TSTP Solution File: HWV069-1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : HWV069-1 : TPTP v8.1.0. Bugfixed v5.5.1.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n005.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 02:15:41 EDT 2022
% Result : Unsatisfiable 16.69s 11.80s
% Output : Proof 17.45s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.14 % Problem : HWV069-1 : TPTP v8.1.0. Bugfixed v5.5.1.
% 0.04/0.15 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.15/0.37 % Computer : n005.cluster.edu
% 0.15/0.37 % Model : x86_64 x86_64
% 0.15/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.37 % Memory : 8042.1875MB
% 0.15/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.37 % CPULimit : 300
% 0.15/0.37 % WCLimit : 300
% 0.15/0.37 % DateTime : Wed Aug 31 23:42:33 EDT 2022
% 0.15/0.37 % CPUTime :
% 0.23/0.37 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.23/0.37 Usage: tptp [options] [-file:]file
% 0.23/0.37 -h, -? prints this message.
% 0.23/0.37 -smt2 print SMT-LIB2 benchmark.
% 0.23/0.37 -m, -model generate model.
% 0.23/0.37 -p, -proof generate proof.
% 0.23/0.37 -c, -core generate unsat core of named formulas.
% 0.23/0.37 -st, -statistics display statistics.
% 0.23/0.37 -t:timeout set timeout (in second).
% 0.23/0.37 -smt2status display status in smt2 format instead of SZS.
% 0.23/0.37 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.23/0.37 -<param>:<value> configuration parameter and value.
% 0.23/0.37 -o:<output-file> file to place output in.
% 16.69/11.80 % SZS status Unsatisfiable
% 16.69/11.80 % SZS output start Proof
% 16.69/11.80 tff(esk9213_4_type, type, (
% 16.69/11.80 esk9213_4: ( $i * $i * $i * $i ) > $o)).
% 16.69/11.80 tff(true_type, type, (
% 16.69/11.80 true: $i)).
% 16.69/11.80 tff(esk7952_4_type, type, (
% 16.69/11.80 esk7952_4: ( $i * $i * $i * $i ) > $o)).
% 16.69/11.80 tff(esk7951_4_type, type, (
% 16.69/11.80 esk7951_4: ( $i * $i * $i * $i ) > $o)).
% 16.69/11.80 tff(esk8752_4_type, type, (
% 16.69/11.80 esk8752_4: ( $i * $i * $i * $i ) > $o)).
% 16.69/11.80 tff(esk9168_4_type, type, (
% 16.69/11.80 esk9168_4: ( $i * $i * $i * $i ) > $o)).
% 16.69/11.80 tff(p_type, type, (
% 16.69/11.80 p: $i > $o)).
% 16.69/11.80 tff(esk1_0_type, type, (
% 16.69/11.80 esk1_0: $o)).
% 16.69/11.80 tff(esk7953_4_type, type, (
% 16.69/11.80 esk7953_4: ( $i * $i * $i * $i ) > $o)).
% 16.69/11.80 tff(esk7824_4_type, type, (
% 16.69/11.80 esk7824_4: ( $i * $i * $i * $i ) > $o)).
% 16.69/11.80 tff(esk7825_4_type, type, (
% 16.69/11.80 esk7825_4: ( $i * $i * $i * $i ) > $o)).
% 16.69/11.80 tff(esk8761_4_type, type, (
% 16.69/11.80 esk8761_4: ( $i * $i * $i * $i ) > $o)).
% 16.69/11.80 tff(esk8120_4_type, type, (
% 16.69/11.80 esk8120_4: ( $i * $i * $i * $i ) > $o)).
% 16.69/11.80 tff(esk7826_4_type, type, (
% 16.69/11.80 esk7826_4: ( $i * $i * $i * $i ) > $o)).
% 16.69/11.80 tff(esk8751_4_type, type, (
% 16.69/11.80 esk8751_4: ( $i * $i * $i * $i ) > $o)).
% 16.69/11.80 tff(esk2_0_type, type, (
% 16.69/11.80 esk2_0: $o)).
% 16.69/11.80 tff(esk9744_4_type, type, (
% 16.69/11.80 esk9744_4: ( $i * $i * $i * $i ) > $o)).
% 16.69/11.80 tff(esk9743_4_type, type, (
% 16.69/11.80 esk9743_4: ( $i * $i * $i * $i ) > $o)).
% 16.69/11.80 tff(esk9741_4_type, type, (
% 16.69/11.80 esk9741_4: ( $i * $i * $i * $i ) > $o)).
% 16.69/11.80 tff(esk9742_4_type, type, (
% 16.69/11.80 esk9742_4: ( $i * $i * $i * $i ) > $o)).
% 16.69/11.80 tff(1,assumption,(esk9168_4(true, true, true, true)), introduced(assumption)).
% 16.69/11.80 tff(2,plain,
% 16.69/11.80 (p(true) <=> p(true)),
% 16.69/11.80 inference(rewrite,[status(thm)],[])).
% 16.69/11.80 tff(3,axiom,(p(true)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','rule_true')).
% 16.69/11.80 tff(4,plain,
% 16.69/11.80 (p(true)),
% 16.69/11.80 inference(modus_ponens,[status(thm)],[3, 2])).
% 16.69/11.80 tff(5,plain,
% 16.69/11.80 (^[X4: $i, X3: $i, X2: $i, X1: $i] : refl(((~p(X3)) | (~p(X1)) | (~p(X4)) | (~p(X2)) | (~esk9168_4(X1, X2, X3, X4))) <=> ((~p(X3)) | (~p(X1)) | (~p(X4)) | (~p(X2)) | (~esk9168_4(X1, X2, X3, X4))))),
% 16.69/11.80 inference(bind,[status(th)],[])).
% 16.69/11.80 tff(6,plain,
% 16.69/11.80 (![X4: $i, X3: $i, X2: $i, X1: $i] : ((~p(X3)) | (~p(X1)) | (~p(X4)) | (~p(X2)) | (~esk9168_4(X1, X2, X3, X4))) <=> ![X4: $i, X3: $i, X2: $i, X1: $i] : ((~p(X3)) | (~p(X1)) | (~p(X4)) | (~p(X2)) | (~esk9168_4(X1, X2, X3, X4)))),
% 16.69/11.80 inference(quant_intro,[status(thm)],[5])).
% 16.69/11.80 tff(7,plain,
% 16.69/11.80 (![X4: $i, X3: $i, X2: $i, X1: $i] : ((~p(X3)) | (~p(X1)) | (~p(X4)) | (~p(X2)) | (~esk9168_4(X1, X2, X3, X4))) <=> ![X4: $i, X3: $i, X2: $i, X1: $i] : ((~p(X3)) | (~p(X1)) | (~p(X4)) | (~p(X2)) | (~esk9168_4(X1, X2, X3, X4)))),
% 16.69/11.80 inference(rewrite,[status(thm)],[])).
% 16.69/11.80 tff(8,plain,
% 16.69/11.80 (^[X4: $i, X3: $i, X2: $i, X1: $i] : trans(monotonicity(iff_false(asserted(~esk1_0), (esk1_0 <=> $false)), (((~p(X3)) | (~p(X1)) | esk1_0 | (~p(X4)) | (~p(X2)) | (~esk9168_4(X1, X2, X3, X4))) <=> ((~p(X3)) | (~p(X1)) | $false | (~p(X4)) | (~p(X2)) | (~esk9168_4(X1, X2, X3, X4))))), rewrite(((~p(X3)) | (~p(X1)) | $false | (~p(X4)) | (~p(X2)) | (~esk9168_4(X1, X2, X3, X4))) <=> ((~p(X3)) | (~p(X1)) | (~p(X4)) | (~p(X2)) | (~esk9168_4(X1, X2, X3, X4)))), (((~p(X3)) | (~p(X1)) | esk1_0 | (~p(X4)) | (~p(X2)) | (~esk9168_4(X1, X2, X3, X4))) <=> ((~p(X3)) | (~p(X1)) | (~p(X4)) | (~p(X2)) | (~esk9168_4(X1, X2, X3, X4)))))),
% 16.69/11.80 inference(bind,[status(th)],[])).
% 16.69/11.80 tff(9,plain,
% 16.69/11.80 (![X4: $i, X3: $i, X2: $i, X1: $i] : ((~p(X3)) | (~p(X1)) | esk1_0 | (~p(X4)) | (~p(X2)) | (~esk9168_4(X1, X2, X3, X4))) <=> ![X4: $i, X3: $i, X2: $i, X1: $i] : ((~p(X3)) | (~p(X1)) | (~p(X4)) | (~p(X2)) | (~esk9168_4(X1, X2, X3, X4)))),
% 16.69/11.80 inference(quant_intro,[status(thm)],[8])).
% 16.69/11.80 tff(10,plain,
% 16.69/11.80 (^[X4: $i, X3: $i, X2: $i, X1: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~p(X3)) | esk1_0) <=> ((~p(X3)) | esk1_0)), ((((~p(X3)) | esk1_0) | (~p(X4))) <=> (((~p(X3)) | esk1_0) | (~p(X4))))), rewrite((((~p(X3)) | esk1_0) | (~p(X4))) <=> ((~p(X3)) | esk1_0 | (~p(X4)))), ((((~p(X3)) | esk1_0) | (~p(X4))) <=> ((~p(X3)) | esk1_0 | (~p(X4))))), (((((~p(X3)) | esk1_0) | (~p(X4))) | (~p(X2))) <=> (((~p(X3)) | esk1_0 | (~p(X4))) | (~p(X2))))), rewrite((((~p(X3)) | esk1_0 | (~p(X4))) | (~p(X2))) <=> ((~p(X3)) | esk1_0 | (~p(X4)) | (~p(X2)))), (((((~p(X3)) | esk1_0) | (~p(X4))) | (~p(X2))) <=> ((~p(X3)) | esk1_0 | (~p(X4)) | (~p(X2))))), ((((((~p(X3)) | esk1_0) | (~p(X4))) | (~p(X2))) | (~esk9168_4(X1, X2, X3, X4))) <=> (((~p(X3)) | esk1_0 | (~p(X4)) | (~p(X2))) | (~esk9168_4(X1, X2, X3, X4))))), rewrite((((~p(X3)) | esk1_0 | (~p(X4)) | (~p(X2))) | (~esk9168_4(X1, X2, X3, X4))) <=> ((~p(X3)) | esk1_0 | (~p(X4)) | (~p(X2)) | (~esk9168_4(X1, X2, X3, X4)))), ((((((~p(X3)) | esk1_0) | (~p(X4))) | (~p(X2))) | (~esk9168_4(X1, X2, X3, X4))) <=> ((~p(X3)) | esk1_0 | (~p(X4)) | (~p(X2)) | (~esk9168_4(X1, X2, X3, X4))))), (((((((~p(X3)) | esk1_0) | (~p(X4))) | (~p(X2))) | (~esk9168_4(X1, X2, X3, X4))) | (~p(X1))) <=> (((~p(X3)) | esk1_0 | (~p(X4)) | (~p(X2)) | (~esk9168_4(X1, X2, X3, X4))) | (~p(X1))))), rewrite((((~p(X3)) | esk1_0 | (~p(X4)) | (~p(X2)) | (~esk9168_4(X1, X2, X3, X4))) | (~p(X1))) <=> ((~p(X3)) | (~p(X1)) | esk1_0 | (~p(X4)) | (~p(X2)) | (~esk9168_4(X1, X2, X3, X4)))), (((((((~p(X3)) | esk1_0) | (~p(X4))) | (~p(X2))) | (~esk9168_4(X1, X2, X3, X4))) | (~p(X1))) <=> ((~p(X3)) | (~p(X1)) | esk1_0 | (~p(X4)) | (~p(X2)) | (~esk9168_4(X1, X2, X3, X4)))))),
% 16.69/11.80 inference(bind,[status(th)],[])).
% 16.69/11.80 tff(11,plain,
% 16.69/11.80 (![X4: $i, X3: $i, X2: $i, X1: $i] : ((((((~p(X3)) | esk1_0) | (~p(X4))) | (~p(X2))) | (~esk9168_4(X1, X2, X3, X4))) | (~p(X1))) <=> ![X4: $i, X3: $i, X2: $i, X1: $i] : ((~p(X3)) | (~p(X1)) | esk1_0 | (~p(X4)) | (~p(X2)) | (~esk9168_4(X1, X2, X3, X4)))),
% 16.69/11.80 inference(quant_intro,[status(thm)],[10])).
% 16.69/11.80 tff(12,axiom,(![X4: $i, X3: $i, X2: $i, X1: $i] : ((((((~p(X3)) | esk1_0) | (~p(X4))) | (~p(X2))) | (~esk9168_4(X1, X2, X3, X4))) | (~p(X1)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','i_0_16826')).
% 16.69/11.80 tff(13,plain,
% 16.69/11.80 (![X4: $i, X3: $i, X2: $i, X1: $i] : ((~p(X3)) | (~p(X1)) | esk1_0 | (~p(X4)) | (~p(X2)) | (~esk9168_4(X1, X2, X3, X4)))),
% 16.69/11.80 inference(modus_ponens,[status(thm)],[12, 11])).
% 16.69/11.80 tff(14,plain,
% 16.69/11.80 (![X4: $i, X3: $i, X2: $i, X1: $i] : ((~p(X3)) | (~p(X1)) | (~p(X4)) | (~p(X2)) | (~esk9168_4(X1, X2, X3, X4)))),
% 16.69/11.80 inference(modus_ponens,[status(thm)],[13, 9])).
% 16.69/11.80 tff(15,plain,
% 16.69/11.80 (![X4: $i, X3: $i, X2: $i, X1: $i] : ((~p(X3)) | (~p(X1)) | (~p(X4)) | (~p(X2)) | (~esk9168_4(X1, X2, X3, X4)))),
% 16.69/11.80 inference(modus_ponens,[status(thm)],[14, 7])).
% 16.69/11.80 tff(16,plain,(
% 16.69/11.80 ![X4: $i, X3: $i, X2: $i, X1: $i] : ((~p(X3)) | (~p(X1)) | (~p(X4)) | (~p(X2)) | (~esk9168_4(X1, X2, X3, X4)))),
% 16.69/11.80 inference(skolemize,[status(sab)],[15])).
% 16.69/11.80 tff(17,plain,
% 16.69/11.80 (![X4: $i, X3: $i, X2: $i, X1: $i] : ((~p(X3)) | (~p(X1)) | (~p(X4)) | (~p(X2)) | (~esk9168_4(X1, X2, X3, X4)))),
% 16.69/11.80 inference(modus_ponens,[status(thm)],[16, 6])).
% 16.69/11.80 tff(18,plain,
% 16.69/11.80 (((~![X4: $i, X3: $i, X2: $i, X1: $i] : ((~p(X3)) | (~p(X1)) | (~p(X4)) | (~p(X2)) | (~esk9168_4(X1, X2, X3, X4)))) | ((~p(true)) | (~esk9168_4(true, true, true, true)))) <=> ((~![X4: $i, X3: $i, X2: $i, X1: $i] : ((~p(X3)) | (~p(X1)) | (~p(X4)) | (~p(X2)) | (~esk9168_4(X1, X2, X3, X4)))) | (~p(true)) | (~esk9168_4(true, true, true, true)))),
% 16.69/11.80 inference(rewrite,[status(thm)],[])).
% 16.69/11.80 tff(19,plain,
% 16.69/11.80 (((~p(true)) | (~p(true)) | (~p(true)) | (~p(true)) | (~esk9168_4(true, true, true, true))) <=> ((~p(true)) | (~esk9168_4(true, true, true, true)))),
% 16.69/11.80 inference(rewrite,[status(thm)],[])).
% 16.69/11.80 tff(20,plain,
% 16.69/11.80 (((~![X4: $i, X3: $i, X2: $i, X1: $i] : ((~p(X3)) | (~p(X1)) | (~p(X4)) | (~p(X2)) | (~esk9168_4(X1, X2, X3, X4)))) | ((~p(true)) | (~p(true)) | (~p(true)) | (~p(true)) | (~esk9168_4(true, true, true, true)))) <=> ((~![X4: $i, X3: $i, X2: $i, X1: $i] : ((~p(X3)) | (~p(X1)) | (~p(X4)) | (~p(X2)) | (~esk9168_4(X1, X2, X3, X4)))) | ((~p(true)) | (~esk9168_4(true, true, true, true))))),
% 16.69/11.80 inference(monotonicity,[status(thm)],[19])).
% 16.69/11.80 tff(21,plain,
% 16.69/11.80 (((~![X4: $i, X3: $i, X2: $i, X1: $i] : ((~p(X3)) | (~p(X1)) | (~p(X4)) | (~p(X2)) | (~esk9168_4(X1, X2, X3, X4)))) | ((~p(true)) | (~p(true)) | (~p(true)) | (~p(true)) | (~esk9168_4(true, true, true, true)))) <=> ((~![X4: $i, X3: $i, X2: $i, X1: $i] : ((~p(X3)) | (~p(X1)) | (~p(X4)) | (~p(X2)) | (~esk9168_4(X1, X2, X3, X4)))) | (~p(true)) | (~esk9168_4(true, true, true, true)))),
% 16.69/11.80 inference(transitivity,[status(thm)],[20, 18])).
% 16.69/11.80 tff(22,plain,
% 16.69/11.80 ((~![X4: $i, X3: $i, X2: $i, X1: $i] : ((~p(X3)) | (~p(X1)) | (~p(X4)) | (~p(X2)) | (~esk9168_4(X1, X2, X3, X4)))) | ((~p(true)) | (~p(true)) | (~p(true)) | (~p(true)) | (~esk9168_4(true, true, true, true)))),
% 16.69/11.80 inference(quant_inst,[status(thm)],[])).
% 16.69/11.80 tff(23,plain,
% 16.69/11.80 ((~![X4: $i, X3: $i, X2: $i, X1: $i] : ((~p(X3)) | (~p(X1)) | (~p(X4)) | (~p(X2)) | (~esk9168_4(X1, X2, X3, X4)))) | (~p(true)) | (~esk9168_4(true, true, true, true))),
% 16.69/11.80 inference(modus_ponens,[status(thm)],[22, 21])).
% 16.69/11.80 tff(24,plain,
% 16.69/11.80 ($false),
% 16.69/11.80 inference(unit_resolution,[status(thm)],[23, 17, 4, 1])).
% 16.69/11.80 tff(25,plain,(~esk9168_4(true, true, true, true)), inference(lemma,lemma(discharge,[]))).
% 16.69/11.80 tff(26,plain,
% 16.69/11.80 (^[X4: $i, X3: $i, X2: $i, X1: $i] : refl(((~esk8752_4(X1, X2, X3, X4)) | esk9168_4(X1, X2, X3, X4)) <=> ((~esk8752_4(X1, X2, X3, X4)) | esk9168_4(X1, X2, X3, X4)))),
% 16.69/11.80 inference(bind,[status(th)],[])).
% 16.69/11.80 tff(27,plain,
% 16.69/11.80 (![X4: $i, X3: $i, X2: $i, X1: $i] : ((~esk8752_4(X1, X2, X3, X4)) | esk9168_4(X1, X2, X3, X4)) <=> ![X4: $i, X3: $i, X2: $i, X1: $i] : ((~esk8752_4(X1, X2, X3, X4)) | esk9168_4(X1, X2, X3, X4))),
% 16.69/11.80 inference(quant_intro,[status(thm)],[26])).
% 16.69/11.80 tff(28,plain,
% 16.69/11.80 (![X4: $i, X3: $i, X2: $i, X1: $i] : ((~esk8752_4(X1, X2, X3, X4)) | esk9168_4(X1, X2, X3, X4)) <=> ![X4: $i, X3: $i, X2: $i, X1: $i] : ((~esk8752_4(X1, X2, X3, X4)) | esk9168_4(X1, X2, X3, X4))),
% 16.69/11.80 inference(rewrite,[status(thm)],[])).
% 16.69/11.80 tff(29,axiom,(![X4: $i, X3: $i, X2: $i, X1: $i] : ((~esk8752_4(X1, X2, X3, X4)) | esk9168_4(X1, X2, X3, X4))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','i_0_6826')).
% 16.69/11.80 tff(30,plain,
% 16.69/11.80 (![X4: $i, X3: $i, X2: $i, X1: $i] : ((~esk8752_4(X1, X2, X3, X4)) | esk9168_4(X1, X2, X3, X4))),
% 16.69/11.80 inference(modus_ponens,[status(thm)],[29, 28])).
% 16.69/11.80 tff(31,plain,(
% 16.69/11.80 ![X4: $i, X3: $i, X2: $i, X1: $i] : ((~esk8752_4(X1, X2, X3, X4)) | esk9168_4(X1, X2, X3, X4))),
% 16.69/11.80 inference(skolemize,[status(sab)],[30])).
% 16.69/11.80 tff(32,plain,
% 16.69/11.80 (![X4: $i, X3: $i, X2: $i, X1: $i] : ((~esk8752_4(X1, X2, X3, X4)) | esk9168_4(X1, X2, X3, X4))),
% 16.69/11.80 inference(modus_ponens,[status(thm)],[31, 27])).
% 16.69/11.80 tff(33,plain,
% 16.69/11.80 (((~![X4: $i, X3: $i, X2: $i, X1: $i] : ((~esk8752_4(X1, X2, X3, X4)) | esk9168_4(X1, X2, X3, X4))) | ((~esk8752_4(true, true, true, true)) | esk9168_4(true, true, true, true))) <=> ((~![X4: $i, X3: $i, X2: $i, X1: $i] : ((~esk8752_4(X1, X2, X3, X4)) | esk9168_4(X1, X2, X3, X4))) | (~esk8752_4(true, true, true, true)) | esk9168_4(true, true, true, true))),
% 16.69/11.80 inference(rewrite,[status(thm)],[])).
% 16.69/11.80 tff(34,plain,
% 16.69/11.80 ((~![X4: $i, X3: $i, X2: $i, X1: $i] : ((~esk8752_4(X1, X2, X3, X4)) | esk9168_4(X1, X2, X3, X4))) | ((~esk8752_4(true, true, true, true)) | esk9168_4(true, true, true, true))),
% 16.69/11.80 inference(quant_inst,[status(thm)],[])).
% 16.69/11.80 tff(35,plain,
% 16.69/11.80 ((~![X4: $i, X3: $i, X2: $i, X1: $i] : ((~esk8752_4(X1, X2, X3, X4)) | esk9168_4(X1, X2, X3, X4))) | (~esk8752_4(true, true, true, true)) | esk9168_4(true, true, true, true)),
% 16.69/11.80 inference(modus_ponens,[status(thm)],[34, 33])).
% 16.69/11.80 tff(36,plain,
% 16.69/11.80 (~esk8752_4(true, true, true, true)),
% 16.69/11.80 inference(unit_resolution,[status(thm)],[35, 32, 25])).
% 16.69/11.80 tff(37,plain,
% 16.69/11.80 (^[X4: $i, X3: $i, X2: $i, X1: $i] : refl((esk8752_4(X1, X2, X3, X4) | (~esk7951_4(X1, X2, X3, X4))) <=> (esk8752_4(X1, X2, X3, X4) | (~esk7951_4(X1, X2, X3, X4))))),
% 16.69/11.80 inference(bind,[status(th)],[])).
% 16.69/11.80 tff(38,plain,
% 16.69/11.80 (![X4: $i, X3: $i, X2: $i, X1: $i] : (esk8752_4(X1, X2, X3, X4) | (~esk7951_4(X1, X2, X3, X4))) <=> ![X4: $i, X3: $i, X2: $i, X1: $i] : (esk8752_4(X1, X2, X3, X4) | (~esk7951_4(X1, X2, X3, X4)))),
% 16.69/11.80 inference(quant_intro,[status(thm)],[37])).
% 16.69/11.80 tff(39,plain,
% 16.69/11.80 (![X4: $i, X3: $i, X2: $i, X1: $i] : (esk8752_4(X1, X2, X3, X4) | (~esk7951_4(X1, X2, X3, X4))) <=> ![X4: $i, X3: $i, X2: $i, X1: $i] : (esk8752_4(X1, X2, X3, X4) | (~esk7951_4(X1, X2, X3, X4)))),
% 16.69/11.80 inference(rewrite,[status(thm)],[])).
% 16.69/11.80 tff(40,axiom,(![X4: $i, X3: $i, X2: $i, X1: $i] : (esk8752_4(X1, X2, X3, X4) | (~esk7951_4(X1, X2, X3, X4)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','i_0_15706')).
% 16.69/11.81 tff(41,plain,
% 16.69/11.81 (![X4: $i, X3: $i, X2: $i, X1: $i] : (esk8752_4(X1, X2, X3, X4) | (~esk7951_4(X1, X2, X3, X4)))),
% 16.69/11.81 inference(modus_ponens,[status(thm)],[40, 39])).
% 16.69/11.81 tff(42,plain,(
% 16.69/11.81 ![X4: $i, X3: $i, X2: $i, X1: $i] : (esk8752_4(X1, X2, X3, X4) | (~esk7951_4(X1, X2, X3, X4)))),
% 16.69/11.81 inference(skolemize,[status(sab)],[41])).
% 16.69/11.81 tff(43,plain,
% 16.69/11.81 (![X4: $i, X3: $i, X2: $i, X1: $i] : (esk8752_4(X1, X2, X3, X4) | (~esk7951_4(X1, X2, X3, X4)))),
% 16.69/11.81 inference(modus_ponens,[status(thm)],[42, 38])).
% 16.69/11.81 tff(44,plain,
% 16.69/11.81 (((~![X4: $i, X3: $i, X2: $i, X1: $i] : (esk8752_4(X1, X2, X3, X4) | (~esk7951_4(X1, X2, X3, X4)))) | ((~esk7951_4(true, true, true, true)) | esk8752_4(true, true, true, true))) <=> ((~![X4: $i, X3: $i, X2: $i, X1: $i] : (esk8752_4(X1, X2, X3, X4) | (~esk7951_4(X1, X2, X3, X4)))) | (~esk7951_4(true, true, true, true)) | esk8752_4(true, true, true, true))),
% 16.69/11.81 inference(rewrite,[status(thm)],[])).
% 16.69/11.81 tff(45,plain,
% 16.69/11.81 ((esk8752_4(true, true, true, true) | (~esk7951_4(true, true, true, true))) <=> ((~esk7951_4(true, true, true, true)) | esk8752_4(true, true, true, true))),
% 16.69/11.81 inference(rewrite,[status(thm)],[])).
% 16.69/11.81 tff(46,plain,
% 16.69/11.81 (((~![X4: $i, X3: $i, X2: $i, X1: $i] : (esk8752_4(X1, X2, X3, X4) | (~esk7951_4(X1, X2, X3, X4)))) | (esk8752_4(true, true, true, true) | (~esk7951_4(true, true, true, true)))) <=> ((~![X4: $i, X3: $i, X2: $i, X1: $i] : (esk8752_4(X1, X2, X3, X4) | (~esk7951_4(X1, X2, X3, X4)))) | ((~esk7951_4(true, true, true, true)) | esk8752_4(true, true, true, true)))),
% 16.69/11.81 inference(monotonicity,[status(thm)],[45])).
% 16.69/11.81 tff(47,plain,
% 16.69/11.81 (((~![X4: $i, X3: $i, X2: $i, X1: $i] : (esk8752_4(X1, X2, X3, X4) | (~esk7951_4(X1, X2, X3, X4)))) | (esk8752_4(true, true, true, true) | (~esk7951_4(true, true, true, true)))) <=> ((~![X4: $i, X3: $i, X2: $i, X1: $i] : (esk8752_4(X1, X2, X3, X4) | (~esk7951_4(X1, X2, X3, X4)))) | (~esk7951_4(true, true, true, true)) | esk8752_4(true, true, true, true))),
% 16.69/11.81 inference(transitivity,[status(thm)],[46, 44])).
% 16.69/11.81 tff(48,plain,
% 16.69/11.81 ((~![X4: $i, X3: $i, X2: $i, X1: $i] : (esk8752_4(X1, X2, X3, X4) | (~esk7951_4(X1, X2, X3, X4)))) | (esk8752_4(true, true, true, true) | (~esk7951_4(true, true, true, true)))),
% 16.69/11.81 inference(quant_inst,[status(thm)],[])).
% 16.69/11.81 tff(49,plain,
% 16.69/11.81 ((~![X4: $i, X3: $i, X2: $i, X1: $i] : (esk8752_4(X1, X2, X3, X4) | (~esk7951_4(X1, X2, X3, X4)))) | (~esk7951_4(true, true, true, true)) | esk8752_4(true, true, true, true)),
% 16.69/11.81 inference(modus_ponens,[status(thm)],[48, 47])).
% 16.69/11.81 tff(50,plain,
% 16.69/11.81 (~esk7951_4(true, true, true, true)),
% 16.69/11.81 inference(unit_resolution,[status(thm)],[49, 43, 36])).
% 16.69/11.81 tff(51,assumption,(esk8120_4(true, true, true, true)), introduced(assumption)).
% 16.69/11.81 tff(52,plain,
% 16.69/11.81 (^[X4: $i, X3: $i, X2: $i, X1: $i] : refl((~esk8120_4(X1, X2, X3, X4)) <=> (~esk8120_4(X1, X2, X3, X4)))),
% 16.69/11.81 inference(bind,[status(th)],[])).
% 16.69/11.81 tff(53,plain,
% 16.69/11.81 (![X4: $i, X3: $i, X2: $i, X1: $i] : (~esk8120_4(X1, X2, X3, X4)) <=> ![X4: $i, X3: $i, X2: $i, X1: $i] : (~esk8120_4(X1, X2, X3, X4))),
% 16.69/11.81 inference(quant_intro,[status(thm)],[52])).
% 16.69/11.81 tff(54,plain,
% 16.69/11.81 (![X4: $i, X3: $i, X2: $i, X1: $i] : (~esk8120_4(X1, X2, X3, X4)) <=> ![X4: $i, X3: $i, X2: $i, X1: $i] : (~esk8120_4(X1, X2, X3, X4))),
% 16.69/11.81 inference(rewrite,[status(thm)],[])).
% 16.69/11.81 tff(55,axiom,(![X4: $i, X3: $i, X2: $i, X1: $i] : (~esk8120_4(X1, X2, X3, X4))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','i_0_18461')).
% 16.69/11.81 tff(56,plain,
% 16.69/11.81 (![X4: $i, X3: $i, X2: $i, X1: $i] : (~esk8120_4(X1, X2, X3, X4))),
% 16.69/11.81 inference(modus_ponens,[status(thm)],[55, 54])).
% 16.69/11.81 tff(57,plain,(
% 16.69/11.81 ![X4: $i, X3: $i, X2: $i, X1: $i] : (~esk8120_4(X1, X2, X3, X4))),
% 16.69/11.81 inference(skolemize,[status(sab)],[56])).
% 16.69/11.81 tff(58,plain,
% 16.69/11.81 (![X4: $i, X3: $i, X2: $i, X1: $i] : (~esk8120_4(X1, X2, X3, X4))),
% 16.69/11.81 inference(modus_ponens,[status(thm)],[57, 53])).
% 16.69/11.81 tff(59,plain,
% 16.69/11.81 ((~![X4: $i, X3: $i, X2: $i, X1: $i] : (~esk8120_4(X1, X2, X3, X4))) | (~esk8120_4(true, true, true, true))),
% 16.69/11.81 inference(quant_inst,[status(thm)],[])).
% 16.69/11.81 tff(60,plain,
% 16.69/11.81 ($false),
% 16.69/11.81 inference(unit_resolution,[status(thm)],[59, 58, 51])).
% 16.69/11.81 tff(61,plain,(~esk8120_4(true, true, true, true)), inference(lemma,lemma(discharge,[]))).
% 16.69/11.81 tff(62,plain,
% 16.69/11.81 (^[X4: $i, X3: $i, X2: $i, X1: $i] : refl(((~esk8761_4(X1, X2, X3, X4)) | esk8120_4(X1, X2, X3, X4)) <=> ((~esk8761_4(X1, X2, X3, X4)) | esk8120_4(X1, X2, X3, X4)))),
% 16.69/11.81 inference(bind,[status(th)],[])).
% 16.69/11.81 tff(63,plain,
% 16.69/11.81 (![X4: $i, X3: $i, X2: $i, X1: $i] : ((~esk8761_4(X1, X2, X3, X4)) | esk8120_4(X1, X2, X3, X4)) <=> ![X4: $i, X3: $i, X2: $i, X1: $i] : ((~esk8761_4(X1, X2, X3, X4)) | esk8120_4(X1, X2, X3, X4))),
% 16.69/11.81 inference(quant_intro,[status(thm)],[62])).
% 16.69/11.81 tff(64,plain,
% 16.69/11.81 (![X4: $i, X3: $i, X2: $i, X1: $i] : ((~esk8761_4(X1, X2, X3, X4)) | esk8120_4(X1, X2, X3, X4)) <=> ![X4: $i, X3: $i, X2: $i, X1: $i] : ((~esk8761_4(X1, X2, X3, X4)) | esk8120_4(X1, X2, X3, X4))),
% 16.69/11.81 inference(rewrite,[status(thm)],[])).
% 16.69/11.81 tff(65,axiom,(![X4: $i, X3: $i, X2: $i, X1: $i] : ((~esk8761_4(X1, X2, X3, X4)) | esk8120_4(X1, X2, X3, X4))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','i_0_27269')).
% 16.69/11.81 tff(66,plain,
% 16.69/11.81 (![X4: $i, X3: $i, X2: $i, X1: $i] : ((~esk8761_4(X1, X2, X3, X4)) | esk8120_4(X1, X2, X3, X4))),
% 16.69/11.81 inference(modus_ponens,[status(thm)],[65, 64])).
% 16.69/11.81 tff(67,plain,(
% 16.69/11.81 ![X4: $i, X3: $i, X2: $i, X1: $i] : ((~esk8761_4(X1, X2, X3, X4)) | esk8120_4(X1, X2, X3, X4))),
% 16.69/11.81 inference(skolemize,[status(sab)],[66])).
% 16.69/11.81 tff(68,plain,
% 16.69/11.81 (![X4: $i, X3: $i, X2: $i, X1: $i] : ((~esk8761_4(X1, X2, X3, X4)) | esk8120_4(X1, X2, X3, X4))),
% 16.69/11.81 inference(modus_ponens,[status(thm)],[67, 63])).
% 16.69/11.81 tff(69,plain,
% 16.69/11.81 (((~![X4: $i, X3: $i, X2: $i, X1: $i] : ((~esk8761_4(X1, X2, X3, X4)) | esk8120_4(X1, X2, X3, X4))) | ((~esk8761_4(true, true, true, true)) | esk8120_4(true, true, true, true))) <=> ((~![X4: $i, X3: $i, X2: $i, X1: $i] : ((~esk8761_4(X1, X2, X3, X4)) | esk8120_4(X1, X2, X3, X4))) | (~esk8761_4(true, true, true, true)) | esk8120_4(true, true, true, true))),
% 16.69/11.81 inference(rewrite,[status(thm)],[])).
% 16.69/11.81 tff(70,plain,
% 16.69/11.81 ((~![X4: $i, X3: $i, X2: $i, X1: $i] : ((~esk8761_4(X1, X2, X3, X4)) | esk8120_4(X1, X2, X3, X4))) | ((~esk8761_4(true, true, true, true)) | esk8120_4(true, true, true, true))),
% 16.69/11.81 inference(quant_inst,[status(thm)],[])).
% 16.69/11.81 tff(71,plain,
% 16.69/11.81 ((~![X4: $i, X3: $i, X2: $i, X1: $i] : ((~esk8761_4(X1, X2, X3, X4)) | esk8120_4(X1, X2, X3, X4))) | (~esk8761_4(true, true, true, true)) | esk8120_4(true, true, true, true)),
% 16.69/11.81 inference(modus_ponens,[status(thm)],[70, 69])).
% 16.69/11.81 tff(72,plain,
% 16.69/11.81 (~esk8761_4(true, true, true, true)),
% 16.69/11.81 inference(unit_resolution,[status(thm)],[71, 68, 61])).
% 16.69/11.81 tff(73,plain,
% 16.69/11.81 (^[X4: $i, X3: $i, X2: $i, X1: $i] : refl(((~esk7825_4(X1, X2, X3, X4)) | esk8761_4(X1, X2, X3, X4)) <=> ((~esk7825_4(X1, X2, X3, X4)) | esk8761_4(X1, X2, X3, X4)))),
% 16.69/11.81 inference(bind,[status(th)],[])).
% 16.69/11.81 tff(74,plain,
% 16.69/11.81 (![X4: $i, X3: $i, X2: $i, X1: $i] : ((~esk7825_4(X1, X2, X3, X4)) | esk8761_4(X1, X2, X3, X4)) <=> ![X4: $i, X3: $i, X2: $i, X1: $i] : ((~esk7825_4(X1, X2, X3, X4)) | esk8761_4(X1, X2, X3, X4))),
% 16.69/11.81 inference(quant_intro,[status(thm)],[73])).
% 16.69/11.81 tff(75,plain,
% 16.69/11.81 (![X4: $i, X3: $i, X2: $i, X1: $i] : ((~esk7825_4(X1, X2, X3, X4)) | esk8761_4(X1, X2, X3, X4)) <=> ![X4: $i, X3: $i, X2: $i, X1: $i] : ((~esk7825_4(X1, X2, X3, X4)) | esk8761_4(X1, X2, X3, X4))),
% 16.69/11.81 inference(rewrite,[status(thm)],[])).
% 16.69/11.81 tff(76,axiom,(![X4: $i, X3: $i, X2: $i, X1: $i] : ((~esk7825_4(X1, X2, X3, X4)) | esk8761_4(X1, X2, X3, X4))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','i_0_17201')).
% 16.69/11.81 tff(77,plain,
% 16.69/11.81 (![X4: $i, X3: $i, X2: $i, X1: $i] : ((~esk7825_4(X1, X2, X3, X4)) | esk8761_4(X1, X2, X3, X4))),
% 16.69/11.81 inference(modus_ponens,[status(thm)],[76, 75])).
% 16.69/11.81 tff(78,plain,(
% 16.69/11.81 ![X4: $i, X3: $i, X2: $i, X1: $i] : ((~esk7825_4(X1, X2, X3, X4)) | esk8761_4(X1, X2, X3, X4))),
% 16.69/11.81 inference(skolemize,[status(sab)],[77])).
% 16.69/11.81 tff(79,plain,
% 16.69/11.81 (![X4: $i, X3: $i, X2: $i, X1: $i] : ((~esk7825_4(X1, X2, X3, X4)) | esk8761_4(X1, X2, X3, X4))),
% 16.69/11.81 inference(modus_ponens,[status(thm)],[78, 74])).
% 16.69/11.81 tff(80,plain,
% 16.69/11.81 (((~![X4: $i, X3: $i, X2: $i, X1: $i] : ((~esk7825_4(X1, X2, X3, X4)) | esk8761_4(X1, X2, X3, X4))) | ((~esk7825_4(true, true, true, true)) | esk8761_4(true, true, true, true))) <=> ((~![X4: $i, X3: $i, X2: $i, X1: $i] : ((~esk7825_4(X1, X2, X3, X4)) | esk8761_4(X1, X2, X3, X4))) | (~esk7825_4(true, true, true, true)) | esk8761_4(true, true, true, true))),
% 16.69/11.81 inference(rewrite,[status(thm)],[])).
% 16.69/11.81 tff(81,plain,
% 16.69/11.81 ((~![X4: $i, X3: $i, X2: $i, X1: $i] : ((~esk7825_4(X1, X2, X3, X4)) | esk8761_4(X1, X2, X3, X4))) | ((~esk7825_4(true, true, true, true)) | esk8761_4(true, true, true, true))),
% 16.69/11.81 inference(quant_inst,[status(thm)],[])).
% 16.69/11.81 tff(82,plain,
% 16.69/11.81 ((~![X4: $i, X3: $i, X2: $i, X1: $i] : ((~esk7825_4(X1, X2, X3, X4)) | esk8761_4(X1, X2, X3, X4))) | (~esk7825_4(true, true, true, true)) | esk8761_4(true, true, true, true)),
% 16.69/11.81 inference(modus_ponens,[status(thm)],[81, 80])).
% 16.69/11.81 tff(83,plain,
% 16.69/11.81 (~esk7825_4(true, true, true, true)),
% 16.69/11.81 inference(unit_resolution,[status(thm)],[82, 79, 72])).
% 16.69/11.81 tff(84,plain,
% 16.69/11.81 (^[X4: $i, X3: $i, X2: $i, X1: $i] : refl(((~p(X3)) | (~p(X1)) | (~p(X4)) | (~p(X2)) | esk8751_4(X1, X2, X3, X4)) <=> ((~p(X3)) | (~p(X1)) | (~p(X4)) | (~p(X2)) | esk8751_4(X1, X2, X3, X4)))),
% 16.69/11.81 inference(bind,[status(th)],[])).
% 16.69/11.81 tff(85,plain,
% 16.69/11.81 (![X4: $i, X3: $i, X2: $i, X1: $i] : ((~p(X3)) | (~p(X1)) | (~p(X4)) | (~p(X2)) | esk8751_4(X1, X2, X3, X4)) <=> ![X4: $i, X3: $i, X2: $i, X1: $i] : ((~p(X3)) | (~p(X1)) | (~p(X4)) | (~p(X2)) | esk8751_4(X1, X2, X3, X4))),
% 16.69/11.81 inference(quant_intro,[status(thm)],[84])).
% 16.69/11.81 tff(86,plain,
% 16.69/11.81 (![X4: $i, X3: $i, X2: $i, X1: $i] : ((~p(X3)) | (~p(X1)) | (~p(X4)) | (~p(X2)) | esk8751_4(X1, X2, X3, X4)) <=> ![X4: $i, X3: $i, X2: $i, X1: $i] : ((~p(X3)) | (~p(X1)) | (~p(X4)) | (~p(X2)) | esk8751_4(X1, X2, X3, X4))),
% 16.69/11.81 inference(rewrite,[status(thm)],[])).
% 16.69/11.81 tff(87,plain,
% 16.69/11.81 (^[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(X1)) | (~p(X4)) | (~p(X2)) | esk8751_4(X1, X2, X3, X4) | (~esk2_0)) <=> ((~p(X3)) | (~p(X1)) | (~p(X4)) | (~p(X2)) | esk8751_4(X1, X2, X3, X4) | $false))), rewrite(((~p(X3)) | (~p(X1)) | (~p(X4)) | (~p(X2)) | esk8751_4(X1, X2, X3, X4) | $false) <=> ((~p(X3)) | (~p(X1)) | (~p(X4)) | (~p(X2)) | esk8751_4(X1, X2, X3, X4))), (((~p(X3)) | (~p(X1)) | (~p(X4)) | (~p(X2)) | esk8751_4(X1, X2, X3, X4) | (~esk2_0)) <=> ((~p(X3)) | (~p(X1)) | (~p(X4)) | (~p(X2)) | esk8751_4(X1, X2, X3, X4))))),
% 16.69/11.81 inference(bind,[status(th)],[])).
% 16.69/11.81 tff(88,plain,
% 16.69/11.81 (![X4: $i, X3: $i, X2: $i, X1: $i] : ((~p(X3)) | (~p(X1)) | (~p(X4)) | (~p(X2)) | esk8751_4(X1, X2, X3, X4) | (~esk2_0)) <=> ![X4: $i, X3: $i, X2: $i, X1: $i] : ((~p(X3)) | (~p(X1)) | (~p(X4)) | (~p(X2)) | esk8751_4(X1, X2, X3, X4))),
% 16.69/11.81 inference(quant_intro,[status(thm)],[87])).
% 16.69/11.81 tff(89,plain,
% 16.69/11.81 (^[X4: $i, X3: $i, X2: $i, X1: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~p(X1)) | (~p(X4))) | (~p(X2))) <=> ((~p(X1)) | (~p(X4)) | (~p(X2)))), (((((~p(X1)) | (~p(X4))) | (~p(X2))) | (~esk2_0)) <=> (((~p(X1)) | (~p(X4)) | (~p(X2))) | (~esk2_0)))), rewrite((((~p(X1)) | (~p(X4)) | (~p(X2))) | (~esk2_0)) <=> ((~p(X1)) | (~p(X4)) | (~p(X2)) | (~esk2_0))), (((((~p(X1)) | (~p(X4))) | (~p(X2))) | (~esk2_0)) <=> ((~p(X1)) | (~p(X4)) | (~p(X2)) | (~esk2_0)))), ((((((~p(X1)) | (~p(X4))) | (~p(X2))) | (~esk2_0)) | (~p(X3))) <=> (((~p(X1)) | (~p(X4)) | (~p(X2)) | (~esk2_0)) | (~p(X3))))), rewrite((((~p(X1)) | (~p(X4)) | (~p(X2)) | (~esk2_0)) | (~p(X3))) <=> ((~p(X3)) | (~p(X1)) | (~p(X4)) | (~p(X2)) | (~esk2_0))), ((((((~p(X1)) | (~p(X4))) | (~p(X2))) | (~esk2_0)) | (~p(X3))) <=> ((~p(X3)) | (~p(X1)) | (~p(X4)) | (~p(X2)) | (~esk2_0)))), (((((((~p(X1)) | (~p(X4))) | (~p(X2))) | (~esk2_0)) | (~p(X3))) | esk8751_4(X1, X2, X3, X4)) <=> (((~p(X3)) | (~p(X1)) | (~p(X4)) | (~p(X2)) | (~esk2_0)) | esk8751_4(X1, X2, X3, X4)))), rewrite((((~p(X3)) | (~p(X1)) | (~p(X4)) | (~p(X2)) | (~esk2_0)) | esk8751_4(X1, X2, X3, X4)) <=> ((~p(X3)) | (~p(X1)) | (~p(X4)) | (~p(X2)) | esk8751_4(X1, X2, X3, X4) | (~esk2_0))), (((((((~p(X1)) | (~p(X4))) | (~p(X2))) | (~esk2_0)) | (~p(X3))) | esk8751_4(X1, X2, X3, X4)) <=> ((~p(X3)) | (~p(X1)) | (~p(X4)) | (~p(X2)) | esk8751_4(X1, X2, X3, X4) | (~esk2_0))))),
% 16.69/11.81 inference(bind,[status(th)],[])).
% 16.69/11.81 tff(90,plain,
% 16.69/11.81 (![X4: $i, X3: $i, X2: $i, X1: $i] : ((((((~p(X1)) | (~p(X4))) | (~p(X2))) | (~esk2_0)) | (~p(X3))) | esk8751_4(X1, X2, X3, X4)) <=> ![X4: $i, X3: $i, X2: $i, X1: $i] : ((~p(X3)) | (~p(X1)) | (~p(X4)) | (~p(X2)) | esk8751_4(X1, X2, X3, X4) | (~esk2_0))),
% 16.69/11.81 inference(quant_intro,[status(thm)],[89])).
% 16.69/11.81 tff(91,axiom,(![X4: $i, X3: $i, X2: $i, X1: $i] : ((((((~p(X1)) | (~p(X4))) | (~p(X2))) | (~esk2_0)) | (~p(X3))) | esk8751_4(X1, X2, X3, X4))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','i_0_14639')).
% 16.69/11.81 tff(92,plain,
% 16.69/11.81 (![X4: $i, X3: $i, X2: $i, X1: $i] : ((~p(X3)) | (~p(X1)) | (~p(X4)) | (~p(X2)) | esk8751_4(X1, X2, X3, X4) | (~esk2_0))),
% 16.69/11.81 inference(modus_ponens,[status(thm)],[91, 90])).
% 16.69/11.81 tff(93,plain,
% 16.69/11.81 (![X4: $i, X3: $i, X2: $i, X1: $i] : ((~p(X3)) | (~p(X1)) | (~p(X4)) | (~p(X2)) | esk8751_4(X1, X2, X3, X4))),
% 16.69/11.81 inference(modus_ponens,[status(thm)],[92, 88])).
% 16.69/11.81 tff(94,plain,
% 16.69/11.81 (![X4: $i, X3: $i, X2: $i, X1: $i] : ((~p(X3)) | (~p(X1)) | (~p(X4)) | (~p(X2)) | esk8751_4(X1, X2, X3, X4))),
% 16.69/11.81 inference(modus_ponens,[status(thm)],[93, 86])).
% 16.69/11.81 tff(95,plain,(
% 16.69/11.81 ![X4: $i, X3: $i, X2: $i, X1: $i] : ((~p(X3)) | (~p(X1)) | (~p(X4)) | (~p(X2)) | esk8751_4(X1, X2, X3, X4))),
% 16.69/11.81 inference(skolemize,[status(sab)],[94])).
% 16.69/11.81 tff(96,plain,
% 16.69/11.81 (![X4: $i, X3: $i, X2: $i, X1: $i] : ((~p(X3)) | (~p(X1)) | (~p(X4)) | (~p(X2)) | esk8751_4(X1, X2, X3, X4))),
% 16.69/11.81 inference(modus_ponens,[status(thm)],[95, 85])).
% 16.69/11.81 tff(97,plain,
% 16.69/11.81 (((~![X4: $i, X3: $i, X2: $i, X1: $i] : ((~p(X3)) | (~p(X1)) | (~p(X4)) | (~p(X2)) | esk8751_4(X1, X2, X3, X4))) | ((~p(true)) | esk8751_4(true, true, true, true))) <=> ((~![X4: $i, X3: $i, X2: $i, X1: $i] : ((~p(X3)) | (~p(X1)) | (~p(X4)) | (~p(X2)) | esk8751_4(X1, X2, X3, X4))) | (~p(true)) | esk8751_4(true, true, true, true))),
% 16.69/11.81 inference(rewrite,[status(thm)],[])).
% 16.69/11.81 tff(98,plain,
% 16.69/11.81 (((~p(true)) | (~p(true)) | (~p(true)) | (~p(true)) | esk8751_4(true, true, true, true)) <=> ((~p(true)) | esk8751_4(true, true, true, true))),
% 16.69/11.81 inference(rewrite,[status(thm)],[])).
% 16.69/11.81 tff(99,plain,
% 16.69/11.81 (((~![X4: $i, X3: $i, X2: $i, X1: $i] : ((~p(X3)) | (~p(X1)) | (~p(X4)) | (~p(X2)) | esk8751_4(X1, X2, X3, X4))) | ((~p(true)) | (~p(true)) | (~p(true)) | (~p(true)) | esk8751_4(true, true, true, true))) <=> ((~![X4: $i, X3: $i, X2: $i, X1: $i] : ((~p(X3)) | (~p(X1)) | (~p(X4)) | (~p(X2)) | esk8751_4(X1, X2, X3, X4))) | ((~p(true)) | esk8751_4(true, true, true, true)))),
% 16.69/11.81 inference(monotonicity,[status(thm)],[98])).
% 16.69/11.81 tff(100,plain,
% 16.69/11.81 (((~![X4: $i, X3: $i, X2: $i, X1: $i] : ((~p(X3)) | (~p(X1)) | (~p(X4)) | (~p(X2)) | esk8751_4(X1, X2, X3, X4))) | ((~p(true)) | (~p(true)) | (~p(true)) | (~p(true)) | esk8751_4(true, true, true, true))) <=> ((~![X4: $i, X3: $i, X2: $i, X1: $i] : ((~p(X3)) | (~p(X1)) | (~p(X4)) | (~p(X2)) | esk8751_4(X1, X2, X3, X4))) | (~p(true)) | esk8751_4(true, true, true, true))),
% 16.69/11.81 inference(transitivity,[status(thm)],[99, 97])).
% 16.69/11.81 tff(101,plain,
% 16.69/11.81 ((~![X4: $i, X3: $i, X2: $i, X1: $i] : ((~p(X3)) | (~p(X1)) | (~p(X4)) | (~p(X2)) | esk8751_4(X1, X2, X3, X4))) | ((~p(true)) | (~p(true)) | (~p(true)) | (~p(true)) | esk8751_4(true, true, true, true))),
% 16.69/11.81 inference(quant_inst,[status(thm)],[])).
% 16.69/11.81 tff(102,plain,
% 16.69/11.81 ((~![X4: $i, X3: $i, X2: $i, X1: $i] : ((~p(X3)) | (~p(X1)) | (~p(X4)) | (~p(X2)) | esk8751_4(X1, X2, X3, X4))) | (~p(true)) | esk8751_4(true, true, true, true)),
% 16.69/11.81 inference(modus_ponens,[status(thm)],[101, 100])).
% 16.69/11.81 tff(103,plain,
% 16.69/11.81 (esk8751_4(true, true, true, true)),
% 16.69/11.81 inference(unit_resolution,[status(thm)],[102, 96, 4])).
% 16.69/11.81 tff(104,plain,
% 16.69/11.81 (^[X4: $i, X3: $i, X2: $i, X1: $i] : refl(((~esk8751_4(X1, X2, X3, X4)) | esk7826_4(X1, X2, X3, X4)) <=> ((~esk8751_4(X1, X2, X3, X4)) | esk7826_4(X1, X2, X3, X4)))),
% 16.69/11.81 inference(bind,[status(th)],[])).
% 16.69/11.81 tff(105,plain,
% 16.69/11.81 (![X4: $i, X3: $i, X2: $i, X1: $i] : ((~esk8751_4(X1, X2, X3, X4)) | esk7826_4(X1, X2, X3, X4)) <=> ![X4: $i, X3: $i, X2: $i, X1: $i] : ((~esk8751_4(X1, X2, X3, X4)) | esk7826_4(X1, X2, X3, X4))),
% 16.69/11.81 inference(quant_intro,[status(thm)],[104])).
% 16.69/11.81 tff(106,plain,
% 16.69/11.81 (![X4: $i, X3: $i, X2: $i, X1: $i] : ((~esk8751_4(X1, X2, X3, X4)) | esk7826_4(X1, X2, X3, X4)) <=> ![X4: $i, X3: $i, X2: $i, X1: $i] : ((~esk8751_4(X1, X2, X3, X4)) | esk7826_4(X1, X2, X3, X4))),
% 16.69/11.81 inference(rewrite,[status(thm)],[])).
% 16.69/11.81 tff(107,axiom,(![X4: $i, X3: $i, X2: $i, X1: $i] : ((~esk8751_4(X1, X2, X3, X4)) | esk7826_4(X1, X2, X3, X4))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','i_0_1548')).
% 16.69/11.81 tff(108,plain,
% 16.69/11.81 (![X4: $i, X3: $i, X2: $i, X1: $i] : ((~esk8751_4(X1, X2, X3, X4)) | esk7826_4(X1, X2, X3, X4))),
% 16.69/11.81 inference(modus_ponens,[status(thm)],[107, 106])).
% 16.69/11.81 tff(109,plain,(
% 16.69/11.81 ![X4: $i, X3: $i, X2: $i, X1: $i] : ((~esk8751_4(X1, X2, X3, X4)) | esk7826_4(X1, X2, X3, X4))),
% 16.69/11.81 inference(skolemize,[status(sab)],[108])).
% 16.69/11.81 tff(110,plain,
% 16.69/11.81 (![X4: $i, X3: $i, X2: $i, X1: $i] : ((~esk8751_4(X1, X2, X3, X4)) | esk7826_4(X1, X2, X3, X4))),
% 16.69/11.81 inference(modus_ponens,[status(thm)],[109, 105])).
% 16.69/11.81 tff(111,plain,
% 16.69/11.81 (((~![X4: $i, X3: $i, X2: $i, X1: $i] : ((~esk8751_4(X1, X2, X3, X4)) | esk7826_4(X1, X2, X3, X4))) | ((~esk8751_4(true, true, true, true)) | esk7826_4(true, true, true, true))) <=> ((~![X4: $i, X3: $i, X2: $i, X1: $i] : ((~esk8751_4(X1, X2, X3, X4)) | esk7826_4(X1, X2, X3, X4))) | (~esk8751_4(true, true, true, true)) | esk7826_4(true, true, true, true))),
% 16.69/11.81 inference(rewrite,[status(thm)],[])).
% 16.69/11.81 tff(112,plain,
% 16.69/11.81 ((~![X4: $i, X3: $i, X2: $i, X1: $i] : ((~esk8751_4(X1, X2, X3, X4)) | esk7826_4(X1, X2, X3, X4))) | ((~esk8751_4(true, true, true, true)) | esk7826_4(true, true, true, true))),
% 16.69/11.81 inference(quant_inst,[status(thm)],[])).
% 16.69/11.81 tff(113,plain,
% 16.69/11.81 ((~![X4: $i, X3: $i, X2: $i, X1: $i] : ((~esk8751_4(X1, X2, X3, X4)) | esk7826_4(X1, X2, X3, X4))) | (~esk8751_4(true, true, true, true)) | esk7826_4(true, true, true, true)),
% 16.69/11.81 inference(modus_ponens,[status(thm)],[112, 111])).
% 16.69/11.81 tff(114,plain,
% 16.69/11.81 (esk7826_4(true, true, true, true)),
% 16.69/11.81 inference(unit_resolution,[status(thm)],[113, 110, 103])).
% 16.69/11.81 tff(115,plain,
% 16.69/11.81 (^[X4: $i, X3: $i, X2: $i, X1: $i] : refl((esk7825_4(X1, X2, X3, X4) | esk7824_4(X1, X2, X3, X4) | (~esk7826_4(X1, X2, X3, X4))) <=> (esk7825_4(X1, X2, X3, X4) | esk7824_4(X1, X2, X3, X4) | (~esk7826_4(X1, X2, X3, X4))))),
% 16.69/11.81 inference(bind,[status(th)],[])).
% 16.69/11.81 tff(116,plain,
% 16.69/11.81 (![X4: $i, X3: $i, X2: $i, X1: $i] : (esk7825_4(X1, X2, X3, X4) | esk7824_4(X1, X2, X3, X4) | (~esk7826_4(X1, X2, X3, X4))) <=> ![X4: $i, X3: $i, X2: $i, X1: $i] : (esk7825_4(X1, X2, X3, X4) | esk7824_4(X1, X2, X3, X4) | (~esk7826_4(X1, X2, X3, X4)))),
% 16.69/11.81 inference(quant_intro,[status(thm)],[115])).
% 16.69/11.81 tff(117,plain,
% 16.69/11.81 (![X4: $i, X3: $i, X2: $i, X1: $i] : (esk7825_4(X1, X2, X3, X4) | esk7824_4(X1, X2, X3, X4) | (~esk7826_4(X1, X2, X3, X4))) <=> ![X4: $i, X3: $i, X2: $i, X1: $i] : (esk7825_4(X1, X2, X3, X4) | esk7824_4(X1, X2, X3, X4) | (~esk7826_4(X1, X2, X3, X4)))),
% 16.69/11.81 inference(rewrite,[status(thm)],[])).
% 16.69/11.81 tff(118,plain,
% 16.69/11.81 (^[X4: $i, X3: $i, X2: $i, X1: $i] : trans(monotonicity(rewrite((esk7825_4(X1, X2, X3, X4) | esk7824_4(X1, X2, X3, X4)) <=> (esk7825_4(X1, X2, X3, X4) | esk7824_4(X1, X2, X3, X4))), (((esk7825_4(X1, X2, X3, X4) | esk7824_4(X1, X2, X3, X4)) | (~esk7826_4(X1, X2, X3, X4))) <=> ((esk7825_4(X1, X2, X3, X4) | esk7824_4(X1, X2, X3, X4)) | (~esk7826_4(X1, X2, X3, X4))))), rewrite(((esk7825_4(X1, X2, X3, X4) | esk7824_4(X1, X2, X3, X4)) | (~esk7826_4(X1, X2, X3, X4))) <=> (esk7825_4(X1, X2, X3, X4) | esk7824_4(X1, X2, X3, X4) | (~esk7826_4(X1, X2, X3, X4)))), (((esk7825_4(X1, X2, X3, X4) | esk7824_4(X1, X2, X3, X4)) | (~esk7826_4(X1, X2, X3, X4))) <=> (esk7825_4(X1, X2, X3, X4) | esk7824_4(X1, X2, X3, X4) | (~esk7826_4(X1, X2, X3, X4)))))),
% 16.69/11.81 inference(bind,[status(th)],[])).
% 16.69/11.81 tff(119,plain,
% 16.69/11.81 (![X4: $i, X3: $i, X2: $i, X1: $i] : ((esk7825_4(X1, X2, X3, X4) | esk7824_4(X1, X2, X3, X4)) | (~esk7826_4(X1, X2, X3, X4))) <=> ![X4: $i, X3: $i, X2: $i, X1: $i] : (esk7825_4(X1, X2, X3, X4) | esk7824_4(X1, X2, X3, X4) | (~esk7826_4(X1, X2, X3, X4)))),
% 16.69/11.81 inference(quant_intro,[status(thm)],[118])).
% 16.69/11.81 tff(120,axiom,(![X4: $i, X3: $i, X2: $i, X1: $i] : ((esk7825_4(X1, X2, X3, X4) | esk7824_4(X1, X2, X3, X4)) | (~esk7826_4(X1, X2, X3, X4)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','i_0_3978')).
% 16.69/11.81 tff(121,plain,
% 16.69/11.81 (![X4: $i, X3: $i, X2: $i, X1: $i] : (esk7825_4(X1, X2, X3, X4) | esk7824_4(X1, X2, X3, X4) | (~esk7826_4(X1, X2, X3, X4)))),
% 16.69/11.81 inference(modus_ponens,[status(thm)],[120, 119])).
% 16.69/11.81 tff(122,plain,
% 16.69/11.81 (![X4: $i, X3: $i, X2: $i, X1: $i] : (esk7825_4(X1, X2, X3, X4) | esk7824_4(X1, X2, X3, X4) | (~esk7826_4(X1, X2, X3, X4)))),
% 16.69/11.81 inference(modus_ponens,[status(thm)],[121, 117])).
% 16.69/11.81 tff(123,plain,(
% 16.69/11.81 ![X4: $i, X3: $i, X2: $i, X1: $i] : (esk7825_4(X1, X2, X3, X4) | esk7824_4(X1, X2, X3, X4) | (~esk7826_4(X1, X2, X3, X4)))),
% 16.69/11.81 inference(skolemize,[status(sab)],[122])).
% 16.69/11.81 tff(124,plain,
% 16.69/11.81 (![X4: $i, X3: $i, X2: $i, X1: $i] : (esk7825_4(X1, X2, X3, X4) | esk7824_4(X1, X2, X3, X4) | (~esk7826_4(X1, X2, X3, X4)))),
% 16.69/11.81 inference(modus_ponens,[status(thm)],[123, 116])).
% 16.69/11.81 tff(125,plain,
% 16.69/11.81 (((~![X4: $i, X3: $i, X2: $i, X1: $i] : (esk7825_4(X1, X2, X3, X4) | esk7824_4(X1, X2, X3, X4) | (~esk7826_4(X1, X2, X3, X4)))) | (esk7825_4(true, true, true, true) | esk7824_4(true, true, true, true) | (~esk7826_4(true, true, true, true)))) <=> ((~![X4: $i, X3: $i, X2: $i, X1: $i] : (esk7825_4(X1, X2, X3, X4) | esk7824_4(X1, X2, X3, X4) | (~esk7826_4(X1, X2, X3, X4)))) | esk7825_4(true, true, true, true) | esk7824_4(true, true, true, true) | (~esk7826_4(true, true, true, true)))),
% 16.69/11.81 inference(rewrite,[status(thm)],[])).
% 16.69/11.81 tff(126,plain,
% 16.69/11.81 ((~![X4: $i, X3: $i, X2: $i, X1: $i] : (esk7825_4(X1, X2, X3, X4) | esk7824_4(X1, X2, X3, X4) | (~esk7826_4(X1, X2, X3, X4)))) | (esk7825_4(true, true, true, true) | esk7824_4(true, true, true, true) | (~esk7826_4(true, true, true, true)))),
% 16.69/11.81 inference(quant_inst,[status(thm)],[])).
% 16.69/11.81 tff(127,plain,
% 16.69/11.81 ((~![X4: $i, X3: $i, X2: $i, X1: $i] : (esk7825_4(X1, X2, X3, X4) | esk7824_4(X1, X2, X3, X4) | (~esk7826_4(X1, X2, X3, X4)))) | esk7825_4(true, true, true, true) | esk7824_4(true, true, true, true) | (~esk7826_4(true, true, true, true))),
% 16.69/11.81 inference(modus_ponens,[status(thm)],[126, 125])).
% 16.69/11.81 tff(128,plain,
% 16.69/11.81 (esk7825_4(true, true, true, true) | esk7824_4(true, true, true, true)),
% 16.69/11.81 inference(unit_resolution,[status(thm)],[127, 124, 114])).
% 16.69/11.81 tff(129,plain,
% 16.69/11.81 (esk7824_4(true, true, true, true)),
% 16.69/11.81 inference(unit_resolution,[status(thm)],[128, 83])).
% 16.69/11.81 tff(130,plain,
% 16.69/11.81 (^[X4: $i, X3: $i, X2: $i, X1: $i] : refl(((~esk7824_4(X1, X2, X3, X4)) | esk7953_4(X1, X2, X3, X4)) <=> ((~esk7824_4(X1, X2, X3, X4)) | esk7953_4(X1, X2, X3, X4)))),
% 16.69/11.81 inference(bind,[status(th)],[])).
% 16.69/11.81 tff(131,plain,
% 16.69/11.81 (![X4: $i, X3: $i, X2: $i, X1: $i] : ((~esk7824_4(X1, X2, X3, X4)) | esk7953_4(X1, X2, X3, X4)) <=> ![X4: $i, X3: $i, X2: $i, X1: $i] : ((~esk7824_4(X1, X2, X3, X4)) | esk7953_4(X1, X2, X3, X4))),
% 16.69/11.81 inference(quant_intro,[status(thm)],[130])).
% 16.69/11.81 tff(132,plain,
% 16.69/11.81 (![X4: $i, X3: $i, X2: $i, X1: $i] : ((~esk7824_4(X1, X2, X3, X4)) | esk7953_4(X1, X2, X3, X4)) <=> ![X4: $i, X3: $i, X2: $i, X1: $i] : ((~esk7824_4(X1, X2, X3, X4)) | esk7953_4(X1, X2, X3, X4))),
% 16.69/11.81 inference(rewrite,[status(thm)],[])).
% 16.69/11.81 tff(133,plain,
% 16.69/11.81 (^[X4: $i, X3: $i, X2: $i, X1: $i] : rewrite((esk7953_4(X1, X2, X3, X4) | (~esk7824_4(X1, X2, X3, X4))) <=> ((~esk7824_4(X1, X2, X3, X4)) | esk7953_4(X1, X2, X3, X4)))),
% 16.69/11.81 inference(bind,[status(th)],[])).
% 16.69/11.81 tff(134,plain,
% 16.69/11.81 (![X4: $i, X3: $i, X2: $i, X1: $i] : (esk7953_4(X1, X2, X3, X4) | (~esk7824_4(X1, X2, X3, X4))) <=> ![X4: $i, X3: $i, X2: $i, X1: $i] : ((~esk7824_4(X1, X2, X3, X4)) | esk7953_4(X1, X2, X3, X4))),
% 16.69/11.81 inference(quant_intro,[status(thm)],[133])).
% 16.69/11.81 tff(135,axiom,(![X4: $i, X3: $i, X2: $i, X1: $i] : (esk7953_4(X1, X2, X3, X4) | (~esk7824_4(X1, X2, X3, X4)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','i_0_8559')).
% 16.69/11.81 tff(136,plain,
% 16.69/11.81 (![X4: $i, X3: $i, X2: $i, X1: $i] : ((~esk7824_4(X1, X2, X3, X4)) | esk7953_4(X1, X2, X3, X4))),
% 16.69/11.81 inference(modus_ponens,[status(thm)],[135, 134])).
% 16.69/11.81 tff(137,plain,
% 16.69/11.81 (![X4: $i, X3: $i, X2: $i, X1: $i] : ((~esk7824_4(X1, X2, X3, X4)) | esk7953_4(X1, X2, X3, X4))),
% 16.69/11.81 inference(modus_ponens,[status(thm)],[136, 132])).
% 16.69/11.81 tff(138,plain,(
% 16.69/11.81 ![X4: $i, X3: $i, X2: $i, X1: $i] : ((~esk7824_4(X1, X2, X3, X4)) | esk7953_4(X1, X2, X3, X4))),
% 16.69/11.81 inference(skolemize,[status(sab)],[137])).
% 16.69/11.81 tff(139,plain,
% 16.69/11.81 (![X4: $i, X3: $i, X2: $i, X1: $i] : ((~esk7824_4(X1, X2, X3, X4)) | esk7953_4(X1, X2, X3, X4))),
% 16.69/11.81 inference(modus_ponens,[status(thm)],[138, 131])).
% 16.69/11.81 tff(140,plain,
% 16.69/11.81 (((~![X4: $i, X3: $i, X2: $i, X1: $i] : ((~esk7824_4(X1, X2, X3, X4)) | esk7953_4(X1, X2, X3, X4))) | ((~esk7824_4(true, true, true, true)) | esk7953_4(true, true, true, true))) <=> ((~![X4: $i, X3: $i, X2: $i, X1: $i] : ((~esk7824_4(X1, X2, X3, X4)) | esk7953_4(X1, X2, X3, X4))) | (~esk7824_4(true, true, true, true)) | esk7953_4(true, true, true, true))),
% 16.69/11.81 inference(rewrite,[status(thm)],[])).
% 16.69/11.81 tff(141,plain,
% 16.69/11.81 ((~![X4: $i, X3: $i, X2: $i, X1: $i] : ((~esk7824_4(X1, X2, X3, X4)) | esk7953_4(X1, X2, X3, X4))) | ((~esk7824_4(true, true, true, true)) | esk7953_4(true, true, true, true))),
% 16.69/11.81 inference(quant_inst,[status(thm)],[])).
% 16.69/11.81 tff(142,plain,
% 16.69/11.81 ((~![X4: $i, X3: $i, X2: $i, X1: $i] : ((~esk7824_4(X1, X2, X3, X4)) | esk7953_4(X1, X2, X3, X4))) | (~esk7824_4(true, true, true, true)) | esk7953_4(true, true, true, true)),
% 16.69/11.81 inference(modus_ponens,[status(thm)],[141, 140])).
% 16.69/11.81 tff(143,plain,
% 16.69/11.81 (esk7953_4(true, true, true, true)),
% 16.69/11.81 inference(unit_resolution,[status(thm)],[142, 139, 129])).
% 16.69/11.81 tff(144,plain,
% 16.69/11.81 (^[X4: $i, X3: $i, X2: $i, X1: $i] : refl((esk7952_4(X1, X2, X3, X4) | esk7951_4(X1, X2, X3, X4) | (~esk7953_4(X1, X2, X3, X4))) <=> (esk7952_4(X1, X2, X3, X4) | esk7951_4(X1, X2, X3, X4) | (~esk7953_4(X1, X2, X3, X4))))),
% 16.69/11.81 inference(bind,[status(th)],[])).
% 16.69/11.81 tff(145,plain,
% 16.69/11.81 (![X4: $i, X3: $i, X2: $i, X1: $i] : (esk7952_4(X1, X2, X3, X4) | esk7951_4(X1, X2, X3, X4) | (~esk7953_4(X1, X2, X3, X4))) <=> ![X4: $i, X3: $i, X2: $i, X1: $i] : (esk7952_4(X1, X2, X3, X4) | esk7951_4(X1, X2, X3, X4) | (~esk7953_4(X1, X2, X3, X4)))),
% 16.69/11.81 inference(quant_intro,[status(thm)],[144])).
% 16.69/11.81 tff(146,plain,
% 16.69/11.81 (![X4: $i, X3: $i, X2: $i, X1: $i] : (esk7952_4(X1, X2, X3, X4) | esk7951_4(X1, X2, X3, X4) | (~esk7953_4(X1, X2, X3, X4))) <=> ![X4: $i, X3: $i, X2: $i, X1: $i] : (esk7952_4(X1, X2, X3, X4) | esk7951_4(X1, X2, X3, X4) | (~esk7953_4(X1, X2, X3, X4)))),
% 16.69/11.81 inference(rewrite,[status(thm)],[])).
% 16.69/11.81 tff(147,plain,
% 16.69/11.81 (^[X4: $i, X3: $i, X2: $i, X1: $i] : rewrite((((~esk7953_4(X1, X2, X3, X4)) | esk7952_4(X1, X2, X3, X4)) | esk7951_4(X1, X2, X3, X4)) <=> (esk7952_4(X1, X2, X3, X4) | esk7951_4(X1, X2, X3, X4) | (~esk7953_4(X1, X2, X3, X4))))),
% 16.69/11.81 inference(bind,[status(th)],[])).
% 16.69/11.81 tff(148,plain,
% 16.69/11.81 (![X4: $i, X3: $i, X2: $i, X1: $i] : (((~esk7953_4(X1, X2, X3, X4)) | esk7952_4(X1, X2, X3, X4)) | esk7951_4(X1, X2, X3, X4)) <=> ![X4: $i, X3: $i, X2: $i, X1: $i] : (esk7952_4(X1, X2, X3, X4) | esk7951_4(X1, X2, X3, X4) | (~esk7953_4(X1, X2, X3, X4)))),
% 16.69/11.81 inference(quant_intro,[status(thm)],[147])).
% 16.69/11.81 tff(149,axiom,(![X4: $i, X3: $i, X2: $i, X1: $i] : (((~esk7953_4(X1, X2, X3, X4)) | esk7952_4(X1, X2, X3, X4)) | esk7951_4(X1, X2, X3, X4))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','i_0_3018')).
% 16.69/11.81 tff(150,plain,
% 16.69/11.81 (![X4: $i, X3: $i, X2: $i, X1: $i] : (esk7952_4(X1, X2, X3, X4) | esk7951_4(X1, X2, X3, X4) | (~esk7953_4(X1, X2, X3, X4)))),
% 16.69/11.81 inference(modus_ponens,[status(thm)],[149, 148])).
% 16.69/11.81 tff(151,plain,
% 16.69/11.81 (![X4: $i, X3: $i, X2: $i, X1: $i] : (esk7952_4(X1, X2, X3, X4) | esk7951_4(X1, X2, X3, X4) | (~esk7953_4(X1, X2, X3, X4)))),
% 16.69/11.81 inference(modus_ponens,[status(thm)],[150, 146])).
% 16.69/11.81 tff(152,plain,(
% 16.69/11.81 ![X4: $i, X3: $i, X2: $i, X1: $i] : (esk7952_4(X1, X2, X3, X4) | esk7951_4(X1, X2, X3, X4) | (~esk7953_4(X1, X2, X3, X4)))),
% 16.69/11.81 inference(skolemize,[status(sab)],[151])).
% 16.69/11.81 tff(153,plain,
% 16.69/11.81 (![X4: $i, X3: $i, X2: $i, X1: $i] : (esk7952_4(X1, X2, X3, X4) | esk7951_4(X1, X2, X3, X4) | (~esk7953_4(X1, X2, X3, X4)))),
% 16.69/11.81 inference(modus_ponens,[status(thm)],[152, 145])).
% 16.69/11.81 tff(154,plain,
% 16.69/11.81 (((~![X4: $i, X3: $i, X2: $i, X1: $i] : (esk7952_4(X1, X2, X3, X4) | esk7951_4(X1, X2, X3, X4) | (~esk7953_4(X1, X2, X3, X4)))) | (esk7952_4(true, true, true, true) | esk7951_4(true, true, true, true) | (~esk7953_4(true, true, true, true)))) <=> ((~![X4: $i, X3: $i, X2: $i, X1: $i] : (esk7952_4(X1, X2, X3, X4) | esk7951_4(X1, X2, X3, X4) | (~esk7953_4(X1, X2, X3, X4)))) | esk7952_4(true, true, true, true) | esk7951_4(true, true, true, true) | (~esk7953_4(true, true, true, true)))),
% 16.69/11.81 inference(rewrite,[status(thm)],[])).
% 16.69/11.81 tff(155,plain,
% 16.69/11.81 ((~![X4: $i, X3: $i, X2: $i, X1: $i] : (esk7952_4(X1, X2, X3, X4) | esk7951_4(X1, X2, X3, X4) | (~esk7953_4(X1, X2, X3, X4)))) | (esk7952_4(true, true, true, true) | esk7951_4(true, true, true, true) | (~esk7953_4(true, true, true, true)))),
% 16.69/11.81 inference(quant_inst,[status(thm)],[])).
% 16.69/11.81 tff(156,plain,
% 16.69/11.81 ((~![X4: $i, X3: $i, X2: $i, X1: $i] : (esk7952_4(X1, X2, X3, X4) | esk7951_4(X1, X2, X3, X4) | (~esk7953_4(X1, X2, X3, X4)))) | esk7952_4(true, true, true, true) | esk7951_4(true, true, true, true) | (~esk7953_4(true, true, true, true))),
% 16.69/11.81 inference(modus_ponens,[status(thm)],[155, 154])).
% 16.69/11.81 tff(157,plain,
% 16.69/11.81 (esk7952_4(true, true, true, true) | esk7951_4(true, true, true, true)),
% 16.69/11.81 inference(unit_resolution,[status(thm)],[156, 153, 143])).
% 16.69/11.81 tff(158,plain,
% 16.69/11.81 (esk7952_4(true, true, true, true)),
% 16.69/11.81 inference(unit_resolution,[status(thm)],[157, 50])).
% 16.69/11.81 tff(159,plain,
% 16.69/11.81 (^[X4: $i, X3: $i, X2: $i, X1: $i] : refl((esk9213_4(X1, X2, X3, X4) | (~esk7952_4(X1, X2, X3, X4))) <=> (esk9213_4(X1, X2, X3, X4) | (~esk7952_4(X1, X2, X3, X4))))),
% 16.69/11.81 inference(bind,[status(th)],[])).
% 16.69/11.81 tff(160,plain,
% 16.69/11.81 (![X4: $i, X3: $i, X2: $i, X1: $i] : (esk9213_4(X1, X2, X3, X4) | (~esk7952_4(X1, X2, X3, X4))) <=> ![X4: $i, X3: $i, X2: $i, X1: $i] : (esk9213_4(X1, X2, X3, X4) | (~esk7952_4(X1, X2, X3, X4)))),
% 16.69/11.81 inference(quant_intro,[status(thm)],[159])).
% 16.69/11.81 tff(161,plain,
% 16.69/11.81 (![X4: $i, X3: $i, X2: $i, X1: $i] : (esk9213_4(X1, X2, X3, X4) | (~esk7952_4(X1, X2, X3, X4))) <=> ![X4: $i, X3: $i, X2: $i, X1: $i] : (esk9213_4(X1, X2, X3, X4) | (~esk7952_4(X1, X2, X3, X4)))),
% 16.69/11.81 inference(rewrite,[status(thm)],[])).
% 16.69/11.81 tff(162,axiom,(![X4: $i, X3: $i, X2: $i, X1: $i] : (esk9213_4(X1, X2, X3, X4) | (~esk7952_4(X1, X2, X3, X4)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','i_0_25867')).
% 16.69/11.81 tff(163,plain,
% 16.69/11.81 (![X4: $i, X3: $i, X2: $i, X1: $i] : (esk9213_4(X1, X2, X3, X4) | (~esk7952_4(X1, X2, X3, X4)))),
% 16.69/11.81 inference(modus_ponens,[status(thm)],[162, 161])).
% 16.69/11.81 tff(164,plain,(
% 16.69/11.81 ![X4: $i, X3: $i, X2: $i, X1: $i] : (esk9213_4(X1, X2, X3, X4) | (~esk7952_4(X1, X2, X3, X4)))),
% 16.69/11.81 inference(skolemize,[status(sab)],[163])).
% 16.69/11.81 tff(165,plain,
% 16.69/11.81 (![X4: $i, X3: $i, X2: $i, X1: $i] : (esk9213_4(X1, X2, X3, X4) | (~esk7952_4(X1, X2, X3, X4)))),
% 16.69/11.81 inference(modus_ponens,[status(thm)],[164, 160])).
% 16.69/11.81 tff(166,plain,
% 16.69/11.81 (((~![X4: $i, X3: $i, X2: $i, X1: $i] : (esk9213_4(X1, X2, X3, X4) | (~esk7952_4(X1, X2, X3, X4)))) | (esk9213_4(true, true, true, true) | (~esk7952_4(true, true, true, true)))) <=> ((~![X4: $i, X3: $i, X2: $i, X1: $i] : (esk9213_4(X1, X2, X3, X4) | (~esk7952_4(X1, X2, X3, X4)))) | esk9213_4(true, true, true, true) | (~esk7952_4(true, true, true, true)))),
% 16.69/11.81 inference(rewrite,[status(thm)],[])).
% 16.69/11.81 tff(167,plain,
% 16.69/11.81 ((~![X4: $i, X3: $i, X2: $i, X1: $i] : (esk9213_4(X1, X2, X3, X4) | (~esk7952_4(X1, X2, X3, X4)))) | (esk9213_4(true, true, true, true) | (~esk7952_4(true, true, true, true)))),
% 16.69/11.81 inference(quant_inst,[status(thm)],[])).
% 16.69/11.81 tff(168,plain,
% 16.69/11.81 ((~![X4: $i, X3: $i, X2: $i, X1: $i] : (esk9213_4(X1, X2, X3, X4) | (~esk7952_4(X1, X2, X3, X4)))) | esk9213_4(true, true, true, true) | (~esk7952_4(true, true, true, true))),
% 16.69/11.81 inference(modus_ponens,[status(thm)],[167, 166])).
% 16.69/11.81 tff(169,plain,
% 16.69/11.81 (esk9213_4(true, true, true, true)),
% 16.69/11.81 inference(unit_resolution,[status(thm)],[168, 165, 158])).
% 16.69/11.81 tff(170,plain,
% 16.69/11.81 (^[X4: $i, X3: $i, X2: $i, X1: $i] : refl((esk8752_4(X1, X2, X3, X4) | (~esk9743_4(X1, X2, X3, X4))) <=> (esk8752_4(X1, X2, X3, X4) | (~esk9743_4(X1, X2, X3, X4))))),
% 16.69/11.81 inference(bind,[status(th)],[])).
% 16.69/11.82 tff(171,plain,
% 16.69/11.82 (![X4: $i, X3: $i, X2: $i, X1: $i] : (esk8752_4(X1, X2, X3, X4) | (~esk9743_4(X1, X2, X3, X4))) <=> ![X4: $i, X3: $i, X2: $i, X1: $i] : (esk8752_4(X1, X2, X3, X4) | (~esk9743_4(X1, X2, X3, X4)))),
% 16.69/11.82 inference(quant_intro,[status(thm)],[170])).
% 16.69/11.82 tff(172,plain,
% 16.69/11.82 (![X4: $i, X3: $i, X2: $i, X1: $i] : (esk8752_4(X1, X2, X3, X4) | (~esk9743_4(X1, X2, X3, X4))) <=> ![X4: $i, X3: $i, X2: $i, X1: $i] : (esk8752_4(X1, X2, X3, X4) | (~esk9743_4(X1, X2, X3, X4)))),
% 16.69/11.82 inference(rewrite,[status(thm)],[])).
% 16.69/11.82 tff(173,axiom,(![X4: $i, X3: $i, X2: $i, X1: $i] : (esk8752_4(X1, X2, X3, X4) | (~esk9743_4(X1, X2, X3, X4)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','i_0_8874')).
% 16.69/11.82 tff(174,plain,
% 16.69/11.82 (![X4: $i, X3: $i, X2: $i, X1: $i] : (esk8752_4(X1, X2, X3, X4) | (~esk9743_4(X1, X2, X3, X4)))),
% 16.69/11.82 inference(modus_ponens,[status(thm)],[173, 172])).
% 16.69/11.82 tff(175,plain,(
% 16.69/11.82 ![X4: $i, X3: $i, X2: $i, X1: $i] : (esk8752_4(X1, X2, X3, X4) | (~esk9743_4(X1, X2, X3, X4)))),
% 16.69/11.82 inference(skolemize,[status(sab)],[174])).
% 16.69/11.82 tff(176,plain,
% 16.69/11.82 (![X4: $i, X3: $i, X2: $i, X1: $i] : (esk8752_4(X1, X2, X3, X4) | (~esk9743_4(X1, X2, X3, X4)))),
% 16.69/11.82 inference(modus_ponens,[status(thm)],[175, 171])).
% 16.69/11.82 tff(177,plain,
% 16.69/11.82 (((~![X4: $i, X3: $i, X2: $i, X1: $i] : (esk8752_4(X1, X2, X3, X4) | (~esk9743_4(X1, X2, X3, X4)))) | ((~esk9743_4(true, true, true, true)) | esk8752_4(true, true, true, true))) <=> ((~![X4: $i, X3: $i, X2: $i, X1: $i] : (esk8752_4(X1, X2, X3, X4) | (~esk9743_4(X1, X2, X3, X4)))) | (~esk9743_4(true, true, true, true)) | esk8752_4(true, true, true, true))),
% 16.69/11.82 inference(rewrite,[status(thm)],[])).
% 16.69/11.82 tff(178,plain,
% 16.69/11.82 ((esk8752_4(true, true, true, true) | (~esk9743_4(true, true, true, true))) <=> ((~esk9743_4(true, true, true, true)) | esk8752_4(true, true, true, true))),
% 16.69/11.82 inference(rewrite,[status(thm)],[])).
% 16.69/11.82 tff(179,plain,
% 16.69/11.82 (((~![X4: $i, X3: $i, X2: $i, X1: $i] : (esk8752_4(X1, X2, X3, X4) | (~esk9743_4(X1, X2, X3, X4)))) | (esk8752_4(true, true, true, true) | (~esk9743_4(true, true, true, true)))) <=> ((~![X4: $i, X3: $i, X2: $i, X1: $i] : (esk8752_4(X1, X2, X3, X4) | (~esk9743_4(X1, X2, X3, X4)))) | ((~esk9743_4(true, true, true, true)) | esk8752_4(true, true, true, true)))),
% 16.69/11.82 inference(monotonicity,[status(thm)],[178])).
% 16.69/11.82 tff(180,plain,
% 16.69/11.82 (((~![X4: $i, X3: $i, X2: $i, X1: $i] : (esk8752_4(X1, X2, X3, X4) | (~esk9743_4(X1, X2, X3, X4)))) | (esk8752_4(true, true, true, true) | (~esk9743_4(true, true, true, true)))) <=> ((~![X4: $i, X3: $i, X2: $i, X1: $i] : (esk8752_4(X1, X2, X3, X4) | (~esk9743_4(X1, X2, X3, X4)))) | (~esk9743_4(true, true, true, true)) | esk8752_4(true, true, true, true))),
% 16.69/11.82 inference(transitivity,[status(thm)],[179, 177])).
% 16.69/11.82 tff(181,plain,
% 16.69/11.82 ((~![X4: $i, X3: $i, X2: $i, X1: $i] : (esk8752_4(X1, X2, X3, X4) | (~esk9743_4(X1, X2, X3, X4)))) | (esk8752_4(true, true, true, true) | (~esk9743_4(true, true, true, true)))),
% 16.69/11.82 inference(quant_inst,[status(thm)],[])).
% 16.69/11.82 tff(182,plain,
% 16.69/11.82 ((~![X4: $i, X3: $i, X2: $i, X1: $i] : (esk8752_4(X1, X2, X3, X4) | (~esk9743_4(X1, X2, X3, X4)))) | (~esk9743_4(true, true, true, true)) | esk8752_4(true, true, true, true)),
% 16.69/11.82 inference(modus_ponens,[status(thm)],[181, 180])).
% 16.69/11.82 tff(183,plain,
% 16.69/11.82 (~esk9743_4(true, true, true, true)),
% 16.69/11.82 inference(unit_resolution,[status(thm)],[182, 176, 36])).
% 16.69/11.82 tff(184,plain,
% 16.69/11.82 (^[X4: $i, X3: $i, X2: $i, X1: $i] : refl(((~esk9741_4(X1, X2, X3, X4)) | esk8120_4(X1, X2, X3, X4)) <=> ((~esk9741_4(X1, X2, X3, X4)) | esk8120_4(X1, X2, X3, X4)))),
% 16.69/11.82 inference(bind,[status(th)],[])).
% 16.69/11.82 tff(185,plain,
% 16.69/11.82 (![X4: $i, X3: $i, X2: $i, X1: $i] : ((~esk9741_4(X1, X2, X3, X4)) | esk8120_4(X1, X2, X3, X4)) <=> ![X4: $i, X3: $i, X2: $i, X1: $i] : ((~esk9741_4(X1, X2, X3, X4)) | esk8120_4(X1, X2, X3, X4))),
% 16.69/11.82 inference(quant_intro,[status(thm)],[184])).
% 16.69/11.82 tff(186,plain,
% 16.69/11.82 (![X4: $i, X3: $i, X2: $i, X1: $i] : ((~esk9741_4(X1, X2, X3, X4)) | esk8120_4(X1, X2, X3, X4)) <=> ![X4: $i, X3: $i, X2: $i, X1: $i] : ((~esk9741_4(X1, X2, X3, X4)) | esk8120_4(X1, X2, X3, X4))),
% 16.69/11.82 inference(rewrite,[status(thm)],[])).
% 16.69/11.82 tff(187,axiom,(![X4: $i, X3: $i, X2: $i, X1: $i] : ((~esk9741_4(X1, X2, X3, X4)) | esk8120_4(X1, X2, X3, X4))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','i_0_6532')).
% 16.69/11.82 tff(188,plain,
% 16.69/11.82 (![X4: $i, X3: $i, X2: $i, X1: $i] : ((~esk9741_4(X1, X2, X3, X4)) | esk8120_4(X1, X2, X3, X4))),
% 16.69/11.82 inference(modus_ponens,[status(thm)],[187, 186])).
% 16.69/11.82 tff(189,plain,(
% 16.69/11.82 ![X4: $i, X3: $i, X2: $i, X1: $i] : ((~esk9741_4(X1, X2, X3, X4)) | esk8120_4(X1, X2, X3, X4))),
% 16.69/11.82 inference(skolemize,[status(sab)],[188])).
% 16.69/11.82 tff(190,plain,
% 16.69/11.82 (![X4: $i, X3: $i, X2: $i, X1: $i] : ((~esk9741_4(X1, X2, X3, X4)) | esk8120_4(X1, X2, X3, X4))),
% 16.69/11.82 inference(modus_ponens,[status(thm)],[189, 185])).
% 16.69/11.82 tff(191,plain,
% 16.69/11.82 (((~![X4: $i, X3: $i, X2: $i, X1: $i] : ((~esk9741_4(X1, X2, X3, X4)) | esk8120_4(X1, X2, X3, X4))) | ((~esk9741_4(true, true, true, true)) | esk8120_4(true, true, true, true))) <=> ((~![X4: $i, X3: $i, X2: $i, X1: $i] : ((~esk9741_4(X1, X2, X3, X4)) | esk8120_4(X1, X2, X3, X4))) | (~esk9741_4(true, true, true, true)) | esk8120_4(true, true, true, true))),
% 16.69/11.82 inference(rewrite,[status(thm)],[])).
% 16.69/11.82 tff(192,plain,
% 16.69/11.82 ((~![X4: $i, X3: $i, X2: $i, X1: $i] : ((~esk9741_4(X1, X2, X3, X4)) | esk8120_4(X1, X2, X3, X4))) | ((~esk9741_4(true, true, true, true)) | esk8120_4(true, true, true, true))),
% 16.69/11.82 inference(quant_inst,[status(thm)],[])).
% 16.69/11.82 tff(193,plain,
% 16.69/11.82 ((~![X4: $i, X3: $i, X2: $i, X1: $i] : ((~esk9741_4(X1, X2, X3, X4)) | esk8120_4(X1, X2, X3, X4))) | (~esk9741_4(true, true, true, true)) | esk8120_4(true, true, true, true)),
% 16.69/11.82 inference(modus_ponens,[status(thm)],[192, 191])).
% 16.69/11.82 tff(194,plain,
% 16.69/11.82 (~esk9741_4(true, true, true, true)),
% 16.69/11.82 inference(unit_resolution,[status(thm)],[193, 190, 61])).
% 16.69/11.82 tff(195,plain,
% 16.69/11.82 (^[X4: $i, X3: $i, X2: $i, X1: $i] : refl(((~esk9742_4(X1, X2, X3, X4)) | esk8120_4(X1, X2, X3, X4)) <=> ((~esk9742_4(X1, X2, X3, X4)) | esk8120_4(X1, X2, X3, X4)))),
% 16.69/11.82 inference(bind,[status(th)],[])).
% 16.69/11.82 tff(196,plain,
% 16.69/11.82 (![X4: $i, X3: $i, X2: $i, X1: $i] : ((~esk9742_4(X1, X2, X3, X4)) | esk8120_4(X1, X2, X3, X4)) <=> ![X4: $i, X3: $i, X2: $i, X1: $i] : ((~esk9742_4(X1, X2, X3, X4)) | esk8120_4(X1, X2, X3, X4))),
% 16.69/11.82 inference(quant_intro,[status(thm)],[195])).
% 16.69/11.82 tff(197,plain,
% 16.69/11.82 (![X4: $i, X3: $i, X2: $i, X1: $i] : ((~esk9742_4(X1, X2, X3, X4)) | esk8120_4(X1, X2, X3, X4)) <=> ![X4: $i, X3: $i, X2: $i, X1: $i] : ((~esk9742_4(X1, X2, X3, X4)) | esk8120_4(X1, X2, X3, X4))),
% 16.69/11.82 inference(rewrite,[status(thm)],[])).
% 16.69/11.82 tff(198,axiom,(![X4: $i, X3: $i, X2: $i, X1: $i] : ((~esk9742_4(X1, X2, X3, X4)) | esk8120_4(X1, X2, X3, X4))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','i_0_21694')).
% 16.69/11.82 tff(199,plain,
% 16.69/11.82 (![X4: $i, X3: $i, X2: $i, X1: $i] : ((~esk9742_4(X1, X2, X3, X4)) | esk8120_4(X1, X2, X3, X4))),
% 16.69/11.82 inference(modus_ponens,[status(thm)],[198, 197])).
% 16.69/11.82 tff(200,plain,(
% 16.69/11.82 ![X4: $i, X3: $i, X2: $i, X1: $i] : ((~esk9742_4(X1, X2, X3, X4)) | esk8120_4(X1, X2, X3, X4))),
% 16.69/11.82 inference(skolemize,[status(sab)],[199])).
% 16.69/11.82 tff(201,plain,
% 16.69/11.82 (![X4: $i, X3: $i, X2: $i, X1: $i] : ((~esk9742_4(X1, X2, X3, X4)) | esk8120_4(X1, X2, X3, X4))),
% 16.69/11.82 inference(modus_ponens,[status(thm)],[200, 196])).
% 16.69/11.82 tff(202,plain,
% 16.69/11.82 (((~![X4: $i, X3: $i, X2: $i, X1: $i] : ((~esk9742_4(X1, X2, X3, X4)) | esk8120_4(X1, X2, X3, X4))) | ((~esk9742_4(true, true, true, true)) | esk8120_4(true, true, true, true))) <=> ((~![X4: $i, X3: $i, X2: $i, X1: $i] : ((~esk9742_4(X1, X2, X3, X4)) | esk8120_4(X1, X2, X3, X4))) | (~esk9742_4(true, true, true, true)) | esk8120_4(true, true, true, true))),
% 16.69/11.82 inference(rewrite,[status(thm)],[])).
% 16.69/11.82 tff(203,plain,
% 16.69/11.82 ((~![X4: $i, X3: $i, X2: $i, X1: $i] : ((~esk9742_4(X1, X2, X3, X4)) | esk8120_4(X1, X2, X3, X4))) | ((~esk9742_4(true, true, true, true)) | esk8120_4(true, true, true, true))),
% 16.69/11.82 inference(quant_inst,[status(thm)],[])).
% 16.69/11.82 tff(204,plain,
% 16.69/11.82 ((~![X4: $i, X3: $i, X2: $i, X1: $i] : ((~esk9742_4(X1, X2, X3, X4)) | esk8120_4(X1, X2, X3, X4))) | (~esk9742_4(true, true, true, true)) | esk8120_4(true, true, true, true)),
% 16.69/11.82 inference(modus_ponens,[status(thm)],[203, 202])).
% 16.69/11.82 tff(205,plain,
% 16.69/11.82 (~esk9742_4(true, true, true, true)),
% 16.69/11.82 inference(unit_resolution,[status(thm)],[204, 201, 61])).
% 16.69/11.82 tff(206,plain,
% 16.69/11.82 (^[X4: $i, X3: $i, X2: $i, X1: $i] : refl((esk9741_4(X1, X2, X3, X4) | (~esk9744_4(X1, X2, X3, X4)) | esk9742_4(X1, X2, X3, X4) | esk9743_4(X1, X2, X3, X4)) <=> (esk9741_4(X1, X2, X3, X4) | (~esk9744_4(X1, X2, X3, X4)) | esk9742_4(X1, X2, X3, X4) | esk9743_4(X1, X2, X3, X4)))),
% 16.69/11.82 inference(bind,[status(th)],[])).
% 16.69/11.82 tff(207,plain,
% 16.69/11.82 (![X4: $i, X3: $i, X2: $i, X1: $i] : (esk9741_4(X1, X2, X3, X4) | (~esk9744_4(X1, X2, X3, X4)) | esk9742_4(X1, X2, X3, X4) | esk9743_4(X1, X2, X3, X4)) <=> ![X4: $i, X3: $i, X2: $i, X1: $i] : (esk9741_4(X1, X2, X3, X4) | (~esk9744_4(X1, X2, X3, X4)) | esk9742_4(X1, X2, X3, X4) | esk9743_4(X1, X2, X3, X4))),
% 16.69/11.82 inference(quant_intro,[status(thm)],[206])).
% 16.69/11.82 tff(208,plain,
% 16.69/11.82 (![X4: $i, X3: $i, X2: $i, X1: $i] : (esk9741_4(X1, X2, X3, X4) | (~esk9744_4(X1, X2, X3, X4)) | esk9742_4(X1, X2, X3, X4) | esk9743_4(X1, X2, X3, X4)) <=> ![X4: $i, X3: $i, X2: $i, X1: $i] : (esk9741_4(X1, X2, X3, X4) | (~esk9744_4(X1, X2, X3, X4)) | esk9742_4(X1, X2, X3, X4) | esk9743_4(X1, X2, X3, X4))),
% 16.69/11.82 inference(rewrite,[status(thm)],[])).
% 16.69/11.82 tff(209,plain,
% 16.69/11.82 (^[X4: $i, X3: $i, X2: $i, X1: $i] : trans(monotonicity(rewrite((((~esk9744_4(X1, X2, X3, X4)) | esk9743_4(X1, X2, X3, X4)) | esk9741_4(X1, X2, X3, X4)) <=> (esk9741_4(X1, X2, X3, X4) | (~esk9744_4(X1, X2, X3, X4)) | esk9743_4(X1, X2, X3, X4))), (((((~esk9744_4(X1, X2, X3, X4)) | esk9743_4(X1, X2, X3, X4)) | esk9741_4(X1, X2, X3, X4)) | esk9742_4(X1, X2, X3, X4)) <=> ((esk9741_4(X1, X2, X3, X4) | (~esk9744_4(X1, X2, X3, X4)) | esk9743_4(X1, X2, X3, X4)) | esk9742_4(X1, X2, X3, X4)))), rewrite(((esk9741_4(X1, X2, X3, X4) | (~esk9744_4(X1, X2, X3, X4)) | esk9743_4(X1, X2, X3, X4)) | esk9742_4(X1, X2, X3, X4)) <=> (esk9741_4(X1, X2, X3, X4) | (~esk9744_4(X1, X2, X3, X4)) | esk9742_4(X1, X2, X3, X4) | esk9743_4(X1, X2, X3, X4))), (((((~esk9744_4(X1, X2, X3, X4)) | esk9743_4(X1, X2, X3, X4)) | esk9741_4(X1, X2, X3, X4)) | esk9742_4(X1, X2, X3, X4)) <=> (esk9741_4(X1, X2, X3, X4) | (~esk9744_4(X1, X2, X3, X4)) | esk9742_4(X1, X2, X3, X4) | esk9743_4(X1, X2, X3, X4))))),
% 16.69/11.82 inference(bind,[status(th)],[])).
% 16.69/11.82 tff(210,plain,
% 16.69/11.82 (![X4: $i, X3: $i, X2: $i, X1: $i] : ((((~esk9744_4(X1, X2, X3, X4)) | esk9743_4(X1, X2, X3, X4)) | esk9741_4(X1, X2, X3, X4)) | esk9742_4(X1, X2, X3, X4)) <=> ![X4: $i, X3: $i, X2: $i, X1: $i] : (esk9741_4(X1, X2, X3, X4) | (~esk9744_4(X1, X2, X3, X4)) | esk9742_4(X1, X2, X3, X4) | esk9743_4(X1, X2, X3, X4))),
% 16.69/11.82 inference(quant_intro,[status(thm)],[209])).
% 16.69/11.82 tff(211,axiom,(![X4: $i, X3: $i, X2: $i, X1: $i] : ((((~esk9744_4(X1, X2, X3, X4)) | esk9743_4(X1, X2, X3, X4)) | esk9741_4(X1, X2, X3, X4)) | esk9742_4(X1, X2, X3, X4))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','i_0_17471')).
% 16.69/11.82 tff(212,plain,
% 16.69/11.82 (![X4: $i, X3: $i, X2: $i, X1: $i] : (esk9741_4(X1, X2, X3, X4) | (~esk9744_4(X1, X2, X3, X4)) | esk9742_4(X1, X2, X3, X4) | esk9743_4(X1, X2, X3, X4))),
% 16.69/11.82 inference(modus_ponens,[status(thm)],[211, 210])).
% 16.69/11.82 tff(213,plain,
% 16.69/11.82 (![X4: $i, X3: $i, X2: $i, X1: $i] : (esk9741_4(X1, X2, X3, X4) | (~esk9744_4(X1, X2, X3, X4)) | esk9742_4(X1, X2, X3, X4) | esk9743_4(X1, X2, X3, X4))),
% 16.69/11.82 inference(modus_ponens,[status(thm)],[212, 208])).
% 16.69/11.82 tff(214,plain,(
% 16.69/11.82 ![X4: $i, X3: $i, X2: $i, X1: $i] : (esk9741_4(X1, X2, X3, X4) | (~esk9744_4(X1, X2, X3, X4)) | esk9742_4(X1, X2, X3, X4) | esk9743_4(X1, X2, X3, X4))),
% 16.69/11.82 inference(skolemize,[status(sab)],[213])).
% 16.69/11.82 tff(215,plain,
% 16.69/11.82 (![X4: $i, X3: $i, X2: $i, X1: $i] : (esk9741_4(X1, X2, X3, X4) | (~esk9744_4(X1, X2, X3, X4)) | esk9742_4(X1, X2, X3, X4) | esk9743_4(X1, X2, X3, X4))),
% 16.69/11.82 inference(modus_ponens,[status(thm)],[214, 207])).
% 16.69/11.82 tff(216,plain,
% 16.69/11.82 (((~![X4: $i, X3: $i, X2: $i, X1: $i] : (esk9741_4(X1, X2, X3, X4) | (~esk9744_4(X1, X2, X3, X4)) | esk9742_4(X1, X2, X3, X4) | esk9743_4(X1, X2, X3, X4))) | (esk9743_4(true, true, true, true) | (~esk9744_4(true, true, true, true)) | esk9742_4(true, true, true, true) | esk9741_4(true, true, true, true))) <=> ((~![X4: $i, X3: $i, X2: $i, X1: $i] : (esk9741_4(X1, X2, X3, X4) | (~esk9744_4(X1, X2, X3, X4)) | esk9742_4(X1, X2, X3, X4) | esk9743_4(X1, X2, X3, X4))) | esk9743_4(true, true, true, true) | (~esk9744_4(true, true, true, true)) | esk9742_4(true, true, true, true) | esk9741_4(true, true, true, true))),
% 16.69/11.82 inference(rewrite,[status(thm)],[])).
% 16.69/11.82 tff(217,plain,
% 16.69/11.82 ((esk9741_4(true, true, true, true) | (~esk9744_4(true, true, true, true)) | esk9742_4(true, true, true, true) | esk9743_4(true, true, true, true)) <=> (esk9743_4(true, true, true, true) | (~esk9744_4(true, true, true, true)) | esk9742_4(true, true, true, true) | esk9741_4(true, true, true, true))),
% 16.69/11.82 inference(rewrite,[status(thm)],[])).
% 16.69/11.82 tff(218,plain,
% 16.69/11.82 (((~![X4: $i, X3: $i, X2: $i, X1: $i] : (esk9741_4(X1, X2, X3, X4) | (~esk9744_4(X1, X2, X3, X4)) | esk9742_4(X1, X2, X3, X4) | esk9743_4(X1, X2, X3, X4))) | (esk9741_4(true, true, true, true) | (~esk9744_4(true, true, true, true)) | esk9742_4(true, true, true, true) | esk9743_4(true, true, true, true))) <=> ((~![X4: $i, X3: $i, X2: $i, X1: $i] : (esk9741_4(X1, X2, X3, X4) | (~esk9744_4(X1, X2, X3, X4)) | esk9742_4(X1, X2, X3, X4) | esk9743_4(X1, X2, X3, X4))) | (esk9743_4(true, true, true, true) | (~esk9744_4(true, true, true, true)) | esk9742_4(true, true, true, true) | esk9741_4(true, true, true, true)))),
% 16.69/11.82 inference(monotonicity,[status(thm)],[217])).
% 16.69/11.82 tff(219,plain,
% 16.69/11.82 (((~![X4: $i, X3: $i, X2: $i, X1: $i] : (esk9741_4(X1, X2, X3, X4) | (~esk9744_4(X1, X2, X3, X4)) | esk9742_4(X1, X2, X3, X4) | esk9743_4(X1, X2, X3, X4))) | (esk9741_4(true, true, true, true) | (~esk9744_4(true, true, true, true)) | esk9742_4(true, true, true, true) | esk9743_4(true, true, true, true))) <=> ((~![X4: $i, X3: $i, X2: $i, X1: $i] : (esk9741_4(X1, X2, X3, X4) | (~esk9744_4(X1, X2, X3, X4)) | esk9742_4(X1, X2, X3, X4) | esk9743_4(X1, X2, X3, X4))) | esk9743_4(true, true, true, true) | (~esk9744_4(true, true, true, true)) | esk9742_4(true, true, true, true) | esk9741_4(true, true, true, true))),
% 16.69/11.82 inference(transitivity,[status(thm)],[218, 216])).
% 16.69/11.82 tff(220,plain,
% 16.69/11.82 ((~![X4: $i, X3: $i, X2: $i, X1: $i] : (esk9741_4(X1, X2, X3, X4) | (~esk9744_4(X1, X2, X3, X4)) | esk9742_4(X1, X2, X3, X4) | esk9743_4(X1, X2, X3, X4))) | (esk9741_4(true, true, true, true) | (~esk9744_4(true, true, true, true)) | esk9742_4(true, true, true, true) | esk9743_4(true, true, true, true))),
% 16.69/11.82 inference(quant_inst,[status(thm)],[])).
% 16.69/11.82 tff(221,plain,
% 16.69/11.82 ((~![X4: $i, X3: $i, X2: $i, X1: $i] : (esk9741_4(X1, X2, X3, X4) | (~esk9744_4(X1, X2, X3, X4)) | esk9742_4(X1, X2, X3, X4) | esk9743_4(X1, X2, X3, X4))) | esk9743_4(true, true, true, true) | (~esk9744_4(true, true, true, true)) | esk9742_4(true, true, true, true) | esk9741_4(true, true, true, true)),
% 16.69/11.82 inference(modus_ponens,[status(thm)],[220, 219])).
% 16.69/11.82 tff(222,plain,
% 16.69/11.82 (esk9743_4(true, true, true, true) | (~esk9744_4(true, true, true, true))),
% 16.69/11.82 inference(unit_resolution,[status(thm)],[221, 215, 205, 194])).
% 16.69/11.82 tff(223,plain,
% 16.69/11.82 (~esk9744_4(true, true, true, true)),
% 16.69/11.82 inference(unit_resolution,[status(thm)],[222, 183])).
% 16.69/11.82 tff(224,plain,
% 16.69/11.82 (^[X4: $i, X3: $i, X2: $i, X1: $i] : refl(((~esk9213_4(X1, X2, X3, X4)) | esk9744_4(X1, X2, X3, X4)) <=> ((~esk9213_4(X1, X2, X3, X4)) | esk9744_4(X1, X2, X3, X4)))),
% 16.69/11.82 inference(bind,[status(th)],[])).
% 16.69/11.82 tff(225,plain,
% 16.69/11.82 (![X4: $i, X3: $i, X2: $i, X1: $i] : ((~esk9213_4(X1, X2, X3, X4)) | esk9744_4(X1, X2, X3, X4)) <=> ![X4: $i, X3: $i, X2: $i, X1: $i] : ((~esk9213_4(X1, X2, X3, X4)) | esk9744_4(X1, X2, X3, X4))),
% 16.69/11.82 inference(quant_intro,[status(thm)],[224])).
% 16.69/11.82 tff(226,plain,
% 16.69/11.82 (![X4: $i, X3: $i, X2: $i, X1: $i] : ((~esk9213_4(X1, X2, X3, X4)) | esk9744_4(X1, X2, X3, X4)) <=> ![X4: $i, X3: $i, X2: $i, X1: $i] : ((~esk9213_4(X1, X2, X3, X4)) | esk9744_4(X1, X2, X3, X4))),
% 16.69/11.82 inference(rewrite,[status(thm)],[])).
% 16.69/11.82 tff(227,axiom,(![X4: $i, X3: $i, X2: $i, X1: $i] : ((~esk9213_4(X1, X2, X3, X4)) | esk9744_4(X1, X2, X3, X4))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','i_0_14455')).
% 16.69/11.82 tff(228,plain,
% 16.69/11.82 (![X4: $i, X3: $i, X2: $i, X1: $i] : ((~esk9213_4(X1, X2, X3, X4)) | esk9744_4(X1, X2, X3, X4))),
% 17.45/12.60 inference(modus_ponens,[status(thm)],[227, 226])).
% 17.45/12.60 tff(229,plain,(
% 17.45/12.60 ![X4: $i, X3: $i, X2: $i, X1: $i] : ((~esk9213_4(X1, X2, X3, X4)) | esk9744_4(X1, X2, X3, X4))),
% 17.45/12.60 inference(skolemize,[status(sab)],[228])).
% 17.45/12.60 tff(230,plain,
% 17.45/12.60 (![X4: $i, X3: $i, X2: $i, X1: $i] : ((~esk9213_4(X1, X2, X3, X4)) | esk9744_4(X1, X2, X3, X4))),
% 17.45/12.60 inference(modus_ponens,[status(thm)],[229, 225])).
% 17.45/12.60 tff(231,plain,
% 17.45/12.60 (((~![X4: $i, X3: $i, X2: $i, X1: $i] : ((~esk9213_4(X1, X2, X3, X4)) | esk9744_4(X1, X2, X3, X4))) | ((~esk9213_4(true, true, true, true)) | esk9744_4(true, true, true, true))) <=> ((~![X4: $i, X3: $i, X2: $i, X1: $i] : ((~esk9213_4(X1, X2, X3, X4)) | esk9744_4(X1, X2, X3, X4))) | (~esk9213_4(true, true, true, true)) | esk9744_4(true, true, true, true))),
% 17.45/12.60 inference(rewrite,[status(thm)],[])).
% 17.45/12.60 tff(232,plain,
% 17.45/12.60 ((~![X4: $i, X3: $i, X2: $i, X1: $i] : ((~esk9213_4(X1, X2, X3, X4)) | esk9744_4(X1, X2, X3, X4))) | ((~esk9213_4(true, true, true, true)) | esk9744_4(true, true, true, true))),
% 17.45/12.60 inference(quant_inst,[status(thm)],[])).
% 17.45/12.60 tff(233,plain,
% 17.45/12.60 ((~![X4: $i, X3: $i, X2: $i, X1: $i] : ((~esk9213_4(X1, X2, X3, X4)) | esk9744_4(X1, X2, X3, X4))) | (~esk9213_4(true, true, true, true)) | esk9744_4(true, true, true, true)),
% 17.45/12.60 inference(modus_ponens,[status(thm)],[232, 231])).
% 17.45/12.60 tff(234,plain,
% 17.45/12.60 ($false),
% 17.45/12.60 inference(unit_resolution,[status(thm)],[233, 230, 223, 169])).
% 17.45/12.60 % SZS output end Proof
%------------------------------------------------------------------------------