((hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | c3_1(U) | c1_1(V) | (~c0_1(V)) | (~c3_1(V))) <=> (hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | c3_1(U) | c1_1(V) | (~c0_1(V)) | (~c3_1(V))))),
% 0.96/0.87 inference(bind,[status(th)],[])).
% 0.96/0.87 tff(1249,plain,
% 0.96/0.87 (![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | c3_1(U) | c1_1(V) | (~c0_1(V)) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | c3_1(U) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)))),
% 0.96/0.87 inference(quant_intro,[status(thm)],[1248])).
% 0.96/0.87 tff(1250,plain,
% 0.96/0.87 (![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | c3_1(U) | c1_1(V) | (~c0_1(V)) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | c3_1(U) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)))),
% 0.96/0.87 inference(rewrite,[status(thm)],[])).
% 0.96/0.87 tff(1251,plain,
% 0.96/0.87 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c1_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)))), ((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c1_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(V)))), ((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(V))))), (((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(V)) | (~c3_1(V)))), (((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(V)) | (~c3_1(V))))), ((((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c2_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(V)) | (~c3_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(V)) | (~c3_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(V)) | (~c3_1(V)))), ((((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(V)) | (~c3_1(V))))), (((((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(V)) | (~c3_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(V)) | (~c3_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | c3_1(U) | (~c0_1(V)) | (~c3_1(V)))), (((((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | c3_1(U) | (~c0_1(V)) | (~c3_1(V))))), ((((((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | c3_1(U) | (~c0_1(V)) | (~c3_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | c3_1(U) | (~c0_1(V)) | (~c3_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | c3_1(U) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)))), ((((((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | c3_1(U) | c1_1(V) | (~c0_1(V)) | (~c3_1(V))))), (((((((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | hskp22) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | c3_1(U) | c1_1(V) | (~c0_1(V)) | (~c3_1(V))) | hskp22))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | c3_1(U) | c1_1(V) | (~c0_1(V)) | (~c3_1(V))) | hskp22) <=> (hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | c3_1(U) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)))), (((((((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | hskp22) <=> (hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | c3_1(U) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)))))),
% 0.96/0.88 inference(bind,[status(th)],[])).
% 0.96/0.88 tff(1252,plain,
% 0.96/0.88 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | hskp22) <=> ![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | c3_1(U) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)))),
% 0.96/0.88 inference(quant_intro,[status(thm)],[1251])).
% 0.96/0.88 tff(1253,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | hskp22)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause172')).
% 0.96/0.88 tff(1254,plain,
% 0.96/0.88 (![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | c3_1(U) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)))),
% 0.96/0.88 inference(modus_ponens,[status(thm)],[1253, 1252])).
% 0.96/0.88 tff(1255,plain,
% 0.96/0.88 (![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | c3_1(U) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)))),
% 0.96/0.88 inference(modus_ponens,[status(thm)],[1254, 1250])).
% 0.96/0.88 tff(1256,plain,(
% 0.96/0.88 ![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | c3_1(U) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)))),
% 0.96/0.88 inference(skolemize,[status(sab)],[1255])).
% 0.96/0.88 tff(1257,plain,
% 0.96/0.88 (![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | c3_1(U) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)))),
% 0.96/0.88 inference(modus_ponens,[status(thm)],[1256, 1249])).
% 0.96/0.88 tff(1258,plain,
% 0.96/0.88 (((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | c3_1(U) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)))) | (hskp22 | c3_1(a1044) | c1_1(a1010) | (~ndr1_0) | (~c0_1(a1010)) | (~c3_1(a1010)) | c2_1(a1044) | (~c1_1(a1044)))) <=> ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | c3_1(U) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)))) | hskp22 | c3_1(a1044) | c1_1(a1010) | (~ndr1_0) | (~c0_1(a1010)) | (~c3_1(a1010)) | c2_1(a1044) | (~c1_1(a1044)))),
% 0.96/0.88 inference(rewrite,[status(thm)],[])).
% 0.96/0.88 tff(1259,plain,
% 0.96/0.88 ((hskp22 | (~ndr1_0) | c2_1(a1044) | (~c1_1(a1044)) | c3_1(a1044) | c1_1(a1010) | (~c0_1(a1010)) | (~c3_1(a1010))) <=> (hskp22 | c3_1(a1044) | c1_1(a1010) | (~ndr1_0) | (~c0_1(a1010)) | (~c3_1(a1010)) | c2_1(a1044) | (~c1_1(a1044)))),
% 0.96/0.88 inference(rewrite,[status(thm)],[])).
% 0.96/0.88 tff(1260,plain,
% 0.96/0.88 (((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | c3_1(U) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)))) | (hskp22 | (~ndr1_0) | c2_1(a1044) | (~c1_1(a1044)) | c3_1(a1044) | c1_1(a1010) | (~c0_1(a1010)) | (~c3_1(a1010)))) <=> ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | c3_1(U) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)))) | (hskp22 | c3_1(a1044) | c1_1(a1010) | (~ndr1_0) | (~c0_1(a1010)) | (~c3_1(a1010)) | c2_1(a1044) | (~c1_1(a1044))))),
% 0.96/0.88 inference(monotonicity,[status(thm)],[1259])).
% 0.96/0.88 tff(1261,plain,
% 0.96/0.88 (((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | c3_1(U) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)))) | (hskp22 | (~ndr1_0) | c2_1(a1044) | (~c1_1(a1044)) | c3_1(a1044) | c1_1(a1010) | (~c0_1(a1010)) | (~c3_1(a1010)))) <=> ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | c3_1(U) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)))) | hskp22 | c3_1(a1044) | c1_1(a1010) | (~ndr1_0) | (~c0_1(a1010)) | (~c3_1(a1010)) | c2_1(a1044) | (~c1_1(a1044)))),
% 0.96/0.88 inference(transitivity,[status(thm)],[1260, 1258])).
% 0.96/0.88 tff(1262,plain,
% 0.96/0.88 ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | c3_1(U) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)))) | (hskp22 | (~ndr1_0) | c2_1(a1044) | (~c1_1(a1044)) | c3_1(a1044) | c1_1(a1010) | (~c0_1(a1010)) | (~c3_1(a1010)))),
% 0.96/0.88 inference(quant_inst,[status(thm)],[])).
% 0.96/0.88 tff(1263,plain,
% 0.96/0.88 ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | c3_1(U) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)))) | hskp22 | c3_1(a1044) | c1_1(a1010) | (~ndr1_0) | (~c0_1(a1010)) | (~c3_1(a1010)) | c2_1(a1044) | (~c1_1(a1044))),
% 0.96/0.88 inference(modus_ponens,[status(thm)],[1262, 1261])).
% 0.96/0.88 tff(1264,plain,
% 0.96/0.88 (hskp22),
% 0.96/0.88 inference(unit_resolution,[status(thm)],[1263, 90, 772, 1141, 1140, 761, 1139, 1257, 1022])).
% 0.96/0.88 tff(1265,plain,
% 0.96/0.88 (((~hskp22) | (~c2_1(a1043))) <=> ((~hskp22) | (~c2_1(a1043)))),
% 0.96/0.88 inference(rewrite,[status(thm)],[])).
% 0.96/0.88 tff(1266,plain,
% 0.96/0.88 (((~c2_1(a1043)) | (~hskp22)) <=> ((~hskp22) | (~c2_1(a1043)))),
% 0.96/0.88 inference(rewrite,[status(thm)],[])).
% 0.96/0.88 tff(1267,axiom,((~c2_1(a1043)) | (~hskp22)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause92')).
% 0.96/0.88 tff(1268,plain,
% 0.96/0.88 ((~hskp22) | (~c2_1(a1043))),
% 0.96/0.88 inference(modus_ponens,[status(thm)],[1267, 1266])).
% 0.96/0.88 tff(1269,plain,
% 0.96/0.88 ((~hskp22) | (~c2_1(a1043))),
% 0.96/0.88 inference(modus_ponens,[status(thm)],[1268, 1265])).
% 0.96/0.88 tff(1270,plain,
% 0.96/0.88 (~c2_1(a1043)),
% 0.96/0.88 inference(unit_resolution,[status(thm)],[1269, 1264])).
% 0.96/0.88 tff(1271,plain,
% 0.96/0.88 (((~hskp22) | (~c1_1(a1043))) <=> ((~hskp22) | (~c1_1(a1043)))),
% 0.96/0.88 inference(rewrite,[status(thm)],[])).
% 0.96/0.88 tff(1272,plain,
% 0.96/0.88 (((~c1_1(a1043)) | (~hskp22)) <=> ((~hskp22) | (~c1_1(a1043)))),
% 0.96/0.88 inference(rewrite,[status(thm)],[])).
% 0.96/0.88 tff(1273,axiom,((~c1_1(a1043)) | (~hskp22)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause91')).
% 0.96/0.88 tff(1274,plain,
% 0.96/0.88 ((~hskp22) | (~c1_1(a1043))),
% 0.96/0.88 inference(modus_ponens,[status(thm)],[1273, 1272])).
% 0.96/0.88 tff(1275,plain,
% 0.96/0.88 ((~hskp22) | (~c1_1(a1043))),
% 0.96/0.88 inference(modus_ponens,[status(thm)],[1274, 1271])).
% 0.96/0.88 tff(1276,plain,
% 0.96/0.88 (~c1_1(a1043)),
% 0.96/0.88 inference(unit_resolution,[status(thm)],[1275, 1264])).
% 0.96/0.88 tff(1277,plain,
% 0.96/0.88 (c1_1(a1003)),
% 0.96/0.88 inference(unit_resolution,[status(thm)],[538, 1245])).
% 0.96/0.88 tff(1278,plain,
% 0.96/0.88 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp7 | c1_1(a1043) | c2_1(a1043) | c0_1(a1003) | c2_1(a1003) | (~ndr1_0) | (~c1_1(a1003)) | (~c3_1(a1043)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp7 | c1_1(a1043) | c2_1(a1043) | c0_1(a1003) | c2_1(a1003) | (~ndr1_0) | (~c1_1(a1003)) | (~c3_1(a1043)))),
% 0.96/0.88 inference(rewrite,[status(thm)],[])).
% 0.96/0.88 tff(1279,plain,
% 0.96/0.88 ((hskp7 | (~ndr1_0) | c2_1(a1043) | c1_1(a1043) | (~c3_1(a1043)) | c0_1(a1003) | c2_1(a1003) | (~c1_1(a1003))) <=> (hskp7 | c1_1(a1043) | c2_1(a1043) | c0_1(a1003) | c2_1(a1003) | (~ndr1_0) | (~c1_1(a1003)) | (~c3_1(a1043)))),
% 0.96/0.88 inference(rewrite,[status(thm)],[])).
% 0.96/0.88 tff(1280,plain,
% 0.96/0.88 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp7 | (~ndr1_0) | c2_1(a1043) | c1_1(a1043) | (~c3_1(a1043)) | c0_1(a1003) | c2_1(a1003) | (~c1_1(a1003)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp7 | c1_1(a1043) | c2_1(a1043) | c0_1(a1003) | c2_1(a1003) | (~ndr1_0) | (~c1_1(a1003)) | (~c3_1(a1043))))),
% 0.96/0.88 inference(monotonicity,[status(thm)],[1279])).
% 0.96/0.88 tff(1281,plain,
% 0.96/0.88 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp7 | (~ndr1_0) | c2_1(a1043) | c1_1(a1043) | (~c3_1(a1043)) | c0_1(a1003) | c2_1(a1003) | (~c1_1(a1003)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp7 | c1_1(a1043) | c2_1(a1043) | c0_1(a1003) | c2_1(a1003) | (~ndr1_0) | (~c1_1(a1003)) | (~c3_1(a1043)))),
% 0.96/0.88 inference(transitivity,[status(thm)],[1280, 1278])).
% 0.96/0.88 tff(1282,plain,
% 0.96/0.88 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp7 | (~ndr1_0) | c2_1(a1043) | c1_1(a1043) | (~c3_1(a1043)) | c0_1(a1003) | c2_1(a1003) | (~c1_1(a1003)))),
% 0.96/0.88 inference(quant_inst,[status(thm)],[])).
% 0.96/0.88 tff(1283,plain,
% 0.96/0.88 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp7 | c1_1(a1043) | c2_1(a1043) | c0_1(a1003) | c2_1(a1003) | (~ndr1_0) | (~c1_1(a1003)) | (~c3_1(a1043))),
% 0.96/0.88 inference(modus_ponens,[status(thm)],[1282, 1281])).
% 0.96/0.88 tff(1284,plain,
% 0.96/0.88 (~c3_1(a1043)),
% 0.96/0.88 inference(unit_resolution,[status(thm)],[1283, 90, 644, 1277, 1276, 1270, 1247, 1246, 1014])).
% 0.96/0.88 tff(1285,plain,
% 0.96/0.88 (((~hskp22) | c0_1(a1043)) <=> ((~hskp22) | c0_1(a1043))),
% 0.96/0.88 inference(rewrite,[status(thm)],[])).
% 0.96/0.88 tff(1286,axiom,((~hskp22) | c0_1(a1043)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause55')).
% 0.96/0.88 tff(1287,plain,
% 0.96/0.88 ((~hskp22) | c0_1(a1043)),
% 0.96/0.88 inference(modus_ponens,[status(thm)],[1286, 1285])).
% 0.96/0.88 tff(1288,plain,
% 0.96/0.88 ((~hskp22) | c0_1(a1043)),
% 0.96/0.88 inference(modus_ponens,[status(thm)],[1287, 1285])).
% 0.96/0.88 tff(1289,plain,
% 0.96/0.88 ((~hskp22) | c0_1(a1043)),
% 0.96/0.88 inference(modus_ponens,[status(thm)],[1288, 1285])).
% 0.96/0.88 tff(1290,plain,
% 0.96/0.88 ((~hskp22) | c0_1(a1043)),
% 0.96/0.88 inference(modus_ponens,[status(thm)],[1289, 1285])).
% 0.96/0.88 tff(1291,plain,
% 0.96/0.88 ((~hskp22) | c0_1(a1043)),
% 0.96/0.88 inference(modus_ponens,[status(thm)],[1290, 1285])).
% 0.96/0.88 tff(1292,plain,
% 0.96/0.88 ((~hskp22) | c0_1(a1043)),
% 0.96/0.88 inference(modus_ponens,[status(thm)],[1291, 1285])).
% 0.96/0.88 tff(1293,plain,
% 0.96/0.88 ((~hskp22) | c0_1(a1043)),
% 0.96/0.88 inference(modus_ponens,[status(thm)],[1292, 1285])).
% 0.96/0.88 tff(1294,plain,
% 0.96/0.88 ((~hskp22) | c0_1(a1043)),
% 0.96/0.88 inference(modus_ponens,[status(thm)],[1293, 1285])).
% 0.96/0.88 tff(1295,plain,
% 0.96/0.88 (c0_1(a1043)),
% 0.96/0.88 inference(unit_resolution,[status(thm)],[1294, 1264])).
% 0.96/0.88 tff(1296,plain,
% 0.96/0.88 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp13 | c1_1(a1043) | c2_1(a1043) | (~ndr1_0) | (~c0_1(a1043)) | c3_1(a1043))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp13 | c1_1(a1043) | c2_1(a1043) | (~ndr1_0) | (~c0_1(a1043)) | c3_1(a1043))),
% 0.96/0.88 inference(rewrite,[status(thm)],[])).
% 0.96/0.88 tff(1297,plain,
% 0.96/0.88 ((hskp13 | (~ndr1_0) | c1_1(a1043) | c3_1(a1043) | (~c0_1(a1043)) | c3_1(a1043) | c1_1(a1043) | c2_1(a1043)) <=> (hskp13 | c1_1(a1043) | c2_1(a1043) | (~ndr1_0) | (~c0_1(a1043)) | c3_1(a1043))),
% 0.96/0.88 inference(rewrite,[status(thm)],[])).
% 0.96/0.88 tff(1298,plain,
% 0.96/0.88 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp13 | (~ndr1_0) | c1_1(a1043) | c3_1(a1043) | (~c0_1(a1043)) | c3_1(a1043) | c1_1(a1043) | c2_1(a1043))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp13 | c1_1(a1043) | c2_1(a1043) | (~ndr1_0) | (~c0_1(a1043)) | c3_1(a1043)))),
% 0.96/0.88 inference(monotonicity,[status(thm)],[1297])).
% 0.96/0.88 tff(1299,plain,
% 0.96/0.88 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp13 | (~ndr1_0) | c1_1(a1043) | c3_1(a1043) | (~c0_1(a1043)) | c3_1(a1043) | c1_1(a1043) | c2_1(a1043))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp13 | c1_1(a1043) | c2_1(a1043) | (~ndr1_0) | (~c0_1(a1043)) | c3_1(a1043))),
% 0.96/0.88 inference(transitivity,[status(thm)],[1298, 1296])).
% 0.96/0.88 tff(1300,plain,
% 0.96/0.88 ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp13 | (~ndr1_0) | c1_1(a1043) | c3_1(a1043) | (~c0_1(a1043)) | c3_1(a1043) | c1_1(a1043) | c2_1(a1043))),
% 0.96/0.88 inference(quant_inst,[status(thm)],[])).
% 0.96/0.88 tff(1301,plain,
% 0.96/0.88 ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp13 | c1_1(a1043) | c2_1(a1043) | (~ndr1_0) | (~c0_1(a1043)) | c3_1(a1043)),
% 0.96/0.88 inference(modus_ponens,[status(thm)],[1300, 1299])).
% 0.96/0.88 tff(1302,plain,
% 0.96/0.88 ($false),
% 0.96/0.88 inference(unit_resolution,[status(thm)],[1301, 90, 624, 1295, 1276, 1270, 107, 1284])).
% 0.96/0.88 tff(1303,plain,(hskp7 | hskp13 | (~c2_1(a1001)) | (~c3_1(a1001)) | c1_1(a1001)), inference(lemma,lemma(discharge,[]))).
% 0.96/0.88 tff(1304,plain,
% 0.96/0.88 (hskp7),
% 0.96/0.88 inference(unit_resolution,[status(thm)],[1303, 624, 926, 925, 923])).
% 0.96/0.88 tff(1305,plain,
% 0.96/0.88 (c2_1(a1008)),
% 0.96/0.88 inference(unit_resolution,[status(thm)],[248, 1304])).
% 0.96/0.88 tff(1306,plain,
% 0.96/0.88 (~c3_1(a1008)),
% 0.96/0.88 inference(unit_resolution,[status(thm)],[231, 1304])).
% 0.96/0.88 tff(1307,plain,
% 0.96/0.88 (~c1_1(a1008)),
% 0.96/0.88 inference(unit_resolution,[status(thm)],[237, 1304])).
% 0.96/0.88 tff(1308,plain,
% 0.96/0.88 (hskp26),
% 0.96/0.88 inference(unit_resolution,[status(thm)],[1040, 1023, 1147])).
% 0.96/0.88 tff(1309,plain,
% 0.96/0.88 (~c2_1(a1052)),
% 0.96/0.88 inference(unit_resolution,[status(thm)],[1046, 1308])).
% 0.96/0.88 tff(1310,plain,
% 0.96/0.88 (~c0_1(a1052)),
% 0.96/0.88 inference(unit_resolution,[status(thm)],[1052, 1308])).
% 0.96/0.88 tff(1311,plain,
% 0.96/0.88 (c3_1(a1052)),
% 0.96/0.88 inference(unit_resolution,[status(thm)],[1115, 1308])).
% 0.96/0.88 tff(1312,plain,
% 0.96/0.88 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))) | (c0_1(a1052) | c2_1(a1052) | c1_1(a1008) | c3_1(a1008) | (~ndr1_0) | (~c2_1(a1008)) | c1_1(a1052) | (~c3_1(a1052)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))) | c0_1(a1052) | c2_1(a1052) | c1_1(a1008) | c3_1(a1008) | (~ndr1_0) | (~c2_1(a1008)) | c1_1(a1052) | (~c3_1(a1052)))),
% 0.96/0.88 inference(rewrite,[status(thm)],[])).
% 0.96/0.88 tff(1313,plain,
% 0.96/0.88 (((~ndr1_0) | c1_1(a1008) | c3_1(a1008) | (~c2_1(a1008)) | c0_1(a1052) | c2_1(a1052) | (~c3_1(a1052)) | c0_1(a1052) | c1_1(a1052) | (~c3_1(a1052))) <=> (c0_1(a1052) | c2_1(a1052) | c1_1(a1008) | c3_1(a1008) | (~ndr1_0) | (~c2_1(a1008)) | c1_1(a1052) | (~c3_1(a1052)))),
% 0.96/0.88 inference(rewrite,[status(thm)],[])).
% 0.96/0.88 tff(1314,plain,
% 0.96/0.88 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a1008) | c3_1(a1008) | (~c2_1(a1008)) | c0_1(a1052) | c2_1(a1052) | (~c3_1(a1052)) | c0_1(a1052) | c1_1(a1052) | (~c3_1(a1052)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))) | (c0_1(a1052) | c2_1(a1052) | c1_1(a1008) | c3_1(a1008) | (~ndr1_0) | (~c2_1(a1008)) | c1_1(a1052) | (~c3_1(a1052))))),
% 0.96/0.88 inference(monotonicity,[status(thm)],[1313])).
% 0.96/0.88 tff(1315,plain,
% 0.96/0.88 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a1008) | c3_1(a1008) | (~c2_1(a1008)) | c0_1(a1052) | c2_1(a1052) | (~c3_1(a1052)) | c0_1(a1052) | c1_1(a1052) | (~c3_1(a1052)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))) | c0_1(a1052) | c2_1(a1052) | c1_1(a1008) | c3_1(a1008) | (~ndr1_0) | (~c2_1(a1008)) | c1_1(a1052) | (~c3_1(a1052)))),
% 0.96/0.88 inference(transitivity,[status(thm)],[1314, 1312])).
% 0.96/0.88 tff(1316,plain,
% 0.96/0.88 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a1008) | c3_1(a1008) | (~c2_1(a1008)) | c0_1(a1052) | c2_1(a1052) | (~c3_1(a1052)) | c0_1(a1052) | c1_1(a1052) | (~c3_1(a1052)))),
% 0.96/0.88 inference(quant_inst,[status(thm)],[])).
% 0.96/0.88 tff(1317,plain,
% 0.96/0.88 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))) | c0_1(a1052) | c2_1(a1052) | c1_1(a1008) | c3_1(a1008) | (~ndr1_0) | (~c2_1(a1008)) | c1_1(a1052) | (~c3_1(a1052))),
% 0.96/0.88 inference(modus_ponens,[status(thm)],[1316, 1315])).
% 0.96/0.88 tff(1318,plain,
% 0.96/0.88 (c1_1(a1052)),
% 0.96/0.88 inference(unit_resolution,[status(thm)],[1317, 90, 1311, 681, 1310, 1309, 690, 680, 225])).
% 0.96/0.88 tff(1319,plain,
% 0.96/0.88 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp8 | c0_1(a1052) | c2_1(a1052) | c1_1(a1008) | c3_1(a1008) | (~ndr1_0) | (~c2_1(a1008)) | (~c1_1(a1052)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp8 | c0_1(a1052) | c2_1(a1052) | c1_1(a1008) | c3_1(a1008) | (~ndr1_0) | (~c2_1(a1008)) | (~c1_1(a1052)))),
% 0.96/0.88 inference(rewrite,[status(thm)],[])).
% 0.96/0.88 tff(1320,plain,
% 0.96/0.88 ((hskp8 | (~ndr1_0) | c1_1(a1008) | c3_1(a1008) | (~c2_1(a1008)) | c0_1(a1052) | c2_1(a1052) | (~c1_1(a1052))) <=> (hskp8 | c0_1(a1052) | c2_1(a1052) | c1_1(a1008) | c3_1(a1008) | (~ndr1_0) | (~c2_1(a1008)) | (~c1_1(a1052)))),
% 0.96/0.88 inference(rewrite,[status(thm)],[])).
% 0.96/0.88 tff(1321,plain,
% 0.96/0.88 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp8 | (~ndr1_0) | c1_1(a1008) | c3_1(a1008) | (~c2_1(a1008)) | c0_1(a1052) | c2_1(a1052) | (~c1_1(a1052)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp8 | c0_1(a1052) | c2_1(a1052) | c1_1(a1008) | c3_1(a1008) | (~ndr1_0) | (~c2_1(a1008)) | (~c1_1(a1052))))),
% 0.96/0.88 inference(monotonicity,[status(thm)],[1320])).
% 0.96/0.88 tff(1322,plain,
% 0.96/0.88 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp8 | (~ndr1_0) | c1_1(a1008) | c3_1(a1008) | (~c2_1(a1008)) | c0_1(a1052) | c2_1(a1052) | (~c1_1(a1052)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp8 | c0_1(a1052) | c2_1(a1052) | c1_1(a1008) | c3_1(a1008) | (~ndr1_0) | (~c2_1(a1008)) | (~c1_1(a1052)))),
% 0.96/0.88 inference(transitivity,[status(thm)],[1321, 1319])).
% 0.96/0.88 tff(1323,plain,
% 0.96/0.88 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp8 | (~ndr1_0) | c1_1(a1008) | c3_1(a1008) | (~c2_1(a1008)) | c0_1(a1052) | c2_1(a1052) | (~c1_1(a1052)))),
% 0.96/0.88 inference(quant_inst,[status(thm)],[])).
% 0.96/0.88 tff(1324,plain,
% 0.96/0.88 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp8 | c0_1(a1052) | c2_1(a1052) | c1_1(a1008) | c3_1(a1008) | (~ndr1_0) | (~c2_1(a1008)) | (~c1_1(a1052))),
% 0.96/0.88 inference(modus_ponens,[status(thm)],[1323, 1322])).
% 0.96/0.88 tff(1325,plain,
% 0.96/0.88 ($false),
% 0.96/0.88 inference(unit_resolution,[status(thm)],[1324, 90, 1023, 681, 1310, 1309, 690, 680, 21, 1318])).
% 0.96/0.88 tff(1326,plain,(hskp8 | (~c2_1(a1008)) | c1_1(a1008) | c3_1(a1008) | c2_1(a1044)), inference(lemma,lemma(discharge,[]))).
% 0.96/0.88 tff(1327,plain,
% 0.96/0.88 (hskp8),
% 0.96/0.88 inference(unit_resolution,[status(thm)],[1326, 1305, 1307, 1306, 983])).
% 0.96/0.88 tff(1328,plain,
% 0.96/0.88 (~c1_1(a1010)),
% 0.96/0.88 inference(unit_resolution,[status(thm)],[545, 1327])).
% 0.96/0.88 tff(1329,plain,
% 0.96/0.88 (c0_1(a1010)),
% 0.96/0.88 inference(unit_resolution,[status(thm)],[567, 1327])).
% 0.96/0.88 tff(1330,plain,
% 0.96/0.88 (c3_1(a1010)),
% 0.96/0.88 inference(unit_resolution,[status(thm)],[556, 1327])).
% 0.96/0.88 tff(1331,plain,
% 0.96/0.88 (hskp3),
% 0.96/0.88 inference(unit_resolution,[status(thm)],[1244, 1330, 1329, 926, 925, 1002, 923, 1004, 1003, 1328, 983])).
% 0.96/0.88 tff(1332,plain,
% 0.96/0.88 (~c2_1(a1003)),
% 0.96/0.88 inference(unit_resolution,[status(thm)],[521, 1331])).
% 0.96/0.88 tff(1333,plain,
% 0.96/0.88 (~c0_1(a1003)),
% 0.96/0.88 inference(unit_resolution,[status(thm)],[527, 1331])).
% 0.96/0.88 tff(1334,plain,
% 0.96/0.88 (c1_1(a1003)),
% 0.96/0.88 inference(unit_resolution,[status(thm)],[538, 1331])).
% 0.96/0.88 tff(1335,assumption,(~hskp4), introduced(assumption)).
% 0.96/0.88 tff(1336,plain,
% 0.96/0.88 (^[V: $i, U: $i] : refl((hskp4 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))) <=> (hskp4 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))))),
% 0.96/0.88 inference(bind,[status(th)],[])).
% 0.96/0.88 tff(1337,plain,
% 0.96/0.88 (![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 0.96/0.88 inference(quant_intro,[status(thm)],[1336])).
% 0.96/0.88 tff(1338,plain,
% 0.96/0.88 (![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 0.96/0.88 inference(rewrite,[status(thm)],[])).
% 0.96/0.88 tff(1339,plain,
% 0.96/0.88 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V))))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V))))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V))))), ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c0_1(V)) | c1_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))), ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c0_1(V)) | c1_1(V)) | hskp4) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))) | hskp4))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))) | hskp4) <=> (hskp4 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c0_1(V)) | c1_1(V)) | hskp4) <=> (hskp4 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))))),
% 0.96/0.88 inference(bind,[status(th)],[])).
% 0.96/0.88 tff(1340,plain,
% 0.96/0.88 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c0_1(V)) | c1_1(V)) | hskp4) <=> ![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 0.96/0.88 inference(quant_intro,[status(thm)],[1339])).
% 0.96/0.88 tff(1341,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c0_1(V)) | c1_1(V)) | hskp4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause164')).
% 0.96/0.88 tff(1342,plain,
% 0.96/0.88 (![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 0.96/0.88 inference(modus_ponens,[status(thm)],[1341, 1340])).
% 0.96/0.88 tff(1343,plain,
% 0.96/0.88 (![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 0.96/0.88 inference(modus_ponens,[status(thm)],[1342, 1338])).
% 0.96/0.88 tff(1344,plain,(
% 0.96/0.88 ![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 0.96/0.88 inference(skolemize,[status(sab)],[1343])).
% 0.96/0.88 tff(1345,plain,
% 0.96/0.88 (![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 0.96/0.88 inference(modus_ponens,[status(thm)],[1344, 1337])).
% 0.96/0.88 tff(1346,plain,
% 0.96/0.88 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp4 | c1_1(a1008) | c2_1(a1006) | (~ndr1_0) | (~c0_1(a1006)) | (~c3_1(a1006)) | (~c2_1(a1008)) | c0_1(a1008))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp4 | c1_1(a1008) | c2_1(a1006) | (~ndr1_0) | (~c0_1(a1006)) | (~c3_1(a1006)) | (~c2_1(a1008)) | c0_1(a1008))),
% 0.96/0.88 inference(rewrite,[status(thm)],[])).
% 0.96/0.88 tff(1347,plain,
% 0.96/0.88 ((hskp4 | (~ndr1_0) | c2_1(a1006) | (~c3_1(a1006)) | (~c0_1(a1006)) | c1_1(a1008) | c0_1(a1008) | (~c2_1(a1008))) <=> (hskp4 | c1_1(a1008) | c2_1(a1006) | (~ndr1_0) | (~c0_1(a1006)) | (~c3_1(a1006)) | (~c2_1(a1008)) | c0_1(a1008))),
% 0.96/0.88 inference(rewrite,[status(thm)],[])).
% 0.96/0.88 tff(1348,plain,
% 0.96/0.88 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp4 | (~ndr1_0) | c2_1(a1006) | (~c3_1(a1006)) | (~c0_1(a1006)) | c1_1(a1008) | c0_1(a1008) | (~c2_1(a1008)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp4 | c1_1(a1008) | c2_1(a1006) | (~ndr1_0) | (~c0_1(a1006)) | (~c3_1(a1006)) | (~c2_1(a1008)) | c0_1(a1008)))),
% 0.96/0.88 inference(monotonicity,[status(thm)],[1347])).
% 0.96/0.88 tff(1349,plain,
% 0.96/0.88 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp4 | (~ndr1_0) | c2_1(a1006) | (~c3_1(a1006)) | (~c0_1(a1006)) | c1_1(a1008) | c0_1(a1008) | (~c2_1(a1008)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp4 | c1_1(a1008) | c2_1(a1006) | (~ndr1_0) | (~c0_1(a1006)) | (~c3_1(a1006)) | (~c2_1(a1008)) | c0_1(a1008))),
% 0.96/0.88 inference(transitivity,[status(thm)],[1348, 1346])).
% 0.96/0.88 tff(1350,plain,
% 0.96/0.88 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp4 | (~ndr1_0) | c2_1(a1006) | (~c3_1(a1006)) | (~c0_1(a1006)) | c1_1(a1008) | c0_1(a1008) | (~c2_1(a1008)))),
% 0.96/0.88 inference(quant_inst,[status(thm)],[])).
% 0.96/0.88 tff(1351,plain,
% 0.96/0.88 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp4 | c1_1(a1008) | c2_1(a1006) | (~ndr1_0) | (~c0_1(a1006)) | (~c3_1(a1006)) | (~c2_1(a1008)) | c0_1(a1008)),
% 0.96/0.88 inference(modus_ponens,[status(thm)],[1350, 1349])).
% 0.96/0.88 tff(1352,plain,
% 0.96/0.88 (hskp4 | c0_1(a1008)),
% 0.96/0.88 inference(unit_resolution,[status(thm)],[1351, 90, 681, 1156, 1155, 690, 1146, 1345])).
% 0.96/0.88 tff(1353,plain,
% 0.96/0.88 (c0_1(a1008)),
% 0.96/0.88 inference(unit_resolution,[status(thm)],[1352, 1335])).
% 0.96/0.88 tff(1354,plain,
% 0.96/0.88 (^[V: $i, U: $i] : refl((hskp4 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V))) <=> (hskp4 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V))))),
% 0.96/0.88 inference(bind,[status(th)],[])).
% 0.96/0.88 tff(1355,plain,
% 0.96/0.88 (![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))),
% 0.96/0.88 inference(quant_intro,[status(thm)],[1354])).
% 0.96/0.88 tff(1356,plain,
% 0.96/0.88 (![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))),
% 0.96/0.88 inference(rewrite,[status(thm)],[])).
% 0.96/0.88 tff(1357,plain,
% 0.96/0.88 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c0_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c0_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(V)))), ((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(V))))), (((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c1_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c1_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c1_1(V)))), (((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c1_1(V))))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c1_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c1_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | (~c1_1(V)))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | (~c1_1(V))))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | (~c1_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | (~c1_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V))))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V))) | c2_1(V)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V))))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | hskp4) <=> (((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V))) | hskp4))), rewrite((((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V))) | hskp4) <=> (hskp4 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | hskp4) <=> (hskp4 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))))),
% 0.96/0.89 inference(bind,[status(th)],[])).
% 0.96/0.89 tff(1358,plain,
% 0.96/0.89 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | hskp4) <=> ![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))),
% 0.96/0.89 inference(quant_intro,[status(thm)],[1357])).
% 0.96/0.89 tff(1359,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | hskp4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause157')).
% 0.96/0.89 tff(1360,plain,
% 0.96/0.89 (![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))),
% 0.96/0.89 inference(modus_ponens,[status(thm)],[1359, 1358])).
% 0.96/0.89 tff(1361,plain,
% 0.96/0.89 (![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))),
% 0.96/0.89 inference(modus_ponens,[status(thm)],[1360, 1356])).
% 0.96/0.89 tff(1362,plain,(
% 0.96/0.89 ![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))),
% 0.96/0.89 inference(skolemize,[status(sab)],[1361])).
% 0.96/0.89 tff(1363,plain,
% 0.96/0.89 (![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))),
% 0.96/0.89 inference(modus_ponens,[status(thm)],[1362, 1355])).
% 0.96/0.89 tff(1364,assumption,(~c2_1(a1003)), introduced(assumption)).
% 0.96/0.89 tff(1365,assumption,(~c0_1(a1003)), introduced(assumption)).
% 0.96/0.89 tff(1366,assumption,(c1_1(a1003)), introduced(assumption)).
% 0.96/0.89 tff(1367,plain,
% 0.96/0.89 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp4 | c1_1(a1008) | c3_1(a1008) | c0_1(a1003) | c2_1(a1003) | (~ndr1_0) | (~c1_1(a1003)) | (~c0_1(a1008)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp4 | c1_1(a1008) | c3_1(a1008) | c0_1(a1003) | c2_1(a1003) | (~ndr1_0) | (~c1_1(a1003)) | (~c0_1(a1008)))),
% 0.96/0.89 inference(rewrite,[status(thm)],[])).
% 0.96/0.89 tff(1368,plain,
% 0.96/0.89 ((hskp4 | (~ndr1_0) | c1_1(a1008) | c3_1(a1008) | (~c0_1(a1008)) | c0_1(a1003) | c2_1(a1003) | (~c1_1(a1003))) <=> (hskp4 | c1_1(a1008) | c3_1(a1008) | c0_1(a1003) | c2_1(a1003) | (~ndr1_0) | (~c1_1(a1003)) | (~c0_1(a1008)))),
% 0.96/0.89 inference(rewrite,[status(thm)],[])).
% 0.96/0.89 tff(1369,plain,
% 0.96/0.89 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp4 | (~ndr1_0) | c1_1(a1008) | c3_1(a1008) | (~c0_1(a1008)) | c0_1(a1003) | c2_1(a1003) | (~c1_1(a1003)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp4 | c1_1(a1008) | c3_1(a1008) | c0_1(a1003) | c2_1(a1003) | (~ndr1_0) | (~c1_1(a1003)) | (~c0_1(a1008))))),
% 0.96/0.89 inference(monotonicity,[status(thm)],[1368])).
% 0.96/0.89 tff(1370,plain,
% 0.96/0.89 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp4 | (~ndr1_0) | c1_1(a1008) | c3_1(a1008) | (~c0_1(a1008)) | c0_1(a1003) | c2_1(a1003) | (~c1_1(a1003)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp4 | c1_1(a1008) | c3_1(a1008) | c0_1(a1003) | c2_1(a1003) | (~ndr1_0) | (~c1_1(a1003)) | (~c0_1(a1008)))),
% 0.96/0.89 inference(transitivity,[status(thm)],[1369, 1367])).
% 0.96/0.89 tff(1371,plain,
% 0.96/0.89 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp4 | (~ndr1_0) | c1_1(a1008) | c3_1(a1008) | (~c0_1(a1008)) | c0_1(a1003) | c2_1(a1003) | (~c1_1(a1003)))),
% 0.96/0.89 inference(quant_inst,[status(thm)],[])).
% 0.96/0.89 tff(1372,plain,
% 0.96/0.89 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp4 | c1_1(a1008) | c3_1(a1008) | c0_1(a1003) | c2_1(a1003) | (~ndr1_0) | (~c1_1(a1003)) | (~c0_1(a1008))),
% 0.96/0.89 inference(modus_ponens,[status(thm)],[1371, 1370])).
% 0.96/0.89 tff(1373,plain,
% 0.96/0.89 (hskp4 | (~c0_1(a1008))),
% 0.96/0.89 inference(unit_resolution,[status(thm)],[1372, 90, 1366, 690, 680, 1365, 1364, 1363])).
% 0.96/0.89 tff(1374,plain,
% 0.96/0.89 ($false),
% 0.96/0.89 inference(unit_resolution,[status(thm)],[1373, 1353, 1335])).
% 0.96/0.89 tff(1375,plain,(hskp4 | (~c1_1(a1003)) | c1_1(a1008) | c3_1(a1008) | c0_1(a1003) | c2_1(a1003) | (~c2_1(a1008)) | (~c0_1(a1006)) | (~c3_1(a1006)) | c2_1(a1006)), inference(lemma,lemma(discharge,[]))).
% 0.96/0.89 tff(1376,plain,
% 0.96/0.89 (hskp4),
% 0.96/0.89 inference(unit_resolution,[status(thm)],[1375, 1334, 1307, 1306, 1333, 1332, 1305, 1004, 1003, 1002])).
% 0.96/0.89 tff(1377,plain,
% 0.96/0.89 (~c3_1(a1004)),
% 0.96/0.89 inference(unit_resolution,[status(thm)],[865, 1376])).
% 0.96/0.89 tff(1378,plain,
% 0.96/0.89 (c2_1(a1004)),
% 0.96/0.89 inference(unit_resolution,[status(thm)],[841, 1376])).
% 0.96/0.89 tff(1379,plain,
% 0.96/0.89 (c1_1(a1004)),
% 0.96/0.89 inference(unit_resolution,[status(thm)],[852, 1376])).
% 0.96/0.89 tff(1380,plain,
% 0.96/0.89 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c1_1(W) | (~c3_1(W)) | (~c2_1(W)))) | (c2_1(a1006) | c3_1(a1004) | c1_1(a1001) | (~ndr1_0) | (~c3_1(a1001)) | (~c2_1(a1001)) | (~c2_1(a1004)) | (~c1_1(a1004)) | (~c0_1(a1006)) | (~c3_1(a1006)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c1_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c2_1(a1006) | c3_1(a1004) | c1_1(a1001) | (~ndr1_0) | (~c3_1(a1001)) | (~c2_1(a1001)) | (~c2_1(a1004)) | (~c1_1(a1004)) | (~c0_1(a1006)) | (~c3_1(a1006)))),
% 0.96/0.89 inference(rewrite,[status(thm)],[])).
% 0.96/0.89 tff(1381,plain,
% 0.96/0.89 (((~ndr1_0) | (~c1_1(a1004)) | c3_1(a1004) | (~c2_1(a1004)) | c2_1(a1006) | (~c0_1(a1006)) | (~c3_1(a1006)) | c1_1(a1001) | (~c3_1(a1001)) | (~c2_1(a1001))) <=> (c2_1(a1006) | c3_1(a1004) | c1_1(a1001) | (~ndr1_0) | (~c3_1(a1001)) | (~c2_1(a1001)) | (~c2_1(a1004)) | (~c1_1(a1004)) | (~c0_1(a1006)) | (~c3_1(a1006)))),
% 0.96/0.89 inference(rewrite,[status(thm)],[])).
% 0.96/0.89 tff(1382,plain,
% 0.96/0.89 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c1_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c1_1(a1004)) | c3_1(a1004) | (~c2_1(a1004)) | c2_1(a1006) | (~c0_1(a1006)) | (~c3_1(a1006)) | c1_1(a1001) | (~c3_1(a1001)) | (~c2_1(a1001)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c1_1(W) | (~c3_1(W)) | (~c2_1(W)))) | (c2_1(a1006) | c3_1(a1004) | c1_1(a1001) | (~ndr1_0) | (~c3_1(a1001)) | (~c2_1(a1001)) | (~c2_1(a1004)) | (~c1_1(a1004)) | (~c0_1(a1006)) | (~c3_1(a1006))))),
% 0.96/0.89 inference(monotonicity,[status(thm)],[1381])).
% 0.96/0.89 tff(1383,plain,
% 0.96/0.89 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c1_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c1_1(a1004)) | c3_1(a1004) | (~c2_1(a1004)) | c2_1(a1006) | (~c0_1(a1006)) | (~c3_1(a1006)) | c1_1(a1001) | (~c3_1(a1001)) | (~c2_1(a1001)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c1_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c2_1(a1006) | c3_1(a1004) | c1_1(a1001) | (~ndr1_0) | (~c3_1(a1001)) | (~c2_1(a1001)) | (~c2_1(a1004)) | (~c1_1(a1004)) | (~c0_1(a1006)) | (~c3_1(a1006)))),
% 0.96/0.89 inference(transitivity,[status(thm)],[1382, 1380])).
% 0.96/0.89 tff(1384,plain,
% 0.96/0.89 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c1_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c1_1(a1004)) | c3_1(a1004) | (~c2_1(a1004)) | c2_1(a1006) | (~c0_1(a1006)) | (~c3_1(a1006)) | c1_1(a1001) | (~c3_1(a1001)) | (~c2_1(a1001)))),
% 0.96/0.89 inference(quant_inst,[status(thm)],[])).
% 0.96/0.89 tff(1385,plain,
% 0.96/0.89 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c1_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c2_1(a1006) | c3_1(a1004) | c1_1(a1001) | (~ndr1_0) | (~c3_1(a1001)) | (~c2_1(a1001)) | (~c2_1(a1004)) | (~c1_1(a1004)) | (~c0_1(a1006)) | (~c3_1(a1006))),
% 0.96/0.89 inference(modus_ponens,[status(thm)],[1384, 1383])).
% 0.96/0.89 tff(1386,plain,
% 0.96/0.89 ($false),
% 0.96/0.89 inference(unit_resolution,[status(thm)],[1385, 90, 1004, 1003, 1379, 1378, 926, 925, 1002, 1377, 923, 817])).
% 0.96/0.89 tff(1387,plain,(hskp13 | hskp2), inference(lemma,lemma(discharge,[]))).
% 0.96/0.89 tff(1388,plain,
% 0.96/0.89 (hskp13),
% 0.96/0.89 inference(unit_resolution,[status(thm)],[1387, 616])).
% 0.96/0.89 tff(1389,plain,
% 0.96/0.89 (c3_1(a1023)),
% 0.96/0.89 inference(unit_resolution,[status(thm)],[164, 1388])).
% 0.96/0.89 tff(1390,plain,
% 0.96/0.89 (~c2_1(a1023)),
% 0.96/0.89 inference(unit_resolution,[status(thm)],[177, 1388])).
% 0.96/0.89 tff(1391,plain,
% 0.96/0.89 (~c1_1(a1023)),
% 0.96/0.89 inference(unit_resolution,[status(thm)],[153, 1388])).
% 0.96/0.89 tff(1392,plain,
% 0.96/0.89 (~hskp4),
% 0.96/0.89 inference(unit_resolution,[status(thm)],[874, 679, 616, 644])).
% 0.96/0.89 tff(1393,plain,
% 0.96/0.89 (hskp21),
% 0.96/0.89 inference(unit_resolution,[status(thm)],[889, 1392, 644])).
% 0.96/0.89 tff(1394,plain,
% 0.96/0.89 (~c3_1(a1041)),
% 0.96/0.89 inference(unit_resolution,[status(thm)],[895, 1393])).
% 0.96/0.89 tff(1395,plain,
% 0.96/0.89 (~c0_1(a1041)),
% 0.96/0.89 inference(unit_resolution,[status(thm)],[901, 1393])).
% 0.96/0.89 tff(1396,plain,
% 0.96/0.89 (c2_1(a1041)),
% 0.96/0.89 inference(unit_resolution,[status(thm)],[912, 1393])).
% 0.96/0.89 tff(1397,plain,
% 0.96/0.89 ($false),
% 0.96/0.89 inference(unit_resolution,[status(thm)],[919, 90, 616, 679, 1396, 1395, 1394, 678])).
% 0.96/0.89 tff(1398,plain,(hskp1 | hskp2 | hskp7), inference(lemma,lemma(discharge,[]))).
% 0.96/0.89 tff(1399,plain,
% 0.96/0.89 (hskp1),
% 0.96/0.89 inference(unit_resolution,[status(thm)],[1398, 644, 616])).
% 0.96/0.89 tff(1400,plain,
% 0.96/0.89 (~c1_1(a1001)),
% 0.96/0.89 inference(unit_resolution,[status(thm)],[303, 1399])).
% 0.96/0.89 tff(1401,plain,
% 0.96/0.89 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W))) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W))))),
% 0.96/0.89 inference(bind,[status(th)],[])).
% 0.96/0.89 tff(1402,plain,
% 0.96/0.89 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))),
% 0.96/0.89 inference(quant_intro,[status(thm)],[1401])).
% 0.96/0.89 tff(1403,plain,
% 0.96/0.89 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))),
% 0.96/0.89 inference(rewrite,[status(thm)],[])).
% 0.96/0.89 tff(1404,plain,
% 0.96/0.89 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c0_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c0_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c0_1(V)))), ((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c0_1(V))))), (((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c0_1(V))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c0_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V)))), (((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V))))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c2_1(W))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V))) | (~c2_1(W))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V)) | (~c2_1(W)))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V)) | (~c2_1(W))))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c2_1(W))) | c2_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V)) | (~c2_1(W))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V)) | (~c2_1(W))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V)) | (~c2_1(W)))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c2_1(W))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V)) | (~c2_1(W))))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c2_1(W))) | c2_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V)) | (~c2_1(W))) | c3_1(U)))), rewrite((((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V)) | (~c2_1(W))) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V)) | (~c2_1(W)))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c2_1(W))) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V)) | (~c2_1(W))))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c2_1(W))) | c2_1(U)) | c3_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V)) | (~c2_1(W))) | c1_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V)) | (~c2_1(W))) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | (~c2_1(W)))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c2_1(W))) | c2_1(U)) | c3_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | (~c2_1(W))))), ((((((((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c2_1(W))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | (~c2_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | (~c2_1(W))) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)))), ((((((((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c2_1(W))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c2_1(W))))), (((((((((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c2_1(W))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c0_1(W)) | c3_1(W)) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c2_1(W))) | c3_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c2_1(W))) | c3_1(W)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))), (((((((((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c2_1(W))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c0_1(W)) | c3_1(W)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))))),
% 0.96/0.89 inference(bind,[status(th)],[])).
% 0.96/0.89 tff(1405,plain,
% 0.96/0.89 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c2_1(W))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c0_1(W)) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))),
% 0.96/0.89 inference(quant_intro,[status(thm)],[1404])).
% 0.96/0.89 tff(1406,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c2_1(W))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c0_1(W)) | c3_1(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause186')).
% 0.96/0.89 tff(1407,plain,
% 0.96/0.89 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))),
% 0.96/0.89 inference(modus_ponens,[status(thm)],[1406, 1405])).
% 0.96/0.89 tff(1408,plain,
% 0.96/0.89 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))),
% 0.96/0.89 inference(modus_ponens,[status(thm)],[1407, 1403])).
% 0.96/0.89 tff(1409,plain,(
% 0.96/0.89 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))),
% 0.96/0.89 inference(skolemize,[status(sab)],[1408])).
% 0.96/0.89 tff(1410,plain,
% 0.96/0.89 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))),
% 0.96/0.89 inference(modus_ponens,[status(thm)],[1409, 1402])).
% 0.96/0.89 tff(1411,plain,
% 0.96/0.89 (hskp21),
% 0.96/0.89 inference(unit_resolution,[status(thm)],[889, 1335, 644])).
% 0.96/0.89 tff(1412,plain,
% 0.96/0.89 (~c3_1(a1041)),
% 0.96/0.89 inference(unit_resolution,[status(thm)],[895, 1411])).
% 0.96/0.89 tff(1413,plain,
% 0.96/0.89 (~c0_1(a1041)),
% 0.96/0.89 inference(unit_resolution,[status(thm)],[901, 1411])).
% 0.96/0.89 tff(1414,plain,
% 0.96/0.89 (c2_1(a1001)),
% 0.96/0.89 inference(unit_resolution,[status(thm)],[342, 1399])).
% 0.96/0.89 tff(1415,plain,
% 0.96/0.89 (c2_1(a1041)),
% 0.96/0.89 inference(unit_resolution,[status(thm)],[912, 1411])).
% 0.96/0.89 tff(1416,plain,
% 0.96/0.89 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | (c3_1(a1044) | c0_1(a1041) | c3_1(a1041) | c1_1(a1001) | (~ndr1_0) | (~c0_1(a1001)) | (~c2_1(a1001)) | (~c2_1(a1041)) | c2_1(a1044) | (~c0_1(a1044)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c3_1(a1044) | c0_1(a1041) | c3_1(a1041) | c1_1(a1001) | (~ndr1_0) | (~c0_1(a1001)) | (~c2_1(a1001)) | (~c2_1(a1041)) | c2_1(a1044) | (~c0_1(a1044)))),
% 0.96/0.89 inference(rewrite,[status(thm)],[])).
% 0.96/0.89 tff(1417,plain,
% 0.96/0.89 (((~ndr1_0) | c2_1(a1044) | c3_1(a1044) | (~c0_1(a1044)) | c1_1(a1001) | (~c2_1(a1001)) | (~c0_1(a1001)) | c3_1(a1041) | c0_1(a1041) | (~c2_1(a1041))) <=> (c3_1(a1044) | c0_1(a1041) | c3_1(a1041) | c1_1(a1001) | (~ndr1_0) | (~c0_1(a1001)) | (~c2_1(a1001)) | (~c2_1(a1041)) | c2_1(a1044) | (~c0_1(a1044)))),
% 0.96/0.89 inference(rewrite,[status(thm)],[])).
% 0.96/0.89 tff(1418,plain,
% 0.96/0.89 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a1044) | c3_1(a1044) | (~c0_1(a1044)) | c1_1(a1001) | (~c2_1(a1001)) | (~c0_1(a1001)) | c3_1(a1041) | c0_1(a1041) | (~c2_1(a1041)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | (c3_1(a1044) | c0_1(a1041) | c3_1(a1041) | c1_1(a1001) | (~ndr1_0) | (~c0_1(a1001)) | (~c2_1(a1001)) | (~c2_1(a1041)) | c2_1(a1044) | (~c0_1(a1044))))),
% 0.96/0.89 inference(monotonicity,[status(thm)],[1417])).
% 0.96/0.89 tff(1419,plain,
% 0.96/0.89 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a1044) | c3_1(a1044) | (~c0_1(a1044)) | c1_1(a1001) | (~c2_1(a1001)) | (~c0_1(a1001)) | c3_1(a1041) | c0_1(a1041) | (~c2_1(a1041)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c3_1(a1044) | c0_1(a1041) | c3_1(a1041) | c1_1(a1001) | (~ndr1_0) | (~c0_1(a1001)) | (~c2_1(a1001)) | (~c2_1(a1041)) | c2_1(a1044) | (~c0_1(a1044)))),
% 0.96/0.89 inference(transitivity,[status(thm)],[1418, 1416])).
% 0.96/0.89 tff(1420,plain,
% 0.96/0.89 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a1044) | c3_1(a1044) | (~c0_1(a1044)) | c1_1(a1001) | (~c2_1(a1001)) | (~c0_1(a1001)) | c3_1(a1041) | c0_1(a1041) | (~c2_1(a1041)))),
% 0.96/0.89 inference(quant_inst,[status(thm)],[])).
% 0.96/0.89 tff(1421,plain,
% 0.96/0.89 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c3_1(a1044) | c0_1(a1041) | c3_1(a1041) | c1_1(a1001) | (~ndr1_0) | (~c0_1(a1001)) | (~c2_1(a1001)) | (~c2_1(a1041)) | c2_1(a1044) | (~c0_1(a1044))),
% 0.96/0.89 inference(modus_ponens,[status(thm)],[1420, 1419])).
% 0.96/0.89 tff(1422,plain,
% 0.96/0.89 (~c0_1(a1001)),
% 0.96/0.89 inference(unit_resolution,[status(thm)],[1421, 90, 783, 1415, 1414, 761, 1413, 1412, 1400, 1410, 1022])).
% 0.96/0.89 tff(1423,plain,
% 0.96/0.89 (^[U: $i] : refl((hskp19 | hskp4 | (~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c0_1(U))) <=> (hskp19 | hskp4 | (~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c0_1(U))))),
% 0.96/0.89 inference(bind,[status(th)],[])).
% 0.96/0.89 tff(1424,plain,
% 0.96/0.89 (![U: $i] : (hskp19 | hskp4 | (~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c0_1(U))) <=> ![U: $i] : (hskp19 | hskp4 | (~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c0_1(U)))),
% 0.96/0.89 inference(quant_intro,[status(thm)],[1423])).
% 0.96/0.89 tff(1425,plain,
% 0.96/0.89 (![U: $i] : (hskp19 | hskp4 | (~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c0_1(U))) <=> ![U: $i] : (hskp19 | hskp4 | (~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c0_1(U)))),
% 0.96/0.89 inference(rewrite,[status(thm)],[])).
% 0.96/0.89 tff(1426,plain,
% 0.96/0.89 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | c3_1(U)) <=> ((~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) <=> ((~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp4) <=> (((~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c0_1(U))) | hskp4))), rewrite((((~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c0_1(U))) | hskp4) <=> (hskp4 | (~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c0_1(U)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp4) <=> (hskp4 | (~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c0_1(U))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp4) | hskp19) <=> ((hskp4 | (~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c0_1(U))) | hskp19))), rewrite(((hskp4 | (~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c0_1(U))) | hskp19) <=> (hskp19 | hskp4 | (~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c0_1(U)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp4) | hskp19) <=> (hskp19 | hskp4 | (~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c0_1(U)))))),
% 0.96/0.89 inference(bind,[status(th)],[])).
% 0.96/0.89 tff(1427,plain,
% 0.96/0.89 (![U: $i] : ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp4) | hskp19) <=> ![U: $i] : (hskp19 | hskp4 | (~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c0_1(U)))),
% 0.96/0.89 inference(quant_intro,[status(thm)],[1426])).
% 0.96/0.89 tff(1428,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp4) | hskp19)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause145')).
% 0.96/0.89 tff(1429,plain,
% 0.96/0.89 (![U: $i] : (hskp19 | hskp4 | (~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c0_1(U)))),
% 0.96/0.89 inference(modus_ponens,[status(thm)],[1428, 1427])).
% 0.96/0.89 tff(1430,plain,
% 0.96/0.89 (![U: $i] : (hskp19 | hskp4 | (~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c0_1(U)))),
% 0.96/0.89 inference(modus_ponens,[status(thm)],[1429, 1425])).
% 0.96/0.89 tff(1431,plain,(
% 0.96/0.89 ![U: $i] : (hskp19 | hskp4 | (~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c0_1(U)))),
% 0.96/0.89 inference(skolemize,[status(sab)],[1430])).
% 0.96/0.89 tff(1432,plain,
% 0.96/0.89 (![U: $i] : (hskp19 | hskp4 | (~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c0_1(U)))),
% 0.96/0.89 inference(modus_ponens,[status(thm)],[1431, 1424])).
% 0.96/0.89 tff(1433,plain,
% 0.96/0.89 (((~![U: $i] : (hskp19 | hskp4 | (~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c0_1(U)))) | (hskp19 | hskp4 | c3_1(a1044) | (~ndr1_0) | (~c0_1(a1044)) | (~c1_1(a1044)))) <=> ((~![U: $i] : (hskp19 | hskp4 | (~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c0_1(U)))) | hskp19 | hskp4 | c3_1(a1044) | (~ndr1_0) | (~c0_1(a1044)) | (~c1_1(a1044)))),
% 0.96/0.89 inference(rewrite,[status(thm)],[])).
% 0.96/0.89 tff(1434,plain,
% 0.96/0.89 ((hskp19 | hskp4 | (~ndr1_0) | (~c1_1(a1044)) | c3_1(a1044) | (~c0_1(a1044))) <=> (hskp19 | hskp4 | c3_1(a1044) | (~ndr1_0) | (~c0_1(a1044)) | (~c1_1(a1044)))),
% 0.96/0.89 inference(rewrite,[status(thm)],[])).
% 0.96/0.89 tff(1435,plain,
% 0.96/0.89 (((~![U: $i] : (hskp19 | hskp4 | (~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c0_1(U)))) | (hskp19 | hskp4 | (~ndr1_0) | (~c1_1(a1044)) | c3_1(a1044) | (~c0_1(a1044)))) <=> ((~![U: $i] : (hskp19 | hskp4 | (~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c0_1(U)))) | (hskp19 | hskp4 | c3_1(a1044) | (~ndr1_0) | (~c0_1(a1044)) | (~c1_1(a1044))))),
% 0.96/0.89 inference(monotonicity,[status(thm)],[1434])).
% 0.96/0.89 tff(1436,plain,
% 0.96/0.89 (((~![U: $i] : (hskp19 | hskp4 | (~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c0_1(U)))) | (hskp19 | hskp4 | (~ndr1_0) | (~c1_1(a1044)) | c3_1(a1044) | (~c0_1(a1044)))) <=> ((~![U: $i] : (hskp19 | hskp4 | (~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c0_1(U)))) | hskp19 | hskp4 | c3_1(a1044) | (~ndr1_0) | (~c0_1(a1044)) | (~c1_1(a1044)))),
% 0.96/0.89 inference(transitivity,[status(thm)],[1435, 1433])).
% 0.96/0.89 tff(1437,plain,
% 0.96/0.89 ((~![U: $i] : (hskp19 | hskp4 | (~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c0_1(U)))) | (hskp19 | hskp4 | (~ndr1_0) | (~c1_1(a1044)) | c3_1(a1044) | (~c0_1(a1044)))),
% 0.96/0.89 inference(quant_inst,[status(thm)],[])).
% 0.96/0.89 tff(1438,plain,
% 0.96/0.89 ((~![U: $i] : (hskp19 | hskp4 | (~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c0_1(U)))) | hskp19 | hskp4 | c3_1(a1044) | (~ndr1_0) | (~c0_1(a1044)) | (~c1_1(a1044))),
% 0.96/0.89 inference(modus_ponens,[status(thm)],[1437, 1436])).
% 0.96/0.89 tff(1439,plain,
% 0.96/0.89 (hskp19 | hskp4),
% 0.96/0.89 inference(unit_resolution,[status(thm)],[1438, 90, 783, 772, 761, 1432])).
% 0.96/0.89 tff(1440,plain,
% 0.96/0.89 (hskp19),
% 0.96/0.89 inference(unit_resolution,[status(thm)],[1439, 1335])).
% 0.96/0.89 tff(1441,plain,
% 0.96/0.89 (~c3_1(a1037)),
% 0.96/0.89 inference(unit_resolution,[status(thm)],[140, 1440])).
% 0.96/0.89 tff(1442,plain,
% 0.96/0.89 (~c1_1(a1037)),
% 0.96/0.89 inference(unit_resolution,[status(thm)],[146, 1440])).
% 0.96/0.89 tff(1443,plain,
% 0.96/0.89 (~c0_1(a1037)),
% 0.96/0.89 inference(unit_resolution,[status(thm)],[704, 1440])).
% 0.96/0.89 tff(1444,assumption,(hskp28), introduced(assumption)).
% 0.96/0.89 tff(1445,plain,
% 0.96/0.89 (((~hskp28) | c2_1(a1033)) <=> ((~hskp28) | c2_1(a1033))),
% 0.96/0.89 inference(rewrite,[status(thm)],[])).
% 0.96/0.89 tff(1446,axiom,((~hskp28) | c2_1(a1033)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause45')).
% 0.96/0.89 tff(1447,plain,
% 0.96/0.89 ((~hskp28) | c2_1(a1033)),
% 0.96/0.89 inference(modus_ponens,[status(thm)],[1446, 1445])).
% 0.96/0.89 tff(1448,plain,
% 0.96/0.89 ((~hskp28) | c2_1(a1033)),
% 0.96/0.89 inference(modus_ponens,[status(thm)],[1447, 1445])).
% 0.96/0.89 tff(1449,plain,
% 0.96/0.89 ((~hskp28) | c2_1(a1033)),
% 0.96/0.89 inference(modus_ponens,[status(thm)],[1448, 1445])).
% 0.96/0.89 tff(1450,plain,
% 0.96/0.89 ((~hskp28) | c2_1(a1033)),
% 0.96/0.89 inference(modus_ponens,[status(thm)],[1449, 1445])).
% 0.96/0.89 tff(1451,plain,
% 0.96/0.89 ((~hskp28) | c2_1(a1033)),
% 0.96/0.89 inference(modus_ponens,[status(thm)],[1450, 1445])).
% 0.96/0.89 tff(1452,plain,
% 0.96/0.89 ((~hskp28) | c2_1(a1033)),
% 0.96/0.89 inference(modus_ponens,[status(thm)],[1451, 1445])).
% 0.96/0.89 tff(1453,plain,
% 0.96/0.89 ((~hskp28) | c2_1(a1033)),
% 0.96/0.89 inference(modus_ponens,[status(thm)],[1452, 1445])).
% 0.96/0.89 tff(1454,plain,
% 0.96/0.89 ((~hskp28) | c2_1(a1033)),
% 0.96/0.89 inference(modus_ponens,[status(thm)],[1453, 1445])).
% 0.96/0.89 tff(1455,plain,
% 0.96/0.89 (c2_1(a1033)),
% 0.96/0.89 inference(unit_resolution,[status(thm)],[1454, 1444])).
% 0.96/0.89 tff(1456,plain,
% 0.96/0.89 (((~hskp28) | c1_1(a1033)) <=> ((~hskp28) | c1_1(a1033))),
% 0.96/0.89 inference(rewrite,[status(thm)],[])).
% 0.96/0.89 tff(1457,axiom,((~hskp28) | c1_1(a1033)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause44')).
% 0.96/0.89 tff(1458,plain,
% 0.96/0.89 ((~hskp28) | c1_1(a1033)),
% 0.96/0.89 inference(modus_ponens,[status(thm)],[1457, 1456])).
% 0.96/0.89 tff(1459,plain,
% 0.96/0.89 ((~hskp28) | c1_1(a1033)),
% 0.96/0.89 inference(modus_ponens,[status(thm)],[1458, 1456])).
% 0.96/0.89 tff(1460,plain,
% 0.96/0.89 ((~hskp28) | c1_1(a1033)),
% 0.96/0.89 inference(modus_ponens,[status(thm)],[1459, 1456])).
% 0.96/0.89 tff(1461,plain,
% 0.96/0.89 ((~hskp28) | c1_1(a1033)),
% 0.96/0.89 inference(modus_ponens,[status(thm)],[1460, 1456])).
% 0.96/0.89 tff(1462,plain,
% 0.96/0.89 ((~hskp28) | c1_1(a1033)),
% 0.96/0.89 inference(modus_ponens,[status(thm)],[1461, 1456])).
% 0.96/0.89 tff(1463,plain,
% 0.96/0.89 ((~hskp28) | c1_1(a1033)),
% 0.96/0.89 inference(modus_ponens,[status(thm)],[1462, 1456])).
% 0.96/0.89 tff(1464,plain,
% 0.96/0.89 ((~hskp28) | c1_1(a1033)),
% 0.96/0.89 inference(modus_ponens,[status(thm)],[1463, 1456])).
% 0.96/0.89 tff(1465,plain,
% 0.96/0.89 ((~hskp28) | c1_1(a1033)),
% 0.96/0.89 inference(modus_ponens,[status(thm)],[1464, 1456])).
% 0.96/0.89 tff(1466,plain,
% 0.96/0.89 (c1_1(a1033)),
% 0.96/0.89 inference(unit_resolution,[status(thm)],[1465, 1444])).
% 0.96/0.89 tff(1467,plain,
% 0.96/0.89 (((~hskp28) | c0_1(a1033)) <=> ((~hskp28) | c0_1(a1033))),
% 0.96/0.89 inference(rewrite,[status(thm)],[])).
% 0.96/0.89 tff(1468,axiom,((~hskp28) | c0_1(a1033)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause43')).
% 0.96/0.89 tff(1469,plain,
% 0.96/0.89 ((~hskp28) | c0_1(a1033)),
% 0.96/0.89 inference(modus_ponens,[status(thm)],[1468, 1467])).
% 0.96/0.89 tff(1470,plain,
% 0.96/0.89 ((~hskp28) | c0_1(a1033)),
% 0.96/0.89 inference(modus_ponens,[status(thm)],[1469, 1467])).
% 0.96/0.89 tff(1471,plain,
% 0.96/0.89 ((~hskp28) | c0_1(a1033)),
% 0.96/0.89 inference(modus_ponens,[status(thm)],[1470, 1467])).
% 0.96/0.89 tff(1472,plain,
% 0.96/0.89 ((~hskp28) | c0_1(a1033)),
% 0.96/0.89 inference(modus_ponens,[status(thm)],[1471, 1467])).
% 0.96/0.89 tff(1473,plain,
% 0.96/0.89 ((~hskp28) | c0_1(a1033)),
% 0.96/0.89 inference(modus_ponens,[status(thm)],[1472, 1467])).
% 0.96/0.89 tff(1474,plain,
% 0.96/0.89 ((~hskp28) | c0_1(a1033)),
% 0.96/0.89 inference(modus_ponens,[status(thm)],[1473, 1467])).
% 0.96/0.89 tff(1475,plain,
% 0.96/0.89 ((~hskp28) | c0_1(a1033)),
% 0.96/0.89 inference(modus_ponens,[status(thm)],[1474, 1467])).
% 0.96/0.89 tff(1476,plain,
% 0.96/0.89 ((~hskp28) | c0_1(a1033)),
% 0.96/0.89 inference(modus_ponens,[status(thm)],[1475, 1467])).
% 0.96/0.89 tff(1477,plain,
% 0.96/0.89 (c0_1(a1033)),
% 0.96/0.89 inference(unit_resolution,[status(thm)],[1476, 1444])).
% 0.96/0.89 tff(1478,plain,
% 0.96/0.89 (((~![U: $i] : (hskp7 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)))) | (hskp7 | (~ndr1_0) | (~c2_1(a1033)) | (~c0_1(a1033)) | (~c1_1(a1033)))) <=> ((~![U: $i] : (hskp7 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)))) | hskp7 | (~ndr1_0) | (~c2_1(a1033)) | (~c0_1(a1033)) | (~c1_1(a1033)))),
% 0.96/0.89 inference(rewrite,[status(thm)],[])).
% 0.96/0.89 tff(1479,plain,
% 0.96/0.89 ((hskp7 | (~ndr1_0) | (~c1_1(a1033)) | (~c2_1(a1033)) | (~c0_1(a1033))) <=> (hskp7 | (~ndr1_0) | (~c2_1(a1033)) | (~c0_1(a1033)) | (~c1_1(a1033)))),
% 0.96/0.89 inference(rewrite,[status(thm)],[])).
% 0.96/0.89 tff(1480,plain,
% 0.96/0.89 (((~![U: $i] : (hskp7 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)))) | (hskp7 | (~ndr1_0) | (~c1_1(a1033)) | (~c2_1(a1033)) | (~c0_1(a1033)))) <=> ((~![U: $i] : (hskp7 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)))) | (hskp7 | (~ndr1_0) | (~c2_1(a1033)) | (~c0_1(a1033)) | (~c1_1(a1033))))),
% 0.96/0.89 inference(monotonicity,[status(thm)],[1479])).
% 0.96/0.89 tff(1481,plain,
% 0.96/0.89 (((~![U: $i] : (hskp7 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)))) | (hskp7 | (~ndr1_0) | (~c1_1(a1033)) | (~c2_1(a1033)) | (~c0_1(a1033)))) <=> ((~![U: $i] : (hskp7 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)))) | hskp7 | (~ndr1_0) | (~c2_1(a1033)) | (~c0_1(a1033)) | (~c1_1(a1033)))),
% 0.96/0.89 inference(transitivity,[status(thm)],[1480, 1478])).
% 0.96/0.89 tff(1482,plain,
% 0.96/0.89 ((~![U: $i] : (hskp7 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)))) | (hskp7 | (~ndr1_0) | (~c1_1(a1033)) | (~c2_1(a1033)) | (~c0_1(a1033)))),
% 0.96/0.89 inference(quant_inst,[status(thm)],[])).
% 0.96/0.89 tff(1483,plain,
% 0.96/0.89 ((~![U: $i] : (hskp7 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)))) | hskp7 | (~ndr1_0) | (~c2_1(a1033)) | (~c0_1(a1033)) | (~c1_1(a1033))),
% 0.96/0.89 inference(modus_ponens,[status(thm)],[1482, 1481])).
% 0.96/0.90 tff(1484,plain,
% 0.96/0.90 ($false),
% 0.96/0.90 inference(unit_resolution,[status(thm)],[1483, 90, 644, 1477, 1466, 1455, 188])).
% 0.96/0.90 tff(1485,plain,((~hskp28) | hskp7), inference(lemma,lemma(discharge,[]))).
% 0.96/0.90 tff(1486,plain,
% 0.96/0.90 (~hskp28),
% 0.96/0.90 inference(unit_resolution,[status(thm)],[1485, 644])).
% 0.96/0.90 tff(1487,plain,
% 0.96/0.90 (^[U: $i] : refl((hskp28 | hskp8 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U))) <=> (hskp28 | hskp8 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U))))),
% 0.96/0.90 inference(bind,[status(th)],[])).
% 0.96/0.90 tff(1488,plain,
% 0.96/0.90 (![U: $i] : (hskp28 | hskp8 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U))) <=> ![U: $i] : (hskp28 | hskp8 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))),
% 0.96/0.90 inference(quant_intro,[status(thm)],[1487])).
% 0.96/0.90 tff(1489,plain,
% 0.96/0.90 (![U: $i] : (hskp28 | hskp8 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U))) <=> ![U: $i] : (hskp28 | hskp8 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))),
% 0.96/0.90 inference(rewrite,[status(thm)],[])).
% 0.96/0.90 tff(1490,plain,
% 0.96/0.90 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c3_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)))), ((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) <=> (((~ndr1_0) | (~c3_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)))), ((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U))))), (((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))), (((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U))))), ((((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp28) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U))) | hskp28))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U))) | hskp28) <=> (hskp28 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))), ((((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp28) <=> (hskp28 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U))))), (((((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp28) | hskp8) <=> ((hskp28 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U))) | hskp8))), rewrite(((hskp28 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U))) | hskp8) <=> (hskp28 | hskp8 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))), (((((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp28) | hskp8) <=> (hskp28 | hskp8 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))))),
% 0.96/0.90 inference(bind,[status(th)],[])).
% 0.96/0.90 tff(1491,plain,
% 0.96/0.90 (![U: $i] : ((((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp28) | hskp8) <=> ![U: $i] : (hskp28 | hskp8 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))),
% 0.96/0.90 inference(quant_intro,[status(thm)],[1490])).
% 0.96/0.90 tff(1492,axiom,(![U: $i] : ((((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp28) | hskp8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause135')).
% 0.96/0.90 tff(1493,plain,
% 0.96/0.90 (![U: $i] : (hskp28 | hskp8 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))),
% 0.96/0.90 inference(modus_ponens,[status(thm)],[1492, 1491])).
% 0.96/0.90 tff(1494,plain,
% 0.96/0.90 (![U: $i] : (hskp28 | hskp8 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))),
% 0.96/0.90 inference(modus_ponens,[status(thm)],[1493, 1489])).
% 0.96/0.90 tff(1495,plain,(
% 0.96/0.90 ![U: $i] : (hskp28 | hskp8 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))),
% 0.96/0.90 inference(skolemize,[status(sab)],[1494])).
% 0.96/0.90 tff(1496,plain,
% 0.96/0.90 (![U: $i] : (hskp28 | hskp8 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))),
% 0.96/0.90 inference(modus_ponens,[status(thm)],[1495, 1488])).
% 0.96/0.90 tff(1497,plain,
% 0.96/0.90 (((~![U: $i] : (hskp28 | hskp8 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | (hskp28 | hskp8 | c1_1(a1023) | c2_1(a1023) | (~ndr1_0) | (~c3_1(a1023)))) <=> ((~![U: $i] : (hskp28 | hskp8 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | hskp28 | hskp8 | c1_1(a1023) | c2_1(a1023) | (~ndr1_0) | (~c3_1(a1023)))),
% 0.96/0.90 inference(rewrite,[status(thm)],[])).
% 0.96/0.90 tff(1498,plain,
% 0.96/0.90 ((hskp28 | hskp8 | (~ndr1_0) | c2_1(a1023) | c1_1(a1023) | (~c3_1(a1023))) <=> (hskp28 | hskp8 | c1_1(a1023) | c2_1(a1023) | (~ndr1_0) | (~c3_1(a1023)))),
% 0.96/0.90 inference(rewrite,[status(thm)],[])).
% 0.96/0.90 tff(1499,plain,
% 0.96/0.90 (((~![U: $i] : (hskp28 | hskp8 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | (hskp28 | hskp8 | (~ndr1_0) | c2_1(a1023) | c1_1(a1023) | (~c3_1(a1023)))) <=> ((~![U: $i] : (hskp28 | hskp8 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | (hskp28 | hskp8 | c1_1(a1023) | c2_1(a1023) | (~ndr1_0) | (~c3_1(a1023))))),
% 0.96/0.90 inference(monotonicity,[status(thm)],[1498])).
% 0.96/0.90 tff(1500,plain,
% 0.96/0.90 (((~![U: $i] : (hskp28 | hskp8 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | (hskp28 | hskp8 | (~ndr1_0) | c2_1(a1023) | c1_1(a1023) | (~c3_1(a1023)))) <=> ((~![U: $i] : (hskp28 | hskp8 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | hskp28 | hskp8 | c1_1(a1023) | c2_1(a1023) | (~ndr1_0) | (~c3_1(a1023)))),
% 0.96/0.90 inference(transitivity,[status(thm)],[1499, 1497])).
% 0.96/0.90 tff(1501,plain,
% 0.96/0.90 ((~![U: $i] : (hskp28 | hskp8 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | (hskp28 | hskp8 | (~ndr1_0) | c2_1(a1023) | c1_1(a1023) | (~c3_1(a1023)))),
% 0.96/0.90 inference(quant_inst,[status(thm)],[])).
% 0.96/0.90 tff(1502,plain,
% 0.96/0.90 ((~![U: $i] : (hskp28 | hskp8 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | hskp28 | hskp8 | c1_1(a1023) | c2_1(a1023) | (~ndr1_0) | (~c3_1(a1023))),
% 0.96/0.90 inference(modus_ponens,[status(thm)],[1501, 1500])).
% 0.96/0.90 tff(1503,plain,
% 0.96/0.90 (hskp28 | hskp8),
% 0.96/0.90 inference(unit_resolution,[status(thm)],[1502, 90, 1389, 1391, 1390, 1496])).
% 0.96/0.90 tff(1504,plain,
% 0.96/0.90 (hskp8),
% 0.96/0.90 inference(unit_resolution,[status(thm)],[1503, 1486])).
% 0.96/0.90 tff(1505,plain,
% 0.96/0.90 (~c1_1(a1010)),
% 0.96/0.90 inference(unit_resolution,[status(thm)],[545, 1504])).
% 0.96/0.90 tff(1506,plain,
% 0.96/0.90 (c3_1(a1010)),
% 0.96/0.90 inference(unit_resolution,[status(thm)],[556, 1504])).
% 0.96/0.90 tff(1507,plain,
% 0.96/0.90 (c0_1(a1010)),
% 0.96/0.90 inference(unit_resolution,[status(thm)],[567, 1504])).
% 0.96/0.90 tff(1508,plain,
% 0.96/0.90 (hskp22),
% 0.96/0.90 inference(unit_resolution,[status(thm)],[1263, 90, 772, 1507, 1506, 761, 1505, 1257, 1022])).
% 0.96/0.90 tff(1509,plain,
% 0.96/0.90 (~c2_1(a1043)),
% 0.96/0.90 inference(unit_resolution,[status(thm)],[1269, 1508])).
% 0.96/0.90 tff(1510,plain,
% 0.96/0.90 (~c1_1(a1043)),
% 0.96/0.90 inference(unit_resolution,[status(thm)],[1275, 1508])).
% 0.96/0.90 tff(1511,plain,
% 0.96/0.90 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | c1_1(a1043) | c2_1(a1043) | c0_1(a1037) | c1_1(a1037) | c3_1(a1037) | (~ndr1_0) | c3_1(a1043))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp2 | c1_1(a1043) | c2_1(a1043) | c0_1(a1037) | c1_1(a1037) | c3_1(a1037) | (~ndr1_0) | c3_1(a1043))),
% 0.96/0.90 inference(rewrite,[status(thm)],[])).
% 0.96/0.90 tff(1512,plain,
% 0.96/0.90 ((hskp2 | (~ndr1_0) | c2_1(a1043) | c1_1(a1043) | c3_1(a1043) | c3_1(a1037) | c1_1(a1037) | c0_1(a1037)) <=> (hskp2 | c1_1(a1043) | c2_1(a1043) | c0_1(a1037) | c1_1(a1037) | c3_1(a1037) | (~ndr1_0) | c3_1(a1043))),
% 0.96/0.90 inference(rewrite,[status(thm)],[])).
% 0.96/0.90 tff(1513,plain,
% 0.96/0.90 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | (~ndr1_0) | c2_1(a1043) | c1_1(a1043) | c3_1(a1043) | c3_1(a1037) | c1_1(a1037) | c0_1(a1037))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | c1_1(a1043) | c2_1(a1043) | c0_1(a1037) | c1_1(a1037) | c3_1(a1037) | (~ndr1_0) | c3_1(a1043)))),
% 0.96/0.90 inference(monotonicity,[status(thm)],[1512])).
% 0.96/0.90 tff(1514,plain,
% 0.96/0.90 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | (~ndr1_0) | c2_1(a1043) | c1_1(a1043) | c3_1(a1043) | c3_1(a1037) | c1_1(a1037) | c0_1(a1037))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp2 | c1_1(a1043) | c2_1(a1043) | c0_1(a1037) | c1_1(a1037) | c3_1(a1037) | (~ndr1_0) | c3_1(a1043))),
% 0.96/0.90 inference(transitivity,[status(thm)],[1513, 1511])).
% 0.96/0.90 tff(1515,plain,
% 0.96/0.90 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | (~ndr1_0) | c2_1(a1043) | c1_1(a1043) | c3_1(a1043) | c3_1(a1037) | c1_1(a1037) | c0_1(a1037))),
% 0.96/0.90 inference(quant_inst,[status(thm)],[])).
% 0.96/0.90 tff(1516,plain,
% 0.96/0.90 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp2 | c1_1(a1043) | c2_1(a1043) | c0_1(a1037) | c1_1(a1037) | c3_1(a1037) | (~ndr1_0) | c3_1(a1043)),
% 0.96/0.90 inference(modus_ponens,[status(thm)],[1515, 1514])).
% 0.96/0.90 tff(1517,plain,
% 0.96/0.90 (c3_1(a1043)),
% 0.96/0.90 inference(unit_resolution,[status(thm)],[1516, 90, 616, 1510, 1509, 1443, 1442, 1441, 596])).
% 0.96/0.90 tff(1518,plain,
% 0.96/0.90 (c0_1(a1043)),
% 0.96/0.90 inference(unit_resolution,[status(thm)],[1294, 1508])).
% 0.96/0.90 tff(1519,plain,
% 0.96/0.90 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp4 | c2_1(a1043) | c1_1(a1001) | (~ndr1_0) | c0_1(a1001) | (~c2_1(a1001)) | (~c0_1(a1043)) | (~c3_1(a1043)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp4 | c2_1(a1043) | c1_1(a1001) | (~ndr1_0) | c0_1(a1001) | (~c2_1(a1001)) | (~c0_1(a1043)) | (~c3_1(a1043)))),
% 0.96/0.90 inference(rewrite,[status(thm)],[])).
% 0.96/0.90 tff(1520,plain,
% 0.96/0.90 ((hskp4 | (~ndr1_0) | c2_1(a1043) | (~c3_1(a1043)) | (~c0_1(a1043)) | c1_1(a1001) | c0_1(a1001) | (~c2_1(a1001))) <=> (hskp4 | c2_1(a1043) | c1_1(a1001) | (~ndr1_0) | c0_1(a1001) | (~c2_1(a1001)) | (~c0_1(a1043)) | (~c3_1(a1043)))),
% 0.96/0.90 inference(rewrite,[status(thm)],[])).
% 0.96/0.90 tff(1521,plain,
% 0.96/0.90 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp4 | (~ndr1_0) | c2_1(a1043) | (~c3_1(a1043)) | (~c0_1(a1043)) | c1_1(a1001) | c0_1(a1001) | (~c2_1(a1001)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp4 | c2_1(a1043) | c1_1(a1001) | (~ndr1_0) | c0_1(a1001) | (~c2_1(a1001)) | (~c0_1(a1043)) | (~c3_1(a1043))))),
% 0.96/0.90 inference(monotonicity,[status(thm)],[1520])).
% 0.96/0.90 tff(1522,plain,
% 0.96/0.90 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp4 | (~ndr1_0) | c2_1(a1043) | (~c3_1(a1043)) | (~c0_1(a1043)) | c1_1(a1001) | c0_1(a1001) | (~c2_1(a1001)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp4 | c2_1(a1043) | c1_1(a1001) | (~ndr1_0) | c0_1(a1001) | (~c2_1(a1001)) | (~c0_1(a1043)) | (~c3_1(a1043)))),
% 0.96/0.90 inference(transitivity,[status(thm)],[1521, 1519])).
% 0.96/0.90 tff(1523,plain,
% 0.96/0.90 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp4 | (~ndr1_0) | c2_1(a1043) | (~c3_1(a1043)) | (~c0_1(a1043)) | c1_1(a1001) | c0_1(a1001) | (~c2_1(a1001)))),
% 0.96/0.90 inference(quant_inst,[status(thm)],[])).
% 0.96/0.90 tff(1524,plain,
% 0.96/0.90 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp4 | c2_1(a1043) | c1_1(a1001) | (~ndr1_0) | c0_1(a1001) | (~c2_1(a1001)) | (~c0_1(a1043)) | (~c3_1(a1043))),
% 0.96/0.90 inference(modus_ponens,[status(thm)],[1523, 1522])).
% 0.96/0.90 tff(1525,plain,
% 0.96/0.90 (hskp4 | c0_1(a1001) | (~c3_1(a1043))),
% 0.96/0.90 inference(unit_resolution,[status(thm)],[1524, 90, 1518, 1414, 1509, 1400, 1345])).
% 0.96/0.90 tff(1526,plain,
% 0.96/0.90 ($false),
% 0.96/0.90 inference(unit_resolution,[status(thm)],[1525, 1517, 1422, 1335])).
% 0.96/0.90 tff(1527,plain,(hskp4 | hskp2 | hskp7), inference(lemma,lemma(discharge,[]))).
% 0.96/0.90 tff(1528,plain,
% 0.96/0.90 (hskp4),
% 0.96/0.90 inference(unit_resolution,[status(thm)],[1527, 644, 616])).
% 0.96/0.90 tff(1529,plain,
% 0.96/0.90 (~c3_1(a1004)),
% 0.96/0.90 inference(unit_resolution,[status(thm)],[865, 1528])).
% 0.96/0.90 tff(1530,plain,
% 0.96/0.90 (c3_1(a1001)),
% 0.96/0.90 inference(unit_resolution,[status(thm)],[314, 1399])).
% 0.96/0.90 tff(1531,plain,
% 0.96/0.90 (c2_1(a1004)),
% 0.96/0.90 inference(unit_resolution,[status(thm)],[841, 1528])).
% 0.96/0.90 tff(1532,plain,
% 0.96/0.90 (c1_1(a1004)),
% 0.96/0.90 inference(unit_resolution,[status(thm)],[852, 1528])).
% 0.96/0.90 tff(1533,plain,
% 0.96/0.90 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c1_1(W) | (~c3_1(W)) | (~c2_1(W)))) | (c2_1(a1023) | c3_1(a1004) | c1_1(a1001) | (~ndr1_0) | (~c3_1(a1001)) | (~c2_1(a1001)) | (~c2_1(a1004)) | (~c1_1(a1004)) | (~c0_1(a1023)) | (~c3_1(a1023)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c1_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c2_1(a1023) | c3_1(a1004) | c1_1(a1001) | (~ndr1_0) | (~c3_1(a1001)) | (~c2_1(a1001)) | (~c2_1(a1004)) | (~c1_1(a1004)) | (~c0_1(a1023)) | (~c3_1(a1023)))),
% 0.96/0.90 inference(rewrite,[status(thm)],[])).
% 0.96/0.90 tff(1534,plain,
% 0.96/0.90 (((~ndr1_0) | (~c1_1(a1004)) | c3_1(a1004) | (~c2_1(a1004)) | c2_1(a1023) | (~c0_1(a1023)) | (~c3_1(a1023)) | c1_1(a1001) | (~c3_1(a1001)) | (~c2_1(a1001))) <=> (c2_1(a1023) | c3_1(a1004) | c1_1(a1001) | (~ndr1_0) | (~c3_1(a1001)) | (~c2_1(a1001)) | (~c2_1(a1004)) | (~c1_1(a1004)) | (~c0_1(a1023)) | (~c3_1(a1023)))),
% 0.96/0.90 inference(rewrite,[status(thm)],[])).
% 0.96/0.90 tff(1535,plain,
% 0.96/0.90 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c1_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c1_1(a1004)) | c3_1(a1004) | (~c2_1(a1004)) | c2_1(a1023) | (~c0_1(a1023)) | (~c3_1(a1023)) | c1_1(a1001) | (~c3_1(a1001)) | (~c2_1(a1001)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c1_1(W) | (~c3_1(W)) | (~c2_1(W)))) | (c2_1(a1023) | c3_1(a1004) | c1_1(a1001) | (~ndr1_0) | (~c3_1(a1001)) | (~c2_1(a1001)) | (~c2_1(a1004)) | (~c1_1(a1004)) | (~c0_1(a1023)) | (~c3_1(a1023))))),
% 0.96/0.90 inference(monotonicity,[status(thm)],[1534])).
% 0.96/0.90 tff(1536,plain,
% 0.96/0.90 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c1_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c1_1(a1004)) | c3_1(a1004) | (~c2_1(a1004)) | c2_1(a1023) | (~c0_1(a1023)) | (~c3_1(a1023)) | c1_1(a1001) | (~c3_1(a1001)) | (~c2_1(a1001)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c1_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c2_1(a1023) | c3_1(a1004) | c1_1(a1001) | (~ndr1_0) | (~c3_1(a1001)) | (~c2_1(a1001)) | (~c2_1(a1004)) | (~c1_1(a1004)) | (~c0_1(a1023)) | (~c3_1(a1023)))),
% 0.96/0.90 inference(transitivity,[status(thm)],[1535, 1533])).
% 0.96/0.90 tff(1537,plain,
% 0.96/0.90 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c1_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c1_1(a1004)) | c3_1(a1004) | (~c2_1(a1004)) | c2_1(a1023) | (~c0_1(a1023)) | (~c3_1(a1023)) | c1_1(a1001) | (~c3_1(a1001)) | (~c2_1(a1001)))),
% 0.96/0.90 inference(quant_inst,[status(thm)],[])).
% 0.96/0.90 tff(1538,plain,
% 0.96/0.90 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c1_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c2_1(a1023) | c3_1(a1004) | c1_1(a1001) | (~ndr1_0) | (~c3_1(a1001)) | (~c2_1(a1001)) | (~c2_1(a1004)) | (~c1_1(a1004)) | (~c0_1(a1023)) | (~c3_1(a1023))),
% 0.96/0.90 inference(modus_ponens,[status(thm)],[1537, 1536])).
% 0.96/0.90 tff(1539,plain,
% 0.96/0.90 (~c0_1(a1023)),
% 0.96/0.90 inference(unit_resolution,[status(thm)],[1538, 90, 1389, 1532, 1531, 1414, 1530, 1390, 1529, 1400, 817])).
% 0.96/0.90 tff(1540,plain,
% 0.96/0.90 (~c0_1(a1004)),
% 0.96/0.90 inference(unit_resolution,[status(thm)],[859, 90, 644, 1532, 1531, 188])).
% 0.96/0.90 tff(1541,plain,
% 0.96/0.90 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c1_1(W) | (~c3_1(W)) | (~c2_1(W)))) | (c2_1(a1043) | c3_1(a1004) | c1_1(a1001) | (~ndr1_0) | (~c3_1(a1001)) | (~c2_1(a1001)) | (~c2_1(a1004)) | (~c1_1(a1004)) | (~c0_1(a1043)) | (~c3_1(a1043)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c1_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c2_1(a1043) | c3_1(a1004) | c1_1(a1001) | (~ndr1_0) | (~c3_1(a1001)) | (~c2_1(a1001)) | (~c2_1(a1004)) | (~c1_1(a1004)) | (~c0_1(a1043)) | (~c3_1(a1043)))),
% 0.96/0.90 inference(rewrite,[status(thm)],[])).
% 0.96/0.90 tff(1542,plain,
% 0.96/0.90 (((~ndr1_0) | (~c1_1(a1004)) | c3_1(a1004) | (~c2_1(a1004)) | c2_1(a1043) | (~c0_1(a1043)) | (~c3_1(a1043)) | c1_1(a1001) | (~c3_1(a1001)) | (~c2_1(a1001))) <=> (c2_1(a1043) | c3_1(a1004) | c1_1(a1001) | (~ndr1_0) | (~c3_1(a1001)) | (~c2_1(a1001)) | (~c2_1(a1004)) | (~c1_1(a1004)) | (~c0_1(a1043)) | (~c3_1(a1043)))),
% 0.96/0.90 inference(rewrite,[status(thm)],[])).
% 0.96/0.90 tff(1543,plain,
% 0.96/0.90 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c1_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c1_1(a1004)) | c3_1(a1004) | (~c2_1(a1004)) | c2_1(a1043) | (~c0_1(a1043)) | (~c3_1(a1043)) | c1_1(a1001) | (~c3_1(a1001)) | (~c2_1(a1001)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c1_1(W) | (~c3_1(W)) | (~c2_1(W)))) | (c2_1(a1043) | c3_1(a1004) | c1_1(a1001) | (~ndr1_0) | (~c3_1(a1001)) | (~c2_1(a1001)) | (~c2_1(a1004)) | (~c1_1(a1004)) | (~c0_1(a1043)) | (~c3_1(a1043))))),
% 0.96/0.90 inference(monotonicity,[status(thm)],[1542])).
% 0.96/0.90 tff(1544,plain,
% 0.96/0.90 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c1_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c1_1(a1004)) | c3_1(a1004) | (~c2_1(a1004)) | c2_1(a1043) | (~c0_1(a1043)) | (~c3_1(a1043)) | c1_1(a1001) | (~c3_1(a1001)) | (~c2_1(a1001)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c1_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c2_1(a1043) | c3_1(a1004) | c1_1(a1001) | (~ndr1_0) | (~c3_1(a1001)) | (~c2_1(a1001)) | (~c2_1(a1004)) | (~c1_1(a1004)) | (~c0_1(a1043)) | (~c3_1(a1043)))),
% 0.96/0.90 inference(transitivity,[status(thm)],[1543, 1541])).
% 0.96/0.90 tff(1545,plain,
% 0.96/0.90 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c1_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c1_1(a1004)) | c3_1(a1004) | (~c2_1(a1004)) | c2_1(a1043) | (~c0_1(a1043)) | (~c3_1(a1043)) | c1_1(a1001) | (~c3_1(a1001)) | (~c2_1(a1001)))),
% 0.96/0.90 inference(quant_inst,[status(thm)],[])).
% 0.96/0.90 tff(1546,plain,
% 0.96/0.90 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c1_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c2_1(a1043) | c3_1(a1004) | c1_1(a1001) | (~ndr1_0) | (~c3_1(a1001)) | (~c2_1(a1001)) | (~c2_1(a1004)) | (~c1_1(a1004)) | (~c0_1(a1043)) | (~c3_1(a1043))),
% 0.96/0.90 inference(modus_ponens,[status(thm)],[1545, 1544])).
% 0.96/0.90 tff(1547,plain,
% 0.96/0.90 (~c3_1(a1043)),
% 0.96/0.90 inference(unit_resolution,[status(thm)],[1546, 90, 1518, 1532, 1531, 1414, 1530, 1509, 1529, 1400, 817])).
% 0.96/0.90 tff(1548,plain,
% 0.96/0.90 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | (c2_1(a1043) | c3_1(a1004) | c1_1(a1001) | (~ndr1_0) | (~c0_1(a1001)) | (~c2_1(a1001)) | (~c2_1(a1004)) | c0_1(a1004) | (~c0_1(a1043)) | c3_1(a1043))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c2_1(a1043) | c3_1(a1004) | c1_1(a1001) | (~ndr1_0) | (~c0_1(a1001)) | (~c2_1(a1001)) | (~c2_1(a1004)) | c0_1(a1004) | (~c0_1(a1043)) | c3_1(a1043))),
% 0.96/0.90 inference(rewrite,[status(thm)],[])).
% 0.96/0.90 tff(1549,plain,
% 0.96/0.90 (((~ndr1_0) | c2_1(a1043) | c3_1(a1043) | (~c0_1(a1043)) | c1_1(a1001) | (~c2_1(a1001)) | (~c0_1(a1001)) | c3_1(a1004) | c0_1(a1004) | (~c2_1(a1004))) <=> (c2_1(a1043) | c3_1(a1004) | c1_1(a1001) | (~ndr1_0) | (~c0_1(a1001)) | (~c2_1(a1001)) | (~c2_1(a1004)) | c0_1(a1004) | (~c0_1(a1043)) | c3_1(a1043))),
% 0.96/0.90 inference(rewrite,[status(thm)],[])).
% 0.96/0.90 tff(1550,plain,
% 0.96/0.90 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a1043) | c3_1(a1043) | (~c0_1(a1043)) | c1_1(a1001) | (~c2_1(a1001)) | (~c0_1(a1001)) | c3_1(a1004) | c0_1(a1004) | (~c2_1(a1004)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | (c2_1(a1043) | c3_1(a1004) | c1_1(a1001) | (~ndr1_0) | (~c0_1(a1001)) | (~c2_1(a1001)) | (~c2_1(a1004)) | c0_1(a1004) | (~c0_1(a1043)) | c3_1(a1043)))),
% 0.96/0.90 inference(monotonicity,[status(thm)],[1549])).
% 0.96/0.90 tff(1551,plain,
% 0.96/0.90 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a1043) | c3_1(a1043) | (~c0_1(a1043)) | c1_1(a1001) | (~c2_1(a1001)) | (~c0_1(a1001)) | c3_1(a1004) | c0_1(a1004) | (~c2_1(a1004)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c2_1(a1043) | c3_1(a1004) | c1_1(a1001) | (~ndr1_0) | (~c0_1(a1001)) | (~c2_1(a1001)) | (~c2_1(a1004)) | c0_1(a1004) | (~c0_1(a1043)) | c3_1(a1043))),
% 0.96/0.90 inference(transitivity,[status(thm)],[1550, 1548])).
% 0.96/0.90 tff(1552,plain,
% 0.96/0.90 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a1043) | c3_1(a1043) | (~c0_1(a1043)) | c1_1(a1001) | (~c2_1(a1001)) | (~c0_1(a1001)) | c3_1(a1004) | c0_1(a1004) | (~c2_1(a1004)))),
% 0.96/0.90 inference(quant_inst,[status(thm)],[])).
% 0.96/0.90 tff(1553,plain,
% 0.96/0.90 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c2_1(a1043) | c3_1(a1004) | c1_1(a1001) | (~ndr1_0) | (~c0_1(a1001)) | (~c2_1(a1001)) | (~c2_1(a1004)) | c0_1(a1004) | (~c0_1(a1043)) | c3_1(a1043)),
% 0.96/0.90 inference(modus_ponens,[status(thm)],[1552, 1551])).
% 0.96/0.90 tff(1554,plain,
% 0.96/0.90 (~c0_1(a1001)),
% 0.96/0.90 inference(unit_resolution,[status(thm)],[1553, 90, 1518, 1531, 1414, 1509, 1529, 1400, 1410, 1547, 1540])).
% 0.96/0.90 tff(1555,plain,
% 0.96/0.90 (c0_1(a1001) | c0_1(a1023)),
% 0.96/0.90 inference(unit_resolution,[status(thm)],[349, 90, 1389, 1414, 1391, 1390, 1400, 332])).
% 0.96/0.90 tff(1556,plain,
% 0.96/0.90 ($false),
% 0.96/0.90 inference(unit_resolution,[status(thm)],[1555, 1554, 1539])).
% 0.96/0.90 tff(1557,plain,(hskp7 | hskp2), inference(lemma,lemma(discharge,[]))).
% 0.96/0.90 tff(1558,plain,
% 0.96/0.90 (hskp7),
% 0.96/0.90 inference(unit_resolution,[status(thm)],[1557, 616])).
% 0.96/0.90 tff(1559,plain,
% 0.96/0.90 (c0_1(a1023)),
% 0.96/0.90 inference(unit_resolution,[status(thm)],[257, 1558, 1391, 1390, 1389])).
% 0.96/0.90 tff(1560,plain,
% 0.96/0.90 (~c3_1(a1008)),
% 0.96/0.90 inference(unit_resolution,[status(thm)],[231, 1558])).
% 0.96/0.90 tff(1561,plain,
% 0.96/0.90 (c2_1(a1008)),
% 0.96/0.90 inference(unit_resolution,[status(thm)],[248, 1558])).
% 0.96/0.90 tff(1562,plain,
% 0.96/0.90 (hskp1 | c0_1(a1008)),
% 0.96/0.90 inference(unit_resolution,[status(thm)],[687, 90, 616, 1561, 1560, 678])).
% 0.96/0.90 tff(1563,plain,
% 0.96/0.90 (c0_1(a1008)),
% 0.96/0.90 inference(unit_resolution,[status(thm)],[1562, 679])).
% 0.96/0.90 tff(1564,plain,
% 0.96/0.90 (~c1_1(a1008)),
% 0.96/0.90 inference(unit_resolution,[status(thm)],[237, 1558])).
% 0.96/0.90 tff(1565,plain,
% 0.96/0.90 (hskp19 | (~c0_1(a1008))),
% 0.96/0.90 inference(unit_resolution,[status(thm)],[696, 90, 1561, 1564, 1560, 117])).
% 0.96/0.90 tff(1566,plain,
% 0.96/0.90 (hskp19),
% 0.96/0.90 inference(unit_resolution,[status(thm)],[1565, 1563])).
% 0.96/0.90 tff(1567,plain,
% 0.96/0.90 (~c3_1(a1037)),
% 0.96/0.90 inference(unit_resolution,[status(thm)],[140, 1566])).
% 0.96/0.90 tff(1568,plain,
% 0.96/0.90 (~c0_1(a1037)),
% 0.96/0.90 inference(unit_resolution,[status(thm)],[704, 1566])).
% 0.96/0.90 tff(1569,plain,
% 0.96/0.90 (~c2_1(a1037)),
% 0.96/0.90 inference(unit_resolution,[status(thm)],[711, 90, 616, 679, 1568, 1567, 678])).
% 0.96/0.90 tff(1570,plain,
% 0.96/0.90 (~c1_1(a1037)),
% 0.96/0.90 inference(unit_resolution,[status(thm)],[146, 1566])).
% 0.96/0.90 tff(1571,plain,
% 0.96/0.90 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | c0_1(a1037) | c1_1(a1037) | c3_1(a1037) | (~ndr1_0) | c2_1(a1037))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp2 | c0_1(a1037) | c1_1(a1037) | c3_1(a1037) | (~ndr1_0) | c2_1(a1037))),
% 0.96/0.90 inference(rewrite,[status(thm)],[])).
% 0.96/0.90 tff(1572,plain,
% 0.96/0.90 ((hskp2 | (~ndr1_0) | c2_1(a1037) | c1_1(a1037) | c3_1(a1037) | c3_1(a1037) | c1_1(a1037) | c0_1(a1037)) <=> (hskp2 | c0_1(a1037) | c1_1(a1037) | c3_1(a1037) | (~ndr1_0) | c2_1(a1037))),
% 0.96/0.90 inference(rewrite,[status(thm)],[])).
% 0.96/0.90 tff(1573,plain,
% 0.96/0.90 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | (~ndr1_0) | c2_1(a1037) | c1_1(a1037) | c3_1(a1037) | c3_1(a1037) | c1_1(a1037) | c0_1(a1037))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | c0_1(a1037) | c1_1(a1037) | c3_1(a1037) | (~ndr1_0) | c2_1(a1037)))),
% 0.96/0.90 inference(monotonicity,[status(thm)],[1572])).
% 0.96/0.90 tff(1574,plain,
% 0.96/0.90 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | (~ndr1_0) | c2_1(a1037) | c1_1(a1037) | c3_1(a1037) | c3_1(a1037) | c1_1(a1037) | c0_1(a1037))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp2 | c0_1(a1037) | c1_1(a1037) | c3_1(a1037) | (~ndr1_0) | c2_1(a1037))),
% 0.96/0.90 inference(transitivity,[status(thm)],[1573, 1571])).
% 0.96/0.90 tff(1575,plain,
% 0.96/0.90 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | (~ndr1_0) | c2_1(a1037) | c1_1(a1037) | c3_1(a1037) | c3_1(a1037) | c1_1(a1037) | c0_1(a1037))),
% 0.96/0.90 inference(quant_inst,[status(thm)],[])).
% 0.96/0.90 tff(1576,plain,
% 0.96/0.90 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp2 | c0_1(a1037) | c1_1(a1037) | c3_1(a1037) | (~ndr1_0) | c2_1(a1037)),
% 0.96/0.90 inference(modus_ponens,[status(thm)],[1575, 1574])).
% 0.96/0.90 tff(1577,plain,
% 0.96/0.90 ($false),
% 0.96/0.90 inference(unit_resolution,[status(thm)],[1576, 90, 616, 1568, 1570, 1567, 596, 1569])).
% 0.96/0.90 tff(1578,plain,(hskp1 | hskp2), inference(lemma,lemma(discharge,[]))).
% 0.96/0.90 tff(1579,plain,
% 0.96/0.90 (hskp1),
% 0.96/0.90 inference(unit_resolution,[status(thm)],[1578, 616])).
% 0.96/0.90 tff(1580,plain,
% 0.96/0.90 (~c1_1(a1001)),
% 0.96/0.90 inference(unit_resolution,[status(thm)],[303, 1579])).
% 0.96/0.90 tff(1581,plain,
% 0.96/0.90 (c2_1(a1001)),
% 0.96/0.90 inference(unit_resolution,[status(thm)],[342, 1579])).
% 0.96/0.90 tff(1582,plain,
% 0.96/0.90 (c3_1(a1001)),
% 0.96/0.90 inference(unit_resolution,[status(thm)],[314, 1579])).
% 0.96/0.90 tff(1583,assumption,(c0_1(a1023)), introduced(assumption)).
% 0.96/0.90 tff(1584,plain,
% 0.96/0.90 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp4 | c2_1(a1023) | c1_1(a1008) | (~ndr1_0) | (~c2_1(a1008)) | c0_1(a1008) | (~c0_1(a1023)) | (~c3_1(a1023)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp4 | c2_1(a1023) | c1_1(a1008) | (~ndr1_0) | (~c2_1(a1008)) | c0_1(a1008) | (~c0_1(a1023)) | (~c3_1(a1023)))),
% 0.96/0.90 inference(rewrite,[status(thm)],[])).
% 0.96/0.90 tff(1585,plain,
% 0.96/0.90 ((hskp4 | (~ndr1_0) | c2_1(a1023) | (~c3_1(a1023)) | (~c0_1(a1023)) | c1_1(a1008) | c0_1(a1008) | (~c2_1(a1008))) <=> (hskp4 | c2_1(a1023) | c1_1(a1008) | (~ndr1_0) | (~c2_1(a1008)) | c0_1(a1008) | (~c0_1(a1023)) | (~c3_1(a1023)))),
% 0.96/0.90 inference(rewrite,[status(thm)],[])).
% 0.96/0.90 tff(1586,plain,
% 0.96/0.90 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp4 | (~ndr1_0) | c2_1(a1023) | (~c3_1(a1023)) | (~c0_1(a1023)) | c1_1(a1008) | c0_1(a1008) | (~c2_1(a1008)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp4 | c2_1(a1023) | c1_1(a1008) | (~ndr1_0) | (~c2_1(a1008)) | c0_1(a1008) | (~c0_1(a1023)) | (~c3_1(a1023))))),
% 0.96/0.90 inference(monotonicity,[status(thm)],[1585])).
% 0.96/0.90 tff(1587,plain,
% 0.96/0.90 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp4 | (~ndr1_0) | c2_1(a1023) | (~c3_1(a1023)) | (~c0_1(a1023)) | c1_1(a1008) | c0_1(a1008) | (~c2_1(a1008)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp4 | c2_1(a1023) | c1_1(a1008) | (~ndr1_0) | (~c2_1(a1008)) | c0_1(a1008) | (~c0_1(a1023)) | (~c3_1(a1023)))),
% 0.96/0.90 inference(transitivity,[status(thm)],[1586, 1584])).
% 0.96/0.90 tff(1588,plain,
% 0.96/0.90 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp4 | (~ndr1_0) | c2_1(a1023) | (~c3_1(a1023)) | (~c0_1(a1023)) | c1_1(a1008) | c0_1(a1008) | (~c2_1(a1008)))),
% 0.96/0.90 inference(quant_inst,[status(thm)],[])).
% 0.96/0.90 tff(1589,plain,
% 0.96/0.91 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp4 | c2_1(a1023) | c1_1(a1008) | (~ndr1_0) | (~c2_1(a1008)) | c0_1(a1008) | (~c0_1(a1023)) | (~c3_1(a1023))),
% 0.96/0.91 inference(modus_ponens,[status(thm)],[1588, 1587])).
% 0.96/0.91 tff(1590,plain,
% 0.96/0.91 (hskp4 | c0_1(a1008)),
% 0.96/0.91 inference(unit_resolution,[status(thm)],[1589, 90, 215, 681, 213, 690, 1345, 1583])).
% 0.96/0.91 tff(1591,plain,
% 0.96/0.91 (c0_1(a1008)),
% 0.96/0.91 inference(unit_resolution,[status(thm)],[1590, 1335])).
% 0.96/0.91 tff(1592,plain,
% 0.96/0.91 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp6 | c1_1(a1008) | c1_1(a1001) | (~ndr1_0) | (~c3_1(a1001)) | (~c2_1(a1001)) | (~c2_1(a1008)) | (~c0_1(a1008)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp6 | c1_1(a1008) | c1_1(a1001) | (~ndr1_0) | (~c3_1(a1001)) | (~c2_1(a1001)) | (~c2_1(a1008)) | (~c0_1(a1008)))),
% 0.96/0.91 inference(rewrite,[status(thm)],[])).
% 0.96/0.91 tff(1593,plain,
% 0.96/0.91 ((hskp6 | (~ndr1_0) | c1_1(a1001) | (~c2_1(a1001)) | (~c3_1(a1001)) | c1_1(a1008) | (~c2_1(a1008)) | (~c0_1(a1008))) <=> (hskp6 | c1_1(a1008) | c1_1(a1001) | (~ndr1_0) | (~c3_1(a1001)) | (~c2_1(a1001)) | (~c2_1(a1008)) | (~c0_1(a1008)))),
% 0.96/0.91 inference(rewrite,[status(thm)],[])).
% 0.96/0.91 tff(1594,plain,
% 0.96/0.91 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp6 | (~ndr1_0) | c1_1(a1001) | (~c2_1(a1001)) | (~c3_1(a1001)) | c1_1(a1008) | (~c2_1(a1008)) | (~c0_1(a1008)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp6 | c1_1(a1008) | c1_1(a1001) | (~ndr1_0) | (~c3_1(a1001)) | (~c2_1(a1001)) | (~c2_1(a1008)) | (~c0_1(a1008))))),
% 0.96/0.91 inference(monotonicity,[status(thm)],[1593])).
% 0.96/0.91 tff(1595,plain,
% 0.96/0.91 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp6 | (~ndr1_0) | c1_1(a1001) | (~c2_1(a1001)) | (~c3_1(a1001)) | c1_1(a1008) | (~c2_1(a1008)) | (~c0_1(a1008)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp6 | c1_1(a1008) | c1_1(a1001) | (~ndr1_0) | (~c3_1(a1001)) | (~c2_1(a1001)) | (~c2_1(a1008)) | (~c0_1(a1008)))),
% 0.96/0.91 inference(transitivity,[status(thm)],[1594, 1592])).
% 0.96/0.91 tff(1596,plain,
% 0.96/0.91 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp6 | (~ndr1_0) | c1_1(a1001) | (~c2_1(a1001)) | (~c3_1(a1001)) | c1_1(a1008) | (~c2_1(a1008)) | (~c0_1(a1008)))),
% 0.96/0.91 inference(quant_inst,[status(thm)],[])).
% 0.96/0.91 tff(1597,plain,
% 0.96/0.91 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp6 | c1_1(a1008) | c1_1(a1001) | (~ndr1_0) | (~c3_1(a1001)) | (~c2_1(a1001)) | (~c2_1(a1008)) | (~c0_1(a1008))),
% 0.96/0.91 inference(modus_ponens,[status(thm)],[1596, 1595])).
% 0.96/0.91 tff(1598,plain,
% 0.96/0.91 (hskp6 | (~c0_1(a1008))),
% 0.96/0.91 inference(unit_resolution,[status(thm)],[1597, 90, 681, 938, 928, 690, 927, 827])).
% 0.96/0.91 tff(1599,plain,
% 0.96/0.91 (hskp6),
% 0.96/0.91 inference(unit_resolution,[status(thm)],[1598, 1591])).
% 0.96/0.91 tff(1600,plain,
% 0.96/0.91 (~c2_1(a1006)),
% 0.96/0.91 inference(unit_resolution,[status(thm)],[951, 1599])).
% 0.96/0.91 tff(1601,plain,
% 0.96/0.91 (c3_1(a1006)),
% 0.96/0.91 inference(unit_resolution,[status(thm)],[962, 1599])).
% 0.96/0.91 tff(1602,plain,
% 0.96/0.91 (c0_1(a1006)),
% 0.96/0.91 inference(unit_resolution,[status(thm)],[973, 1599])).
% 0.96/0.91 tff(1603,plain,
% 0.96/0.91 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c1_1(W) | (~c3_1(W)) | (~c2_1(W)))) | (c3_1(a1044) | c2_1(a1023) | c1_1(a1001) | (~ndr1_0) | (~c3_1(a1001)) | (~c2_1(a1001)) | (~c0_1(a1023)) | (~c3_1(a1023)) | (~c2_1(a1044)) | (~c1_1(a1044)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c1_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c3_1(a1044) | c2_1(a1023) | c1_1(a1001) | (~ndr1_0) | (~c3_1(a1001)) | (~c2_1(a1001)) | (~c0_1(a1023)) | (~c3_1(a1023)) | (~c2_1(a1044)) | (~c1_1(a1044)))),
% 0.96/0.91 inference(rewrite,[status(thm)],[])).
% 0.96/0.91 tff(1604,plain,
% 0.96/0.91 (((~ndr1_0) | (~c1_1(a1044)) | c3_1(a1044) | (~c2_1(a1044)) | c2_1(a1023) | (~c0_1(a1023)) | (~c3_1(a1023)) | c1_1(a1001) | (~c3_1(a1001)) | (~c2_1(a1001))) <=> (c3_1(a1044) | c2_1(a1023) | c1_1(a1001) | (~ndr1_0) | (~c3_1(a1001)) | (~c2_1(a1001)) | (~c0_1(a1023)) | (~c3_1(a1023)) | (~c2_1(a1044)) | (~c1_1(a1044)))),
% 0.96/0.91 inference(rewrite,[status(thm)],[])).
% 0.96/0.91 tff(1605,plain,
% 0.96/0.91 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c1_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c1_1(a1044)) | c3_1(a1044) | (~c2_1(a1044)) | c2_1(a1023) | (~c0_1(a1023)) | (~c3_1(a1023)) | c1_1(a1001) | (~c3_1(a1001)) | (~c2_1(a1001)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c1_1(W) | (~c3_1(W)) | (~c2_1(W)))) | (c3_1(a1044) | c2_1(a1023) | c1_1(a1001) | (~ndr1_0) | (~c3_1(a1001)) | (~c2_1(a1001)) | (~c0_1(a1023)) | (~c3_1(a1023)) | (~c2_1(a1044)) | (~c1_1(a1044))))),
% 0.96/0.91 inference(monotonicity,[status(thm)],[1604])).
% 0.96/0.91 tff(1606,plain,
% 0.96/0.91 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c1_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c1_1(a1044)) | c3_1(a1044) | (~c2_1(a1044)) | c2_1(a1023) | (~c0_1(a1023)) | (~c3_1(a1023)) | c1_1(a1001) | (~c3_1(a1001)) | (~c2_1(a1001)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c1_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c3_1(a1044) | c2_1(a1023) | c1_1(a1001) | (~ndr1_0) | (~c3_1(a1001)) | (~c2_1(a1001)) | (~c0_1(a1023)) | (~c3_1(a1023)) | (~c2_1(a1044)) | (~c1_1(a1044)))),
% 0.96/0.91 inference(transitivity,[status(thm)],[1605, 1603])).
% 0.96/0.91 tff(1607,plain,
% 0.96/0.91 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c1_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c1_1(a1044)) | c3_1(a1044) | (~c2_1(a1044)) | c2_1(a1023) | (~c0_1(a1023)) | (~c3_1(a1023)) | c1_1(a1001) | (~c3_1(a1001)) | (~c2_1(a1001)))),
% 0.96/0.91 inference(quant_inst,[status(thm)],[])).
% 0.96/0.91 tff(1608,plain,
% 0.96/0.91 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c1_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c3_1(a1044) | c2_1(a1023) | c1_1(a1001) | (~ndr1_0) | (~c3_1(a1001)) | (~c2_1(a1001)) | (~c0_1(a1023)) | (~c3_1(a1023)) | (~c2_1(a1044)) | (~c1_1(a1044))),
% 0.96/0.91 inference(modus_ponens,[status(thm)],[1607, 1606])).
% 0.96/0.91 tff(1609,plain,
% 0.96/0.91 (~c2_1(a1044)),
% 0.96/0.91 inference(unit_resolution,[status(thm)],[1608, 90, 772, 215, 938, 928, 761, 213, 927, 817, 1583])).
% 0.96/0.91 tff(1610,plain,
% 0.96/0.91 (hskp8),
% 0.96/0.91 inference(unit_resolution,[status(thm)],[1326, 1609, 690, 680, 681])).
% 0.96/0.91 tff(1611,plain,
% 0.96/0.91 (~c1_1(a1010)),
% 0.96/0.91 inference(unit_resolution,[status(thm)],[545, 1610])).
% 0.96/0.91 tff(1612,plain,
% 0.96/0.91 (c3_1(a1010)),
% 0.96/0.91 inference(unit_resolution,[status(thm)],[556, 1610])).
% 0.96/0.91 tff(1613,plain,
% 0.96/0.91 (c0_1(a1010)),
% 0.96/0.91 inference(unit_resolution,[status(thm)],[567, 1610])).
% 0.96/0.91 tff(1614,plain,
% 0.96/0.91 (hskp3),
% 0.96/0.91 inference(unit_resolution,[status(thm)],[1244, 1600, 1613, 1612, 928, 938, 927, 1602, 1601, 1611, 1609])).
% 0.96/0.91 tff(1615,plain,
% 0.96/0.91 (~c2_1(a1003)),
% 0.96/0.91 inference(unit_resolution,[status(thm)],[521, 1614])).
% 0.96/0.91 tff(1616,plain,
% 0.96/0.91 (c1_1(a1003)),
% 0.96/0.91 inference(unit_resolution,[status(thm)],[538, 1614])).
% 0.96/0.91 tff(1617,plain,
% 0.96/0.91 (~c0_1(a1003)),
% 0.96/0.91 inference(unit_resolution,[status(thm)],[527, 1614])).
% 0.96/0.91 tff(1618,plain,
% 0.96/0.91 ($false),
% 0.96/0.91 inference(unit_resolution,[status(thm)],[1375, 1617, 1616, 690, 680, 1335, 1615, 681, 1602, 1601, 1600])).
% 0.96/0.91 tff(1619,plain,(hskp4 | c1_1(a1008) | c3_1(a1008) | (~c2_1(a1008)) | (~c3_1(a1001)) | (~c2_1(a1001)) | c1_1(a1001) | (~c3_1(a1023)) | c2_1(a1023) | (~c0_1(a1023))), inference(lemma,lemma(discharge,[]))).
% 0.96/0.91 tff(1620,plain,
% 0.96/0.91 (hskp4),
% 0.96/0.91 inference(unit_resolution,[status(thm)],[1619, 1564, 1560, 1561, 1582, 1581, 1580, 1389, 1390, 1559])).
% 0.96/0.91 tff(1621,plain,
% 0.96/0.91 (~c3_1(a1004)),
% 0.96/0.91 inference(unit_resolution,[status(thm)],[865, 1620])).
% 0.96/0.91 tff(1622,plain,
% 0.96/0.91 (c2_1(a1004)),
% 0.96/0.91 inference(unit_resolution,[status(thm)],[841, 1620])).
% 0.96/0.91 tff(1623,plain,
% 0.96/0.91 (c1_1(a1004)),
% 0.96/0.91 inference(unit_resolution,[status(thm)],[852, 1620])).
% 0.96/0.91 tff(1624,plain,
% 0.96/0.91 ($false),
% 0.96/0.91 inference(unit_resolution,[status(thm)],[1538, 90, 1389, 1623, 1622, 1581, 1582, 1390, 1621, 1580, 817, 1559])).
% 0.96/0.91 tff(1625,plain,(hskp2), inference(lemma,lemma(discharge,[]))).
% 0.96/0.91 tff(1626,plain,
% 0.96/0.91 (~c1_1(a1002)),
% 0.96/0.91 inference(unit_resolution,[status(thm)],[38, 1625])).
% 0.96/0.91 tff(1627,plain,
% 0.96/0.91 (c2_1(a1002)),
% 0.96/0.91 inference(unit_resolution,[status(thm)],[127, 1625])).
% 0.96/0.91 tff(1628,plain,
% 0.96/0.91 (c0_1(a1002)),
% 0.96/0.91 inference(unit_resolution,[status(thm)],[49, 1625])).
% 0.96/0.91 tff(1629,plain,
% 0.96/0.91 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp6 | c1_1(a1002) | (~ndr1_0) | (~c0_1(a1002)) | (~c2_1(a1002)) | c1_1(a1032) | (~c2_1(a1032)) | (~c3_1(a1032)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp6 | c1_1(a1002) | (~ndr1_0) | (~c0_1(a1002)) | (~c2_1(a1002)) | c1_1(a1032) | (~c2_1(a1032)) | (~c3_1(a1032)))),
% 0.96/0.91 inference(rewrite,[status(thm)],[])).
% 0.96/0.91 tff(1630,plain,
% 0.96/0.91 ((hskp6 | (~ndr1_0) | c1_1(a1032) | (~c2_1(a1032)) | (~c3_1(a1032)) | c1_1(a1002) | (~c2_1(a1002)) | (~c0_1(a1002))) <=> (hskp6 | c1_1(a1002) | (~ndr1_0) | (~c0_1(a1002)) | (~c2_1(a1002)) | c1_1(a1032) | (~c2_1(a1032)) | (~c3_1(a1032)))),
% 0.96/0.91 inference(rewrite,[status(thm)],[])).
% 0.96/0.91 tff(1631,plain,
% 0.96/0.91 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp6 | (~ndr1_0) | c1_1(a1032) | (~c2_1(a1032)) | (~c3_1(a1032)) | c1_1(a1002) | (~c2_1(a1002)) | (~c0_1(a1002)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp6 | c1_1(a1002) | (~ndr1_0) | (~c0_1(a1002)) | (~c2_1(a1002)) | c1_1(a1032) | (~c2_1(a1032)) | (~c3_1(a1032))))),
% 0.96/0.91 inference(monotonicity,[status(thm)],[1630])).
% 0.96/0.91 tff(1632,plain,
% 0.96/0.91 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp6 | (~ndr1_0) | c1_1(a1032) | (~c2_1(a1032)) | (~c3_1(a1032)) | c1_1(a1002) | (~c2_1(a1002)) | (~c0_1(a1002)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp6 | c1_1(a1002) | (~ndr1_0) | (~c0_1(a1002)) | (~c2_1(a1002)) | c1_1(a1032) | (~c2_1(a1032)) | (~c3_1(a1032)))),
% 0.96/0.91 inference(transitivity,[status(thm)],[1631, 1629])).
% 0.96/0.91 tff(1633,plain,
% 0.96/0.91 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp6 | (~ndr1_0) | c1_1(a1032) | (~c2_1(a1032)) | (~c3_1(a1032)) | c1_1(a1002) | (~c2_1(a1002)) | (~c0_1(a1002)))),
% 0.96/0.91 inference(quant_inst,[status(thm)],[])).
% 0.96/0.91 tff(1634,plain,
% 0.96/0.91 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp6 | c1_1(a1002) | (~ndr1_0) | (~c0_1(a1002)) | (~c2_1(a1002)) | c1_1(a1032) | (~c2_1(a1032)) | (~c3_1(a1032))),
% 0.96/0.91 inference(modus_ponens,[status(thm)],[1633, 1632])).
% 0.96/0.91 tff(1635,plain,
% 0.96/0.91 (hskp6),
% 0.96/0.91 inference(unit_resolution,[status(thm)],[1634, 90, 794, 793, 1628, 1627, 1626, 827, 807])).
% 0.96/0.91 tff(1636,plain,
% 0.96/0.91 (~c2_1(a1006)),
% 0.96/0.91 inference(unit_resolution,[status(thm)],[951, 1635])).
% 0.96/0.91 tff(1637,plain,
% 0.96/0.91 (c3_1(a1006)),
% 0.96/0.91 inference(unit_resolution,[status(thm)],[962, 1635])).
% 0.96/0.91 tff(1638,plain,
% 0.96/0.91 (c0_1(a1006)),
% 0.96/0.91 inference(unit_resolution,[status(thm)],[973, 1635])).
% 0.96/0.91 tff(1639,plain,
% 0.96/0.91 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c1_1(W) | (~c3_1(W)) | (~c2_1(W)))) | (c3_1(a1044) | c2_1(a1006) | (~ndr1_0) | (~c0_1(a1006)) | (~c3_1(a1006)) | c1_1(a1032) | (~c2_1(a1032)) | (~c3_1(a1032)) | (~c2_1(a1044)) | (~c1_1(a1044)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c1_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c3_1(a1044) | c2_1(a1006) | (~ndr1_0) | (~c0_1(a1006)) | (~c3_1(a1006)) | c1_1(a1032) | (~c2_1(a1032)) | (~c3_1(a1032)) | (~c2_1(a1044)) | (~c1_1(a1044)))),
% 0.96/0.91 inference(rewrite,[status(thm)],[])).
% 0.96/0.91 tff(1640,plain,
% 0.96/0.91 (((~ndr1_0) | (~c1_1(a1044)) | c3_1(a1044) | (~c2_1(a1044)) | c2_1(a1006) | (~c0_1(a1006)) | (~c3_1(a1006)) | c1_1(a1032) | (~c3_1(a1032)) | (~c2_1(a1032))) <=> (c3_1(a1044) | c2_1(a1006) | (~ndr1_0) | (~c0_1(a1006)) | (~c3_1(a1006)) | c1_1(a1032) | (~c2_1(a1032)) | (~c3_1(a1032)) | (~c2_1(a1044)) | (~c1_1(a1044)))),
% 0.96/0.91 inference(rewrite,[status(thm)],[])).
% 0.96/0.91 tff(1641,plain,
% 0.96/0.91 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c1_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c1_1(a1044)) | c3_1(a1044) | (~c2_1(a1044)) | c2_1(a1006) | (~c0_1(a1006)) | (~c3_1(a1006)) | c1_1(a1032) | (~c3_1(a1032)) | (~c2_1(a1032)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c1_1(W) | (~c3_1(W)) | (~c2_1(W)))) | (c3_1(a1044) | c2_1(a1006) | (~ndr1_0) | (~c0_1(a1006)) | (~c3_1(a1006)) | c1_1(a1032) | (~c2_1(a1032)) | (~c3_1(a1032)) | (~c2_1(a1044)) | (~c1_1(a1044))))),
% 0.96/0.91 inference(monotonicity,[status(thm)],[1640])).
% 0.96/0.91 tff(1642,plain,
% 0.96/0.91 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c1_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c1_1(a1044)) | c3_1(a1044) | (~c2_1(a1044)) | c2_1(a1006) | (~c0_1(a1006)) | (~c3_1(a1006)) | c1_1(a1032) | (~c3_1(a1032)) | (~c2_1(a1032)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c1_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c3_1(a1044) | c2_1(a1006) | (~ndr1_0) | (~c0_1(a1006)) | (~c3_1(a1006)) | c1_1(a1032) | (~c2_1(a1032)) | (~c3_1(a1032)) | (~c2_1(a1044)) | (~c1_1(a1044)))),
% 0.96/0.91 inference(transitivity,[status(thm)],[1641, 1639])).
% 0.96/0.91 tff(1643,plain,
% 0.96/0.91 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c1_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c1_1(a1044)) | c3_1(a1044) | (~c2_1(a1044)) | c2_1(a1006) | (~c0_1(a1006)) | (~c3_1(a1006)) | c1_1(a1032) | (~c3_1(a1032)) | (~c2_1(a1032)))),
% 0.96/0.91 inference(quant_inst,[status(thm)],[])).
% 0.96/0.91 tff(1644,plain,
% 0.96/0.91 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c1_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c3_1(a1044) | c2_1(a1006) | (~ndr1_0) | (~c0_1(a1006)) | (~c3_1(a1006)) | c1_1(a1032) | (~c2_1(a1032)) | (~c3_1(a1032)) | (~c2_1(a1044)) | (~c1_1(a1044))),
% 0.96/0.91 inference(modus_ponens,[status(thm)],[1643, 1642])).
% 0.96/0.91 tff(1645,plain,
% 0.96/0.91 ($false),
% 0.96/0.91 inference(unit_resolution,[status(thm)],[1644, 90, 772, 794, 793, 1638, 1637, 761, 1636, 817, 1, 807])).
% 0.96/0.91 tff(1646,plain,(~c2_1(a1044)), inference(lemma,lemma(discharge,[]))).
% 0.96/0.91 tff(1647,plain,
% 0.96/0.91 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W))) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W))))),
% 0.96/0.91 inference(bind,[status(th)],[])).
% 0.96/0.91 tff(1648,plain,
% 0.96/0.91 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))),
% 0.96/0.91 inference(quant_intro,[status(thm)],[1647])).
% 0.96/0.91 tff(1649,plain,
% 0.96/0.91 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))),
% 0.96/0.91 inference(rewrite,[status(thm)],[])).
% 0.96/0.91 tff(1650,plain,
% 0.96/0.91 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c2_1(W))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V))) | (~c2_1(W))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V)) | (~c2_1(W)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V)) | (~c2_1(W))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c2_1(W))) | c2_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V)) | (~c2_1(W))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V)) | (~c2_1(W))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V)) | (~c2_1(W)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c2_1(W))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V)) | (~c2_1(W))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c2_1(W))) | c2_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V)) | (~c2_1(W))) | c1_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V)) | (~c2_1(W))) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | (~c2_1(W)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c2_1(W))) | c2_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | (~c2_1(W))))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c2_1(W))) | c2_1(U)) | c1_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | (~c2_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | (~c2_1(W))) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c2_1(W))) | c2_1(U)) | c1_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c2_1(W))))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c2_1(W))) | c2_1(U)) | c1_1(V)) | c0_1(W)) | c1_1(W)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c2_1(W))) | c1_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c2_1(W))) | c1_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c2_1(W))) | c2_1(U)) | c1_1(V)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))))),
% 0.96/0.91 inference(bind,[status(th)],[])).
% 0.96/0.91 tff(1651,plain,
% 0.96/0.91 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c2_1(W))) | c2_1(U)) | c1_1(V)) | c0_1(W)) | c1_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))),
% 0.96/0.91 inference(quant_intro,[status(thm)],[1650])).
% 0.96/0.91 tff(1652,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c2_1(W))) | c2_1(U)) | c1_1(V)) | c0_1(W)) | c1_1(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause187')).
% 0.96/0.91 tff(1653,plain,
% 0.96/0.91 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))),
% 0.96/0.91 inference(modus_ponens,[status(thm)],[1652, 1651])).
% 0.96/0.91 tff(1654,plain,
% 0.96/0.91 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))),
% 0.96/0.91 inference(modus_ponens,[status(thm)],[1653, 1649])).
% 0.96/0.91 tff(1655,plain,(
% 0.96/0.91 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))),
% 0.96/0.91 inference(skolemize,[status(sab)],[1654])).
% 0.96/0.91 tff(1656,plain,
% 0.96/0.91 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))),
% 0.96/0.91 inference(modus_ponens,[status(thm)],[1655, 1648])).
% 0.96/0.91 tff(1657,plain,
% 0.96/0.91 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | (c0_1(a1041) | c1_1(a1002) | (~ndr1_0) | (~c0_1(a1002)) | (~c2_1(a1002)) | (~c2_1(a1041)) | c1_1(a1041) | c2_1(a1044) | (~c0_1(a1044)) | (~c1_1(a1044)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | c0_1(a1041) | c1_1(a1002) | (~ndr1_0) | (~c0_1(a1002)) | (~c2_1(a1002)) | (~c2_1(a1041)) | c1_1(a1041) | c2_1(a1044) | (~c0_1(a1044)) | (~c1_1(a1044)))),
% 0.96/0.91 inference(rewrite,[status(thm)],[])).
% 0.96/0.91 tff(1658,plain,
% 0.96/0.91 (((~ndr1_0) | c2_1(a1044) | (~c1_1(a1044)) | (~c0_1(a1044)) | c1_1(a1002) | (~c2_1(a1002)) | (~c0_1(a1002)) | c0_1(a1041) | c1_1(a1041) | (~c2_1(a1041))) <=> (c0_1(a1041) | c1_1(a1002) | (~ndr1_0) | (~c0_1(a1002)) | (~c2_1(a1002)) | (~c2_1(a1041)) | c1_1(a1041) | c2_1(a1044) | (~c0_1(a1044)) | (~c1_1(a1044)))),
% 0.96/0.91 inference(rewrite,[status(thm)],[])).
% 0.96/0.91 tff(1659,plain,
% 0.96/0.91 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a1044) | (~c1_1(a1044)) | (~c0_1(a1044)) | c1_1(a1002) | (~c2_1(a1002)) | (~c0_1(a1002)) | c0_1(a1041) | c1_1(a1041) | (~c2_1(a1041)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | (c0_1(a1041) | c1_1(a1002) | (~ndr1_0) | (~c0_1(a1002)) | (~c2_1(a1002)) | (~c2_1(a1041)) | c1_1(a1041) | c2_1(a1044) | (~c0_1(a1044)) | (~c1_1(a1044))))),
% 0.96/0.91 inference(monotonicity,[status(thm)],[1658])).
% 0.96/0.91 tff(1660,plain,
% 0.96/0.91 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a1044) | (~c1_1(a1044)) | (~c0_1(a1044)) | c1_1(a1002) | (~c2_1(a1002)) | (~c0_1(a1002)) | c0_1(a1041) | c1_1(a1041) | (~c2_1(a1041)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | c0_1(a1041) | c1_1(a1002) | (~ndr1_0) | (~c0_1(a1002)) | (~c2_1(a1002)) | (~c2_1(a1041)) | c1_1(a1041) | c2_1(a1044) | (~c0_1(a1044)) | (~c1_1(a1044)))),
% 0.96/0.91 inference(transitivity,[status(thm)],[1659, 1657])).
% 0.96/0.91 tff(1661,plain,
% 0.96/0.91 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a1044) | (~c1_1(a1044)) | (~c0_1(a1044)) | c1_1(a1002) | (~c2_1(a1002)) | (~c0_1(a1002)) | c0_1(a1041) | c1_1(a1041) | (~c2_1(a1041)))),
% 0.96/0.91 inference(quant_inst,[status(thm)],[])).
% 0.96/0.91 tff(1662,plain,
% 0.96/0.91 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | c0_1(a1041) | c1_1(a1002) | (~ndr1_0) | (~c0_1(a1002)) | (~c2_1(a1002)) | (~c2_1(a1041)) | c1_1(a1041) | c2_1(a1044) | (~c0_1(a1044)) | (~c1_1(a1044))),
% 0.96/0.91 inference(modus_ponens,[status(thm)],[1661, 1660])).
% 0.96/0.91 tff(1663,plain,
% 0.96/0.91 (c1_1(a1041)),
% 0.96/0.91 inference(unit_resolution,[status(thm)],[1662, 90, 783, 772, 1415, 1628, 1627, 1413, 1626, 1656, 1022])).
% 0.96/0.91 tff(1664,plain,
% 0.96/0.91 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | (c0_1(a1037) | c1_1(a1037) | c1_1(a1002) | (~ndr1_0) | (~c0_1(a1002)) | (~c2_1(a1002)) | (~c2_1(a1037)) | c2_1(a1044) | (~c0_1(a1044)) | (~c1_1(a1044)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | c0_1(a1037) | c1_1(a1037) | c1_1(a1002) | (~ndr1_0) | (~c0_1(a1002)) | (~c2_1(a1002)) | (~c2_1(a1037)) | c2_1(a1044) | (~c0_1(a1044)) | (~c1_1(a1044)))),
% 0.96/0.91 inference(rewrite,[status(thm)],[])).
% 0.96/0.91 tff(1665,plain,
% 0.96/0.91 (((~ndr1_0) | c2_1(a1044) | (~c1_1(a1044)) | (~c0_1(a1044)) | c1_1(a1002) | (~c2_1(a1002)) | (~c0_1(a1002)) | c0_1(a1037) | c1_1(a1037) | (~c2_1(a1037))) <=> (c0_1(a1037) | c1_1(a1037) | c1_1(a1002) | (~ndr1_0) | (~c0_1(a1002)) | (~c2_1(a1002)) | (~c2_1(a1037)) | c2_1(a1044) | (~c0_1(a1044)) | (~c1_1(a1044)))),
% 0.96/0.91 inference(rewrite,[status(thm)],[])).
% 0.96/0.91 tff(1666,plain,
% 0.96/0.91 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a1044) | (~c1_1(a1044)) | (~c0_1(a1044)) | c1_1(a1002) | (~c2_1(a1002)) | (~c0_1(a1002)) | c0_1(a1037) | c1_1(a1037) | (~c2_1(a1037)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | (c0_1(a1037) | c1_1(a1037) | c1_1(a1002) | (~ndr1_0) | (~c0_1(a1002)) | (~c2_1(a1002)) | (~c2_1(a1037)) | c2_1(a1044) | (~c0_1(a1044)) | (~c1_1(a1044))))),
% 0.96/0.91 inference(monotonicity,[status(thm)],[1665])).
% 0.96/0.91 tff(1667,plain,
% 0.96/0.91 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a1044) | (~c1_1(a1044)) | (~c0_1(a1044)) | c1_1(a1002) | (~c2_1(a1002)) | (~c0_1(a1002)) | c0_1(a1037) | c1_1(a1037) | (~c2_1(a1037)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | c0_1(a1037) | c1_1(a1037) | c1_1(a1002) | (~ndr1_0) | (~c0_1(a1002)) | (~c2_1(a1002)) | (~c2_1(a1037)) | c2_1(a1044) | (~c0_1(a1044)) | (~c1_1(a1044)))),
% 0.96/0.91 inference(transitivity,[status(thm)],[1666, 1664])).
% 0.96/0.91 tff(1668,plain,
% 0.96/0.91 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a1044) | (~c1_1(a1044)) | (~c0_1(a1044)) | c1_1(a1002) | (~c2_1(a1002)) | (~c0_1(a1002)) | c0_1(a1037) | c1_1(a1037) | (~c2_1(a1037)))),
% 0.96/0.91 inference(quant_inst,[status(thm)],[])).
% 0.96/0.91 tff(1669,plain,
% 0.96/0.91 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | c0_1(a1037) | c1_1(a1037) | c1_1(a1002) | (~ndr1_0) | (~c0_1(a1002)) | (~c2_1(a1002)) | (~c2_1(a1037)) | c2_1(a1044) | (~c0_1(a1044)) | (~c1_1(a1044))),
% 0.96/0.91 inference(modus_ponens,[status(thm)],[1668, 1667])).
% 0.96/0.91 tff(1670,plain,
% 0.96/0.91 (~c2_1(a1037)),
% 0.96/0.92 inference(unit_resolution,[status(thm)],[1669, 90, 783, 772, 1628, 1627, 1443, 1442, 1626, 1656, 1022])).
% 0.96/0.92 tff(1671,plain,
% 0.96/0.92 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c0_1(U) | (~c1_1(U)) | c3_1(U) | c3_1(V) | c1_1(V) | c2_1(V) | c3_1(W) | c2_1(W) | c0_1(W)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | c3_1(U) | c3_1(V) | c1_1(V) | c2_1(V) | c3_1(W) | c2_1(W) | c0_1(W)))),
% 0.96/0.92 inference(bind,[status(th)],[])).
% 0.96/0.92 tff(1672,plain,
% 0.96/0.92 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | c3_1(U) | c3_1(V) | c1_1(V) | c2_1(V) | c3_1(W) | c2_1(W) | c0_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | c3_1(U) | c3_1(V) | c1_1(V) | c2_1(V) | c3_1(W) | c2_1(W) | c0_1(W))),
% 0.96/0.92 inference(quant_intro,[status(thm)],[1671])).
% 0.96/0.92 tff(1673,plain,
% 0.96/0.92 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | c3_1(U) | c3_1(V) | c1_1(V) | c2_1(V) | c3_1(W) | c2_1(W) | c0_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | c3_1(U) | c3_1(V) | c1_1(V) | c2_1(V) | c3_1(W) | c2_1(W) | c0_1(W))),
% 0.96/0.92 inference(rewrite,[status(thm)],[])).
% 0.96/0.92 tff(1674,plain,
% 0.96/0.92 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~ndr1_0) | (~c1_1(U))) | c1_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | c1_1(V))), (((((~ndr1_0) | (~c1_1(U))) | c1_1(V)) | c2_1(V)) <=> (((~ndr1_0) | (~c1_1(U)) | c1_1(V)) | c2_1(V)))), rewrite((((~ndr1_0) | (~c1_1(U)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | c1_1(V) | c2_1(V))), (((((~ndr1_0) | (~c1_1(U))) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | c1_1(V) | c2_1(V)))), ((((((~ndr1_0) | (~c1_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) <=> (((~ndr1_0) | (~c1_1(U)) | c1_1(V) | c2_1(V)) | c3_1(V)))), rewrite((((~ndr1_0) | (~c1_1(U)) | c1_1(V) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))), ((((((~ndr1_0) | (~c1_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V)))), (((((((~ndr1_0) | (~c1_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V)) | c0_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))), (((((((~ndr1_0) | (~c1_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V)))), ((((((((~ndr1_0) | (~c1_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V)) | c3_1(U)))), rewrite((((~ndr1_0) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V)) | c3_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | c3_1(U) | c3_1(V) | c1_1(V) | c2_1(V))), ((((((((~ndr1_0) | (~c1_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | c3_1(U) | c3_1(V) | c1_1(V) | c2_1(V)))), (((((((((~ndr1_0) | (~c1_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(U)) | c3_1(U)) | c0_1(W)) <=> (((~ndr1_0) | c0_1(U) | (~c1_1(U)) | c3_1(U) | c3_1(V) | c1_1(V) | c2_1(V)) | c0_1(W)))), rewrite((((~ndr1_0) | c0_1(U) | (~c1_1(U)) | c3_1(U) | c3_1(V) | c1_1(V) | c2_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | c3_1(U) | c3_1(V) | c1_1(V) | c2_1(V) | c0_1(W))), (((((((((~ndr1_0) | (~c1_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(U)) | c3_1(U)) | c0_1(W)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | c3_1(U) | c3_1(V) | c1_1(V) | c2_1(V) | c0_1(W)))), ((((((((((~ndr1_0) | (~c1_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(U)) | c3_1(U)) | c0_1(W)) | c2_1(W)) <=> (((~ndr1_0) | c0_1(U) | (~c1_1(U)) | c3_1(U) | c3_1(V) | c1_1(V) | c2_1(V) | c0_1(W)) | c2_1(W)))), rewrite((((~ndr1_0) | c0_1(U) | (~c1_1(U)) | c3_1(U) | c3_1(V) | c1_1(V) | c2_1(V) | c0_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | c3_1(U) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c0_1(W))), ((((((((((~ndr1_0) | (~c1_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(U)) | c3_1(U)) | c0_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | c3_1(U) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c0_1(W)))), (((((((((((~ndr1_0) | (~c1_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(U)) | c3_1(U)) | c0_1(W)) | c2_1(W)) | c3_1(W)) <=> (((~ndr1_0) | c0_1(U) | (~c1_1(U)) | c3_1(U) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c0_1(W)) | c3_1(W)))), rewrite((((~ndr1_0) | c0_1(U) | (~c1_1(U)) | c3_1(U) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c0_1(W)) | c3_1(W)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | c3_1(U) | c3_1(V) | c1_1(V) | c2_1(V) | c3_1(W) | c2_1(W) | c0_1(W))), (((((((((((~ndr1_0) | (~c1_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(U)) | c3_1(U)) | c0_1(W)) | c2_1(W)) | c3_1(W)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | c3_1(U) | c3_1(V) | c1_1(V) | c2_1(V) | c3_1(W) | c2_1(W) | c0_1(W))))),
% 0.96/0.92 inference(bind,[status(th)],[])).
% 0.96/0.92 tff(1675,plain,
% 0.96/0.92 (![W: $i, V: $i, U: $i] : ((((((((((~ndr1_0) | (~c1_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(U)) | c3_1(U)) | c0_1(W)) | c2_1(W)) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | c3_1(U) | c3_1(V) | c1_1(V) | c2_1(V) | c3_1(W) | c2_1(W) | c0_1(W))),
% 0.96/0.92 inference(quant_intro,[status(thm)],[1674])).
% 0.96/0.92 tff(1676,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~ndr1_0) | (~c1_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(U)) | c3_1(U)) | c0_1(W)) | c2_1(W)) | c3_1(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause180')).
% 0.96/0.92 tff(1677,plain,
% 0.96/0.92 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | c3_1(U) | c3_1(V) | c1_1(V) | c2_1(V) | c3_1(W) | c2_1(W) | c0_1(W))),
% 0.96/0.92 inference(modus_ponens,[status(thm)],[1676, 1675])).
% 0.96/0.92 tff(1678,plain,
% 0.96/0.92 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | c3_1(U) | c3_1(V) | c1_1(V) | c2_1(V) | c3_1(W) | c2_1(W) | c0_1(W))),
% 0.96/0.92 inference(modus_ponens,[status(thm)],[1677, 1673])).
% 0.96/0.92 tff(1679,plain,(
% 0.96/0.92 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | c3_1(U) | c3_1(V) | c1_1(V) | c2_1(V) | c3_1(W) | c2_1(W) | c0_1(W))),
% 0.96/0.92 inference(skolemize,[status(sab)],[1678])).
% 0.96/0.92 tff(1680,plain,
% 0.96/0.92 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | c3_1(U) | c3_1(V) | c1_1(V) | c2_1(V) | c3_1(W) | c2_1(W) | c0_1(W))),
% 0.96/0.92 inference(modus_ponens,[status(thm)],[1679, 1672])).
% 0.96/0.92 tff(1681,plain,
% 0.96/0.92 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | c3_1(U) | c3_1(V) | c1_1(V) | c2_1(V) | c3_1(W) | c2_1(W) | c0_1(W))) | (c0_1(a1041) | c3_1(a1041) | c0_1(a1037) | c1_1(a1037) | c3_1(a1037) | (~ndr1_0) | c2_1(a1037) | (~c1_1(a1041)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | c3_1(U) | c3_1(V) | c1_1(V) | c2_1(V) | c3_1(W) | c2_1(W) | c0_1(W))) | c0_1(a1041) | c3_1(a1041) | c0_1(a1037) | c1_1(a1037) | c3_1(a1037) | (~ndr1_0) | c2_1(a1037) | (~c1_1(a1041)))),
% 0.96/0.92 inference(rewrite,[status(thm)],[])).
% 0.96/0.92 tff(1682,plain,
% 0.96/0.92 (((~ndr1_0) | c0_1(a1041) | (~c1_1(a1041)) | c3_1(a1041) | c3_1(a1037) | c1_1(a1037) | c2_1(a1037) | c3_1(a1037) | c2_1(a1037) | c0_1(a1037)) <=> (c0_1(a1041) | c3_1(a1041) | c0_1(a1037) | c1_1(a1037) | c3_1(a1037) | (~ndr1_0) | c2_1(a1037) | (~c1_1(a1041)))),
% 0.96/0.92 inference(rewrite,[status(thm)],[])).
% 0.96/0.92 tff(1683,plain,
% 0.96/0.92 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | c3_1(U) | c3_1(V) | c1_1(V) | c2_1(V) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | c0_1(a1041) | (~c1_1(a1041)) | c3_1(a1041) | c3_1(a1037) | c1_1(a1037) | c2_1(a1037) | c3_1(a1037) | c2_1(a1037) | c0_1(a1037))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | c3_1(U) | c3_1(V) | c1_1(V) | c2_1(V) | c3_1(W) | c2_1(W) | c0_1(W))) | (c0_1(a1041) | c3_1(a1041) | c0_1(a1037) | c1_1(a1037) | c3_1(a1037) | (~ndr1_0) | c2_1(a1037) | (~c1_1(a1041))))),
% 0.96/0.92 inference(monotonicity,[status(thm)],[1682])).
% 0.96/0.92 tff(1684,plain,
% 0.96/0.92 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | c3_1(U) | c3_1(V) | c1_1(V) | c2_1(V) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | c0_1(a1041) | (~c1_1(a1041)) | c3_1(a1041) | c3_1(a1037) | c1_1(a1037) | c2_1(a1037) | c3_1(a1037) | c2_1(a1037) | c0_1(a1037))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | c3_1(U) | c3_1(V) | c1_1(V) | c2_1(V) | c3_1(W) | c2_1(W) | c0_1(W))) | c0_1(a1041) | c3_1(a1041) | c0_1(a1037) | c1_1(a1037) | c3_1(a1037) | (~ndr1_0) | c2_1(a1037) | (~c1_1(a1041)))),
% 0.96/0.92 inference(transitivity,[status(thm)],[1683, 1681])).
% 0.96/0.92 tff(1685,plain,
% 0.96/0.92 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | c3_1(U) | c3_1(V) | c1_1(V) | c2_1(V) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | c0_1(a1041) | (~c1_1(a1041)) | c3_1(a1041) | c3_1(a1037) | c1_1(a1037) | c2_1(a1037) | c3_1(a1037) | c2_1(a1037) | c0_1(a1037))),
% 0.96/0.92 inference(quant_inst,[status(thm)],[])).
% 0.96/0.92 tff(1686,plain,
% 0.96/0.92 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | c3_1(U) | c3_1(V) | c1_1(V) | c2_1(V) | c3_1(W) | c2_1(W) | c0_1(W))) | c0_1(a1041) | c3_1(a1041) | c0_1(a1037) | c1_1(a1037) | c3_1(a1037) | (~ndr1_0) | c2_1(a1037) | (~c1_1(a1041))),
% 0.96/0.92 inference(modus_ponens,[status(thm)],[1685, 1684])).
% 0.96/0.92 tff(1687,plain,
% 0.96/0.92 ($false),
% 0.96/0.92 inference(unit_resolution,[status(thm)],[1686, 90, 1413, 1412, 1443, 1442, 1441, 1680, 1670, 1663])).
% 0.96/0.92 tff(1688,plain,(hskp4 | hskp7), inference(lemma,lemma(discharge,[]))).
% 0.96/0.92 tff(1689,plain,
% 0.96/0.92 (hskp4),
% 0.96/0.92 inference(unit_resolution,[status(thm)],[1688, 644])).
% 0.96/0.92 tff(1690,plain,
% 0.96/0.92 (c2_1(a1004)),
% 0.96/0.92 inference(unit_resolution,[status(thm)],[841, 1689])).
% 0.96/0.92 tff(1691,plain,
% 0.96/0.92 (c1_1(a1004)),
% 0.96/0.92 inference(unit_resolution,[status(thm)],[852, 1689])).
% 0.96/0.92 tff(1692,plain,
% 0.96/0.92 (~c0_1(a1004)),
% 0.96/0.92 inference(unit_resolution,[status(thm)],[859, 90, 644, 1691, 1690, 188])).
% 0.96/0.92 tff(1693,plain,
% 0.96/0.92 (~c3_1(a1004)),
% 0.96/0.92 inference(unit_resolution,[status(thm)],[865, 1689])).
% 0.96/0.92 tff(1694,plain,
% 0.96/0.92 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | (c3_1(a1044) | c3_1(a1004) | c1_1(a1002) | (~ndr1_0) | (~c0_1(a1002)) | (~c2_1(a1002)) | (~c2_1(a1004)) | c0_1(a1004) | c2_1(a1044) | (~c0_1(a1044)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c3_1(a1044) | c3_1(a1004) | c1_1(a1002) | (~ndr1_0) | (~c0_1(a1002)) | (~c2_1(a1002)) | (~c2_1(a1004)) | c0_1(a1004) | c2_1(a1044) | (~c0_1(a1044)))),
% 0.96/0.92 inference(rewrite,[status(thm)],[])).
% 0.96/0.92 tff(1695,plain,
% 0.96/0.92 (((~ndr1_0) | c2_1(a1044) | c3_1(a1044) | (~c0_1(a1044)) | c1_1(a1002) | (~c2_1(a1002)) | (~c0_1(a1002)) | c3_1(a1004) | c0_1(a1004) | (~c2_1(a1004))) <=> (c3_1(a1044) | c3_1(a1004) | c1_1(a1002) | (~ndr1_0) | (~c0_1(a1002)) | (~c2_1(a1002)) | (~c2_1(a1004)) | c0_1(a1004) | c2_1(a1044) | (~c0_1(a1044)))),
% 0.96/0.92 inference(rewrite,[status(thm)],[])).
% 0.96/0.92 tff(1696,plain,
% 0.96/0.92 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a1044) | c3_1(a1044) | (~c0_1(a1044)) | c1_1(a1002) | (~c2_1(a1002)) | (~c0_1(a1002)) | c3_1(a1004) | c0_1(a1004) | (~c2_1(a1004)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | (c3_1(a1044) | c3_1(a1004) | c1_1(a1002) | (~ndr1_0) | (~c0_1(a1002)) | (~c2_1(a1002)) | (~c2_1(a1004)) | c0_1(a1004) | c2_1(a1044) | (~c0_1(a1044))))),
% 0.96/0.92 inference(monotonicity,[status(thm)],[1695])).
% 0.96/0.92 tff(1697,plain,
% 0.96/0.92 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a1044) | c3_1(a1044) | (~c0_1(a1044)) | c1_1(a1002) | (~c2_1(a1002)) | (~c0_1(a1002)) | c3_1(a1004) | c0_1(a1004) | (~c2_1(a1004)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c3_1(a1044) | c3_1(a1004) | c1_1(a1002) | (~ndr1_0) | (~c0_1(a1002)) | (~c2_1(a1002)) | (~c2_1(a1004)) | c0_1(a1004) | c2_1(a1044) | (~c0_1(a1044)))),
% 0.96/0.92 inference(transitivity,[status(thm)],[1696, 1694])).
% 0.96/0.92 tff(1698,plain,
% 0.96/0.92 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a1044) | c3_1(a1044) | (~c0_1(a1044)) | c1_1(a1002) | (~c2_1(a1002)) | (~c0_1(a1002)) | c3_1(a1004) | c0_1(a1004) | (~c2_1(a1004)))),
% 0.96/0.92 inference(quant_inst,[status(thm)],[])).
% 0.96/0.92 tff(1699,plain,
% 0.96/0.92 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c3_1(a1044) | c3_1(a1004) | c1_1(a1002) | (~ndr1_0) | (~c0_1(a1002)) | (~c2_1(a1002)) | (~c2_1(a1004)) | c0_1(a1004) | c2_1(a1044) | (~c0_1(a1044))),
% 0.96/0.92 inference(modus_ponens,[status(thm)],[1698, 1697])).
% 0.96/0.92 tff(1700,plain,
% 0.96/0.92 ($false),
% 0.96/0.92 inference(unit_resolution,[status(thm)],[1699, 90, 783, 1690, 1628, 1627, 761, 1693, 1626, 1410, 1022, 1692])).
% 0.96/0.92 tff(1701,plain,(hskp7), inference(lemma,lemma(discharge,[]))).
% 0.96/0.92 tff(1702,plain,
% 0.96/0.92 (~c3_1(a1008)),
% 0.96/0.92 inference(unit_resolution,[status(thm)],[231, 1701])).
% 0.96/0.92 tff(1703,plain,
% 0.96/0.92 (c2_1(a1008)),
% 0.96/0.92 inference(unit_resolution,[status(thm)],[248, 1701])).
% 0.96/0.92 tff(1704,plain,
% 0.96/0.92 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | (c3_1(a1044) | c3_1(a1008) | c1_1(a1002) | (~ndr1_0) | (~c0_1(a1002)) | (~c2_1(a1002)) | (~c2_1(a1008)) | c0_1(a1008) | c2_1(a1044) | (~c0_1(a1044)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c3_1(a1044) | c3_1(a1008) | c1_1(a1002) | (~ndr1_0) | (~c0_1(a1002)) | (~c2_1(a1002)) | (~c2_1(a1008)) | c0_1(a1008) | c2_1(a1044) | (~c0_1(a1044)))),
% 0.96/0.92 inference(rewrite,[status(thm)],[])).
% 0.96/0.92 tff(1705,plain,
% 0.96/0.92 (((~ndr1_0) | c2_1(a1044) | c3_1(a1044) | (~c0_1(a1044)) | c1_1(a1002) | (~c2_1(a1002)) | (~c0_1(a1002)) | c3_1(a1008) | c0_1(a1008) | (~c2_1(a1008))) <=> (c3_1(a1044) | c3_1(a1008) | c1_1(a1002) | (~ndr1_0) | (~c0_1(a1002)) | (~c2_1(a1002)) | (~c2_1(a1008)) | c0_1(a1008) | c2_1(a1044) | (~c0_1(a1044)))),
% 0.96/0.92 inference(rewrite,[status(thm)],[])).
% 0.96/0.92 tff(1706,plain,
% 0.96/0.92 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a1044) | c3_1(a1044) | (~c0_1(a1044)) | c1_1(a1002) | (~c2_1(a1002)) | (~c0_1(a1002)) | c3_1(a1008) | c0_1(a1008) | (~c2_1(a1008)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | (c3_1(a1044) | c3_1(a1008) | c1_1(a1002) | (~ndr1_0) | (~c0_1(a1002)) | (~c2_1(a1002)) | (~c2_1(a1008)) | c0_1(a1008) | c2_1(a1044) | (~c0_1(a1044))))),
% 0.96/0.92 inference(monotonicity,[status(thm)],[1705])).
% 0.96/0.92 tff(1707,plain,
% 0.96/0.92 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a1044) | c3_1(a1044) | (~c0_1(a1044)) | c1_1(a1002) | (~c2_1(a1002)) | (~c0_1(a1002)) | c3_1(a1008) | c0_1(a1008) | (~c2_1(a1008)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c3_1(a1044) | c3_1(a1008) | c1_1(a1002) | (~ndr1_0) | (~c0_1(a1002)) | (~c2_1(a1002)) | (~c2_1(a1008)) | c0_1(a1008) | c2_1(a1044) | (~c0_1(a1044)))),
% 0.96/0.92 inference(transitivity,[status(thm)],[1706, 1704])).
% 0.96/0.92 tff(1708,plain,
% 0.96/0.92 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a1044) | c3_1(a1044) | (~c0_1(a1044)) | c1_1(a1002) | (~c2_1(a1002)) | (~c0_1(a1002)) | c3_1(a1008) | c0_1(a1008) | (~c2_1(a1008)))),
% 0.96/0.92 inference(quant_inst,[status(thm)],[])).
% 0.96/0.92 tff(1709,plain,
% 0.96/0.92 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c3_1(a1044) | c3_1(a1008) | c1_1(a1002) | (~ndr1_0) | (~c0_1(a1002)) | (~c2_1(a1002)) | (~c2_1(a1008)) | c0_1(a1008) | c2_1(a1044) | (~c0_1(a1044))),
% 0.96/0.92 inference(modus_ponens,[status(thm)],[1708, 1707])).
% 0.96/0.92 tff(1710,plain,
% 0.96/0.92 (c0_1(a1008)),
% 0.96/0.92 inference(unit_resolution,[status(thm)],[1709, 90, 783, 1703, 1628, 1627, 761, 1702, 1626, 1410, 1646])).
% 0.96/0.92 tff(1711,plain,
% 0.96/0.92 (~c1_1(a1008)),
% 0.96/0.92 inference(unit_resolution,[status(thm)],[237, 1701])).
% 0.96/0.92 tff(1712,plain,
% 0.96/0.92 (hskp19 | (~c0_1(a1008))),
% 0.96/0.92 inference(unit_resolution,[status(thm)],[696, 90, 1703, 1711, 1702, 117])).
% 0.96/0.92 tff(1713,plain,
% 0.96/0.92 (hskp19),
% 0.96/0.92 inference(unit_resolution,[status(thm)],[1712, 1710])).
% 0.96/0.92 tff(1714,plain,
% 0.96/0.92 (~c1_1(a1037)),
% 0.96/0.92 inference(unit_resolution,[status(thm)],[146, 1713])).
% 0.96/0.92 tff(1715,plain,
% 0.96/0.92 (~c0_1(a1037)),
% 0.96/0.92 inference(unit_resolution,[status(thm)],[704, 1713])).
% 0.96/0.92 tff(1716,plain,
% 0.96/0.92 (~c3_1(a1037)),
% 0.96/0.92 inference(unit_resolution,[status(thm)],[140, 1713])).
% 0.96/0.92 tff(1717,assumption,(~c1_1(a1037)), introduced(assumption)).
% 0.96/0.92 tff(1718,assumption,(~c0_1(a1037)), introduced(assumption)).
% 0.96/0.92 tff(1719,plain,
% 0.96/0.92 (~c2_1(a1037)),
% 0.96/0.92 inference(unit_resolution,[status(thm)],[1669, 90, 783, 772, 1628, 1627, 1718, 1717, 1626, 1656, 1147])).
% 0.96/0.92 tff(1720,plain,
% 0.96/0.92 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c2_1(W) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c2_1(W) | c0_1(W)))),
% 0.96/0.92 inference(bind,[status(th)],[])).
% 0.96/0.92 tff(1721,plain,
% 0.96/0.92 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c2_1(W) | c0_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))),
% 0.96/0.92 inference(quant_intro,[status(thm)],[1720])).
% 0.96/0.92 tff(1722,plain,
% 0.96/0.92 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c2_1(W) | c0_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))),
% 0.96/0.92 inference(rewrite,[status(thm)],[])).
% 0.96/0.92 tff(1723,plain,
% 0.96/0.92 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c0_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c0_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(V)))), ((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(V))))), (((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c2_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c2_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c2_1(V)))), (((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c2_1(V))))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c2_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c2_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | (~c2_1(V)))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | (~c2_1(V))))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | (~c2_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | (~c2_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V))))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V))) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V))))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c3_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V))) | c0_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V))) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c3_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W)))), ((((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c3_1(V)) | c0_1(W)) | c2_1(W)) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W)) | c2_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W))), ((((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c3_1(V)) | c0_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W)))), (((((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c3_1(V)) | c0_1(W)) | c2_1(W)) | c3_1(W)) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W)) | c3_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W)) | c3_1(W)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))), (((((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c3_1(V)) | c0_1(W)) | c2_1(W)) | c3_1(W)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))))),
% 0.96/0.92 inference(bind,[status(th)],[])).
% 0.96/0.92 tff(1724,plain,
% 0.96/0.92 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c3_1(V)) | c0_1(W)) | c2_1(W)) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))),
% 0.96/0.92 inference(quant_intro,[status(thm)],[1723])).
% 0.96/0.92 tff(1725,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c3_1(V)) | c0_1(W)) | c2_1(W)) | c3_1(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause184')).
% 0.96/0.92 tff(1726,plain,
% 0.96/0.92 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))),
% 0.96/0.92 inference(modus_ponens,[status(thm)],[1725, 1724])).
% 0.96/0.92 tff(1727,plain,
% 0.96/0.92 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))),
% 0.96/0.92 inference(modus_ponens,[status(thm)],[1726, 1722])).
% 0.96/0.92 tff(1728,plain,(
% 0.96/0.92 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))),
% 0.96/0.92 inference(skolemize,[status(sab)],[1727])).
% 0.96/0.92 tff(1729,plain,
% 0.96/0.92 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))),
% 0.96/0.92 inference(modus_ponens,[status(thm)],[1728, 1721])).
% 0.96/0.92 tff(1730,assumption,(~c3_1(a1037)), introduced(assumption)).
% 0.96/0.92 tff(1731,plain,
% 0.96/0.92 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | (c3_1(a1044) | c0_1(a1037) | c3_1(a1037) | c1_1(a1008) | c3_1(a1008) | (~ndr1_0) | (~c2_1(a1008)) | c2_1(a1037) | c2_1(a1044) | (~c0_1(a1044)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | c3_1(a1044) | c0_1(a1037) | c3_1(a1037) | c1_1(a1008) | c3_1(a1008) | (~ndr1_0) | (~c2_1(a1008)) | c2_1(a1037) | c2_1(a1044) | (~c0_1(a1044)))),
% 1.02/0.93 inference(rewrite,[status(thm)],[])).
% 1.02/0.93 tff(1732,plain,
% 1.02/0.93 (((~ndr1_0) | c2_1(a1044) | c3_1(a1044) | (~c0_1(a1044)) | c3_1(a1008) | c1_1(a1008) | (~c2_1(a1008)) | c3_1(a1037) | c2_1(a1037) | c0_1(a1037)) <=> (c3_1(a1044) | c0_1(a1037) | c3_1(a1037) | c1_1(a1008) | c3_1(a1008) | (~ndr1_0) | (~c2_1(a1008)) | c2_1(a1037) | c2_1(a1044) | (~c0_1(a1044)))),
% 1.02/0.93 inference(rewrite,[status(thm)],[])).
% 1.02/0.93 tff(1733,plain,
% 1.02/0.93 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a1044) | c3_1(a1044) | (~c0_1(a1044)) | c3_1(a1008) | c1_1(a1008) | (~c2_1(a1008)) | c3_1(a1037) | c2_1(a1037) | c0_1(a1037))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | (c3_1(a1044) | c0_1(a1037) | c3_1(a1037) | c1_1(a1008) | c3_1(a1008) | (~ndr1_0) | (~c2_1(a1008)) | c2_1(a1037) | c2_1(a1044) | (~c0_1(a1044))))),
% 1.02/0.93 inference(monotonicity,[status(thm)],[1732])).
% 1.02/0.93 tff(1734,plain,
% 1.02/0.93 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a1044) | c3_1(a1044) | (~c0_1(a1044)) | c3_1(a1008) | c1_1(a1008) | (~c2_1(a1008)) | c3_1(a1037) | c2_1(a1037) | c0_1(a1037))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | c3_1(a1044) | c0_1(a1037) | c3_1(a1037) | c1_1(a1008) | c3_1(a1008) | (~ndr1_0) | (~c2_1(a1008)) | c2_1(a1037) | c2_1(a1044) | (~c0_1(a1044)))),
% 1.02/0.93 inference(transitivity,[status(thm)],[1733, 1731])).
% 1.02/0.93 tff(1735,plain,
% 1.02/0.93 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a1044) | c3_1(a1044) | (~c0_1(a1044)) | c3_1(a1008) | c1_1(a1008) | (~c2_1(a1008)) | c3_1(a1037) | c2_1(a1037) | c0_1(a1037))),
% 1.02/0.93 inference(quant_inst,[status(thm)],[])).
% 1.02/0.93 tff(1736,plain,
% 1.02/0.93 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | c3_1(a1044) | c0_1(a1037) | c3_1(a1037) | c1_1(a1008) | c3_1(a1008) | (~ndr1_0) | (~c2_1(a1008)) | c2_1(a1037) | c2_1(a1044) | (~c0_1(a1044))),
% 1.02/0.93 inference(modus_ponens,[status(thm)],[1735, 1734])).
% 1.02/0.93 tff(1737,plain,
% 1.02/0.93 ($false),
% 1.02/0.93 inference(unit_resolution,[status(thm)],[1736, 90, 783, 1703, 761, 1718, 1730, 1711, 1702, 1729, 1147, 1719])).
% 1.02/0.93 tff(1738,plain,(c2_1(a1044) | c0_1(a1037) | c3_1(a1037) | c1_1(a1037)), inference(lemma,lemma(discharge,[]))).
% 1.02/0.93 tff(1739,plain,
% 1.02/0.93 ($false),
% 1.02/0.93 inference(unit_resolution,[status(thm)],[1738, 1716, 1715, 1646, 1714])).
% 1.02/0.93 % SZS output end Proof
%------------------------------------------------------------------------------