TSTP Solution File: HWV068-1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : HWV068-1 : TPTP v8.1.0. Bugfixed v5.5.1.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n014.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 : Sat Sep 17 02:15:40 EDT 2022
% Result : Unsatisfiable 26.04s 18.25s
% Output : Proof 27.43s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : HWV068-1 : TPTP v8.1.0. Bugfixed v5.5.1.
% 0.06/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33 % Computer : n014.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 : Wed Aug 31 23:41:47 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.34 Usage: tptp [options] [-file:]file
% 0.12/0.34 -h, -? prints this message.
% 0.12/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.34 -m, -model generate model.
% 0.12/0.34 -p, -proof generate proof.
% 0.12/0.34 -c, -core generate unsat core of named formulas.
% 0.12/0.34 -st, -statistics display statistics.
% 0.12/0.34 -t:timeout set timeout (in second).
% 0.12/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.34 -<param>:<value> configuration parameter and value.
% 0.12/0.34 -o:<output-file> file to place output in.
% 26.04/18.25 % SZS status Unsatisfiable
% 26.04/18.25 % SZS output start Proof
% 26.04/18.25 tff(esk17564_4_type, type, (
% 26.04/18.25 esk17564_4: ( $i * $i * $i * $i ) > $o)).
% 26.04/18.25 tff(true_type, type, (
% 26.04/18.25 true: $i)).
% 26.04/18.25 tff(esk17148_4_type, type, (
% 26.04/18.25 esk17148_4: ( $i * $i * $i * $i ) > $o)).
% 26.04/18.25 tff(esk16347_4_type, type, (
% 26.04/18.25 esk16347_4: ( $i * $i * $i * $i ) > $o)).
% 26.04/18.25 tff(esk16348_4_type, type, (
% 26.04/18.25 esk16348_4: ( $i * $i * $i * $i ) > $o)).
% 26.04/18.25 tff(esk17504_4_type, type, (
% 26.04/18.25 esk17504_4: ( $i * $i * $i * $i ) > $o)).
% 26.04/18.25 tff(esk16333_4_type, type, (
% 26.04/18.25 esk16333_4: ( $i * $i * $i * $i ) > $o)).
% 26.04/18.25 tff(p_type, type, (
% 26.04/18.25 p: $i > $o)).
% 26.04/18.25 tff(esk1_0_type, type, (
% 26.04/18.25 esk1_0: $o)).
% 26.04/18.25 tff(esk16349_4_type, type, (
% 26.04/18.25 esk16349_4: ( $i * $i * $i * $i ) > $o)).
% 26.04/18.25 tff(esk16220_4_type, type, (
% 26.04/18.25 esk16220_4: ( $i * $i * $i * $i ) > $o)).
% 26.04/18.25 tff(esk16221_4_type, type, (
% 26.04/18.25 esk16221_4: ( $i * $i * $i * $i ) > $o)).
% 26.04/18.25 tff(esk16569_4_type, type, (
% 26.04/18.25 esk16569_4: ( $i * $i * $i * $i ) > $o)).
% 26.04/18.25 tff(esk16375_4_type, type, (
% 26.04/18.25 esk16375_4: ( $i * $i * $i * $i ) > $o)).
% 26.04/18.25 tff(esk17139_4_type, type, (
% 26.04/18.25 esk17139_4: ( $i * $i * $i * $i ) > $o)).
% 26.04/18.25 tff(esk17437_4_type, type, (
% 26.04/18.25 esk17437_4: ( $i * $i * $i * $i ) > $o)).
% 26.04/18.25 tff(esk17438_4_type, type, (
% 26.04/18.25 esk17438_4: ( $i * $i * $i * $i ) > $o)).
% 26.04/18.25 tff(esk17439_4_type, type, (
% 26.04/18.25 esk17439_4: ( $i * $i * $i * $i ) > $o)).
% 26.04/18.25 tff(esk16556_4_type, type, (
% 26.04/18.25 esk16556_4: ( $i * $i * $i * $i ) > $o)).
% 26.04/18.25 tff(esk16115_4_type, type, (
% 26.04/18.25 esk16115_4: ( $i * $i * $i * $i ) > $o)).
% 26.04/18.25 tff(esk17440_4_type, type, (
% 26.04/18.25 esk17440_4: ( $i * $i * $i * $i ) > $o)).
% 26.04/18.25 tff(esk17487_4_type, type, (
% 26.04/18.25 esk17487_4: ( $i * $i * $i * $i ) > $o)).
% 26.04/18.25 tff(esk2_0_type, type, (
% 26.04/18.25 esk2_0: $o)).
% 26.04/18.25 tff(esk16222_4_type, type, (
% 26.04/18.25 esk16222_4: ( $i * $i * $i * $i ) > $o)).
% 26.04/18.25 tff(esk17147_4_type, type, (
% 26.04/18.25 esk17147_4: ( $i * $i * $i * $i ) > $o)).
% 26.04/18.25 tff(1,assumption,(esk16333_4(true, true, true, true)), introduced(assumption)).
% 26.04/18.25 tff(2,plain,
% 26.04/18.25 (p(true) <=> p(true)),
% 26.04/18.25 inference(rewrite,[status(thm)],[])).
% 26.04/18.25 tff(3,axiom,(p(true)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','rule_true')).
% 26.04/18.25 tff(4,plain,
% 26.04/18.25 (p(true)),
% 26.04/18.25 inference(modus_ponens,[status(thm)],[3, 2])).
% 26.04/18.25 tff(5,plain,
% 26.04/18.25 (^[X4: $i, X3: $i, X2: $i, X1: $i] : refl(((~p(X3)) | (~p(X4)) | (~p(X2)) | (~p(X1)) | (~esk16333_4(X1, X2, X3, X4))) <=> ((~p(X3)) | (~p(X4)) | (~p(X2)) | (~p(X1)) | (~esk16333_4(X1, X2, X3, X4))))),
% 26.04/18.25 inference(bind,[status(th)],[])).
% 26.04/18.25 tff(6,plain,
% 26.04/18.25 (![X4: $i, X3: $i, X2: $i, X1: $i] : ((~p(X3)) | (~p(X4)) | (~p(X2)) | (~p(X1)) | (~esk16333_4(X1, X2, X3, X4))) <=> ![X4: $i, X3: $i, X2: $i, X1: $i] : ((~p(X3)) | (~p(X4)) | (~p(X2)) | (~p(X1)) | (~esk16333_4(X1, X2, X3, X4)))),
% 26.04/18.25 inference(quant_intro,[status(thm)],[5])).
% 26.04/18.25 tff(7,plain,
% 26.04/18.25 (![X4: $i, X3: $i, X2: $i, X1: $i] : ((~p(X3)) | (~p(X4)) | (~p(X2)) | (~p(X1)) | (~esk16333_4(X1, X2, X3, X4))) <=> ![X4: $i, X3: $i, X2: $i, X1: $i] : ((~p(X3)) | (~p(X4)) | (~p(X2)) | (~p(X1)) | (~esk16333_4(X1, X2, X3, X4)))),
% 26.04/18.25 inference(rewrite,[status(thm)],[])).
% 26.04/18.25 tff(8,plain,
% 26.04/18.25 (^[X4: $i, X3: $i, X2: $i, X1: $i] : trans(monotonicity(iff_false(asserted(~esk1_0), (esk1_0 <=> $false)), (((~p(X3)) | (~p(X4)) | (~p(X2)) | (~p(X1)) | esk1_0 | (~esk16333_4(X1, X2, X3, X4))) <=> ((~p(X3)) | (~p(X4)) | (~p(X2)) | (~p(X1)) | $false | (~esk16333_4(X1, X2, X3, X4))))), rewrite(((~p(X3)) | (~p(X4)) | (~p(X2)) | (~p(X1)) | $false | (~esk16333_4(X1, X2, X3, X4))) <=> ((~p(X3)) | (~p(X4)) | (~p(X2)) | (~p(X1)) | (~esk16333_4(X1, X2, X3, X4)))), (((~p(X3)) | (~p(X4)) | (~p(X2)) | (~p(X1)) | esk1_0 | (~esk16333_4(X1, X2, X3, X4))) <=> ((~p(X3)) | (~p(X4)) | (~p(X2)) | (~p(X1)) | (~esk16333_4(X1, X2, X3, X4)))))),
% 26.04/18.25 inference(bind,[status(th)],[])).
% 26.04/18.25 tff(9,plain,
% 26.04/18.25 (![X4: $i, X3: $i, X2: $i, X1: $i] : ((~p(X3)) | (~p(X4)) | (~p(X2)) | (~p(X1)) | esk1_0 | (~esk16333_4(X1, X2, X3, X4))) <=> ![X4: $i, X3: $i, X2: $i, X1: $i] : ((~p(X3)) | (~p(X4)) | (~p(X2)) | (~p(X1)) | (~esk16333_4(X1, X2, X3, X4)))),
% 26.04/18.25 inference(quant_intro,[status(thm)],[8])).
% 26.04/18.25 tff(10,plain,
% 26.04/18.25 (^[X4: $i, X3: $i, X2: $i, X1: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~p(X3)) | (~esk16333_4(X1, X2, X3, X4))) | (~p(X2))) <=> ((~p(X3)) | (~p(X2)) | (~esk16333_4(X1, X2, X3, X4)))), (((((~p(X3)) | (~esk16333_4(X1, X2, X3, X4))) | (~p(X2))) | esk1_0) <=> (((~p(X3)) | (~p(X2)) | (~esk16333_4(X1, X2, X3, X4))) | esk1_0))), rewrite((((~p(X3)) | (~p(X2)) | (~esk16333_4(X1, X2, X3, X4))) | esk1_0) <=> ((~p(X3)) | (~p(X2)) | esk1_0 | (~esk16333_4(X1, X2, X3, X4)))), (((((~p(X3)) | (~esk16333_4(X1, X2, X3, X4))) | (~p(X2))) | esk1_0) <=> ((~p(X3)) | (~p(X2)) | esk1_0 | (~esk16333_4(X1, X2, X3, X4))))), ((((((~p(X3)) | (~esk16333_4(X1, X2, X3, X4))) | (~p(X2))) | esk1_0) | (~p(X1))) <=> (((~p(X3)) | (~p(X2)) | esk1_0 | (~esk16333_4(X1, X2, X3, X4))) | (~p(X1))))), rewrite((((~p(X3)) | (~p(X2)) | esk1_0 | (~esk16333_4(X1, X2, X3, X4))) | (~p(X1))) <=> ((~p(X3)) | (~p(X2)) | (~p(X1)) | esk1_0 | (~esk16333_4(X1, X2, X3, X4)))), ((((((~p(X3)) | (~esk16333_4(X1, X2, X3, X4))) | (~p(X2))) | esk1_0) | (~p(X1))) <=> ((~p(X3)) | (~p(X2)) | (~p(X1)) | esk1_0 | (~esk16333_4(X1, X2, X3, X4))))), (((((((~p(X3)) | (~esk16333_4(X1, X2, X3, X4))) | (~p(X2))) | esk1_0) | (~p(X1))) | (~p(X4))) <=> (((~p(X3)) | (~p(X2)) | (~p(X1)) | esk1_0 | (~esk16333_4(X1, X2, X3, X4))) | (~p(X4))))), rewrite((((~p(X3)) | (~p(X2)) | (~p(X1)) | esk1_0 | (~esk16333_4(X1, X2, X3, X4))) | (~p(X4))) <=> ((~p(X3)) | (~p(X4)) | (~p(X2)) | (~p(X1)) | esk1_0 | (~esk16333_4(X1, X2, X3, X4)))), (((((((~p(X3)) | (~esk16333_4(X1, X2, X3, X4))) | (~p(X2))) | esk1_0) | (~p(X1))) | (~p(X4))) <=> ((~p(X3)) | (~p(X4)) | (~p(X2)) | (~p(X1)) | esk1_0 | (~esk16333_4(X1, X2, X3, X4)))))),
% 26.04/18.25 inference(bind,[status(th)],[])).
% 26.04/18.25 tff(11,plain,
% 26.04/18.25 (![X4: $i, X3: $i, X2: $i, X1: $i] : ((((((~p(X3)) | (~esk16333_4(X1, X2, X3, X4))) | (~p(X2))) | esk1_0) | (~p(X1))) | (~p(X4))) <=> ![X4: $i, X3: $i, X2: $i, X1: $i] : ((~p(X3)) | (~p(X4)) | (~p(X2)) | (~p(X1)) | esk1_0 | (~esk16333_4(X1, X2, X3, X4)))),
% 26.04/18.25 inference(quant_intro,[status(thm)],[10])).
% 26.04/18.25 tff(12,axiom,(![X4: $i, X3: $i, X2: $i, X1: $i] : ((((((~p(X3)) | (~esk16333_4(X1, X2, X3, X4))) | (~p(X2))) | esk1_0) | (~p(X1))) | (~p(X4)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','i_0_14736')).
% 26.04/18.25 tff(13,plain,
% 26.04/18.25 (![X4: $i, X3: $i, X2: $i, X1: $i] : ((~p(X3)) | (~p(X4)) | (~p(X2)) | (~p(X1)) | esk1_0 | (~esk16333_4(X1, X2, X3, X4)))),
% 26.04/18.25 inference(modus_ponens,[status(thm)],[12, 11])).
% 26.04/18.25 tff(14,plain,
% 26.04/18.25 (![X4: $i, X3: $i, X2: $i, X1: $i] : ((~p(X3)) | (~p(X4)) | (~p(X2)) | (~p(X1)) | (~esk16333_4(X1, X2, X3, X4)))),
% 26.04/18.25 inference(modus_ponens,[status(thm)],[13, 9])).
% 26.04/18.25 tff(15,plain,
% 26.04/18.25 (![X4: $i, X3: $i, X2: $i, X1: $i] : ((~p(X3)) | (~p(X4)) | (~p(X2)) | (~p(X1)) | (~esk16333_4(X1, X2, X3, X4)))),
% 26.04/18.25 inference(modus_ponens,[status(thm)],[14, 7])).
% 26.04/18.25 tff(16,plain,(
% 26.04/18.25 ![X4: $i, X3: $i, X2: $i, X1: $i] : ((~p(X3)) | (~p(X4)) | (~p(X2)) | (~p(X1)) | (~esk16333_4(X1, X2, X3, X4)))),
% 26.04/18.25 inference(skolemize,[status(sab)],[15])).
% 26.04/18.25 tff(17,plain,
% 26.04/18.25 (![X4: $i, X3: $i, X2: $i, X1: $i] : ((~p(X3)) | (~p(X4)) | (~p(X2)) | (~p(X1)) | (~esk16333_4(X1, X2, X3, X4)))),
% 26.04/18.25 inference(modus_ponens,[status(thm)],[16, 6])).
% 26.04/18.25 tff(18,plain,
% 26.04/18.25 (((~![X4: $i, X3: $i, X2: $i, X1: $i] : ((~p(X3)) | (~p(X4)) | (~p(X2)) | (~p(X1)) | (~esk16333_4(X1, X2, X3, X4)))) | ((~p(true)) | (~esk16333_4(true, true, true, true)))) <=> ((~![X4: $i, X3: $i, X2: $i, X1: $i] : ((~p(X3)) | (~p(X4)) | (~p(X2)) | (~p(X1)) | (~esk16333_4(X1, X2, X3, X4)))) | (~p(true)) | (~esk16333_4(true, true, true, true)))),
% 26.04/18.25 inference(rewrite,[status(thm)],[])).
% 26.04/18.25 tff(19,plain,
% 26.04/18.25 (((~p(true)) | (~p(true)) | (~p(true)) | (~p(true)) | (~esk16333_4(true, true, true, true))) <=> ((~p(true)) | (~esk16333_4(true, true, true, true)))),
% 26.04/18.25 inference(rewrite,[status(thm)],[])).
% 26.04/18.25 tff(20,plain,
% 26.04/18.25 (((~![X4: $i, X3: $i, X2: $i, X1: $i] : ((~p(X3)) | (~p(X4)) | (~p(X2)) | (~p(X1)) | (~esk16333_4(X1, X2, X3, X4)))) | ((~p(true)) | (~p(true)) | (~p(true)) | (~p(true)) | (~esk16333_4(true, true, true, true)))) <=> ((~![X4: $i, X3: $i, X2: $i, X1: $i] : ((~p(X3)) | (~p(X4)) | (~p(X2)) | (~p(X1)) | (~esk16333_4(X1, X2, X3, X4)))) | ((~p(true)) | (~esk16333_4(true, true, true, true))))),
% 26.04/18.25 inference(monotonicity,[status(thm)],[19])).
% 26.04/18.25 tff(21,plain,
% 26.04/18.25 (((~![X4: $i, X3: $i, X2: $i, X1: $i] : ((~p(X3)) | (~p(X4)) | (~p(X2)) | (~p(X1)) | (~esk16333_4(X1, X2, X3, X4)))) | ((~p(true)) | (~p(true)) | (~p(true)) | (~p(true)) | (~esk16333_4(true, true, true, true)))) <=> ((~![X4: $i, X3: $i, X2: $i, X1: $i] : ((~p(X3)) | (~p(X4)) | (~p(X2)) | (~p(X1)) | (~esk16333_4(X1, X2, X3, X4)))) | (~p(true)) | (~esk16333_4(true, true, true, true)))),
% 26.04/18.25 inference(transitivity,[status(thm)],[20, 18])).
% 26.04/18.25 tff(22,plain,
% 26.04/18.25 ((~![X4: $i, X3: $i, X2: $i, X1: $i] : ((~p(X3)) | (~p(X4)) | (~p(X2)) | (~p(X1)) | (~esk16333_4(X1, X2, X3, X4)))) | ((~p(true)) | (~p(true)) | (~p(true)) | (~p(true)) | (~esk16333_4(true, true, true, true)))),
% 26.04/18.25 inference(quant_inst,[status(thm)],[])).
% 26.04/18.25 tff(23,plain,
% 26.04/18.25 ((~![X4: $i, X3: $i, X2: $i, X1: $i] : ((~p(X3)) | (~p(X4)) | (~p(X2)) | (~p(X1)) | (~esk16333_4(X1, X2, X3, X4)))) | (~p(true)) | (~esk16333_4(true, true, true, true))),
% 26.04/18.25 inference(modus_ponens,[status(thm)],[22, 21])).
% 26.04/18.25 tff(24,plain,
% 26.04/18.25 ($false),
% 26.04/18.25 inference(unit_resolution,[status(thm)],[23, 17, 4, 1])).
% 26.04/18.25 tff(25,plain,(~esk16333_4(true, true, true, true)), inference(lemma,lemma(discharge,[]))).
% 26.04/18.25 tff(26,plain,
% 26.04/18.25 (^[X4: $i, X3: $i, X2: $i, X1: $i] : refl(((~esk17504_4(X1, X2, X3, X4)) | esk16333_4(X1, X2, X3, X4)) <=> ((~esk17504_4(X1, X2, X3, X4)) | esk16333_4(X1, X2, X3, X4)))),
% 26.04/18.25 inference(bind,[status(th)],[])).
% 26.04/18.25 tff(27,plain,
% 26.04/18.25 (![X4: $i, X3: $i, X2: $i, X1: $i] : ((~esk17504_4(X1, X2, X3, X4)) | esk16333_4(X1, X2, X3, X4)) <=> ![X4: $i, X3: $i, X2: $i, X1: $i] : ((~esk17504_4(X1, X2, X3, X4)) | esk16333_4(X1, X2, X3, X4))),
% 26.04/18.25 inference(quant_intro,[status(thm)],[26])).
% 26.04/18.25 tff(28,plain,
% 26.04/18.25 (![X4: $i, X3: $i, X2: $i, X1: $i] : ((~esk17504_4(X1, X2, X3, X4)) | esk16333_4(X1, X2, X3, X4)) <=> ![X4: $i, X3: $i, X2: $i, X1: $i] : ((~esk17504_4(X1, X2, X3, X4)) | esk16333_4(X1, X2, X3, X4))),
% 26.04/18.25 inference(rewrite,[status(thm)],[])).
% 26.04/18.25 tff(29,axiom,(![X4: $i, X3: $i, X2: $i, X1: $i] : ((~esk17504_4(X1, X2, X3, X4)) | esk16333_4(X1, X2, X3, X4))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','i_0_20513')).
% 26.04/18.25 tff(30,plain,
% 26.04/18.25 (![X4: $i, X3: $i, X2: $i, X1: $i] : ((~esk17504_4(X1, X2, X3, X4)) | esk16333_4(X1, X2, X3, X4))),
% 26.04/18.25 inference(modus_ponens,[status(thm)],[29, 28])).
% 26.04/18.25 tff(31,plain,(
% 26.04/18.25 ![X4: $i, X3: $i, X2: $i, X1: $i] : ((~esk17504_4(X1, X2, X3, X4)) | esk16333_4(X1, X2, X3, X4))),
% 26.04/18.25 inference(skolemize,[status(sab)],[30])).
% 26.04/18.25 tff(32,plain,
% 26.04/18.25 (![X4: $i, X3: $i, X2: $i, X1: $i] : ((~esk17504_4(X1, X2, X3, X4)) | esk16333_4(X1, X2, X3, X4))),
% 26.04/18.25 inference(modus_ponens,[status(thm)],[31, 27])).
% 26.04/18.25 tff(33,plain,
% 26.04/18.25 (((~![X4: $i, X3: $i, X2: $i, X1: $i] : ((~esk17504_4(X1, X2, X3, X4)) | esk16333_4(X1, X2, X3, X4))) | ((~esk17504_4(true, true, true, true)) | esk16333_4(true, true, true, true))) <=> ((~![X4: $i, X3: $i, X2: $i, X1: $i] : ((~esk17504_4(X1, X2, X3, X4)) | esk16333_4(X1, X2, X3, X4))) | (~esk17504_4(true, true, true, true)) | esk16333_4(true, true, true, true))),
% 26.04/18.25 inference(rewrite,[status(thm)],[])).
% 26.04/18.25 tff(34,plain,
% 26.04/18.25 ((~![X4: $i, X3: $i, X2: $i, X1: $i] : ((~esk17504_4(X1, X2, X3, X4)) | esk16333_4(X1, X2, X3, X4))) | ((~esk17504_4(true, true, true, true)) | esk16333_4(true, true, true, true))),
% 26.04/18.25 inference(quant_inst,[status(thm)],[])).
% 26.04/18.25 tff(35,plain,
% 26.04/18.25 ((~![X4: $i, X3: $i, X2: $i, X1: $i] : ((~esk17504_4(X1, X2, X3, X4)) | esk16333_4(X1, X2, X3, X4))) | (~esk17504_4(true, true, true, true)) | esk16333_4(true, true, true, true)),
% 26.04/18.25 inference(modus_ponens,[status(thm)],[34, 33])).
% 26.04/18.25 tff(36,plain,
% 26.04/18.25 (~esk17504_4(true, true, true, true)),
% 26.04/18.25 inference(unit_resolution,[status(thm)],[35, 32, 25])).
% 26.04/18.25 tff(37,plain,
% 26.04/18.25 (^[X4: $i, X3: $i, X2: $i, X1: $i] : refl(((~esk16348_4(X1, X2, X3, X4)) | esk17504_4(X1, X2, X3, X4)) <=> ((~esk16348_4(X1, X2, X3, X4)) | esk17504_4(X1, X2, X3, X4)))),
% 26.04/18.25 inference(bind,[status(th)],[])).
% 26.04/18.25 tff(38,plain,
% 26.04/18.25 (![X4: $i, X3: $i, X2: $i, X1: $i] : ((~esk16348_4(X1, X2, X3, X4)) | esk17504_4(X1, X2, X3, X4)) <=> ![X4: $i, X3: $i, X2: $i, X1: $i] : ((~esk16348_4(X1, X2, X3, X4)) | esk17504_4(X1, X2, X3, X4))),
% 26.04/18.25 inference(quant_intro,[status(thm)],[37])).
% 26.04/18.25 tff(39,plain,
% 26.04/18.25 (![X4: $i, X3: $i, X2: $i, X1: $i] : ((~esk16348_4(X1, X2, X3, X4)) | esk17504_4(X1, X2, X3, X4)) <=> ![X4: $i, X3: $i, X2: $i, X1: $i] : ((~esk16348_4(X1, X2, X3, X4)) | esk17504_4(X1, X2, X3, X4))),
% 26.04/18.25 inference(rewrite,[status(thm)],[])).
% 26.04/18.25 tff(40,axiom,(![X4: $i, X3: $i, X2: $i, X1: $i] : ((~esk16348_4(X1, X2, X3, X4)) | esk17504_4(X1, X2, X3, X4))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','i_0_32779')).
% 26.04/18.25 tff(41,plain,
% 26.04/18.25 (![X4: $i, X3: $i, X2: $i, X1: $i] : ((~esk16348_4(X1, X2, X3, X4)) | esk17504_4(X1, X2, X3, X4))),
% 26.04/18.25 inference(modus_ponens,[status(thm)],[40, 39])).
% 26.04/18.25 tff(42,plain,(
% 26.04/18.25 ![X4: $i, X3: $i, X2: $i, X1: $i] : ((~esk16348_4(X1, X2, X3, X4)) | esk17504_4(X1, X2, X3, X4))),
% 26.04/18.25 inference(skolemize,[status(sab)],[41])).
% 26.04/18.25 tff(43,plain,
% 26.04/18.25 (![X4: $i, X3: $i, X2: $i, X1: $i] : ((~esk16348_4(X1, X2, X3, X4)) | esk17504_4(X1, X2, X3, X4))),
% 26.04/18.25 inference(modus_ponens,[status(thm)],[42, 38])).
% 26.04/18.25 tff(44,plain,
% 26.04/18.25 (((~![X4: $i, X3: $i, X2: $i, X1: $i] : ((~esk16348_4(X1, X2, X3, X4)) | esk17504_4(X1, X2, X3, X4))) | ((~esk16348_4(true, true, true, true)) | esk17504_4(true, true, true, true))) <=> ((~![X4: $i, X3: $i, X2: $i, X1: $i] : ((~esk16348_4(X1, X2, X3, X4)) | esk17504_4(X1, X2, X3, X4))) | (~esk16348_4(true, true, true, true)) | esk17504_4(true, true, true, true))),
% 26.04/18.25 inference(rewrite,[status(thm)],[])).
% 26.04/18.25 tff(45,plain,
% 26.04/18.25 ((~![X4: $i, X3: $i, X2: $i, X1: $i] : ((~esk16348_4(X1, X2, X3, X4)) | esk17504_4(X1, X2, X3, X4))) | ((~esk16348_4(true, true, true, true)) | esk17504_4(true, true, true, true))),
% 26.04/18.25 inference(quant_inst,[status(thm)],[])).
% 26.04/18.25 tff(46,plain,
% 26.04/18.25 ((~![X4: $i, X3: $i, X2: $i, X1: $i] : ((~esk16348_4(X1, X2, X3, X4)) | esk17504_4(X1, X2, X3, X4))) | (~esk16348_4(true, true, true, true)) | esk17504_4(true, true, true, true)),
% 26.04/18.25 inference(modus_ponens,[status(thm)],[45, 44])).
% 26.04/18.25 tff(47,plain,
% 26.04/18.25 (~esk16348_4(true, true, true, true)),
% 26.04/18.25 inference(unit_resolution,[status(thm)],[46, 43, 36])).
% 26.04/18.25 tff(48,assumption,(esk16115_4(true, true, true, true)), introduced(assumption)).
% 26.04/18.25 tff(49,plain,
% 26.04/18.25 (^[X4: $i, X3: $i, X2: $i, X1: $i] : refl((~esk16115_4(X1, X2, X3, X4)) <=> (~esk16115_4(X1, X2, X3, X4)))),
% 26.04/18.25 inference(bind,[status(th)],[])).
% 26.04/18.25 tff(50,plain,
% 26.04/18.25 (![X4: $i, X3: $i, X2: $i, X1: $i] : (~esk16115_4(X1, X2, X3, X4)) <=> ![X4: $i, X3: $i, X2: $i, X1: $i] : (~esk16115_4(X1, X2, X3, X4))),
% 26.04/18.25 inference(quant_intro,[status(thm)],[49])).
% 26.04/18.25 tff(51,plain,
% 26.04/18.25 (![X4: $i, X3: $i, X2: $i, X1: $i] : (~esk16115_4(X1, X2, X3, X4)) <=> ![X4: $i, X3: $i, X2: $i, X1: $i] : (~esk16115_4(X1, X2, X3, X4))),
% 26.04/18.25 inference(rewrite,[status(thm)],[])).
% 26.04/18.25 tff(52,axiom,(![X4: $i, X3: $i, X2: $i, X1: $i] : (~esk16115_4(X1, X2, X3, X4))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','i_0_29772')).
% 26.04/18.25 tff(53,plain,
% 26.04/18.25 (![X4: $i, X3: $i, X2: $i, X1: $i] : (~esk16115_4(X1, X2, X3, X4))),
% 26.04/18.25 inference(modus_ponens,[status(thm)],[52, 51])).
% 26.04/18.25 tff(54,plain,(
% 26.04/18.25 ![X4: $i, X3: $i, X2: $i, X1: $i] : (~esk16115_4(X1, X2, X3, X4))),
% 26.04/18.25 inference(skolemize,[status(sab)],[53])).
% 26.04/18.25 tff(55,plain,
% 26.04/18.25 (![X4: $i, X3: $i, X2: $i, X1: $i] : (~esk16115_4(X1, X2, X3, X4))),
% 26.04/18.25 inference(modus_ponens,[status(thm)],[54, 50])).
% 26.04/18.25 tff(56,plain,
% 26.04/18.25 ((~![X4: $i, X3: $i, X2: $i, X1: $i] : (~esk16115_4(X1, X2, X3, X4))) | (~esk16115_4(true, true, true, true))),
% 26.04/18.25 inference(quant_inst,[status(thm)],[])).
% 26.04/18.25 tff(57,plain,
% 26.04/18.25 ($false),
% 26.04/18.25 inference(unit_resolution,[status(thm)],[56, 55, 48])).
% 26.04/18.25 tff(58,plain,(~esk16115_4(true, true, true, true)), inference(lemma,lemma(discharge,[]))).
% 26.04/18.25 tff(59,plain,
% 26.04/18.25 (^[X4: $i, X3: $i, X2: $i, X1: $i] : refl(((~esk16556_4(X1, X2, X3, X4)) | esk16115_4(X1, X2, X3, X4)) <=> ((~esk16556_4(X1, X2, X3, X4)) | esk16115_4(X1, X2, X3, X4)))),
% 26.04/18.25 inference(bind,[status(th)],[])).
% 26.04/18.25 tff(60,plain,
% 26.04/18.25 (![X4: $i, X3: $i, X2: $i, X1: $i] : ((~esk16556_4(X1, X2, X3, X4)) | esk16115_4(X1, X2, X3, X4)) <=> ![X4: $i, X3: $i, X2: $i, X1: $i] : ((~esk16556_4(X1, X2, X3, X4)) | esk16115_4(X1, X2, X3, X4))),
% 26.04/18.25 inference(quant_intro,[status(thm)],[59])).
% 26.04/18.26 tff(61,plain,
% 26.04/18.26 (![X4: $i, X3: $i, X2: $i, X1: $i] : ((~esk16556_4(X1, X2, X3, X4)) | esk16115_4(X1, X2, X3, X4)) <=> ![X4: $i, X3: $i, X2: $i, X1: $i] : ((~esk16556_4(X1, X2, X3, X4)) | esk16115_4(X1, X2, X3, X4))),
% 26.04/18.26 inference(rewrite,[status(thm)],[])).
% 26.04/18.26 tff(62,plain,
% 26.04/18.26 (^[X4: $i, X3: $i, X2: $i, X1: $i] : rewrite((esk16115_4(X1, X2, X3, X4) | (~esk16556_4(X1, X2, X3, X4))) <=> ((~esk16556_4(X1, X2, X3, X4)) | esk16115_4(X1, X2, X3, X4)))),
% 26.04/18.26 inference(bind,[status(th)],[])).
% 26.04/18.26 tff(63,plain,
% 26.04/18.26 (![X4: $i, X3: $i, X2: $i, X1: $i] : (esk16115_4(X1, X2, X3, X4) | (~esk16556_4(X1, X2, X3, X4))) <=> ![X4: $i, X3: $i, X2: $i, X1: $i] : ((~esk16556_4(X1, X2, X3, X4)) | esk16115_4(X1, X2, X3, X4))),
% 26.04/18.26 inference(quant_intro,[status(thm)],[62])).
% 26.04/18.26 tff(64,axiom,(![X4: $i, X3: $i, X2: $i, X1: $i] : (esk16115_4(X1, X2, X3, X4) | (~esk16556_4(X1, X2, X3, X4)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','i_0_22790')).
% 26.04/18.26 tff(65,plain,
% 26.04/18.26 (![X4: $i, X3: $i, X2: $i, X1: $i] : ((~esk16556_4(X1, X2, X3, X4)) | esk16115_4(X1, X2, X3, X4))),
% 26.04/18.26 inference(modus_ponens,[status(thm)],[64, 63])).
% 26.04/18.26 tff(66,plain,
% 26.04/18.26 (![X4: $i, X3: $i, X2: $i, X1: $i] : ((~esk16556_4(X1, X2, X3, X4)) | esk16115_4(X1, X2, X3, X4))),
% 26.04/18.26 inference(modus_ponens,[status(thm)],[65, 61])).
% 26.04/18.26 tff(67,plain,(
% 26.04/18.26 ![X4: $i, X3: $i, X2: $i, X1: $i] : ((~esk16556_4(X1, X2, X3, X4)) | esk16115_4(X1, X2, X3, X4))),
% 26.04/18.26 inference(skolemize,[status(sab)],[66])).
% 26.04/18.26 tff(68,plain,
% 26.04/18.26 (![X4: $i, X3: $i, X2: $i, X1: $i] : ((~esk16556_4(X1, X2, X3, X4)) | esk16115_4(X1, X2, X3, X4))),
% 26.04/18.26 inference(modus_ponens,[status(thm)],[67, 60])).
% 26.04/18.26 tff(69,plain,
% 26.04/18.26 (((~![X4: $i, X3: $i, X2: $i, X1: $i] : ((~esk16556_4(X1, X2, X3, X4)) | esk16115_4(X1, X2, X3, X4))) | ((~esk16556_4(true, true, true, true)) | esk16115_4(true, true, true, true))) <=> ((~![X4: $i, X3: $i, X2: $i, X1: $i] : ((~esk16556_4(X1, X2, X3, X4)) | esk16115_4(X1, X2, X3, X4))) | (~esk16556_4(true, true, true, true)) | esk16115_4(true, true, true, true))),
% 26.04/18.26 inference(rewrite,[status(thm)],[])).
% 26.04/18.26 tff(70,plain,
% 26.04/18.26 ((~![X4: $i, X3: $i, X2: $i, X1: $i] : ((~esk16556_4(X1, X2, X3, X4)) | esk16115_4(X1, X2, X3, X4))) | ((~esk16556_4(true, true, true, true)) | esk16115_4(true, true, true, true))),
% 26.04/18.26 inference(quant_inst,[status(thm)],[])).
% 26.04/18.26 tff(71,plain,
% 26.04/18.26 ((~![X4: $i, X3: $i, X2: $i, X1: $i] : ((~esk16556_4(X1, X2, X3, X4)) | esk16115_4(X1, X2, X3, X4))) | (~esk16556_4(true, true, true, true)) | esk16115_4(true, true, true, true)),
% 26.04/18.26 inference(modus_ponens,[status(thm)],[70, 69])).
% 26.04/18.26 tff(72,plain,
% 26.04/18.26 (~esk16556_4(true, true, true, true)),
% 26.04/18.26 inference(unit_resolution,[status(thm)],[71, 68, 58])).
% 26.04/18.26 tff(73,plain,
% 26.04/18.26 (^[X4: $i, X3: $i, X2: $i, X1: $i] : refl((esk16556_4(X1, X2, X3, X4) | (~esk17439_4(X1, X2, X3, X4))) <=> (esk16556_4(X1, X2, X3, X4) | (~esk17439_4(X1, X2, X3, X4))))),
% 26.04/18.26 inference(bind,[status(th)],[])).
% 26.04/18.26 tff(74,plain,
% 26.04/18.26 (![X4: $i, X3: $i, X2: $i, X1: $i] : (esk16556_4(X1, X2, X3, X4) | (~esk17439_4(X1, X2, X3, X4))) <=> ![X4: $i, X3: $i, X2: $i, X1: $i] : (esk16556_4(X1, X2, X3, X4) | (~esk17439_4(X1, X2, X3, X4)))),
% 26.04/18.26 inference(quant_intro,[status(thm)],[73])).
% 26.04/18.26 tff(75,plain,
% 26.04/18.26 (![X4: $i, X3: $i, X2: $i, X1: $i] : (esk16556_4(X1, X2, X3, X4) | (~esk17439_4(X1, X2, X3, X4))) <=> ![X4: $i, X3: $i, X2: $i, X1: $i] : (esk16556_4(X1, X2, X3, X4) | (~esk17439_4(X1, X2, X3, X4)))),
% 26.04/18.26 inference(rewrite,[status(thm)],[])).
% 26.04/18.26 tff(76,axiom,(![X4: $i, X3: $i, X2: $i, X1: $i] : (esk16556_4(X1, X2, X3, X4) | (~esk17439_4(X1, X2, X3, X4)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','i_0_43224')).
% 26.04/18.26 tff(77,plain,
% 26.04/18.26 (![X4: $i, X3: $i, X2: $i, X1: $i] : (esk16556_4(X1, X2, X3, X4) | (~esk17439_4(X1, X2, X3, X4)))),
% 26.04/18.26 inference(modus_ponens,[status(thm)],[76, 75])).
% 26.04/18.26 tff(78,plain,(
% 26.04/18.26 ![X4: $i, X3: $i, X2: $i, X1: $i] : (esk16556_4(X1, X2, X3, X4) | (~esk17439_4(X1, X2, X3, X4)))),
% 26.04/18.26 inference(skolemize,[status(sab)],[77])).
% 26.04/18.26 tff(79,plain,
% 26.04/18.26 (![X4: $i, X3: $i, X2: $i, X1: $i] : (esk16556_4(X1, X2, X3, X4) | (~esk17439_4(X1, X2, X3, X4)))),
% 26.04/18.26 inference(modus_ponens,[status(thm)],[78, 74])).
% 26.04/18.26 tff(80,plain,
% 26.04/18.26 (((~![X4: $i, X3: $i, X2: $i, X1: $i] : (esk16556_4(X1, X2, X3, X4) | (~esk17439_4(X1, X2, X3, X4)))) | ((~esk17439_4(true, true, true, true)) | esk16556_4(true, true, true, true))) <=> ((~![X4: $i, X3: $i, X2: $i, X1: $i] : (esk16556_4(X1, X2, X3, X4) | (~esk17439_4(X1, X2, X3, X4)))) | (~esk17439_4(true, true, true, true)) | esk16556_4(true, true, true, true))),
% 26.04/18.26 inference(rewrite,[status(thm)],[])).
% 26.04/18.26 tff(81,plain,
% 26.04/18.26 ((esk16556_4(true, true, true, true) | (~esk17439_4(true, true, true, true))) <=> ((~esk17439_4(true, true, true, true)) | esk16556_4(true, true, true, true))),
% 26.04/18.26 inference(rewrite,[status(thm)],[])).
% 26.04/18.26 tff(82,plain,
% 26.04/18.26 (((~![X4: $i, X3: $i, X2: $i, X1: $i] : (esk16556_4(X1, X2, X3, X4) | (~esk17439_4(X1, X2, X3, X4)))) | (esk16556_4(true, true, true, true) | (~esk17439_4(true, true, true, true)))) <=> ((~![X4: $i, X3: $i, X2: $i, X1: $i] : (esk16556_4(X1, X2, X3, X4) | (~esk17439_4(X1, X2, X3, X4)))) | ((~esk17439_4(true, true, true, true)) | esk16556_4(true, true, true, true)))),
% 26.04/18.26 inference(monotonicity,[status(thm)],[81])).
% 26.04/18.26 tff(83,plain,
% 26.04/18.26 (((~![X4: $i, X3: $i, X2: $i, X1: $i] : (esk16556_4(X1, X2, X3, X4) | (~esk17439_4(X1, X2, X3, X4)))) | (esk16556_4(true, true, true, true) | (~esk17439_4(true, true, true, true)))) <=> ((~![X4: $i, X3: $i, X2: $i, X1: $i] : (esk16556_4(X1, X2, X3, X4) | (~esk17439_4(X1, X2, X3, X4)))) | (~esk17439_4(true, true, true, true)) | esk16556_4(true, true, true, true))),
% 26.04/18.26 inference(transitivity,[status(thm)],[82, 80])).
% 26.04/18.26 tff(84,plain,
% 26.04/18.26 ((~![X4: $i, X3: $i, X2: $i, X1: $i] : (esk16556_4(X1, X2, X3, X4) | (~esk17439_4(X1, X2, X3, X4)))) | (esk16556_4(true, true, true, true) | (~esk17439_4(true, true, true, true)))),
% 26.04/18.26 inference(quant_inst,[status(thm)],[])).
% 26.04/18.26 tff(85,plain,
% 26.04/18.26 ((~![X4: $i, X3: $i, X2: $i, X1: $i] : (esk16556_4(X1, X2, X3, X4) | (~esk17439_4(X1, X2, X3, X4)))) | (~esk17439_4(true, true, true, true)) | esk16556_4(true, true, true, true)),
% 26.04/18.26 inference(modus_ponens,[status(thm)],[84, 83])).
% 26.04/18.26 tff(86,plain,
% 26.04/18.26 (~esk17439_4(true, true, true, true)),
% 26.04/18.26 inference(unit_resolution,[status(thm)],[85, 79, 72])).
% 26.04/18.26 tff(87,plain,
% 26.04/18.26 (^[X4: $i, X3: $i, X2: $i, X1: $i] : refl(((~p(X3)) | (~p(X4)) | (~p(X2)) | (~p(X1)) | esk17487_4(X1, X2, X3, X4)) <=> ((~p(X3)) | (~p(X4)) | (~p(X2)) | (~p(X1)) | esk17487_4(X1, X2, X3, X4)))),
% 26.04/18.26 inference(bind,[status(th)],[])).
% 26.04/18.26 tff(88,plain,
% 26.04/18.26 (![X4: $i, X3: $i, X2: $i, X1: $i] : ((~p(X3)) | (~p(X4)) | (~p(X2)) | (~p(X1)) | esk17487_4(X1, X2, X3, X4)) <=> ![X4: $i, X3: $i, X2: $i, X1: $i] : ((~p(X3)) | (~p(X4)) | (~p(X2)) | (~p(X1)) | esk17487_4(X1, X2, X3, X4))),
% 26.04/18.26 inference(quant_intro,[status(thm)],[87])).
% 26.04/18.26 tff(89,plain,
% 26.04/18.26 (![X4: $i, X3: $i, X2: $i, X1: $i] : ((~p(X3)) | (~p(X4)) | (~p(X2)) | (~p(X1)) | esk17487_4(X1, X2, X3, X4)) <=> ![X4: $i, X3: $i, X2: $i, X1: $i] : ((~p(X3)) | (~p(X4)) | (~p(X2)) | (~p(X1)) | esk17487_4(X1, X2, X3, X4))),
% 26.04/18.26 inference(rewrite,[status(thm)],[])).
% 26.04/18.26 tff(90,plain,
% 26.04/18.26 (^[X4: $i, X3: $i, X2: $i, X1: $i] : trans(monotonicity(trans(monotonicity(iff_true(asserted(esk2_0), (esk2_0 <=> $true)), ((~esk2_0) <=> (~$true))), rewrite((~$true) <=> $false), ((~esk2_0) <=> $false)), (((~p(X3)) | (~p(X4)) | (~p(X2)) | (~p(X1)) | (~esk2_0) | esk17487_4(X1, X2, X3, X4)) <=> ((~p(X3)) | (~p(X4)) | (~p(X2)) | (~p(X1)) | $false | esk17487_4(X1, X2, X3, X4)))), rewrite(((~p(X3)) | (~p(X4)) | (~p(X2)) | (~p(X1)) | $false | esk17487_4(X1, X2, X3, X4)) <=> ((~p(X3)) | (~p(X4)) | (~p(X2)) | (~p(X1)) | esk17487_4(X1, X2, X3, X4))), (((~p(X3)) | (~p(X4)) | (~p(X2)) | (~p(X1)) | (~esk2_0) | esk17487_4(X1, X2, X3, X4)) <=> ((~p(X3)) | (~p(X4)) | (~p(X2)) | (~p(X1)) | esk17487_4(X1, X2, X3, X4))))),
% 26.04/18.26 inference(bind,[status(th)],[])).
% 26.04/18.26 tff(91,plain,
% 26.04/18.26 (![X4: $i, X3: $i, X2: $i, X1: $i] : ((~p(X3)) | (~p(X4)) | (~p(X2)) | (~p(X1)) | (~esk2_0) | esk17487_4(X1, X2, X3, X4)) <=> ![X4: $i, X3: $i, X2: $i, X1: $i] : ((~p(X3)) | (~p(X4)) | (~p(X2)) | (~p(X1)) | esk17487_4(X1, X2, X3, X4))),
% 26.04/18.26 inference(quant_intro,[status(thm)],[90])).
% 26.04/18.26 tff(92,plain,
% 26.04/18.26 (^[X4: $i, X3: $i, X2: $i, X1: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~esk2_0) | (~p(X1))) | (~p(X4))) <=> ((~p(X4)) | (~p(X1)) | (~esk2_0))), (((((~esk2_0) | (~p(X1))) | (~p(X4))) | (~p(X2))) <=> (((~p(X4)) | (~p(X1)) | (~esk2_0)) | (~p(X2))))), rewrite((((~p(X4)) | (~p(X1)) | (~esk2_0)) | (~p(X2))) <=> ((~p(X4)) | (~p(X2)) | (~p(X1)) | (~esk2_0))), (((((~esk2_0) | (~p(X1))) | (~p(X4))) | (~p(X2))) <=> ((~p(X4)) | (~p(X2)) | (~p(X1)) | (~esk2_0)))), ((((((~esk2_0) | (~p(X1))) | (~p(X4))) | (~p(X2))) | (~p(X3))) <=> (((~p(X4)) | (~p(X2)) | (~p(X1)) | (~esk2_0)) | (~p(X3))))), rewrite((((~p(X4)) | (~p(X2)) | (~p(X1)) | (~esk2_0)) | (~p(X3))) <=> ((~p(X3)) | (~p(X4)) | (~p(X2)) | (~p(X1)) | (~esk2_0))), ((((((~esk2_0) | (~p(X1))) | (~p(X4))) | (~p(X2))) | (~p(X3))) <=> ((~p(X3)) | (~p(X4)) | (~p(X2)) | (~p(X1)) | (~esk2_0)))), (((((((~esk2_0) | (~p(X1))) | (~p(X4))) | (~p(X2))) | (~p(X3))) | esk17487_4(X1, X2, X3, X4)) <=> (((~p(X3)) | (~p(X4)) | (~p(X2)) | (~p(X1)) | (~esk2_0)) | esk17487_4(X1, X2, X3, X4)))), rewrite((((~p(X3)) | (~p(X4)) | (~p(X2)) | (~p(X1)) | (~esk2_0)) | esk17487_4(X1, X2, X3, X4)) <=> ((~p(X3)) | (~p(X4)) | (~p(X2)) | (~p(X1)) | (~esk2_0) | esk17487_4(X1, X2, X3, X4))), (((((((~esk2_0) | (~p(X1))) | (~p(X4))) | (~p(X2))) | (~p(X3))) | esk17487_4(X1, X2, X3, X4)) <=> ((~p(X3)) | (~p(X4)) | (~p(X2)) | (~p(X1)) | (~esk2_0) | esk17487_4(X1, X2, X3, X4))))),
% 26.04/18.26 inference(bind,[status(th)],[])).
% 26.04/18.26 tff(93,plain,
% 26.04/18.26 (![X4: $i, X3: $i, X2: $i, X1: $i] : ((((((~esk2_0) | (~p(X1))) | (~p(X4))) | (~p(X2))) | (~p(X3))) | esk17487_4(X1, X2, X3, X4)) <=> ![X4: $i, X3: $i, X2: $i, X1: $i] : ((~p(X3)) | (~p(X4)) | (~p(X2)) | (~p(X1)) | (~esk2_0) | esk17487_4(X1, X2, X3, X4))),
% 26.04/18.26 inference(quant_intro,[status(thm)],[92])).
% 26.04/18.26 tff(94,axiom,(![X4: $i, X3: $i, X2: $i, X1: $i] : ((((((~esk2_0) | (~p(X1))) | (~p(X4))) | (~p(X2))) | (~p(X3))) | esk17487_4(X1, X2, X3, X4))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','i_0_41776')).
% 26.04/18.26 tff(95,plain,
% 26.04/18.26 (![X4: $i, X3: $i, X2: $i, X1: $i] : ((~p(X3)) | (~p(X4)) | (~p(X2)) | (~p(X1)) | (~esk2_0) | esk17487_4(X1, X2, X3, X4))),
% 26.04/18.26 inference(modus_ponens,[status(thm)],[94, 93])).
% 26.04/18.26 tff(96,plain,
% 26.04/18.26 (![X4: $i, X3: $i, X2: $i, X1: $i] : ((~p(X3)) | (~p(X4)) | (~p(X2)) | (~p(X1)) | esk17487_4(X1, X2, X3, X4))),
% 26.04/18.26 inference(modus_ponens,[status(thm)],[95, 91])).
% 26.04/18.26 tff(97,plain,
% 26.04/18.26 (![X4: $i, X3: $i, X2: $i, X1: $i] : ((~p(X3)) | (~p(X4)) | (~p(X2)) | (~p(X1)) | esk17487_4(X1, X2, X3, X4))),
% 26.04/18.26 inference(modus_ponens,[status(thm)],[96, 89])).
% 26.04/18.26 tff(98,plain,(
% 26.04/18.26 ![X4: $i, X3: $i, X2: $i, X1: $i] : ((~p(X3)) | (~p(X4)) | (~p(X2)) | (~p(X1)) | esk17487_4(X1, X2, X3, X4))),
% 26.04/18.26 inference(skolemize,[status(sab)],[97])).
% 26.04/18.26 tff(99,plain,
% 26.04/18.26 (![X4: $i, X3: $i, X2: $i, X1: $i] : ((~p(X3)) | (~p(X4)) | (~p(X2)) | (~p(X1)) | esk17487_4(X1, X2, X3, X4))),
% 26.04/18.26 inference(modus_ponens,[status(thm)],[98, 88])).
% 26.04/18.26 tff(100,plain,
% 26.04/18.26 (((~![X4: $i, X3: $i, X2: $i, X1: $i] : ((~p(X3)) | (~p(X4)) | (~p(X2)) | (~p(X1)) | esk17487_4(X1, X2, X3, X4))) | ((~p(true)) | esk17487_4(true, true, true, true))) <=> ((~![X4: $i, X3: $i, X2: $i, X1: $i] : ((~p(X3)) | (~p(X4)) | (~p(X2)) | (~p(X1)) | esk17487_4(X1, X2, X3, X4))) | (~p(true)) | esk17487_4(true, true, true, true))),
% 26.04/18.26 inference(rewrite,[status(thm)],[])).
% 26.04/18.26 tff(101,plain,
% 26.04/18.26 (((~p(true)) | (~p(true)) | (~p(true)) | (~p(true)) | esk17487_4(true, true, true, true)) <=> ((~p(true)) | esk17487_4(true, true, true, true))),
% 26.04/18.26 inference(rewrite,[status(thm)],[])).
% 26.04/18.26 tff(102,plain,
% 26.04/18.26 (((~![X4: $i, X3: $i, X2: $i, X1: $i] : ((~p(X3)) | (~p(X4)) | (~p(X2)) | (~p(X1)) | esk17487_4(X1, X2, X3, X4))) | ((~p(true)) | (~p(true)) | (~p(true)) | (~p(true)) | esk17487_4(true, true, true, true))) <=> ((~![X4: $i, X3: $i, X2: $i, X1: $i] : ((~p(X3)) | (~p(X4)) | (~p(X2)) | (~p(X1)) | esk17487_4(X1, X2, X3, X4))) | ((~p(true)) | esk17487_4(true, true, true, true)))),
% 26.04/18.26 inference(monotonicity,[status(thm)],[101])).
% 26.04/18.26 tff(103,plain,
% 26.04/18.26 (((~![X4: $i, X3: $i, X2: $i, X1: $i] : ((~p(X3)) | (~p(X4)) | (~p(X2)) | (~p(X1)) | esk17487_4(X1, X2, X3, X4))) | ((~p(true)) | (~p(true)) | (~p(true)) | (~p(true)) | esk17487_4(true, true, true, true))) <=> ((~![X4: $i, X3: $i, X2: $i, X1: $i] : ((~p(X3)) | (~p(X4)) | (~p(X2)) | (~p(X1)) | esk17487_4(X1, X2, X3, X4))) | (~p(true)) | esk17487_4(true, true, true, true))),
% 26.04/18.26 inference(transitivity,[status(thm)],[102, 100])).
% 26.04/18.26 tff(104,plain,
% 26.04/18.26 ((~![X4: $i, X3: $i, X2: $i, X1: $i] : ((~p(X3)) | (~p(X4)) | (~p(X2)) | (~p(X1)) | esk17487_4(X1, X2, X3, X4))) | ((~p(true)) | (~p(true)) | (~p(true)) | (~p(true)) | esk17487_4(true, true, true, true))),
% 26.04/18.26 inference(quant_inst,[status(thm)],[])).
% 26.04/18.26 tff(105,plain,
% 26.04/18.26 ((~![X4: $i, X3: $i, X2: $i, X1: $i] : ((~p(X3)) | (~p(X4)) | (~p(X2)) | (~p(X1)) | esk17487_4(X1, X2, X3, X4))) | (~p(true)) | esk17487_4(true, true, true, true)),
% 26.04/18.26 inference(modus_ponens,[status(thm)],[104, 103])).
% 26.04/18.26 tff(106,plain,
% 26.04/18.26 (esk17487_4(true, true, true, true)),
% 26.04/18.26 inference(unit_resolution,[status(thm)],[105, 99, 4])).
% 26.04/18.26 tff(107,plain,
% 26.04/18.26 (^[X4: $i, X3: $i, X2: $i, X1: $i] : refl(((~esk17487_4(X1, X2, X3, X4)) | esk17440_4(X1, X2, X3, X4)) <=> ((~esk17487_4(X1, X2, X3, X4)) | esk17440_4(X1, X2, X3, X4)))),
% 26.04/18.26 inference(bind,[status(th)],[])).
% 26.04/18.26 tff(108,plain,
% 26.04/18.26 (![X4: $i, X3: $i, X2: $i, X1: $i] : ((~esk17487_4(X1, X2, X3, X4)) | esk17440_4(X1, X2, X3, X4)) <=> ![X4: $i, X3: $i, X2: $i, X1: $i] : ((~esk17487_4(X1, X2, X3, X4)) | esk17440_4(X1, X2, X3, X4))),
% 26.04/18.26 inference(quant_intro,[status(thm)],[107])).
% 26.04/18.26 tff(109,plain,
% 26.04/18.26 (![X4: $i, X3: $i, X2: $i, X1: $i] : ((~esk17487_4(X1, X2, X3, X4)) | esk17440_4(X1, X2, X3, X4)) <=> ![X4: $i, X3: $i, X2: $i, X1: $i] : ((~esk17487_4(X1, X2, X3, X4)) | esk17440_4(X1, X2, X3, X4))),
% 26.04/18.26 inference(rewrite,[status(thm)],[])).
% 26.04/18.26 tff(110,plain,
% 26.04/18.26 (^[X4: $i, X3: $i, X2: $i, X1: $i] : rewrite((esk17440_4(X1, X2, X3, X4) | (~esk17487_4(X1, X2, X3, X4))) <=> ((~esk17487_4(X1, X2, X3, X4)) | esk17440_4(X1, X2, X3, X4)))),
% 26.04/18.26 inference(bind,[status(th)],[])).
% 26.04/18.26 tff(111,plain,
% 26.04/18.26 (![X4: $i, X3: $i, X2: $i, X1: $i] : (esk17440_4(X1, X2, X3, X4) | (~esk17487_4(X1, X2, X3, X4))) <=> ![X4: $i, X3: $i, X2: $i, X1: $i] : ((~esk17487_4(X1, X2, X3, X4)) | esk17440_4(X1, X2, X3, X4))),
% 26.04/18.26 inference(quant_intro,[status(thm)],[110])).
% 26.04/18.26 tff(112,axiom,(![X4: $i, X3: $i, X2: $i, X1: $i] : (esk17440_4(X1, X2, X3, X4) | (~esk17487_4(X1, X2, X3, X4)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','i_0_15234')).
% 26.04/18.26 tff(113,plain,
% 26.04/18.26 (![X4: $i, X3: $i, X2: $i, X1: $i] : ((~esk17487_4(X1, X2, X3, X4)) | esk17440_4(X1, X2, X3, X4))),
% 26.04/18.26 inference(modus_ponens,[status(thm)],[112, 111])).
% 26.04/18.26 tff(114,plain,
% 26.04/18.26 (![X4: $i, X3: $i, X2: $i, X1: $i] : ((~esk17487_4(X1, X2, X3, X4)) | esk17440_4(X1, X2, X3, X4))),
% 26.04/18.26 inference(modus_ponens,[status(thm)],[113, 109])).
% 26.04/18.26 tff(115,plain,(
% 26.04/18.26 ![X4: $i, X3: $i, X2: $i, X1: $i] : ((~esk17487_4(X1, X2, X3, X4)) | esk17440_4(X1, X2, X3, X4))),
% 26.04/18.26 inference(skolemize,[status(sab)],[114])).
% 26.04/18.26 tff(116,plain,
% 26.04/18.26 (![X4: $i, X3: $i, X2: $i, X1: $i] : ((~esk17487_4(X1, X2, X3, X4)) | esk17440_4(X1, X2, X3, X4))),
% 26.04/18.26 inference(modus_ponens,[status(thm)],[115, 108])).
% 26.04/18.26 tff(117,plain,
% 26.04/18.26 (((~![X4: $i, X3: $i, X2: $i, X1: $i] : ((~esk17487_4(X1, X2, X3, X4)) | esk17440_4(X1, X2, X3, X4))) | ((~esk17487_4(true, true, true, true)) | esk17440_4(true, true, true, true))) <=> ((~![X4: $i, X3: $i, X2: $i, X1: $i] : ((~esk17487_4(X1, X2, X3, X4)) | esk17440_4(X1, X2, X3, X4))) | (~esk17487_4(true, true, true, true)) | esk17440_4(true, true, true, true))),
% 26.04/18.26 inference(rewrite,[status(thm)],[])).
% 26.04/18.26 tff(118,plain,
% 26.04/18.26 ((~![X4: $i, X3: $i, X2: $i, X1: $i] : ((~esk17487_4(X1, X2, X3, X4)) | esk17440_4(X1, X2, X3, X4))) | ((~esk17487_4(true, true, true, true)) | esk17440_4(true, true, true, true))),
% 26.04/18.26 inference(quant_inst,[status(thm)],[])).
% 26.04/18.26 tff(119,plain,
% 26.04/18.26 ((~![X4: $i, X3: $i, X2: $i, X1: $i] : ((~esk17487_4(X1, X2, X3, X4)) | esk17440_4(X1, X2, X3, X4))) | (~esk17487_4(true, true, true, true)) | esk17440_4(true, true, true, true)),
% 26.04/18.26 inference(modus_ponens,[status(thm)],[118, 117])).
% 26.04/18.26 tff(120,plain,
% 26.04/18.26 (esk17440_4(true, true, true, true)),
% 26.04/18.26 inference(unit_resolution,[status(thm)],[119, 116, 106])).
% 26.04/18.26 tff(121,plain,
% 26.04/18.26 (^[X4: $i, X3: $i, X2: $i, X1: $i] : refl((esk17438_4(X1, X2, X3, X4) | esk17439_4(X1, X2, X3, X4) | (~esk17440_4(X1, X2, X3, X4))) <=> (esk17438_4(X1, X2, X3, X4) | esk17439_4(X1, X2, X3, X4) | (~esk17440_4(X1, X2, X3, X4))))),
% 26.04/18.26 inference(bind,[status(th)],[])).
% 26.04/18.26 tff(122,plain,
% 26.04/18.26 (![X4: $i, X3: $i, X2: $i, X1: $i] : (esk17438_4(X1, X2, X3, X4) | esk17439_4(X1, X2, X3, X4) | (~esk17440_4(X1, X2, X3, X4))) <=> ![X4: $i, X3: $i, X2: $i, X1: $i] : (esk17438_4(X1, X2, X3, X4) | esk17439_4(X1, X2, X3, X4) | (~esk17440_4(X1, X2, X3, X4)))),
% 26.04/18.26 inference(quant_intro,[status(thm)],[121])).
% 26.04/18.26 tff(123,plain,
% 26.04/18.26 (![X4: $i, X3: $i, X2: $i, X1: $i] : (esk17438_4(X1, X2, X3, X4) | esk17439_4(X1, X2, X3, X4) | (~esk17440_4(X1, X2, X3, X4))) <=> ![X4: $i, X3: $i, X2: $i, X1: $i] : (esk17438_4(X1, X2, X3, X4) | esk17439_4(X1, X2, X3, X4) | (~esk17440_4(X1, X2, X3, X4)))),
% 26.04/18.26 inference(rewrite,[status(thm)],[])).
% 26.04/18.26 tff(124,plain,
% 26.04/18.26 (^[X4: $i, X3: $i, X2: $i, X1: $i] : trans(monotonicity(rewrite((esk17439_4(X1, X2, X3, X4) | esk17438_4(X1, X2, X3, X4)) <=> (esk17438_4(X1, X2, X3, X4) | esk17439_4(X1, X2, X3, X4))), (((esk17439_4(X1, X2, X3, X4) | esk17438_4(X1, X2, X3, X4)) | (~esk17440_4(X1, X2, X3, X4))) <=> ((esk17438_4(X1, X2, X3, X4) | esk17439_4(X1, X2, X3, X4)) | (~esk17440_4(X1, X2, X3, X4))))), rewrite(((esk17438_4(X1, X2, X3, X4) | esk17439_4(X1, X2, X3, X4)) | (~esk17440_4(X1, X2, X3, X4))) <=> (esk17438_4(X1, X2, X3, X4) | esk17439_4(X1, X2, X3, X4) | (~esk17440_4(X1, X2, X3, X4)))), (((esk17439_4(X1, X2, X3, X4) | esk17438_4(X1, X2, X3, X4)) | (~esk17440_4(X1, X2, X3, X4))) <=> (esk17438_4(X1, X2, X3, X4) | esk17439_4(X1, X2, X3, X4) | (~esk17440_4(X1, X2, X3, X4)))))),
% 26.04/18.26 inference(bind,[status(th)],[])).
% 26.04/18.26 tff(125,plain,
% 26.04/18.26 (![X4: $i, X3: $i, X2: $i, X1: $i] : ((esk17439_4(X1, X2, X3, X4) | esk17438_4(X1, X2, X3, X4)) | (~esk17440_4(X1, X2, X3, X4))) <=> ![X4: $i, X3: $i, X2: $i, X1: $i] : (esk17438_4(X1, X2, X3, X4) | esk17439_4(X1, X2, X3, X4) | (~esk17440_4(X1, X2, X3, X4)))),
% 26.04/18.26 inference(quant_intro,[status(thm)],[124])).
% 26.04/18.26 tff(126,axiom,(![X4: $i, X3: $i, X2: $i, X1: $i] : ((esk17439_4(X1, X2, X3, X4) | esk17438_4(X1, X2, X3, X4)) | (~esk17440_4(X1, X2, X3, X4)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','i_0_49341')).
% 26.04/18.26 tff(127,plain,
% 26.04/18.26 (![X4: $i, X3: $i, X2: $i, X1: $i] : (esk17438_4(X1, X2, X3, X4) | esk17439_4(X1, X2, X3, X4) | (~esk17440_4(X1, X2, X3, X4)))),
% 26.04/18.26 inference(modus_ponens,[status(thm)],[126, 125])).
% 26.04/18.26 tff(128,plain,
% 26.04/18.26 (![X4: $i, X3: $i, X2: $i, X1: $i] : (esk17438_4(X1, X2, X3, X4) | esk17439_4(X1, X2, X3, X4) | (~esk17440_4(X1, X2, X3, X4)))),
% 26.04/18.26 inference(modus_ponens,[status(thm)],[127, 123])).
% 26.04/18.26 tff(129,plain,(
% 26.04/18.26 ![X4: $i, X3: $i, X2: $i, X1: $i] : (esk17438_4(X1, X2, X3, X4) | esk17439_4(X1, X2, X3, X4) | (~esk17440_4(X1, X2, X3, X4)))),
% 26.04/18.26 inference(skolemize,[status(sab)],[128])).
% 26.04/18.26 tff(130,plain,
% 26.04/18.26 (![X4: $i, X3: $i, X2: $i, X1: $i] : (esk17438_4(X1, X2, X3, X4) | esk17439_4(X1, X2, X3, X4) | (~esk17440_4(X1, X2, X3, X4)))),
% 26.04/18.26 inference(modus_ponens,[status(thm)],[129, 122])).
% 26.04/18.26 tff(131,plain,
% 26.04/18.26 (((~![X4: $i, X3: $i, X2: $i, X1: $i] : (esk17438_4(X1, X2, X3, X4) | esk17439_4(X1, X2, X3, X4) | (~esk17440_4(X1, X2, X3, X4)))) | (esk17438_4(true, true, true, true) | esk17439_4(true, true, true, true) | (~esk17440_4(true, true, true, true)))) <=> ((~![X4: $i, X3: $i, X2: $i, X1: $i] : (esk17438_4(X1, X2, X3, X4) | esk17439_4(X1, X2, X3, X4) | (~esk17440_4(X1, X2, X3, X4)))) | esk17438_4(true, true, true, true) | esk17439_4(true, true, true, true) | (~esk17440_4(true, true, true, true)))),
% 26.04/18.26 inference(rewrite,[status(thm)],[])).
% 26.04/18.26 tff(132,plain,
% 26.04/18.26 ((~![X4: $i, X3: $i, X2: $i, X1: $i] : (esk17438_4(X1, X2, X3, X4) | esk17439_4(X1, X2, X3, X4) | (~esk17440_4(X1, X2, X3, X4)))) | (esk17438_4(true, true, true, true) | esk17439_4(true, true, true, true) | (~esk17440_4(true, true, true, true)))),
% 26.04/18.26 inference(quant_inst,[status(thm)],[])).
% 26.04/18.26 tff(133,plain,
% 26.04/18.26 ((~![X4: $i, X3: $i, X2: $i, X1: $i] : (esk17438_4(X1, X2, X3, X4) | esk17439_4(X1, X2, X3, X4) | (~esk17440_4(X1, X2, X3, X4)))) | esk17438_4(true, true, true, true) | esk17439_4(true, true, true, true) | (~esk17440_4(true, true, true, true))),
% 26.04/18.26 inference(modus_ponens,[status(thm)],[132, 131])).
% 26.04/18.26 tff(134,plain,
% 26.04/18.26 (esk17438_4(true, true, true, true) | esk17439_4(true, true, true, true)),
% 26.04/18.26 inference(unit_resolution,[status(thm)],[133, 130, 120])).
% 26.04/18.26 tff(135,plain,
% 26.04/18.26 (esk17438_4(true, true, true, true)),
% 26.04/18.26 inference(unit_resolution,[status(thm)],[134, 86])).
% 26.04/18.26 tff(136,plain,
% 26.04/18.26 (^[X4: $i, X3: $i, X2: $i, X1: $i] : refl(((~esk17438_4(X1, X2, X3, X4)) | esk17437_4(X1, X2, X3, X4)) <=> ((~esk17438_4(X1, X2, X3, X4)) | esk17437_4(X1, X2, X3, X4)))),
% 26.04/18.26 inference(bind,[status(th)],[])).
% 26.04/18.26 tff(137,plain,
% 26.04/18.26 (![X4: $i, X3: $i, X2: $i, X1: $i] : ((~esk17438_4(X1, X2, X3, X4)) | esk17437_4(X1, X2, X3, X4)) <=> ![X4: $i, X3: $i, X2: $i, X1: $i] : ((~esk17438_4(X1, X2, X3, X4)) | esk17437_4(X1, X2, X3, X4))),
% 26.04/18.26 inference(quant_intro,[status(thm)],[136])).
% 26.04/18.26 tff(138,plain,
% 26.04/18.26 (![X4: $i, X3: $i, X2: $i, X1: $i] : ((~esk17438_4(X1, X2, X3, X4)) | esk17437_4(X1, X2, X3, X4)) <=> ![X4: $i, X3: $i, X2: $i, X1: $i] : ((~esk17438_4(X1, X2, X3, X4)) | esk17437_4(X1, X2, X3, X4))),
% 26.04/18.26 inference(rewrite,[status(thm)],[])).
% 26.04/18.26 tff(139,plain,
% 26.04/18.26 (^[X4: $i, X3: $i, X2: $i, X1: $i] : rewrite((esk17437_4(X1, X2, X3, X4) | (~esk17438_4(X1, X2, X3, X4))) <=> ((~esk17438_4(X1, X2, X3, X4)) | esk17437_4(X1, X2, X3, X4)))),
% 26.04/18.26 inference(bind,[status(th)],[])).
% 26.04/18.26 tff(140,plain,
% 26.04/18.26 (![X4: $i, X3: $i, X2: $i, X1: $i] : (esk17437_4(X1, X2, X3, X4) | (~esk17438_4(X1, X2, X3, X4))) <=> ![X4: $i, X3: $i, X2: $i, X1: $i] : ((~esk17438_4(X1, X2, X3, X4)) | esk17437_4(X1, X2, X3, X4))),
% 26.04/18.26 inference(quant_intro,[status(thm)],[139])).
% 26.04/18.26 tff(141,axiom,(![X4: $i, X3: $i, X2: $i, X1: $i] : (esk17437_4(X1, X2, X3, X4) | (~esk17438_4(X1, X2, X3, X4)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','i_0_2135')).
% 26.04/18.26 tff(142,plain,
% 26.04/18.26 (![X4: $i, X3: $i, X2: $i, X1: $i] : ((~esk17438_4(X1, X2, X3, X4)) | esk17437_4(X1, X2, X3, X4))),
% 26.04/18.26 inference(modus_ponens,[status(thm)],[141, 140])).
% 26.04/18.26 tff(143,plain,
% 26.04/18.26 (![X4: $i, X3: $i, X2: $i, X1: $i] : ((~esk17438_4(X1, X2, X3, X4)) | esk17437_4(X1, X2, X3, X4))),
% 26.04/18.26 inference(modus_ponens,[status(thm)],[142, 138])).
% 26.04/18.26 tff(144,plain,(
% 26.04/18.26 ![X4: $i, X3: $i, X2: $i, X1: $i] : ((~esk17438_4(X1, X2, X3, X4)) | esk17437_4(X1, X2, X3, X4))),
% 26.04/18.26 inference(skolemize,[status(sab)],[143])).
% 26.04/18.26 tff(145,plain,
% 26.04/18.26 (![X4: $i, X3: $i, X2: $i, X1: $i] : ((~esk17438_4(X1, X2, X3, X4)) | esk17437_4(X1, X2, X3, X4))),
% 26.04/18.26 inference(modus_ponens,[status(thm)],[144, 137])).
% 26.04/18.26 tff(146,plain,
% 26.04/18.26 (((~![X4: $i, X3: $i, X2: $i, X1: $i] : ((~esk17438_4(X1, X2, X3, X4)) | esk17437_4(X1, X2, X3, X4))) | ((~esk17438_4(true, true, true, true)) | esk17437_4(true, true, true, true))) <=> ((~![X4: $i, X3: $i, X2: $i, X1: $i] : ((~esk17438_4(X1, X2, X3, X4)) | esk17437_4(X1, X2, X3, X4))) | (~esk17438_4(true, true, true, true)) | esk17437_4(true, true, true, true))),
% 26.04/18.26 inference(rewrite,[status(thm)],[])).
% 26.04/18.26 tff(147,plain,
% 26.04/18.26 ((~![X4: $i, X3: $i, X2: $i, X1: $i] : ((~esk17438_4(X1, X2, X3, X4)) | esk17437_4(X1, X2, X3, X4))) | ((~esk17438_4(true, true, true, true)) | esk17437_4(true, true, true, true))),
% 26.04/18.26 inference(quant_inst,[status(thm)],[])).
% 26.04/18.26 tff(148,plain,
% 26.04/18.26 ((~![X4: $i, X3: $i, X2: $i, X1: $i] : ((~esk17438_4(X1, X2, X3, X4)) | esk17437_4(X1, X2, X3, X4))) | (~esk17438_4(true, true, true, true)) | esk17437_4(true, true, true, true)),
% 26.04/18.26 inference(modus_ponens,[status(thm)],[147, 146])).
% 26.04/18.26 tff(149,plain,
% 26.04/18.26 (esk17437_4(true, true, true, true)),
% 26.04/18.26 inference(unit_resolution,[status(thm)],[148, 145, 135])).
% 26.04/18.26 tff(150,plain,
% 26.04/18.26 (^[X4: $i, X3: $i, X2: $i, X1: $i] : refl(((~esk17139_4(X1, X2, X3, X4)) | (~esk17437_4(X1, X2, X3, X4))) <=> ((~esk17139_4(X1, X2, X3, X4)) | (~esk17437_4(X1, X2, X3, X4))))),
% 26.04/18.26 inference(bind,[status(th)],[])).
% 26.04/18.26 tff(151,plain,
% 26.04/18.26 (![X4: $i, X3: $i, X2: $i, X1: $i] : ((~esk17139_4(X1, X2, X3, X4)) | (~esk17437_4(X1, X2, X3, X4))) <=> ![X4: $i, X3: $i, X2: $i, X1: $i] : ((~esk17139_4(X1, X2, X3, X4)) | (~esk17437_4(X1, X2, X3, X4)))),
% 26.04/18.26 inference(quant_intro,[status(thm)],[150])).
% 26.04/18.26 tff(152,plain,
% 26.04/18.26 (![X4: $i, X3: $i, X2: $i, X1: $i] : ((~esk17139_4(X1, X2, X3, X4)) | (~esk17437_4(X1, X2, X3, X4))) <=> ![X4: $i, X3: $i, X2: $i, X1: $i] : ((~esk17139_4(X1, X2, X3, X4)) | (~esk17437_4(X1, X2, X3, X4)))),
% 26.04/18.26 inference(rewrite,[status(thm)],[])).
% 26.04/18.26 tff(153,axiom,(![X4: $i, X3: $i, X2: $i, X1: $i] : ((~esk17139_4(X1, X2, X3, X4)) | (~esk17437_4(X1, X2, X3, X4)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','i_0_21673')).
% 26.04/18.26 tff(154,plain,
% 26.04/18.26 (![X4: $i, X3: $i, X2: $i, X1: $i] : ((~esk17139_4(X1, X2, X3, X4)) | (~esk17437_4(X1, X2, X3, X4)))),
% 26.04/18.26 inference(modus_ponens,[status(thm)],[153, 152])).
% 26.04/18.26 tff(155,plain,(
% 26.04/18.26 ![X4: $i, X3: $i, X2: $i, X1: $i] : ((~esk17139_4(X1, X2, X3, X4)) | (~esk17437_4(X1, X2, X3, X4)))),
% 26.04/18.26 inference(skolemize,[status(sab)],[154])).
% 26.04/18.26 tff(156,plain,
% 26.04/18.26 (![X4: $i, X3: $i, X2: $i, X1: $i] : ((~esk17139_4(X1, X2, X3, X4)) | (~esk17437_4(X1, X2, X3, X4)))),
% 26.04/18.26 inference(modus_ponens,[status(thm)],[155, 151])).
% 26.04/18.26 tff(157,plain,
% 26.04/18.26 (((~![X4: $i, X3: $i, X2: $i, X1: $i] : ((~esk17139_4(X1, X2, X3, X4)) | (~esk17437_4(X1, X2, X3, X4)))) | ((~esk17139_4(true, true, true, true)) | (~esk17437_4(true, true, true, true)))) <=> ((~![X4: $i, X3: $i, X2: $i, X1: $i] : ((~esk17139_4(X1, X2, X3, X4)) | (~esk17437_4(X1, X2, X3, X4)))) | (~esk17139_4(true, true, true, true)) | (~esk17437_4(true, true, true, true)))),
% 26.04/18.26 inference(rewrite,[status(thm)],[])).
% 26.04/18.26 tff(158,plain,
% 26.04/18.26 ((~![X4: $i, X3: $i, X2: $i, X1: $i] : ((~esk17139_4(X1, X2, X3, X4)) | (~esk17437_4(X1, X2, X3, X4)))) | ((~esk17139_4(true, true, true, true)) | (~esk17437_4(true, true, true, true)))),
% 26.04/18.26 inference(quant_inst,[status(thm)],[])).
% 26.04/18.26 tff(159,plain,
% 26.04/18.26 ((~![X4: $i, X3: $i, X2: $i, X1: $i] : ((~esk17139_4(X1, X2, X3, X4)) | (~esk17437_4(X1, X2, X3, X4)))) | (~esk17139_4(true, true, true, true)) | (~esk17437_4(true, true, true, true))),
% 26.04/18.26 inference(modus_ponens,[status(thm)],[158, 157])).
% 26.04/18.26 tff(160,plain,
% 26.04/18.26 (~esk17139_4(true, true, true, true)),
% 26.04/18.26 inference(unit_resolution,[status(thm)],[159, 156, 149])).
% 26.04/18.26 tff(161,plain,
% 26.04/18.26 (^[X4: $i, X3: $i, X2: $i, X1: $i] : refl((esk17139_4(X1, X2, X3, X4) | esk16375_4(X1, X2, X3, X4)) <=> (esk17139_4(X1, X2, X3, X4) | esk16375_4(X1, X2, X3, X4)))),
% 26.04/18.26 inference(bind,[status(th)],[])).
% 26.04/18.26 tff(162,plain,
% 26.04/18.26 (![X4: $i, X3: $i, X2: $i, X1: $i] : (esk17139_4(X1, X2, X3, X4) | esk16375_4(X1, X2, X3, X4)) <=> ![X4: $i, X3: $i, X2: $i, X1: $i] : (esk17139_4(X1, X2, X3, X4) | esk16375_4(X1, X2, X3, X4))),
% 26.04/18.26 inference(quant_intro,[status(thm)],[161])).
% 26.04/18.26 tff(163,plain,
% 26.04/18.26 (![X4: $i, X3: $i, X2: $i, X1: $i] : (esk17139_4(X1, X2, X3, X4) | esk16375_4(X1, X2, X3, X4)) <=> ![X4: $i, X3: $i, X2: $i, X1: $i] : (esk17139_4(X1, X2, X3, X4) | esk16375_4(X1, X2, X3, X4))),
% 26.04/18.26 inference(rewrite,[status(thm)],[])).
% 26.04/18.26 tff(164,axiom,(![X4: $i, X3: $i, X2: $i, X1: $i] : (esk17139_4(X1, X2, X3, X4) | esk16375_4(X1, X2, X3, X4))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','i_0_21084')).
% 26.04/18.26 tff(165,plain,
% 26.04/18.26 (![X4: $i, X3: $i, X2: $i, X1: $i] : (esk17139_4(X1, X2, X3, X4) | esk16375_4(X1, X2, X3, X4))),
% 26.04/18.26 inference(modus_ponens,[status(thm)],[164, 163])).
% 26.04/18.26 tff(166,plain,(
% 26.04/18.26 ![X4: $i, X3: $i, X2: $i, X1: $i] : (esk17139_4(X1, X2, X3, X4) | esk16375_4(X1, X2, X3, X4))),
% 26.04/18.26 inference(skolemize,[status(sab)],[165])).
% 26.04/18.26 tff(167,plain,
% 26.04/18.26 (![X4: $i, X3: $i, X2: $i, X1: $i] : (esk17139_4(X1, X2, X3, X4) | esk16375_4(X1, X2, X3, X4))),
% 26.04/18.26 inference(modus_ponens,[status(thm)],[166, 162])).
% 26.04/18.26 tff(168,plain,
% 26.04/18.26 (((~![X4: $i, X3: $i, X2: $i, X1: $i] : (esk17139_4(X1, X2, X3, X4) | esk16375_4(X1, X2, X3, X4))) | (esk17139_4(true, true, true, true) | esk16375_4(true, true, true, true))) <=> ((~![X4: $i, X3: $i, X2: $i, X1: $i] : (esk17139_4(X1, X2, X3, X4) | esk16375_4(X1, X2, X3, X4))) | esk17139_4(true, true, true, true) | esk16375_4(true, true, true, true))),
% 26.04/18.26 inference(rewrite,[status(thm)],[])).
% 26.04/18.26 tff(169,plain,
% 26.04/18.26 ((~![X4: $i, X3: $i, X2: $i, X1: $i] : (esk17139_4(X1, X2, X3, X4) | esk16375_4(X1, X2, X3, X4))) | (esk17139_4(true, true, true, true) | esk16375_4(true, true, true, true))),
% 26.04/18.26 inference(quant_inst,[status(thm)],[])).
% 26.04/18.26 tff(170,plain,
% 26.04/18.26 ((~![X4: $i, X3: $i, X2: $i, X1: $i] : (esk17139_4(X1, X2, X3, X4) | esk16375_4(X1, X2, X3, X4))) | esk17139_4(true, true, true, true) | esk16375_4(true, true, true, true)),
% 26.04/18.26 inference(modus_ponens,[status(thm)],[169, 168])).
% 26.04/18.26 tff(171,plain,
% 26.04/18.26 (esk16375_4(true, true, true, true)),
% 26.04/18.26 inference(unit_resolution,[status(thm)],[170, 167, 160])).
% 26.04/18.26 tff(172,plain,
% 26.04/18.26 (^[X4: $i, X3: $i, X2: $i, X1: $i] : refl(((~esk16375_4(X1, X2, X3, X4)) | (~esk16569_4(X1, X2, X3, X4))) <=> ((~esk16375_4(X1, X2, X3, X4)) | (~esk16569_4(X1, X2, X3, X4))))),
% 26.04/18.26 inference(bind,[status(th)],[])).
% 26.04/18.26 tff(173,plain,
% 26.04/18.26 (![X4: $i, X3: $i, X2: $i, X1: $i] : ((~esk16375_4(X1, X2, X3, X4)) | (~esk16569_4(X1, X2, X3, X4))) <=> ![X4: $i, X3: $i, X2: $i, X1: $i] : ((~esk16375_4(X1, X2, X3, X4)) | (~esk16569_4(X1, X2, X3, X4)))),
% 26.04/18.26 inference(quant_intro,[status(thm)],[172])).
% 26.04/18.26 tff(174,plain,
% 26.04/18.26 (![X4: $i, X3: $i, X2: $i, X1: $i] : ((~esk16375_4(X1, X2, X3, X4)) | (~esk16569_4(X1, X2, X3, X4))) <=> ![X4: $i, X3: $i, X2: $i, X1: $i] : ((~esk16375_4(X1, X2, X3, X4)) | (~esk16569_4(X1, X2, X3, X4)))),
% 26.04/18.26 inference(rewrite,[status(thm)],[])).
% 26.04/18.26 tff(175,axiom,(![X4: $i, X3: $i, X2: $i, X1: $i] : ((~esk16375_4(X1, X2, X3, X4)) | (~esk16569_4(X1, X2, X3, X4)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','i_0_29723')).
% 26.04/18.26 tff(176,plain,
% 26.04/18.26 (![X4: $i, X3: $i, X2: $i, X1: $i] : ((~esk16375_4(X1, X2, X3, X4)) | (~esk16569_4(X1, X2, X3, X4)))),
% 26.04/18.26 inference(modus_ponens,[status(thm)],[175, 174])).
% 26.04/18.26 tff(177,plain,(
% 26.04/18.26 ![X4: $i, X3: $i, X2: $i, X1: $i] : ((~esk16375_4(X1, X2, X3, X4)) | (~esk16569_4(X1, X2, X3, X4)))),
% 26.04/18.26 inference(skolemize,[status(sab)],[176])).
% 26.04/18.26 tff(178,plain,
% 26.04/18.26 (![X4: $i, X3: $i, X2: $i, X1: $i] : ((~esk16375_4(X1, X2, X3, X4)) | (~esk16569_4(X1, X2, X3, X4)))),
% 26.04/18.26 inference(modus_ponens,[status(thm)],[177, 173])).
% 26.04/18.26 tff(179,plain,
% 26.04/18.26 (((~![X4: $i, X3: $i, X2: $i, X1: $i] : ((~esk16375_4(X1, X2, X3, X4)) | (~esk16569_4(X1, X2, X3, X4)))) | ((~esk16375_4(true, true, true, true)) | (~esk16569_4(true, true, true, true)))) <=> ((~![X4: $i, X3: $i, X2: $i, X1: $i] : ((~esk16375_4(X1, X2, X3, X4)) | (~esk16569_4(X1, X2, X3, X4)))) | (~esk16375_4(true, true, true, true)) | (~esk16569_4(true, true, true, true)))),
% 26.04/18.26 inference(rewrite,[status(thm)],[])).
% 26.04/18.26 tff(180,plain,
% 26.04/18.26 ((~![X4: $i, X3: $i, X2: $i, X1: $i] : ((~esk16375_4(X1, X2, X3, X4)) | (~esk16569_4(X1, X2, X3, X4)))) | ((~esk16375_4(true, true, true, true)) | (~esk16569_4(true, true, true, true)))),
% 26.04/18.26 inference(quant_inst,[status(thm)],[])).
% 26.04/18.26 tff(181,plain,
% 26.04/18.26 ((~![X4: $i, X3: $i, X2: $i, X1: $i] : ((~esk16375_4(X1, X2, X3, X4)) | (~esk16569_4(X1, X2, X3, X4)))) | (~esk16375_4(true, true, true, true)) | (~esk16569_4(true, true, true, true))),
% 26.04/18.26 inference(modus_ponens,[status(thm)],[180, 179])).
% 26.04/18.26 tff(182,plain,
% 26.04/18.26 (~esk16569_4(true, true, true, true)),
% 26.04/18.26 inference(unit_resolution,[status(thm)],[181, 178, 171])).
% 26.04/18.26 tff(183,plain,
% 26.04/18.26 (^[X4: $i, X3: $i, X2: $i, X1: $i] : refl((esk16569_4(X1, X2, X3, X4) | (~esk16221_4(X1, X2, X3, X4))) <=> (esk16569_4(X1, X2, X3, X4) | (~esk16221_4(X1, X2, X3, X4))))),
% 26.04/18.26 inference(bind,[status(th)],[])).
% 26.04/18.26 tff(184,plain,
% 26.04/18.26 (![X4: $i, X3: $i, X2: $i, X1: $i] : (esk16569_4(X1, X2, X3, X4) | (~esk16221_4(X1, X2, X3, X4))) <=> ![X4: $i, X3: $i, X2: $i, X1: $i] : (esk16569_4(X1, X2, X3, X4) | (~esk16221_4(X1, X2, X3, X4)))),
% 26.04/18.26 inference(quant_intro,[status(thm)],[183])).
% 26.04/18.26 tff(185,plain,
% 26.04/18.26 (![X4: $i, X3: $i, X2: $i, X1: $i] : (esk16569_4(X1, X2, X3, X4) | (~esk16221_4(X1, X2, X3, X4))) <=> ![X4: $i, X3: $i, X2: $i, X1: $i] : (esk16569_4(X1, X2, X3, X4) | (~esk16221_4(X1, X2, X3, X4)))),
% 26.04/18.26 inference(rewrite,[status(thm)],[])).
% 26.04/18.26 tff(186,axiom,(![X4: $i, X3: $i, X2: $i, X1: $i] : (esk16569_4(X1, X2, X3, X4) | (~esk16221_4(X1, X2, X3, X4)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','i_0_40910')).
% 26.04/18.26 tff(187,plain,
% 26.04/18.26 (![X4: $i, X3: $i, X2: $i, X1: $i] : (esk16569_4(X1, X2, X3, X4) | (~esk16221_4(X1, X2, X3, X4)))),
% 26.04/18.27 inference(modus_ponens,[status(thm)],[186, 185])).
% 26.04/18.27 tff(188,plain,(
% 26.04/18.27 ![X4: $i, X3: $i, X2: $i, X1: $i] : (esk16569_4(X1, X2, X3, X4) | (~esk16221_4(X1, X2, X3, X4)))),
% 26.04/18.27 inference(skolemize,[status(sab)],[187])).
% 26.04/18.27 tff(189,plain,
% 26.04/18.27 (![X4: $i, X3: $i, X2: $i, X1: $i] : (esk16569_4(X1, X2, X3, X4) | (~esk16221_4(X1, X2, X3, X4)))),
% 26.04/18.27 inference(modus_ponens,[status(thm)],[188, 184])).
% 26.04/18.27 tff(190,plain,
% 26.04/18.27 (((~![X4: $i, X3: $i, X2: $i, X1: $i] : (esk16569_4(X1, X2, X3, X4) | (~esk16221_4(X1, X2, X3, X4)))) | ((~esk16221_4(true, true, true, true)) | esk16569_4(true, true, true, true))) <=> ((~![X4: $i, X3: $i, X2: $i, X1: $i] : (esk16569_4(X1, X2, X3, X4) | (~esk16221_4(X1, X2, X3, X4)))) | (~esk16221_4(true, true, true, true)) | esk16569_4(true, true, true, true))),
% 26.04/18.27 inference(rewrite,[status(thm)],[])).
% 26.04/18.27 tff(191,plain,
% 26.04/18.27 ((esk16569_4(true, true, true, true) | (~esk16221_4(true, true, true, true))) <=> ((~esk16221_4(true, true, true, true)) | esk16569_4(true, true, true, true))),
% 26.04/18.27 inference(rewrite,[status(thm)],[])).
% 26.04/18.27 tff(192,plain,
% 26.04/18.27 (((~![X4: $i, X3: $i, X2: $i, X1: $i] : (esk16569_4(X1, X2, X3, X4) | (~esk16221_4(X1, X2, X3, X4)))) | (esk16569_4(true, true, true, true) | (~esk16221_4(true, true, true, true)))) <=> ((~![X4: $i, X3: $i, X2: $i, X1: $i] : (esk16569_4(X1, X2, X3, X4) | (~esk16221_4(X1, X2, X3, X4)))) | ((~esk16221_4(true, true, true, true)) | esk16569_4(true, true, true, true)))),
% 26.04/18.27 inference(monotonicity,[status(thm)],[191])).
% 26.04/18.27 tff(193,plain,
% 26.04/18.27 (((~![X4: $i, X3: $i, X2: $i, X1: $i] : (esk16569_4(X1, X2, X3, X4) | (~esk16221_4(X1, X2, X3, X4)))) | (esk16569_4(true, true, true, true) | (~esk16221_4(true, true, true, true)))) <=> ((~![X4: $i, X3: $i, X2: $i, X1: $i] : (esk16569_4(X1, X2, X3, X4) | (~esk16221_4(X1, X2, X3, X4)))) | (~esk16221_4(true, true, true, true)) | esk16569_4(true, true, true, true))),
% 26.04/18.27 inference(transitivity,[status(thm)],[192, 190])).
% 26.04/18.27 tff(194,plain,
% 26.04/18.27 ((~![X4: $i, X3: $i, X2: $i, X1: $i] : (esk16569_4(X1, X2, X3, X4) | (~esk16221_4(X1, X2, X3, X4)))) | (esk16569_4(true, true, true, true) | (~esk16221_4(true, true, true, true)))),
% 26.04/18.27 inference(quant_inst,[status(thm)],[])).
% 26.04/18.27 tff(195,plain,
% 26.04/18.27 ((~![X4: $i, X3: $i, X2: $i, X1: $i] : (esk16569_4(X1, X2, X3, X4) | (~esk16221_4(X1, X2, X3, X4)))) | (~esk16221_4(true, true, true, true)) | esk16569_4(true, true, true, true)),
% 26.04/18.27 inference(modus_ponens,[status(thm)],[194, 193])).
% 26.04/18.27 tff(196,plain,
% 26.04/18.27 (~esk16221_4(true, true, true, true)),
% 26.04/18.27 inference(unit_resolution,[status(thm)],[195, 189, 182])).
% 26.04/18.27 tff(197,plain,
% 26.04/18.27 (^[X4: $i, X3: $i, X2: $i, X1: $i] : refl(((~p(X3)) | (~p(X4)) | (~p(X2)) | (~p(X1)) | esk17147_4(X1, X2, X3, X4)) <=> ((~p(X3)) | (~p(X4)) | (~p(X2)) | (~p(X1)) | esk17147_4(X1, X2, X3, X4)))),
% 26.04/18.27 inference(bind,[status(th)],[])).
% 26.04/18.27 tff(198,plain,
% 26.04/18.27 (![X4: $i, X3: $i, X2: $i, X1: $i] : ((~p(X3)) | (~p(X4)) | (~p(X2)) | (~p(X1)) | esk17147_4(X1, X2, X3, X4)) <=> ![X4: $i, X3: $i, X2: $i, X1: $i] : ((~p(X3)) | (~p(X4)) | (~p(X2)) | (~p(X1)) | esk17147_4(X1, X2, X3, X4))),
% 26.04/18.27 inference(quant_intro,[status(thm)],[197])).
% 26.04/18.27 tff(199,plain,
% 26.04/18.27 (![X4: $i, X3: $i, X2: $i, X1: $i] : ((~p(X3)) | (~p(X4)) | (~p(X2)) | (~p(X1)) | esk17147_4(X1, X2, X3, X4)) <=> ![X4: $i, X3: $i, X2: $i, X1: $i] : ((~p(X3)) | (~p(X4)) | (~p(X2)) | (~p(X1)) | esk17147_4(X1, X2, X3, X4))),
% 26.04/18.27 inference(rewrite,[status(thm)],[])).
% 26.04/18.27 tff(200,plain,
% 26.04/18.27 (^[X4: $i, X3: $i, X2: $i, X1: $i] : trans(monotonicity(trans(monotonicity(iff_true(asserted(esk2_0), (esk2_0 <=> $true)), ((~esk2_0) <=> (~$true))), rewrite((~$true) <=> $false), ((~esk2_0) <=> $false)), (((~p(X3)) | (~p(X4)) | (~p(X2)) | (~p(X1)) | esk17147_4(X1, X2, X3, X4) | (~esk2_0)) <=> ((~p(X3)) | (~p(X4)) | (~p(X2)) | (~p(X1)) | esk17147_4(X1, X2, X3, X4) | $false))), rewrite(((~p(X3)) | (~p(X4)) | (~p(X2)) | (~p(X1)) | esk17147_4(X1, X2, X3, X4) | $false) <=> ((~p(X3)) | (~p(X4)) | (~p(X2)) | (~p(X1)) | esk17147_4(X1, X2, X3, X4))), (((~p(X3)) | (~p(X4)) | (~p(X2)) | (~p(X1)) | esk17147_4(X1, X2, X3, X4) | (~esk2_0)) <=> ((~p(X3)) | (~p(X4)) | (~p(X2)) | (~p(X1)) | esk17147_4(X1, X2, X3, X4))))),
% 26.10/18.27 inference(bind,[status(th)],[])).
% 26.10/18.27 tff(201,plain,
% 26.10/18.27 (![X4: $i, X3: $i, X2: $i, X1: $i] : ((~p(X3)) | (~p(X4)) | (~p(X2)) | (~p(X1)) | esk17147_4(X1, X2, X3, X4) | (~esk2_0)) <=> ![X4: $i, X3: $i, X2: $i, X1: $i] : ((~p(X3)) | (~p(X4)) | (~p(X2)) | (~p(X1)) | esk17147_4(X1, X2, X3, X4))),
% 26.10/18.27 inference(quant_intro,[status(thm)],[200])).
% 26.10/18.27 tff(202,plain,
% 26.10/18.27 (^[X4: $i, X3: $i, X2: $i, X1: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~p(X1)) | (~p(X3))) | (~p(X4))) <=> ((~p(X3)) | (~p(X4)) | (~p(X1)))), (((((~p(X1)) | (~p(X3))) | (~p(X4))) | esk17147_4(X1, X2, X3, X4)) <=> (((~p(X3)) | (~p(X4)) | (~p(X1))) | esk17147_4(X1, X2, X3, X4)))), rewrite((((~p(X3)) | (~p(X4)) | (~p(X1))) | esk17147_4(X1, X2, X3, X4)) <=> ((~p(X3)) | (~p(X4)) | (~p(X1)) | esk17147_4(X1, X2, X3, X4))), (((((~p(X1)) | (~p(X3))) | (~p(X4))) | esk17147_4(X1, X2, X3, X4)) <=> ((~p(X3)) | (~p(X4)) | (~p(X1)) | esk17147_4(X1, X2, X3, X4)))), ((((((~p(X1)) | (~p(X3))) | (~p(X4))) | esk17147_4(X1, X2, X3, X4)) | (~esk2_0)) <=> (((~p(X3)) | (~p(X4)) | (~p(X1)) | esk17147_4(X1, X2, X3, X4)) | (~esk2_0)))), rewrite((((~p(X3)) | (~p(X4)) | (~p(X1)) | esk17147_4(X1, X2, X3, X4)) | (~esk2_0)) <=> ((~p(X3)) | (~p(X4)) | (~p(X1)) | esk17147_4(X1, X2, X3, X4) | (~esk2_0))), ((((((~p(X1)) | (~p(X3))) | (~p(X4))) | esk17147_4(X1, X2, X3, X4)) | (~esk2_0)) <=> ((~p(X3)) | (~p(X4)) | (~p(X1)) | esk17147_4(X1, X2, X3, X4) | (~esk2_0)))), (((((((~p(X1)) | (~p(X3))) | (~p(X4))) | esk17147_4(X1, X2, X3, X4)) | (~esk2_0)) | (~p(X2))) <=> (((~p(X3)) | (~p(X4)) | (~p(X1)) | esk17147_4(X1, X2, X3, X4) | (~esk2_0)) | (~p(X2))))), rewrite((((~p(X3)) | (~p(X4)) | (~p(X1)) | esk17147_4(X1, X2, X3, X4) | (~esk2_0)) | (~p(X2))) <=> ((~p(X3)) | (~p(X4)) | (~p(X2)) | (~p(X1)) | esk17147_4(X1, X2, X3, X4) | (~esk2_0))), (((((((~p(X1)) | (~p(X3))) | (~p(X4))) | esk17147_4(X1, X2, X3, X4)) | (~esk2_0)) | (~p(X2))) <=> ((~p(X3)) | (~p(X4)) | (~p(X2)) | (~p(X1)) | esk17147_4(X1, X2, X3, X4) | (~esk2_0))))),
% 26.10/18.27 inference(bind,[status(th)],[])).
% 26.10/18.27 tff(203,plain,
% 26.10/18.27 (![X4: $i, X3: $i, X2: $i, X1: $i] : ((((((~p(X1)) | (~p(X3))) | (~p(X4))) | esk17147_4(X1, X2, X3, X4)) | (~esk2_0)) | (~p(X2))) <=> ![X4: $i, X3: $i, X2: $i, X1: $i] : ((~p(X3)) | (~p(X4)) | (~p(X2)) | (~p(X1)) | esk17147_4(X1, X2, X3, X4) | (~esk2_0))),
% 26.10/18.27 inference(quant_intro,[status(thm)],[202])).
% 26.10/18.27 tff(204,axiom,(![X4: $i, X3: $i, X2: $i, X1: $i] : ((((((~p(X1)) | (~p(X3))) | (~p(X4))) | esk17147_4(X1, X2, X3, X4)) | (~esk2_0)) | (~p(X2)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','i_0_34555')).
% 26.10/18.27 tff(205,plain,
% 26.10/18.27 (![X4: $i, X3: $i, X2: $i, X1: $i] : ((~p(X3)) | (~p(X4)) | (~p(X2)) | (~p(X1)) | esk17147_4(X1, X2, X3, X4) | (~esk2_0))),
% 26.10/18.27 inference(modus_ponens,[status(thm)],[204, 203])).
% 26.10/18.27 tff(206,plain,
% 26.10/18.27 (![X4: $i, X3: $i, X2: $i, X1: $i] : ((~p(X3)) | (~p(X4)) | (~p(X2)) | (~p(X1)) | esk17147_4(X1, X2, X3, X4))),
% 26.10/18.27 inference(modus_ponens,[status(thm)],[205, 201])).
% 26.10/18.27 tff(207,plain,
% 26.10/18.27 (![X4: $i, X3: $i, X2: $i, X1: $i] : ((~p(X3)) | (~p(X4)) | (~p(X2)) | (~p(X1)) | esk17147_4(X1, X2, X3, X4))),
% 26.10/18.27 inference(modus_ponens,[status(thm)],[206, 199])).
% 26.10/18.27 tff(208,plain,(
% 26.10/18.27 ![X4: $i, X3: $i, X2: $i, X1: $i] : ((~p(X3)) | (~p(X4)) | (~p(X2)) | (~p(X1)) | esk17147_4(X1, X2, X3, X4))),
% 26.10/18.27 inference(skolemize,[status(sab)],[207])).
% 26.10/18.27 tff(209,plain,
% 26.10/18.27 (![X4: $i, X3: $i, X2: $i, X1: $i] : ((~p(X3)) | (~p(X4)) | (~p(X2)) | (~p(X1)) | esk17147_4(X1, X2, X3, X4))),
% 26.10/18.27 inference(modus_ponens,[status(thm)],[208, 198])).
% 26.10/18.27 tff(210,plain,
% 26.10/18.27 (((~![X4: $i, X3: $i, X2: $i, X1: $i] : ((~p(X3)) | (~p(X4)) | (~p(X2)) | (~p(X1)) | esk17147_4(X1, X2, X3, X4))) | ((~p(true)) | esk17147_4(true, true, true, true))) <=> ((~![X4: $i, X3: $i, X2: $i, X1: $i] : ((~p(X3)) | (~p(X4)) | (~p(X2)) | (~p(X1)) | esk17147_4(X1, X2, X3, X4))) | (~p(true)) | esk17147_4(true, true, true, true))),
% 26.10/18.27 inference(rewrite,[status(thm)],[])).
% 26.10/18.27 tff(211,plain,
% 26.10/18.27 (((~p(true)) | (~p(true)) | (~p(true)) | (~p(true)) | esk17147_4(true, true, true, true)) <=> ((~p(true)) | esk17147_4(true, true, true, true))),
% 26.10/18.27 inference(rewrite,[status(thm)],[])).
% 26.10/18.27 tff(212,plain,
% 26.10/18.27 (((~![X4: $i, X3: $i, X2: $i, X1: $i] : ((~p(X3)) | (~p(X4)) | (~p(X2)) | (~p(X1)) | esk17147_4(X1, X2, X3, X4))) | ((~p(true)) | (~p(true)) | (~p(true)) | (~p(true)) | esk17147_4(true, true, true, true))) <=> ((~![X4: $i, X3: $i, X2: $i, X1: $i] : ((~p(X3)) | (~p(X4)) | (~p(X2)) | (~p(X1)) | esk17147_4(X1, X2, X3, X4))) | ((~p(true)) | esk17147_4(true, true, true, true)))),
% 26.10/18.27 inference(monotonicity,[status(thm)],[211])).
% 26.10/18.27 tff(213,plain,
% 26.10/18.27 (((~![X4: $i, X3: $i, X2: $i, X1: $i] : ((~p(X3)) | (~p(X4)) | (~p(X2)) | (~p(X1)) | esk17147_4(X1, X2, X3, X4))) | ((~p(true)) | (~p(true)) | (~p(true)) | (~p(true)) | esk17147_4(true, true, true, true))) <=> ((~![X4: $i, X3: $i, X2: $i, X1: $i] : ((~p(X3)) | (~p(X4)) | (~p(X2)) | (~p(X1)) | esk17147_4(X1, X2, X3, X4))) | (~p(true)) | esk17147_4(true, true, true, true))),
% 26.10/18.27 inference(transitivity,[status(thm)],[212, 210])).
% 26.10/18.27 tff(214,plain,
% 26.10/18.27 ((~![X4: $i, X3: $i, X2: $i, X1: $i] : ((~p(X3)) | (~p(X4)) | (~p(X2)) | (~p(X1)) | esk17147_4(X1, X2, X3, X4))) | ((~p(true)) | (~p(true)) | (~p(true)) | (~p(true)) | esk17147_4(true, true, true, true))),
% 26.10/18.27 inference(quant_inst,[status(thm)],[])).
% 26.10/18.27 tff(215,plain,
% 26.10/18.27 ((~![X4: $i, X3: $i, X2: $i, X1: $i] : ((~p(X3)) | (~p(X4)) | (~p(X2)) | (~p(X1)) | esk17147_4(X1, X2, X3, X4))) | (~p(true)) | esk17147_4(true, true, true, true)),
% 26.10/18.27 inference(modus_ponens,[status(thm)],[214, 213])).
% 26.10/18.27 tff(216,plain,
% 26.10/18.27 (esk17147_4(true, true, true, true)),
% 26.10/18.27 inference(unit_resolution,[status(thm)],[215, 209, 4])).
% 26.10/18.27 tff(217,plain,
% 26.10/18.27 (^[X4: $i, X3: $i, X2: $i, X1: $i] : refl(((~esk17147_4(X1, X2, X3, X4)) | esk16222_4(X1, X2, X3, X4)) <=> ((~esk17147_4(X1, X2, X3, X4)) | esk16222_4(X1, X2, X3, X4)))),
% 26.10/18.27 inference(bind,[status(th)],[])).
% 26.10/18.27 tff(218,plain,
% 26.10/18.27 (![X4: $i, X3: $i, X2: $i, X1: $i] : ((~esk17147_4(X1, X2, X3, X4)) | esk16222_4(X1, X2, X3, X4)) <=> ![X4: $i, X3: $i, X2: $i, X1: $i] : ((~esk17147_4(X1, X2, X3, X4)) | esk16222_4(X1, X2, X3, X4))),
% 26.10/18.27 inference(quant_intro,[status(thm)],[217])).
% 26.10/18.27 tff(219,plain,
% 26.10/18.27 (![X4: $i, X3: $i, X2: $i, X1: $i] : ((~esk17147_4(X1, X2, X3, X4)) | esk16222_4(X1, X2, X3, X4)) <=> ![X4: $i, X3: $i, X2: $i, X1: $i] : ((~esk17147_4(X1, X2, X3, X4)) | esk16222_4(X1, X2, X3, X4))),
% 26.10/18.27 inference(rewrite,[status(thm)],[])).
% 26.10/18.27 tff(220,axiom,(![X4: $i, X3: $i, X2: $i, X1: $i] : ((~esk17147_4(X1, X2, X3, X4)) | esk16222_4(X1, X2, X3, X4))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','i_0_45914')).
% 26.10/18.27 tff(221,plain,
% 26.10/18.27 (![X4: $i, X3: $i, X2: $i, X1: $i] : ((~esk17147_4(X1, X2, X3, X4)) | esk16222_4(X1, X2, X3, X4))),
% 26.10/18.27 inference(modus_ponens,[status(thm)],[220, 219])).
% 26.10/18.27 tff(222,plain,(
% 26.10/18.27 ![X4: $i, X3: $i, X2: $i, X1: $i] : ((~esk17147_4(X1, X2, X3, X4)) | esk16222_4(X1, X2, X3, X4))),
% 26.10/18.27 inference(skolemize,[status(sab)],[221])).
% 26.10/18.27 tff(223,plain,
% 26.10/18.27 (![X4: $i, X3: $i, X2: $i, X1: $i] : ((~esk17147_4(X1, X2, X3, X4)) | esk16222_4(X1, X2, X3, X4))),
% 26.10/18.27 inference(modus_ponens,[status(thm)],[222, 218])).
% 26.10/18.27 tff(224,plain,
% 26.10/18.27 (((~![X4: $i, X3: $i, X2: $i, X1: $i] : ((~esk17147_4(X1, X2, X3, X4)) | esk16222_4(X1, X2, X3, X4))) | ((~esk17147_4(true, true, true, true)) | esk16222_4(true, true, true, true))) <=> ((~![X4: $i, X3: $i, X2: $i, X1: $i] : ((~esk17147_4(X1, X2, X3, X4)) | esk16222_4(X1, X2, X3, X4))) | (~esk17147_4(true, true, true, true)) | esk16222_4(true, true, true, true))),
% 26.10/18.27 inference(rewrite,[status(thm)],[])).
% 26.10/18.27 tff(225,plain,
% 26.10/18.27 ((~![X4: $i, X3: $i, X2: $i, X1: $i] : ((~esk17147_4(X1, X2, X3, X4)) | esk16222_4(X1, X2, X3, X4))) | ((~esk17147_4(true, true, true, true)) | esk16222_4(true, true, true, true))),
% 26.10/18.27 inference(quant_inst,[status(thm)],[])).
% 26.10/18.27 tff(226,plain,
% 26.10/18.27 ((~![X4: $i, X3: $i, X2: $i, X1: $i] : ((~esk17147_4(X1, X2, X3, X4)) | esk16222_4(X1, X2, X3, X4))) | (~esk17147_4(true, true, true, true)) | esk16222_4(true, true, true, true)),
% 26.10/18.27 inference(modus_ponens,[status(thm)],[225, 224])).
% 26.10/18.27 tff(227,plain,
% 26.10/18.27 (esk16222_4(true, true, true, true)),
% 26.10/18.27 inference(unit_resolution,[status(thm)],[226, 223, 216])).
% 26.10/18.27 tff(228,plain,
% 26.10/18.27 (^[X4: $i, X3: $i, X2: $i, X1: $i] : refl(((~esk16222_4(X1, X2, X3, X4)) | esk16220_4(X1, X2, X3, X4) | esk16221_4(X1, X2, X3, X4)) <=> ((~esk16222_4(X1, X2, X3, X4)) | esk16220_4(X1, X2, X3, X4) | esk16221_4(X1, X2, X3, X4)))),
% 26.10/18.27 inference(bind,[status(th)],[])).
% 26.10/18.27 tff(229,plain,
% 26.10/18.27 (![X4: $i, X3: $i, X2: $i, X1: $i] : ((~esk16222_4(X1, X2, X3, X4)) | esk16220_4(X1, X2, X3, X4) | esk16221_4(X1, X2, X3, X4)) <=> ![X4: $i, X3: $i, X2: $i, X1: $i] : ((~esk16222_4(X1, X2, X3, X4)) | esk16220_4(X1, X2, X3, X4) | esk16221_4(X1, X2, X3, X4))),
% 26.10/18.27 inference(quant_intro,[status(thm)],[228])).
% 26.10/18.27 tff(230,plain,
% 26.10/18.27 (![X4: $i, X3: $i, X2: $i, X1: $i] : ((~esk16222_4(X1, X2, X3, X4)) | esk16220_4(X1, X2, X3, X4) | esk16221_4(X1, X2, X3, X4)) <=> ![X4: $i, X3: $i, X2: $i, X1: $i] : ((~esk16222_4(X1, X2, X3, X4)) | esk16220_4(X1, X2, X3, X4) | esk16221_4(X1, X2, X3, X4))),
% 26.10/18.27 inference(rewrite,[status(thm)],[])).
% 26.10/18.27 tff(231,plain,
% 26.10/18.27 (^[X4: $i, X3: $i, X2: $i, X1: $i] : trans(monotonicity(rewrite((esk16221_4(X1, X2, X3, X4) | esk16220_4(X1, X2, X3, X4)) <=> (esk16220_4(X1, X2, X3, X4) | esk16221_4(X1, X2, X3, X4))), (((esk16221_4(X1, X2, X3, X4) | esk16220_4(X1, X2, X3, X4)) | (~esk16222_4(X1, X2, X3, X4))) <=> ((esk16220_4(X1, X2, X3, X4) | esk16221_4(X1, X2, X3, X4)) | (~esk16222_4(X1, X2, X3, X4))))), rewrite(((esk16220_4(X1, X2, X3, X4) | esk16221_4(X1, X2, X3, X4)) | (~esk16222_4(X1, X2, X3, X4))) <=> ((~esk16222_4(X1, X2, X3, X4)) | esk16220_4(X1, X2, X3, X4) | esk16221_4(X1, X2, X3, X4))), (((esk16221_4(X1, X2, X3, X4) | esk16220_4(X1, X2, X3, X4)) | (~esk16222_4(X1, X2, X3, X4))) <=> ((~esk16222_4(X1, X2, X3, X4)) | esk16220_4(X1, X2, X3, X4) | esk16221_4(X1, X2, X3, X4))))),
% 26.10/18.27 inference(bind,[status(th)],[])).
% 26.10/18.27 tff(232,plain,
% 26.10/18.27 (![X4: $i, X3: $i, X2: $i, X1: $i] : ((esk16221_4(X1, X2, X3, X4) | esk16220_4(X1, X2, X3, X4)) | (~esk16222_4(X1, X2, X3, X4))) <=> ![X4: $i, X3: $i, X2: $i, X1: $i] : ((~esk16222_4(X1, X2, X3, X4)) | esk16220_4(X1, X2, X3, X4) | esk16221_4(X1, X2, X3, X4))),
% 26.10/18.27 inference(quant_intro,[status(thm)],[231])).
% 26.10/18.27 tff(233,axiom,(![X4: $i, X3: $i, X2: $i, X1: $i] : ((esk16221_4(X1, X2, X3, X4) | esk16220_4(X1, X2, X3, X4)) | (~esk16222_4(X1, X2, X3, X4)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','i_0_33259')).
% 26.10/18.27 tff(234,plain,
% 26.10/18.27 (![X4: $i, X3: $i, X2: $i, X1: $i] : ((~esk16222_4(X1, X2, X3, X4)) | esk16220_4(X1, X2, X3, X4) | esk16221_4(X1, X2, X3, X4))),
% 26.10/18.27 inference(modus_ponens,[status(thm)],[233, 232])).
% 26.10/18.27 tff(235,plain,
% 26.10/18.27 (![X4: $i, X3: $i, X2: $i, X1: $i] : ((~esk16222_4(X1, X2, X3, X4)) | esk16220_4(X1, X2, X3, X4) | esk16221_4(X1, X2, X3, X4))),
% 26.10/18.27 inference(modus_ponens,[status(thm)],[234, 230])).
% 26.10/18.27 tff(236,plain,(
% 26.10/18.27 ![X4: $i, X3: $i, X2: $i, X1: $i] : ((~esk16222_4(X1, X2, X3, X4)) | esk16220_4(X1, X2, X3, X4) | esk16221_4(X1, X2, X3, X4))),
% 26.10/18.27 inference(skolemize,[status(sab)],[235])).
% 26.10/18.27 tff(237,plain,
% 26.10/18.27 (![X4: $i, X3: $i, X2: $i, X1: $i] : ((~esk16222_4(X1, X2, X3, X4)) | esk16220_4(X1, X2, X3, X4) | esk16221_4(X1, X2, X3, X4))),
% 26.10/18.27 inference(modus_ponens,[status(thm)],[236, 229])).
% 26.10/18.27 tff(238,plain,
% 26.10/18.27 (((~![X4: $i, X3: $i, X2: $i, X1: $i] : ((~esk16222_4(X1, X2, X3, X4)) | esk16220_4(X1, X2, X3, X4) | esk16221_4(X1, X2, X3, X4))) | ((~esk16222_4(true, true, true, true)) | esk16220_4(true, true, true, true) | esk16221_4(true, true, true, true))) <=> ((~![X4: $i, X3: $i, X2: $i, X1: $i] : ((~esk16222_4(X1, X2, X3, X4)) | esk16220_4(X1, X2, X3, X4) | esk16221_4(X1, X2, X3, X4))) | (~esk16222_4(true, true, true, true)) | esk16220_4(true, true, true, true) | esk16221_4(true, true, true, true))),
% 26.10/18.27 inference(rewrite,[status(thm)],[])).
% 26.10/18.27 tff(239,plain,
% 26.10/18.27 ((~![X4: $i, X3: $i, X2: $i, X1: $i] : ((~esk16222_4(X1, X2, X3, X4)) | esk16220_4(X1, X2, X3, X4) | esk16221_4(X1, X2, X3, X4))) | ((~esk16222_4(true, true, true, true)) | esk16220_4(true, true, true, true) | esk16221_4(true, true, true, true))),
% 26.10/18.27 inference(quant_inst,[status(thm)],[])).
% 26.10/18.27 tff(240,plain,
% 26.10/18.27 ((~![X4: $i, X3: $i, X2: $i, X1: $i] : ((~esk16222_4(X1, X2, X3, X4)) | esk16220_4(X1, X2, X3, X4) | esk16221_4(X1, X2, X3, X4))) | (~esk16222_4(true, true, true, true)) | esk16220_4(true, true, true, true) | esk16221_4(true, true, true, true)),
% 26.10/18.27 inference(modus_ponens,[status(thm)],[239, 238])).
% 26.10/18.27 tff(241,plain,
% 26.10/18.27 (esk16220_4(true, true, true, true) | esk16221_4(true, true, true, true)),
% 26.10/18.27 inference(unit_resolution,[status(thm)],[240, 237, 227])).
% 26.10/18.27 tff(242,plain,
% 26.10/18.27 (esk16220_4(true, true, true, true)),
% 26.10/18.27 inference(unit_resolution,[status(thm)],[241, 196])).
% 26.10/18.27 tff(243,plain,
% 26.10/18.27 (^[X4: $i, X3: $i, X2: $i, X1: $i] : refl((esk16349_4(X1, X2, X3, X4) | (~esk16220_4(X1, X2, X3, X4))) <=> (esk16349_4(X1, X2, X3, X4) | (~esk16220_4(X1, X2, X3, X4))))),
% 26.10/18.27 inference(bind,[status(th)],[])).
% 26.10/18.27 tff(244,plain,
% 26.10/18.27 (![X4: $i, X3: $i, X2: $i, X1: $i] : (esk16349_4(X1, X2, X3, X4) | (~esk16220_4(X1, X2, X3, X4))) <=> ![X4: $i, X3: $i, X2: $i, X1: $i] : (esk16349_4(X1, X2, X3, X4) | (~esk16220_4(X1, X2, X3, X4)))),
% 26.10/18.27 inference(quant_intro,[status(thm)],[243])).
% 26.10/18.27 tff(245,plain,
% 26.10/18.27 (![X4: $i, X3: $i, X2: $i, X1: $i] : (esk16349_4(X1, X2, X3, X4) | (~esk16220_4(X1, X2, X3, X4))) <=> ![X4: $i, X3: $i, X2: $i, X1: $i] : (esk16349_4(X1, X2, X3, X4) | (~esk16220_4(X1, X2, X3, X4)))),
% 26.10/18.27 inference(rewrite,[status(thm)],[])).
% 26.10/18.27 tff(246,axiom,(![X4: $i, X3: $i, X2: $i, X1: $i] : (esk16349_4(X1, X2, X3, X4) | (~esk16220_4(X1, X2, X3, X4)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','i_0_47728')).
% 26.10/18.27 tff(247,plain,
% 26.10/18.27 (![X4: $i, X3: $i, X2: $i, X1: $i] : (esk16349_4(X1, X2, X3, X4) | (~esk16220_4(X1, X2, X3, X4)))),
% 26.10/18.27 inference(modus_ponens,[status(thm)],[246, 245])).
% 26.10/18.27 tff(248,plain,(
% 26.10/18.27 ![X4: $i, X3: $i, X2: $i, X1: $i] : (esk16349_4(X1, X2, X3, X4) | (~esk16220_4(X1, X2, X3, X4)))),
% 26.10/18.27 inference(skolemize,[status(sab)],[247])).
% 26.10/18.27 tff(249,plain,
% 26.10/18.27 (![X4: $i, X3: $i, X2: $i, X1: $i] : (esk16349_4(X1, X2, X3, X4) | (~esk16220_4(X1, X2, X3, X4)))),
% 26.10/18.27 inference(modus_ponens,[status(thm)],[248, 244])).
% 26.10/18.27 tff(250,plain,
% 26.10/18.27 (((~![X4: $i, X3: $i, X2: $i, X1: $i] : (esk16349_4(X1, X2, X3, X4) | (~esk16220_4(X1, X2, X3, X4)))) | ((~esk16220_4(true, true, true, true)) | esk16349_4(true, true, true, true))) <=> ((~![X4: $i, X3: $i, X2: $i, X1: $i] : (esk16349_4(X1, X2, X3, X4) | (~esk16220_4(X1, X2, X3, X4)))) | (~esk16220_4(true, true, true, true)) | esk16349_4(true, true, true, true))),
% 26.10/18.27 inference(rewrite,[status(thm)],[])).
% 26.10/18.27 tff(251,plain,
% 26.10/18.27 ((esk16349_4(true, true, true, true) | (~esk16220_4(true, true, true, true))) <=> ((~esk16220_4(true, true, true, true)) | esk16349_4(true, true, true, true))),
% 26.10/18.27 inference(rewrite,[status(thm)],[])).
% 26.10/18.27 tff(252,plain,
% 26.10/18.27 (((~![X4: $i, X3: $i, X2: $i, X1: $i] : (esk16349_4(X1, X2, X3, X4) | (~esk16220_4(X1, X2, X3, X4)))) | (esk16349_4(true, true, true, true) | (~esk16220_4(true, true, true, true)))) <=> ((~![X4: $i, X3: $i, X2: $i, X1: $i] : (esk16349_4(X1, X2, X3, X4) | (~esk16220_4(X1, X2, X3, X4)))) | ((~esk16220_4(true, true, true, true)) | esk16349_4(true, true, true, true)))),
% 26.10/18.27 inference(monotonicity,[status(thm)],[251])).
% 26.10/18.27 tff(253,plain,
% 26.10/18.27 (((~![X4: $i, X3: $i, X2: $i, X1: $i] : (esk16349_4(X1, X2, X3, X4) | (~esk16220_4(X1, X2, X3, X4)))) | (esk16349_4(true, true, true, true) | (~esk16220_4(true, true, true, true)))) <=> ((~![X4: $i, X3: $i, X2: $i, X1: $i] : (esk16349_4(X1, X2, X3, X4) | (~esk16220_4(X1, X2, X3, X4)))) | (~esk16220_4(true, true, true, true)) | esk16349_4(true, true, true, true))),
% 26.10/18.27 inference(transitivity,[status(thm)],[252, 250])).
% 26.10/18.27 tff(254,plain,
% 26.10/18.27 ((~![X4: $i, X3: $i, X2: $i, X1: $i] : (esk16349_4(X1, X2, X3, X4) | (~esk16220_4(X1, X2, X3, X4)))) | (esk16349_4(true, true, true, true) | (~esk16220_4(true, true, true, true)))),
% 26.10/18.27 inference(quant_inst,[status(thm)],[])).
% 26.10/18.27 tff(255,plain,
% 26.10/18.27 ((~![X4: $i, X3: $i, X2: $i, X1: $i] : (esk16349_4(X1, X2, X3, X4) | (~esk16220_4(X1, X2, X3, X4)))) | (~esk16220_4(true, true, true, true)) | esk16349_4(true, true, true, true)),
% 26.10/18.27 inference(modus_ponens,[status(thm)],[254, 253])).
% 26.10/18.27 tff(256,plain,
% 26.10/18.27 (esk16349_4(true, true, true, true)),
% 26.10/18.27 inference(unit_resolution,[status(thm)],[255, 249, 242])).
% 26.10/18.27 tff(257,plain,
% 26.10/18.27 (^[X4: $i, X3: $i, X2: $i, X1: $i] : refl((esk16347_4(X1, X2, X3, X4) | (~esk16349_4(X1, X2, X3, X4)) | esk16348_4(X1, X2, X3, X4)) <=> (esk16347_4(X1, X2, X3, X4) | (~esk16349_4(X1, X2, X3, X4)) | esk16348_4(X1, X2, X3, X4)))),
% 26.10/18.27 inference(bind,[status(th)],[])).
% 26.10/18.27 tff(258,plain,
% 26.10/18.27 (![X4: $i, X3: $i, X2: $i, X1: $i] : (esk16347_4(X1, X2, X3, X4) | (~esk16349_4(X1, X2, X3, X4)) | esk16348_4(X1, X2, X3, X4)) <=> ![X4: $i, X3: $i, X2: $i, X1: $i] : (esk16347_4(X1, X2, X3, X4) | (~esk16349_4(X1, X2, X3, X4)) | esk16348_4(X1, X2, X3, X4))),
% 26.10/18.27 inference(quant_intro,[status(thm)],[257])).
% 26.10/18.27 tff(259,plain,
% 26.10/18.27 (![X4: $i, X3: $i, X2: $i, X1: $i] : (esk16347_4(X1, X2, X3, X4) | (~esk16349_4(X1, X2, X3, X4)) | esk16348_4(X1, X2, X3, X4)) <=> ![X4: $i, X3: $i, X2: $i, X1: $i] : (esk16347_4(X1, X2, X3, X4) | (~esk16349_4(X1, X2, X3, X4)) | esk16348_4(X1, X2, X3, X4))),
% 26.10/18.27 inference(rewrite,[status(thm)],[])).
% 26.10/18.27 tff(260,plain,
% 26.10/18.27 (^[X4: $i, X3: $i, X2: $i, X1: $i] : rewrite((((~esk16349_4(X1, X2, X3, X4)) | esk16348_4(X1, X2, X3, X4)) | esk16347_4(X1, X2, X3, X4)) <=> (esk16347_4(X1, X2, X3, X4) | (~esk16349_4(X1, X2, X3, X4)) | esk16348_4(X1, X2, X3, X4)))),
% 26.10/18.27 inference(bind,[status(th)],[])).
% 26.10/18.27 tff(261,plain,
% 26.10/18.27 (![X4: $i, X3: $i, X2: $i, X1: $i] : (((~esk16349_4(X1, X2, X3, X4)) | esk16348_4(X1, X2, X3, X4)) | esk16347_4(X1, X2, X3, X4)) <=> ![X4: $i, X3: $i, X2: $i, X1: $i] : (esk16347_4(X1, X2, X3, X4) | (~esk16349_4(X1, X2, X3, X4)) | esk16348_4(X1, X2, X3, X4))),
% 26.10/18.27 inference(quant_intro,[status(thm)],[260])).
% 26.10/18.27 tff(262,axiom,(![X4: $i, X3: $i, X2: $i, X1: $i] : (((~esk16349_4(X1, X2, X3, X4)) | esk16348_4(X1, X2, X3, X4)) | esk16347_4(X1, X2, X3, X4))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','i_0_25870')).
% 26.10/18.27 tff(263,plain,
% 26.10/18.27 (![X4: $i, X3: $i, X2: $i, X1: $i] : (esk16347_4(X1, X2, X3, X4) | (~esk16349_4(X1, X2, X3, X4)) | esk16348_4(X1, X2, X3, X4))),
% 26.10/18.27 inference(modus_ponens,[status(thm)],[262, 261])).
% 26.10/18.27 tff(264,plain,
% 26.10/18.27 (![X4: $i, X3: $i, X2: $i, X1: $i] : (esk16347_4(X1, X2, X3, X4) | (~esk16349_4(X1, X2, X3, X4)) | esk16348_4(X1, X2, X3, X4))),
% 26.10/18.27 inference(modus_ponens,[status(thm)],[263, 259])).
% 26.10/18.27 tff(265,plain,(
% 26.10/18.27 ![X4: $i, X3: $i, X2: $i, X1: $i] : (esk16347_4(X1, X2, X3, X4) | (~esk16349_4(X1, X2, X3, X4)) | esk16348_4(X1, X2, X3, X4))),
% 26.10/18.27 inference(skolemize,[status(sab)],[264])).
% 26.10/18.27 tff(266,plain,
% 26.10/18.27 (![X4: $i, X3: $i, X2: $i, X1: $i] : (esk16347_4(X1, X2, X3, X4) | (~esk16349_4(X1, X2, X3, X4)) | esk16348_4(X1, X2, X3, X4))),
% 26.10/18.27 inference(modus_ponens,[status(thm)],[265, 258])).
% 26.10/18.27 tff(267,plain,
% 26.10/18.27 (((~![X4: $i, X3: $i, X2: $i, X1: $i] : (esk16347_4(X1, X2, X3, X4) | (~esk16349_4(X1, X2, X3, X4)) | esk16348_4(X1, X2, X3, X4))) | (esk16347_4(true, true, true, true) | esk16348_4(true, true, true, true) | (~esk16349_4(true, true, true, true)))) <=> ((~![X4: $i, X3: $i, X2: $i, X1: $i] : (esk16347_4(X1, X2, X3, X4) | (~esk16349_4(X1, X2, X3, X4)) | esk16348_4(X1, X2, X3, X4))) | esk16347_4(true, true, true, true) | esk16348_4(true, true, true, true) | (~esk16349_4(true, true, true, true)))),
% 26.10/18.27 inference(rewrite,[status(thm)],[])).
% 26.10/18.27 tff(268,plain,
% 26.10/18.27 ((esk16347_4(true, true, true, true) | (~esk16349_4(true, true, true, true)) | esk16348_4(true, true, true, true)) <=> (esk16347_4(true, true, true, true) | esk16348_4(true, true, true, true) | (~esk16349_4(true, true, true, true)))),
% 26.10/18.27 inference(rewrite,[status(thm)],[])).
% 26.10/18.27 tff(269,plain,
% 26.10/18.27 (((~![X4: $i, X3: $i, X2: $i, X1: $i] : (esk16347_4(X1, X2, X3, X4) | (~esk16349_4(X1, X2, X3, X4)) | esk16348_4(X1, X2, X3, X4))) | (esk16347_4(true, true, true, true) | (~esk16349_4(true, true, true, true)) | esk16348_4(true, true, true, true))) <=> ((~![X4: $i, X3: $i, X2: $i, X1: $i] : (esk16347_4(X1, X2, X3, X4) | (~esk16349_4(X1, X2, X3, X4)) | esk16348_4(X1, X2, X3, X4))) | (esk16347_4(true, true, true, true) | esk16348_4(true, true, true, true) | (~esk16349_4(true, true, true, true))))),
% 26.10/18.27 inference(monotonicity,[status(thm)],[268])).
% 26.10/18.27 tff(270,plain,
% 26.10/18.27 (((~![X4: $i, X3: $i, X2: $i, X1: $i] : (esk16347_4(X1, X2, X3, X4) | (~esk16349_4(X1, X2, X3, X4)) | esk16348_4(X1, X2, X3, X4))) | (esk16347_4(true, true, true, true) | (~esk16349_4(true, true, true, true)) | esk16348_4(true, true, true, true))) <=> ((~![X4: $i, X3: $i, X2: $i, X1: $i] : (esk16347_4(X1, X2, X3, X4) | (~esk16349_4(X1, X2, X3, X4)) | esk16348_4(X1, X2, X3, X4))) | esk16347_4(true, true, true, true) | esk16348_4(true, true, true, true) | (~esk16349_4(true, true, true, true)))),
% 26.10/18.27 inference(transitivity,[status(thm)],[269, 267])).
% 26.10/18.27 tff(271,plain,
% 26.10/18.27 ((~![X4: $i, X3: $i, X2: $i, X1: $i] : (esk16347_4(X1, X2, X3, X4) | (~esk16349_4(X1, X2, X3, X4)) | esk16348_4(X1, X2, X3, X4))) | (esk16347_4(true, true, true, true) | (~esk16349_4(true, true, true, true)) | esk16348_4(true, true, true, true))),
% 26.10/18.27 inference(quant_inst,[status(thm)],[])).
% 26.10/18.27 tff(272,plain,
% 26.10/18.27 ((~![X4: $i, X3: $i, X2: $i, X1: $i] : (esk16347_4(X1, X2, X3, X4) | (~esk16349_4(X1, X2, X3, X4)) | esk16348_4(X1, X2, X3, X4))) | esk16347_4(true, true, true, true) | esk16348_4(true, true, true, true) | (~esk16349_4(true, true, true, true))),
% 26.10/18.27 inference(modus_ponens,[status(thm)],[271, 270])).
% 26.10/18.27 tff(273,plain,
% 26.10/18.27 (esk16347_4(true, true, true, true) | esk16348_4(true, true, true, true)),
% 26.10/18.27 inference(unit_resolution,[status(thm)],[272, 266, 256])).
% 26.10/18.27 tff(274,plain,
% 26.10/18.27 (esk16347_4(true, true, true, true)),
% 26.10/18.27 inference(unit_resolution,[status(thm)],[273, 47])).
% 26.10/18.27 tff(275,plain,
% 26.10/18.27 (^[X4: $i, X3: $i, X2: $i, X1: $i] : refl(((~esk16347_4(X1, X2, X3, X4)) | esk17148_4(X1, X2, X3, X4)) <=> ((~esk16347_4(X1, X2, X3, X4)) | esk17148_4(X1, X2, X3, X4)))),
% 26.10/18.27 inference(bind,[status(th)],[])).
% 26.10/18.27 tff(276,plain,
% 26.10/18.27 (![X4: $i, X3: $i, X2: $i, X1: $i] : ((~esk16347_4(X1, X2, X3, X4)) | esk17148_4(X1, X2, X3, X4)) <=> ![X4: $i, X3: $i, X2: $i, X1: $i] : ((~esk16347_4(X1, X2, X3, X4)) | esk17148_4(X1, X2, X3, X4))),
% 26.10/18.27 inference(quant_intro,[status(thm)],[275])).
% 26.10/18.27 tff(277,plain,
% 26.10/18.27 (![X4: $i, X3: $i, X2: $i, X1: $i] : ((~esk16347_4(X1, X2, X3, X4)) | esk17148_4(X1, X2, X3, X4)) <=> ![X4: $i, X3: $i, X2: $i, X1: $i] : ((~esk16347_4(X1, X2, X3, X4)) | esk17148_4(X1, X2, X3, X4))),
% 26.10/18.27 inference(rewrite,[status(thm)],[])).
% 26.10/18.27 tff(278,plain,
% 26.10/18.27 (^[X4: $i, X3: $i, X2: $i, X1: $i] : rewrite((esk17148_4(X1, X2, X3, X4) | (~esk16347_4(X1, X2, X3, X4))) <=> ((~esk16347_4(X1, X2, X3, X4)) | esk17148_4(X1, X2, X3, X4)))),
% 26.10/18.27 inference(bind,[status(th)],[])).
% 26.10/18.27 tff(279,plain,
% 26.10/18.27 (![X4: $i, X3: $i, X2: $i, X1: $i] : (esk17148_4(X1, X2, X3, X4) | (~esk16347_4(X1, X2, X3, X4))) <=> ![X4: $i, X3: $i, X2: $i, X1: $i] : ((~esk16347_4(X1, X2, X3, X4)) | esk17148_4(X1, X2, X3, X4))),
% 26.10/18.27 inference(quant_intro,[status(thm)],[278])).
% 26.10/18.27 tff(280,axiom,(![X4: $i, X3: $i, X2: $i, X1: $i] : (esk17148_4(X1, X2, X3, X4) | (~esk16347_4(X1, X2, X3, X4)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','i_0_26220')).
% 26.10/18.27 tff(281,plain,
% 26.10/18.27 (![X4: $i, X3: $i, X2: $i, X1: $i] : ((~esk16347_4(X1, X2, X3, X4)) | esk17148_4(X1, X2, X3, X4))),
% 26.10/18.27 inference(modus_ponens,[status(thm)],[280, 279])).
% 26.10/18.27 tff(282,plain,
% 26.10/18.27 (![X4: $i, X3: $i, X2: $i, X1: $i] : ((~esk16347_4(X1, X2, X3, X4)) | esk17148_4(X1, X2, X3, X4))),
% 26.10/18.27 inference(modus_ponens,[status(thm)],[281, 277])).
% 26.10/18.27 tff(283,plain,(
% 26.10/18.27 ![X4: $i, X3: $i, X2: $i, X1: $i] : ((~esk16347_4(X1, X2, X3, X4)) | esk17148_4(X1, X2, X3, X4))),
% 26.10/18.27 inference(skolemize,[status(sab)],[282])).
% 26.10/18.27 tff(284,plain,
% 26.10/18.27 (![X4: $i, X3: $i, X2: $i, X1: $i] : ((~esk16347_4(X1, X2, X3, X4)) | esk17148_4(X1, X2, X3, X4))),
% 26.10/18.27 inference(modus_ponens,[status(thm)],[283, 276])).
% 26.10/18.27 tff(285,plain,
% 26.10/18.27 (((~![X4: $i, X3: $i, X2: $i, X1: $i] : ((~esk16347_4(X1, X2, X3, X4)) | esk17148_4(X1, X2, X3, X4))) | ((~esk16347_4(true, true, true, true)) | esk17148_4(true, true, true, true))) <=> ((~![X4: $i, X3: $i, X2: $i, X1: $i] : ((~esk16347_4(X1, X2, X3, X4)) | esk17148_4(X1, X2, X3, X4))) | (~esk16347_4(true, true, true, true)) | esk17148_4(true, true, true, true))),
% 26.10/18.27 inference(rewrite,[status(thm)],[])).
% 26.10/18.27 tff(286,plain,
% 26.10/18.27 ((~![X4: $i, X3: $i, X2: $i, X1: $i] : ((~esk16347_4(X1, X2, X3, X4)) | esk17148_4(X1, X2, X3, X4))) | ((~esk16347_4(true, true, true, true)) | esk17148_4(true, true, true, true))),
% 26.10/18.28 inference(quant_inst,[status(thm)],[])).
% 26.10/18.28 tff(287,plain,
% 26.10/18.28 ((~![X4: $i, X3: $i, X2: $i, X1: $i] : ((~esk16347_4(X1, X2, X3, X4)) | esk17148_4(X1, X2, X3, X4))) | (~esk16347_4(true, true, true, true)) | esk17148_4(true, true, true, true)),
% 26.10/18.28 inference(modus_ponens,[status(thm)],[286, 285])).
% 26.10/18.28 tff(288,plain,
% 26.10/18.28 (esk17148_4(true, true, true, true)),
% 26.10/18.28 inference(unit_resolution,[status(thm)],[287, 284, 274])).
% 26.10/18.28 tff(289,plain,
% 26.10/18.28 (^[X4: $i, X3: $i, X2: $i, X1: $i] : refl((esk17564_4(X1, X2, X3, X4) | (~esk17148_4(X1, X2, X3, X4))) <=> (esk17564_4(X1, X2, X3, X4) | (~esk17148_4(X1, X2, X3, X4))))),
% 26.10/18.28 inference(bind,[status(th)],[])).
% 26.10/18.28 tff(290,plain,
% 26.10/18.28 (![X4: $i, X3: $i, X2: $i, X1: $i] : (esk17564_4(X1, X2, X3, X4) | (~esk17148_4(X1, X2, X3, X4))) <=> ![X4: $i, X3: $i, X2: $i, X1: $i] : (esk17564_4(X1, X2, X3, X4) | (~esk17148_4(X1, X2, X3, X4)))),
% 26.10/18.28 inference(quant_intro,[status(thm)],[289])).
% 26.10/18.28 tff(291,plain,
% 26.10/18.28 (![X4: $i, X3: $i, X2: $i, X1: $i] : (esk17564_4(X1, X2, X3, X4) | (~esk17148_4(X1, X2, X3, X4))) <=> ![X4: $i, X3: $i, X2: $i, X1: $i] : (esk17564_4(X1, X2, X3, X4) | (~esk17148_4(X1, X2, X3, X4)))),
% 26.10/18.28 inference(rewrite,[status(thm)],[])).
% 26.10/18.28 tff(292,axiom,(![X4: $i, X3: $i, X2: $i, X1: $i] : (esk17564_4(X1, X2, X3, X4) | (~esk17148_4(X1, X2, X3, X4)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','i_0_22074')).
% 26.10/18.28 tff(293,plain,
% 26.10/18.28 (![X4: $i, X3: $i, X2: $i, X1: $i] : (esk17564_4(X1, X2, X3, X4) | (~esk17148_4(X1, X2, X3, X4)))),
% 26.10/18.28 inference(modus_ponens,[status(thm)],[292, 291])).
% 26.10/18.28 tff(294,plain,(
% 26.10/18.28 ![X4: $i, X3: $i, X2: $i, X1: $i] : (esk17564_4(X1, X2, X3, X4) | (~esk17148_4(X1, X2, X3, X4)))),
% 26.10/18.28 inference(skolemize,[status(sab)],[293])).
% 26.10/18.28 tff(295,plain,
% 26.10/18.28 (![X4: $i, X3: $i, X2: $i, X1: $i] : (esk17564_4(X1, X2, X3, X4) | (~esk17148_4(X1, X2, X3, X4)))),
% 26.10/18.28 inference(modus_ponens,[status(thm)],[294, 290])).
% 26.10/18.28 tff(296,plain,
% 26.10/18.28 (((~![X4: $i, X3: $i, X2: $i, X1: $i] : (esk17564_4(X1, X2, X3, X4) | (~esk17148_4(X1, X2, X3, X4)))) | ((~esk17148_4(true, true, true, true)) | esk17564_4(true, true, true, true))) <=> ((~![X4: $i, X3: $i, X2: $i, X1: $i] : (esk17564_4(X1, X2, X3, X4) | (~esk17148_4(X1, X2, X3, X4)))) | (~esk17148_4(true, true, true, true)) | esk17564_4(true, true, true, true))),
% 26.10/18.28 inference(rewrite,[status(thm)],[])).
% 26.10/18.28 tff(297,plain,
% 26.10/18.28 ((esk17564_4(true, true, true, true) | (~esk17148_4(true, true, true, true))) <=> ((~esk17148_4(true, true, true, true)) | esk17564_4(true, true, true, true))),
% 26.10/18.28 inference(rewrite,[status(thm)],[])).
% 26.10/18.28 tff(298,plain,
% 26.10/18.28 (((~![X4: $i, X3: $i, X2: $i, X1: $i] : (esk17564_4(X1, X2, X3, X4) | (~esk17148_4(X1, X2, X3, X4)))) | (esk17564_4(true, true, true, true) | (~esk17148_4(true, true, true, true)))) <=> ((~![X4: $i, X3: $i, X2: $i, X1: $i] : (esk17564_4(X1, X2, X3, X4) | (~esk17148_4(X1, X2, X3, X4)))) | ((~esk17148_4(true, true, true, true)) | esk17564_4(true, true, true, true)))),
% 26.10/18.28 inference(monotonicity,[status(thm)],[297])).
% 26.10/18.28 tff(299,plain,
% 26.10/18.28 (((~![X4: $i, X3: $i, X2: $i, X1: $i] : (esk17564_4(X1, X2, X3, X4) | (~esk17148_4(X1, X2, X3, X4)))) | (esk17564_4(true, true, true, true) | (~esk17148_4(true, true, true, true)))) <=> ((~![X4: $i, X3: $i, X2: $i, X1: $i] : (esk17564_4(X1, X2, X3, X4) | (~esk17148_4(X1, X2, X3, X4)))) | (~esk17148_4(true, true, true, true)) | esk17564_4(true, true, true, true))),
% 26.10/18.28 inference(transitivity,[status(thm)],[298, 296])).
% 26.10/18.28 tff(300,plain,
% 26.10/18.28 ((~![X4: $i, X3: $i, X2: $i, X1: $i] : (esk17564_4(X1, X2, X3, X4) | (~esk17148_4(X1, X2, X3, X4)))) | (esk17564_4(true, true, true, true) | (~esk17148_4(true, true, true, true)))),
% 26.10/18.28 inference(quant_inst,[status(thm)],[])).
% 26.10/18.28 tff(301,plain,
% 26.10/18.28 ((~![X4: $i, X3: $i, X2: $i, X1: $i] : (esk17564_4(X1, X2, X3, X4) | (~esk17148_4(X1, X2, X3, X4)))) | (~esk17148_4(true, true, true, true)) | esk17564_4(true, true, true, true)),
% 26.10/18.28 inference(modus_ponens,[status(thm)],[300, 299])).
% 26.10/18.28 tff(302,plain,
% 26.10/18.28 (esk17564_4(true, true, true, true)),
% 26.10/18.28 inference(unit_resolution,[status(thm)],[301, 295, 288])).
% 26.10/18.28 tff(303,plain,
% 26.10/18.28 (^[X4: $i, X3: $i, X2: $i, X1: $i] : refl(((~p(X3)) | (~p(X4)) | (~p(X2)) | (~p(X1)) | (~esk17564_4(X1, X2, X3, X4))) <=> ((~p(X3)) | (~p(X4)) | (~p(X2)) | (~p(X1)) | (~esk17564_4(X1, X2, X3, X4))))),
% 26.10/18.28 inference(bind,[status(th)],[])).
% 26.10/18.28 tff(304,plain,
% 26.10/18.28 (![X4: $i, X3: $i, X2: $i, X1: $i] : ((~p(X3)) | (~p(X4)) | (~p(X2)) | (~p(X1)) | (~esk17564_4(X1, X2, X3, X4))) <=> ![X4: $i, X3: $i, X2: $i, X1: $i] : ((~p(X3)) | (~p(X4)) | (~p(X2)) | (~p(X1)) | (~esk17564_4(X1, X2, X3, X4)))),
% 26.10/18.28 inference(quant_intro,[status(thm)],[303])).
% 26.10/18.28 tff(305,plain,
% 26.10/18.28 (![X4: $i, X3: $i, X2: $i, X1: $i] : ((~p(X3)) | (~p(X4)) | (~p(X2)) | (~p(X1)) | (~esk17564_4(X1, X2, X3, X4))) <=> ![X4: $i, X3: $i, X2: $i, X1: $i] : ((~p(X3)) | (~p(X4)) | (~p(X2)) | (~p(X1)) | (~esk17564_4(X1, X2, X3, X4)))),
% 26.10/18.28 inference(rewrite,[status(thm)],[])).
% 26.10/18.28 tff(306,plain,
% 26.10/18.28 (^[X4: $i, X3: $i, X2: $i, X1: $i] : trans(monotonicity(iff_false(asserted(~esk1_0), (esk1_0 <=> $false)), (((~p(X3)) | (~p(X4)) | (~p(X2)) | (~p(X1)) | esk1_0 | (~esk17564_4(X1, X2, X3, X4))) <=> ((~p(X3)) | (~p(X4)) | (~p(X2)) | (~p(X1)) | $false | (~esk17564_4(X1, X2, X3, X4))))), rewrite(((~p(X3)) | (~p(X4)) | (~p(X2)) | (~p(X1)) | $false | (~esk17564_4(X1, X2, X3, X4))) <=> ((~p(X3)) | (~p(X4)) | (~p(X2)) | (~p(X1)) | (~esk17564_4(X1, X2, X3, X4)))), (((~p(X3)) | (~p(X4)) | (~p(X2)) | (~p(X1)) | esk1_0 | (~esk17564_4(X1, X2, X3, X4))) <=> ((~p(X3)) | (~p(X4)) | (~p(X2)) | (~p(X1)) | (~esk17564_4(X1, X2, X3, X4)))))),
% 26.10/18.28 inference(bind,[status(th)],[])).
% 26.10/18.28 tff(307,plain,
% 26.10/18.28 (![X4: $i, X3: $i, X2: $i, X1: $i] : ((~p(X3)) | (~p(X4)) | (~p(X2)) | (~p(X1)) | esk1_0 | (~esk17564_4(X1, X2, X3, X4))) <=> ![X4: $i, X3: $i, X2: $i, X1: $i] : ((~p(X3)) | (~p(X4)) | (~p(X2)) | (~p(X1)) | (~esk17564_4(X1, X2, X3, X4)))),
% 26.10/18.28 inference(quant_intro,[status(thm)],[306])).
% 26.10/18.28 tff(308,plain,
% 26.10/18.28 (^[X4: $i, X3: $i, X2: $i, X1: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~p(X4)) | esk1_0) <=> ((~p(X4)) | esk1_0)), ((((~p(X4)) | esk1_0) | (~p(X1))) <=> (((~p(X4)) | esk1_0) | (~p(X1))))), rewrite((((~p(X4)) | esk1_0) | (~p(X1))) <=> ((~p(X4)) | (~p(X1)) | esk1_0)), ((((~p(X4)) | esk1_0) | (~p(X1))) <=> ((~p(X4)) | (~p(X1)) | esk1_0))), (((((~p(X4)) | esk1_0) | (~p(X1))) | (~esk17564_4(X1, X2, X3, X4))) <=> (((~p(X4)) | (~p(X1)) | esk1_0) | (~esk17564_4(X1, X2, X3, X4))))), rewrite((((~p(X4)) | (~p(X1)) | esk1_0) | (~esk17564_4(X1, X2, X3, X4))) <=> ((~p(X4)) | (~p(X1)) | esk1_0 | (~esk17564_4(X1, X2, X3, X4)))), (((((~p(X4)) | esk1_0) | (~p(X1))) | (~esk17564_4(X1, X2, X3, X4))) <=> ((~p(X4)) | (~p(X1)) | esk1_0 | (~esk17564_4(X1, X2, X3, X4))))), ((((((~p(X4)) | esk1_0) | (~p(X1))) | (~esk17564_4(X1, X2, X3, X4))) | (~p(X3))) <=> (((~p(X4)) | (~p(X1)) | esk1_0 | (~esk17564_4(X1, X2, X3, X4))) | (~p(X3))))), rewrite((((~p(X4)) | (~p(X1)) | esk1_0 | (~esk17564_4(X1, X2, X3, X4))) | (~p(X3))) <=> ((~p(X3)) | (~p(X4)) | (~p(X1)) | esk1_0 | (~esk17564_4(X1, X2, X3, X4)))), ((((((~p(X4)) | esk1_0) | (~p(X1))) | (~esk17564_4(X1, X2, X3, X4))) | (~p(X3))) <=> ((~p(X3)) | (~p(X4)) | (~p(X1)) | esk1_0 | (~esk17564_4(X1, X2, X3, X4))))), (((((((~p(X4)) | esk1_0) | (~p(X1))) | (~esk17564_4(X1, X2, X3, X4))) | (~p(X3))) | (~p(X2))) <=> (((~p(X3)) | (~p(X4)) | (~p(X1)) | esk1_0 | (~esk17564_4(X1, X2, X3, X4))) | (~p(X2))))), rewrite((((~p(X3)) | (~p(X4)) | (~p(X1)) | esk1_0 | (~esk17564_4(X1, X2, X3, X4))) | (~p(X2))) <=> ((~p(X3)) | (~p(X4)) | (~p(X2)) | (~p(X1)) | esk1_0 | (~esk17564_4(X1, X2, X3, X4)))), (((((((~p(X4)) | esk1_0) | (~p(X1))) | (~esk17564_4(X1, X2, X3, X4))) | (~p(X3))) | (~p(X2))) <=> ((~p(X3)) | (~p(X4)) | (~p(X2)) | (~p(X1)) | esk1_0 | (~esk17564_4(X1, X2, X3, X4)))))),
% 26.10/18.28 inference(bind,[status(th)],[])).
% 26.10/18.28 tff(309,plain,
% 26.10/18.28 (![X4: $i, X3: $i, X2: $i, X1: $i] : ((((((~p(X4)) | esk1_0) | (~p(X1))) | (~esk17564_4(X1, X2, X3, X4))) | (~p(X3))) | (~p(X2))) <=> ![X4: $i, X3: $i, X2: $i, X1: $i] : ((~p(X3)) | (~p(X4)) | (~p(X2)) | (~p(X1)) | esk1_0 | (~esk17564_4(X1, X2, X3, X4)))),
% 26.10/18.28 inference(quant_intro,[status(thm)],[308])).
% 26.10/18.28 tff(310,axiom,(![X4: $i, X3: $i, X2: $i, X1: $i] : ((((((~p(X4)) | esk1_0) | (~p(X1))) | (~esk17564_4(X1, X2, X3, X4))) | (~p(X3))) | (~p(X2)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','i_0_43176')).
% 27.43/19.60 tff(311,plain,
% 27.43/19.60 (![X4: $i, X3: $i, X2: $i, X1: $i] : ((~p(X3)) | (~p(X4)) | (~p(X2)) | (~p(X1)) | esk1_0 | (~esk17564_4(X1, X2, X3, X4)))),
% 27.43/19.60 inference(modus_ponens,[status(thm)],[310, 309])).
% 27.43/19.60 tff(312,plain,
% 27.43/19.60 (![X4: $i, X3: $i, X2: $i, X1: $i] : ((~p(X3)) | (~p(X4)) | (~p(X2)) | (~p(X1)) | (~esk17564_4(X1, X2, X3, X4)))),
% 27.43/19.60 inference(modus_ponens,[status(thm)],[311, 307])).
% 27.43/19.60 tff(313,plain,
% 27.43/19.60 (![X4: $i, X3: $i, X2: $i, X1: $i] : ((~p(X3)) | (~p(X4)) | (~p(X2)) | (~p(X1)) | (~esk17564_4(X1, X2, X3, X4)))),
% 27.43/19.60 inference(modus_ponens,[status(thm)],[312, 305])).
% 27.43/19.60 tff(314,plain,(
% 27.43/19.60 ![X4: $i, X3: $i, X2: $i, X1: $i] : ((~p(X3)) | (~p(X4)) | (~p(X2)) | (~p(X1)) | (~esk17564_4(X1, X2, X3, X4)))),
% 27.43/19.60 inference(skolemize,[status(sab)],[313])).
% 27.43/19.60 tff(315,plain,
% 27.43/19.60 (![X4: $i, X3: $i, X2: $i, X1: $i] : ((~p(X3)) | (~p(X4)) | (~p(X2)) | (~p(X1)) | (~esk17564_4(X1, X2, X3, X4)))),
% 27.43/19.60 inference(modus_ponens,[status(thm)],[314, 304])).
% 27.43/19.60 tff(316,plain,
% 27.43/19.60 (((~![X4: $i, X3: $i, X2: $i, X1: $i] : ((~p(X3)) | (~p(X4)) | (~p(X2)) | (~p(X1)) | (~esk17564_4(X1, X2, X3, X4)))) | ((~p(true)) | (~esk17564_4(true, true, true, true)))) <=> ((~![X4: $i, X3: $i, X2: $i, X1: $i] : ((~p(X3)) | (~p(X4)) | (~p(X2)) | (~p(X1)) | (~esk17564_4(X1, X2, X3, X4)))) | (~p(true)) | (~esk17564_4(true, true, true, true)))),
% 27.43/19.60 inference(rewrite,[status(thm)],[])).
% 27.43/19.60 tff(317,plain,
% 27.43/19.60 (((~p(true)) | (~p(true)) | (~p(true)) | (~p(true)) | (~esk17564_4(true, true, true, true))) <=> ((~p(true)) | (~esk17564_4(true, true, true, true)))),
% 27.43/19.60 inference(rewrite,[status(thm)],[])).
% 27.43/19.60 tff(318,plain,
% 27.43/19.60 (((~![X4: $i, X3: $i, X2: $i, X1: $i] : ((~p(X3)) | (~p(X4)) | (~p(X2)) | (~p(X1)) | (~esk17564_4(X1, X2, X3, X4)))) | ((~p(true)) | (~p(true)) | (~p(true)) | (~p(true)) | (~esk17564_4(true, true, true, true)))) <=> ((~![X4: $i, X3: $i, X2: $i, X1: $i] : ((~p(X3)) | (~p(X4)) | (~p(X2)) | (~p(X1)) | (~esk17564_4(X1, X2, X3, X4)))) | ((~p(true)) | (~esk17564_4(true, true, true, true))))),
% 27.43/19.60 inference(monotonicity,[status(thm)],[317])).
% 27.43/19.60 tff(319,plain,
% 27.43/19.60 (((~![X4: $i, X3: $i, X2: $i, X1: $i] : ((~p(X3)) | (~p(X4)) | (~p(X2)) | (~p(X1)) | (~esk17564_4(X1, X2, X3, X4)))) | ((~p(true)) | (~p(true)) | (~p(true)) | (~p(true)) | (~esk17564_4(true, true, true, true)))) <=> ((~![X4: $i, X3: $i, X2: $i, X1: $i] : ((~p(X3)) | (~p(X4)) | (~p(X2)) | (~p(X1)) | (~esk17564_4(X1, X2, X3, X4)))) | (~p(true)) | (~esk17564_4(true, true, true, true)))),
% 27.43/19.60 inference(transitivity,[status(thm)],[318, 316])).
% 27.43/19.60 tff(320,plain,
% 27.43/19.60 ((~![X4: $i, X3: $i, X2: $i, X1: $i] : ((~p(X3)) | (~p(X4)) | (~p(X2)) | (~p(X1)) | (~esk17564_4(X1, X2, X3, X4)))) | ((~p(true)) | (~p(true)) | (~p(true)) | (~p(true)) | (~esk17564_4(true, true, true, true)))),
% 27.43/19.60 inference(quant_inst,[status(thm)],[])).
% 27.43/19.60 tff(321,plain,
% 27.43/19.60 ((~![X4: $i, X3: $i, X2: $i, X1: $i] : ((~p(X3)) | (~p(X4)) | (~p(X2)) | (~p(X1)) | (~esk17564_4(X1, X2, X3, X4)))) | (~p(true)) | (~esk17564_4(true, true, true, true))),
% 27.43/19.60 inference(modus_ponens,[status(thm)],[320, 319])).
% 27.43/19.60 tff(322,plain,
% 27.43/19.60 ($false),
% 27.43/19.60 inference(unit_resolution,[status(thm)],[321, 315, 4, 302])).
% 27.43/19.60 % SZS output end Proof
%------------------------------------------------------------------------------