TSTP Solution File: SWV001-1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SWV001-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n024.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 29 15:09:34 EDT 2022
% Result : Unsatisfiable 0.12s 0.38s
% Output : Proof 0.18s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : SWV001-1 : TPTP v8.1.0. Released v1.0.0.
% 0.06/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33 % Computer : n024.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 : Sun Sep 4 00:58:03 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.33 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.33 Usage: tptp [options] [-file:]file
% 0.12/0.33 -h, -? prints this message.
% 0.12/0.33 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.33 -m, -model generate model.
% 0.12/0.33 -p, -proof generate proof.
% 0.12/0.33 -c, -core generate unsat core of named formulas.
% 0.12/0.33 -st, -statistics display statistics.
% 0.12/0.33 -t:timeout set timeout (in second).
% 0.12/0.33 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.33 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.33 -<param>:<value> configuration parameter and value.
% 0.12/0.33 -o:<output-file> file to place output in.
% 0.12/0.38 % SZS status Unsatisfiable
% 0.12/0.38 % SZS output start Proof
% 0.12/0.38 tff(less_or_equalish_type, type, (
% 0.12/0.38 less_or_equalish: ( $i * $i ) > $o)).
% 0.12/0.38 tff(b_type, type, (
% 0.12/0.38 b: $i)).
% 0.12/0.38 tff(q4_type, type, (
% 0.12/0.38 q4: ( $i * $i * $i ) > $o)).
% 0.12/0.38 tff(a_type, type, (
% 0.12/0.38 a: $i)).
% 0.12/0.38 tff(q2_type, type, (
% 0.12/0.38 q2: ( $i * $i * $i ) > $o)).
% 0.12/0.38 tff(c_type, type, (
% 0.12/0.38 c: $i)).
% 0.12/0.38 tff(q3_type, type, (
% 0.12/0.38 q3: ( $i * $i * $i ) > $o)).
% 0.12/0.38 tff(q1_type, type, (
% 0.12/0.38 q1: ( $i * $i * $i ) > $o)).
% 0.12/0.38 tff(1,assumption,(~less_or_equalish(a, b)), introduced(assumption)).
% 0.12/0.38 tff(2,plain,
% 0.12/0.38 (q1(a, b, c) <=> q1(a, b, c)),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(3,axiom,(q1(a, b, c)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause_5')).
% 0.12/0.38 tff(4,plain,
% 0.12/0.38 (q1(a, b, c)),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[3, 2])).
% 0.12/0.38 tff(5,plain,
% 0.12/0.38 (^[Z: $i, Y: $i, X: $i] : refl((q3(X, Y, Z) | less_or_equalish(X, Y) | (~q1(X, Y, Z))) <=> (q3(X, Y, Z) | less_or_equalish(X, Y) | (~q1(X, Y, Z))))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(6,plain,
% 0.12/0.38 (![Z: $i, Y: $i, X: $i] : (q3(X, Y, Z) | less_or_equalish(X, Y) | (~q1(X, Y, Z))) <=> ![Z: $i, Y: $i, X: $i] : (q3(X, Y, Z) | less_or_equalish(X, Y) | (~q1(X, Y, Z)))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[5])).
% 0.12/0.38 tff(7,plain,
% 0.12/0.38 (![Z: $i, Y: $i, X: $i] : (q3(X, Y, Z) | less_or_equalish(X, Y) | (~q1(X, Y, Z))) <=> ![Z: $i, Y: $i, X: $i] : (q3(X, Y, Z) | less_or_equalish(X, Y) | (~q1(X, Y, Z)))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(8,plain,
% 0.12/0.38 (^[Z: $i, Y: $i, X: $i] : rewrite((((~q1(X, Y, Z)) | less_or_equalish(X, Y)) | q3(X, Y, Z)) <=> (q3(X, Y, Z) | less_or_equalish(X, Y) | (~q1(X, Y, Z))))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(9,plain,
% 0.12/0.38 (![Z: $i, Y: $i, X: $i] : (((~q1(X, Y, Z)) | less_or_equalish(X, Y)) | q3(X, Y, Z)) <=> ![Z: $i, Y: $i, X: $i] : (q3(X, Y, Z) | less_or_equalish(X, Y) | (~q1(X, Y, Z)))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[8])).
% 0.12/0.38 tff(10,axiom,(![Z: $i, Y: $i, X: $i] : (((~q1(X, Y, Z)) | less_or_equalish(X, Y)) | q3(X, Y, Z))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause_2')).
% 0.12/0.38 tff(11,plain,
% 0.12/0.38 (![Z: $i, Y: $i, X: $i] : (q3(X, Y, Z) | less_or_equalish(X, Y) | (~q1(X, Y, Z)))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[10, 9])).
% 0.12/0.38 tff(12,plain,
% 0.12/0.38 (![Z: $i, Y: $i, X: $i] : (q3(X, Y, Z) | less_or_equalish(X, Y) | (~q1(X, Y, Z)))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[11, 7])).
% 0.12/0.38 tff(13,plain,(
% 0.12/0.38 ![Z: $i, Y: $i, X: $i] : (q3(X, Y, Z) | less_or_equalish(X, Y) | (~q1(X, Y, Z)))),
% 0.12/0.38 inference(skolemize,[status(sab)],[12])).
% 0.12/0.38 tff(14,plain,
% 0.12/0.38 (![Z: $i, Y: $i, X: $i] : (q3(X, Y, Z) | less_or_equalish(X, Y) | (~q1(X, Y, Z)))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[13, 6])).
% 0.12/0.38 tff(15,plain,
% 0.12/0.38 (((~![Z: $i, Y: $i, X: $i] : (q3(X, Y, Z) | less_or_equalish(X, Y) | (~q1(X, Y, Z)))) | (less_or_equalish(a, b) | (~q1(a, b, c)) | q3(a, b, c))) <=> ((~![Z: $i, Y: $i, X: $i] : (q3(X, Y, Z) | less_or_equalish(X, Y) | (~q1(X, Y, Z)))) | less_or_equalish(a, b) | (~q1(a, b, c)) | q3(a, b, c))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(16,plain,
% 0.12/0.38 ((q3(a, b, c) | less_or_equalish(a, b) | (~q1(a, b, c))) <=> (less_or_equalish(a, b) | (~q1(a, b, c)) | q3(a, b, c))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(17,plain,
% 0.12/0.38 (((~![Z: $i, Y: $i, X: $i] : (q3(X, Y, Z) | less_or_equalish(X, Y) | (~q1(X, Y, Z)))) | (q3(a, b, c) | less_or_equalish(a, b) | (~q1(a, b, c)))) <=> ((~![Z: $i, Y: $i, X: $i] : (q3(X, Y, Z) | less_or_equalish(X, Y) | (~q1(X, Y, Z)))) | (less_or_equalish(a, b) | (~q1(a, b, c)) | q3(a, b, c)))),
% 0.12/0.38 inference(monotonicity,[status(thm)],[16])).
% 0.12/0.38 tff(18,plain,
% 0.12/0.38 (((~![Z: $i, Y: $i, X: $i] : (q3(X, Y, Z) | less_or_equalish(X, Y) | (~q1(X, Y, Z)))) | (q3(a, b, c) | less_or_equalish(a, b) | (~q1(a, b, c)))) <=> ((~![Z: $i, Y: $i, X: $i] : (q3(X, Y, Z) | less_or_equalish(X, Y) | (~q1(X, Y, Z)))) | less_or_equalish(a, b) | (~q1(a, b, c)) | q3(a, b, c))),
% 0.12/0.38 inference(transitivity,[status(thm)],[17, 15])).
% 0.12/0.38 tff(19,plain,
% 0.12/0.38 ((~![Z: $i, Y: $i, X: $i] : (q3(X, Y, Z) | less_or_equalish(X, Y) | (~q1(X, Y, Z)))) | (q3(a, b, c) | less_or_equalish(a, b) | (~q1(a, b, c)))),
% 0.12/0.38 inference(quant_inst,[status(thm)],[])).
% 0.12/0.38 tff(20,plain,
% 0.12/0.38 ((~![Z: $i, Y: $i, X: $i] : (q3(X, Y, Z) | less_or_equalish(X, Y) | (~q1(X, Y, Z)))) | less_or_equalish(a, b) | (~q1(a, b, c)) | q3(a, b, c)),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[19, 18])).
% 0.12/0.38 tff(21,plain,
% 0.12/0.38 (less_or_equalish(a, b) | q3(a, b, c)),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[20, 14, 4])).
% 0.12/0.38 tff(22,plain,
% 0.12/0.38 (q3(a, b, c)),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[21, 1])).
% 0.12/0.38 tff(23,plain,
% 0.12/0.38 (^[Z: $i, Y: $i, X: $i] : refl(((~q3(X, Y, Z)) | q4(X, Y, X)) <=> ((~q3(X, Y, Z)) | q4(X, Y, X)))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(24,plain,
% 0.12/0.38 (![Z: $i, Y: $i, X: $i] : ((~q3(X, Y, Z)) | q4(X, Y, X)) <=> ![Z: $i, Y: $i, X: $i] : ((~q3(X, Y, Z)) | q4(X, Y, X))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[23])).
% 0.12/0.38 tff(25,plain,
% 0.12/0.38 (![Z: $i, Y: $i, X: $i] : ((~q3(X, Y, Z)) | q4(X, Y, X)) <=> ![Z: $i, Y: $i, X: $i] : ((~q3(X, Y, Z)) | q4(X, Y, X))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(26,axiom,(![Z: $i, Y: $i, X: $i] : ((~q3(X, Y, Z)) | q4(X, Y, X))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause_4')).
% 0.12/0.38 tff(27,plain,
% 0.12/0.38 (![Z: $i, Y: $i, X: $i] : ((~q3(X, Y, Z)) | q4(X, Y, X))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[26, 25])).
% 0.12/0.38 tff(28,plain,(
% 0.12/0.38 ![Z: $i, Y: $i, X: $i] : ((~q3(X, Y, Z)) | q4(X, Y, X))),
% 0.12/0.38 inference(skolemize,[status(sab)],[27])).
% 0.12/0.38 tff(29,plain,
% 0.12/0.38 (![Z: $i, Y: $i, X: $i] : ((~q3(X, Y, Z)) | q4(X, Y, X))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[28, 24])).
% 0.12/0.38 tff(30,plain,
% 0.12/0.38 (((~![Z: $i, Y: $i, X: $i] : ((~q3(X, Y, Z)) | q4(X, Y, X))) | ((~q3(a, b, c)) | q4(a, b, a))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~q3(X, Y, Z)) | q4(X, Y, X))) | (~q3(a, b, c)) | q4(a, b, a))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(31,plain,
% 0.12/0.38 ((~![Z: $i, Y: $i, X: $i] : ((~q3(X, Y, Z)) | q4(X, Y, X))) | ((~q3(a, b, c)) | q4(a, b, a))),
% 0.12/0.38 inference(quant_inst,[status(thm)],[])).
% 0.12/0.38 tff(32,plain,
% 0.12/0.38 ((~![Z: $i, Y: $i, X: $i] : ((~q3(X, Y, Z)) | q4(X, Y, X))) | (~q3(a, b, c)) | q4(a, b, a)),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[31, 30])).
% 0.12/0.38 tff(33,plain,
% 0.12/0.38 (q4(a, b, a)),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[32, 29, 22])).
% 0.12/0.38 tff(34,plain,
% 0.12/0.38 (^[Y: $i, X: $i] : refl((less_or_equalish(X, Y) | less_or_equalish(Y, X)) <=> (less_or_equalish(X, Y) | less_or_equalish(Y, X)))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(35,plain,
% 0.12/0.38 (![Y: $i, X: $i] : (less_or_equalish(X, Y) | less_or_equalish(Y, X)) <=> ![Y: $i, X: $i] : (less_or_equalish(X, Y) | less_or_equalish(Y, X))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[34])).
% 0.12/0.38 tff(36,plain,
% 0.12/0.38 (![Y: $i, X: $i] : (less_or_equalish(X, Y) | less_or_equalish(Y, X)) <=> ![Y: $i, X: $i] : (less_or_equalish(X, Y) | less_or_equalish(Y, X))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(37,axiom,(![Y: $i, X: $i] : (less_or_equalish(X, Y) | less_or_equalish(Y, X))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','all_less_or_equal')).
% 0.12/0.38 tff(38,plain,
% 0.12/0.38 (![Y: $i, X: $i] : (less_or_equalish(X, Y) | less_or_equalish(Y, X))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[37, 36])).
% 0.12/0.38 tff(39,plain,(
% 0.12/0.38 ![Y: $i, X: $i] : (less_or_equalish(X, Y) | less_or_equalish(Y, X))),
% 0.12/0.38 inference(skolemize,[status(sab)],[38])).
% 0.12/0.38 tff(40,plain,
% 0.12/0.38 (![Y: $i, X: $i] : (less_or_equalish(X, Y) | less_or_equalish(Y, X))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[39, 35])).
% 0.12/0.38 tff(41,plain,
% 0.12/0.38 (((~![Y: $i, X: $i] : (less_or_equalish(X, Y) | less_or_equalish(Y, X))) | (less_or_equalish(a, b) | less_or_equalish(b, a))) <=> ((~![Y: $i, X: $i] : (less_or_equalish(X, Y) | less_or_equalish(Y, X))) | less_or_equalish(a, b) | less_or_equalish(b, a))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(42,plain,
% 0.12/0.38 ((less_or_equalish(b, a) | less_or_equalish(a, b)) <=> (less_or_equalish(a, b) | less_or_equalish(b, a))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(43,plain,
% 0.12/0.38 (((~![Y: $i, X: $i] : (less_or_equalish(X, Y) | less_or_equalish(Y, X))) | (less_or_equalish(b, a) | less_or_equalish(a, b))) <=> ((~![Y: $i, X: $i] : (less_or_equalish(X, Y) | less_or_equalish(Y, X))) | (less_or_equalish(a, b) | less_or_equalish(b, a)))),
% 0.12/0.39 inference(monotonicity,[status(thm)],[42])).
% 0.12/0.39 tff(44,plain,
% 0.12/0.39 (((~![Y: $i, X: $i] : (less_or_equalish(X, Y) | less_or_equalish(Y, X))) | (less_or_equalish(b, a) | less_or_equalish(a, b))) <=> ((~![Y: $i, X: $i] : (less_or_equalish(X, Y) | less_or_equalish(Y, X))) | less_or_equalish(a, b) | less_or_equalish(b, a))),
% 0.12/0.39 inference(transitivity,[status(thm)],[43, 41])).
% 0.12/0.39 tff(45,plain,
% 0.12/0.39 ((~![Y: $i, X: $i] : (less_or_equalish(X, Y) | less_or_equalish(Y, X))) | (less_or_equalish(b, a) | less_or_equalish(a, b))),
% 0.12/0.39 inference(quant_inst,[status(thm)],[])).
% 0.12/0.39 tff(46,plain,
% 0.12/0.39 ((~![Y: $i, X: $i] : (less_or_equalish(X, Y) | less_or_equalish(Y, X))) | less_or_equalish(a, b) | less_or_equalish(b, a)),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[45, 44])).
% 0.12/0.39 tff(47,plain,
% 0.12/0.39 (less_or_equalish(b, a)),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[46, 40, 1])).
% 0.12/0.39 tff(48,assumption,(~less_or_equalish(a, a)), introduced(assumption)).
% 0.12/0.39 tff(49,plain,
% 0.12/0.39 (((~![Y: $i, X: $i] : (less_or_equalish(X, Y) | less_or_equalish(Y, X))) | less_or_equalish(a, a)) <=> ((~![Y: $i, X: $i] : (less_or_equalish(X, Y) | less_or_equalish(Y, X))) | less_or_equalish(a, a))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(50,plain,
% 0.12/0.39 ((less_or_equalish(a, a) | less_or_equalish(a, a)) <=> less_or_equalish(a, a)),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(51,plain,
% 0.12/0.39 (((~![Y: $i, X: $i] : (less_or_equalish(X, Y) | less_or_equalish(Y, X))) | (less_or_equalish(a, a) | less_or_equalish(a, a))) <=> ((~![Y: $i, X: $i] : (less_or_equalish(X, Y) | less_or_equalish(Y, X))) | less_or_equalish(a, a))),
% 0.12/0.39 inference(monotonicity,[status(thm)],[50])).
% 0.12/0.39 tff(52,plain,
% 0.12/0.39 (((~![Y: $i, X: $i] : (less_or_equalish(X, Y) | less_or_equalish(Y, X))) | (less_or_equalish(a, a) | less_or_equalish(a, a))) <=> ((~![Y: $i, X: $i] : (less_or_equalish(X, Y) | less_or_equalish(Y, X))) | less_or_equalish(a, a))),
% 0.12/0.39 inference(transitivity,[status(thm)],[51, 49])).
% 0.12/0.39 tff(53,plain,
% 0.12/0.39 ((~![Y: $i, X: $i] : (less_or_equalish(X, Y) | less_or_equalish(Y, X))) | (less_or_equalish(a, a) | less_or_equalish(a, a))),
% 0.12/0.39 inference(quant_inst,[status(thm)],[])).
% 0.12/0.39 tff(54,plain,
% 0.12/0.39 ((~![Y: $i, X: $i] : (less_or_equalish(X, Y) | less_or_equalish(Y, X))) | less_or_equalish(a, a)),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[53, 52])).
% 0.12/0.39 tff(55,plain,
% 0.12/0.39 ($false),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[54, 40, 48])).
% 0.12/0.39 tff(56,plain,(less_or_equalish(a, a)), inference(lemma,lemma(discharge,[]))).
% 0.12/0.39 tff(57,plain,
% 0.12/0.39 (^[W: $i] : refl(((~less_or_equalish(W, a)) | (~less_or_equalish(b, W)) | (~less_or_equalish(a, W)) | (~q4(a, b, W))) <=> ((~less_or_equalish(W, a)) | (~less_or_equalish(b, W)) | (~less_or_equalish(a, W)) | (~q4(a, b, W))))),
% 0.12/0.39 inference(bind,[status(th)],[])).
% 0.12/0.39 tff(58,plain,
% 0.12/0.39 (![W: $i] : ((~less_or_equalish(W, a)) | (~less_or_equalish(b, W)) | (~less_or_equalish(a, W)) | (~q4(a, b, W))) <=> ![W: $i] : ((~less_or_equalish(W, a)) | (~less_or_equalish(b, W)) | (~less_or_equalish(a, W)) | (~q4(a, b, W)))),
% 0.12/0.39 inference(quant_intro,[status(thm)],[57])).
% 0.12/0.39 tff(59,plain,
% 0.12/0.39 (![W: $i] : ((~less_or_equalish(W, a)) | (~less_or_equalish(b, W)) | (~less_or_equalish(a, W)) | (~q4(a, b, W))) <=> ![W: $i] : ((~less_or_equalish(W, a)) | (~less_or_equalish(b, W)) | (~less_or_equalish(a, W)) | (~q4(a, b, W)))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(60,plain,
% 0.12/0.39 (^[W: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~q4(a, b, W)) | (~less_or_equalish(a, W))) <=> ((~less_or_equalish(a, W)) | (~q4(a, b, W)))), ((((~q4(a, b, W)) | (~less_or_equalish(a, W))) | (~less_or_equalish(b, W))) <=> (((~less_or_equalish(a, W)) | (~q4(a, b, W))) | (~less_or_equalish(b, W))))), rewrite((((~less_or_equalish(a, W)) | (~q4(a, b, W))) | (~less_or_equalish(b, W))) <=> ((~less_or_equalish(b, W)) | (~less_or_equalish(a, W)) | (~q4(a, b, W)))), ((((~q4(a, b, W)) | (~less_or_equalish(a, W))) | (~less_or_equalish(b, W))) <=> ((~less_or_equalish(b, W)) | (~less_or_equalish(a, W)) | (~q4(a, b, W))))), (((((~q4(a, b, W)) | (~less_or_equalish(a, W))) | (~less_or_equalish(b, W))) | (~less_or_equalish(W, a))) <=> (((~less_or_equalish(b, W)) | (~less_or_equalish(a, W)) | (~q4(a, b, W))) | (~less_or_equalish(W, a))))), rewrite((((~less_or_equalish(b, W)) | (~less_or_equalish(a, W)) | (~q4(a, b, W))) | (~less_or_equalish(W, a))) <=> ((~less_or_equalish(W, a)) | (~less_or_equalish(b, W)) | (~less_or_equalish(a, W)) | (~q4(a, b, W)))), (((((~q4(a, b, W)) | (~less_or_equalish(a, W))) | (~less_or_equalish(b, W))) | (~less_or_equalish(W, a))) <=> ((~less_or_equalish(W, a)) | (~less_or_equalish(b, W)) | (~less_or_equalish(a, W)) | (~q4(a, b, W)))))),
% 0.18/0.39 inference(bind,[status(th)],[])).
% 0.18/0.39 tff(61,plain,
% 0.18/0.39 (![W: $i] : ((((~q4(a, b, W)) | (~less_or_equalish(a, W))) | (~less_or_equalish(b, W))) | (~less_or_equalish(W, a))) <=> ![W: $i] : ((~less_or_equalish(W, a)) | (~less_or_equalish(b, W)) | (~less_or_equalish(a, W)) | (~q4(a, b, W)))),
% 0.18/0.39 inference(quant_intro,[status(thm)],[60])).
% 0.18/0.39 tff(62,axiom,(![W: $i] : ((((~q4(a, b, W)) | (~less_or_equalish(a, W))) | (~less_or_equalish(b, W))) | (~less_or_equalish(W, a)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause_6')).
% 0.18/0.39 tff(63,plain,
% 0.18/0.39 (![W: $i] : ((~less_or_equalish(W, a)) | (~less_or_equalish(b, W)) | (~less_or_equalish(a, W)) | (~q4(a, b, W)))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[62, 61])).
% 0.18/0.39 tff(64,plain,
% 0.18/0.39 (![W: $i] : ((~less_or_equalish(W, a)) | (~less_or_equalish(b, W)) | (~less_or_equalish(a, W)) | (~q4(a, b, W)))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[63, 59])).
% 0.18/0.39 tff(65,plain,(
% 0.18/0.39 ![W: $i] : ((~less_or_equalish(W, a)) | (~less_or_equalish(b, W)) | (~less_or_equalish(a, W)) | (~q4(a, b, W)))),
% 0.18/0.39 inference(skolemize,[status(sab)],[64])).
% 0.18/0.39 tff(66,plain,
% 0.18/0.39 (![W: $i] : ((~less_or_equalish(W, a)) | (~less_or_equalish(b, W)) | (~less_or_equalish(a, W)) | (~q4(a, b, W)))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[65, 58])).
% 0.18/0.39 tff(67,plain,
% 0.18/0.39 (((~![W: $i] : ((~less_or_equalish(W, a)) | (~less_or_equalish(b, W)) | (~less_or_equalish(a, W)) | (~q4(a, b, W)))) | ((~less_or_equalish(a, a)) | (~less_or_equalish(b, a)) | (~q4(a, b, a)))) <=> ((~![W: $i] : ((~less_or_equalish(W, a)) | (~less_or_equalish(b, W)) | (~less_or_equalish(a, W)) | (~q4(a, b, W)))) | (~less_or_equalish(a, a)) | (~less_or_equalish(b, a)) | (~q4(a, b, a)))),
% 0.18/0.39 inference(rewrite,[status(thm)],[])).
% 0.18/0.39 tff(68,plain,
% 0.18/0.39 (((~less_or_equalish(a, a)) | (~less_or_equalish(b, a)) | (~less_or_equalish(a, a)) | (~q4(a, b, a))) <=> ((~less_or_equalish(a, a)) | (~less_or_equalish(b, a)) | (~q4(a, b, a)))),
% 0.18/0.39 inference(rewrite,[status(thm)],[])).
% 0.18/0.39 tff(69,plain,
% 0.18/0.39 (((~![W: $i] : ((~less_or_equalish(W, a)) | (~less_or_equalish(b, W)) | (~less_or_equalish(a, W)) | (~q4(a, b, W)))) | ((~less_or_equalish(a, a)) | (~less_or_equalish(b, a)) | (~less_or_equalish(a, a)) | (~q4(a, b, a)))) <=> ((~![W: $i] : ((~less_or_equalish(W, a)) | (~less_or_equalish(b, W)) | (~less_or_equalish(a, W)) | (~q4(a, b, W)))) | ((~less_or_equalish(a, a)) | (~less_or_equalish(b, a)) | (~q4(a, b, a))))),
% 0.18/0.39 inference(monotonicity,[status(thm)],[68])).
% 0.18/0.39 tff(70,plain,
% 0.18/0.39 (((~![W: $i] : ((~less_or_equalish(W, a)) | (~less_or_equalish(b, W)) | (~less_or_equalish(a, W)) | (~q4(a, b, W)))) | ((~less_or_equalish(a, a)) | (~less_or_equalish(b, a)) | (~less_or_equalish(a, a)) | (~q4(a, b, a)))) <=> ((~![W: $i] : ((~less_or_equalish(W, a)) | (~less_or_equalish(b, W)) | (~less_or_equalish(a, W)) | (~q4(a, b, W)))) | (~less_or_equalish(a, a)) | (~less_or_equalish(b, a)) | (~q4(a, b, a)))),
% 0.18/0.39 inference(transitivity,[status(thm)],[69, 67])).
% 0.18/0.39 tff(71,plain,
% 0.18/0.39 ((~![W: $i] : ((~less_or_equalish(W, a)) | (~less_or_equalish(b, W)) | (~less_or_equalish(a, W)) | (~q4(a, b, W)))) | ((~less_or_equalish(a, a)) | (~less_or_equalish(b, a)) | (~less_or_equalish(a, a)) | (~q4(a, b, a)))),
% 0.18/0.39 inference(quant_inst,[status(thm)],[])).
% 0.18/0.39 tff(72,plain,
% 0.18/0.39 ((~![W: $i] : ((~less_or_equalish(W, a)) | (~less_or_equalish(b, W)) | (~less_or_equalish(a, W)) | (~q4(a, b, W)))) | (~less_or_equalish(a, a)) | (~less_or_equalish(b, a)) | (~q4(a, b, a))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[71, 70])).
% 0.18/0.39 tff(73,plain,
% 0.18/0.39 ((~less_or_equalish(b, a)) | (~q4(a, b, a))),
% 0.18/0.39 inference(unit_resolution,[status(thm)],[72, 66, 56])).
% 0.18/0.39 tff(74,plain,
% 0.18/0.39 ($false),
% 0.18/0.39 inference(unit_resolution,[status(thm)],[73, 47, 33])).
% 0.18/0.39 tff(75,plain,(less_or_equalish(a, b)), inference(lemma,lemma(discharge,[]))).
% 0.18/0.39 tff(76,plain,
% 0.18/0.39 (^[Z: $i, Y: $i, X: $i] : refl((q2(X, Y, Z) | (~less_or_equalish(X, Y)) | (~q1(X, Y, Z))) <=> (q2(X, Y, Z) | (~less_or_equalish(X, Y)) | (~q1(X, Y, Z))))),
% 0.18/0.39 inference(bind,[status(th)],[])).
% 0.18/0.39 tff(77,plain,
% 0.18/0.39 (![Z: $i, Y: $i, X: $i] : (q2(X, Y, Z) | (~less_or_equalish(X, Y)) | (~q1(X, Y, Z))) <=> ![Z: $i, Y: $i, X: $i] : (q2(X, Y, Z) | (~less_or_equalish(X, Y)) | (~q1(X, Y, Z)))),
% 0.18/0.39 inference(quant_intro,[status(thm)],[76])).
% 0.18/0.39 tff(78,plain,
% 0.18/0.39 (![Z: $i, Y: $i, X: $i] : (q2(X, Y, Z) | (~less_or_equalish(X, Y)) | (~q1(X, Y, Z))) <=> ![Z: $i, Y: $i, X: $i] : (q2(X, Y, Z) | (~less_or_equalish(X, Y)) | (~q1(X, Y, Z)))),
% 0.18/0.39 inference(rewrite,[status(thm)],[])).
% 0.18/0.39 tff(79,plain,
% 0.18/0.39 (^[Z: $i, Y: $i, X: $i] : trans(monotonicity(rewrite(((~q1(X, Y, Z)) | (~less_or_equalish(X, Y))) <=> ((~less_or_equalish(X, Y)) | (~q1(X, Y, Z)))), ((((~q1(X, Y, Z)) | (~less_or_equalish(X, Y))) | q2(X, Y, Z)) <=> (((~less_or_equalish(X, Y)) | (~q1(X, Y, Z))) | q2(X, Y, Z)))), rewrite((((~less_or_equalish(X, Y)) | (~q1(X, Y, Z))) | q2(X, Y, Z)) <=> (q2(X, Y, Z) | (~less_or_equalish(X, Y)) | (~q1(X, Y, Z)))), ((((~q1(X, Y, Z)) | (~less_or_equalish(X, Y))) | q2(X, Y, Z)) <=> (q2(X, Y, Z) | (~less_or_equalish(X, Y)) | (~q1(X, Y, Z)))))),
% 0.18/0.39 inference(bind,[status(th)],[])).
% 0.18/0.39 tff(80,plain,
% 0.18/0.39 (![Z: $i, Y: $i, X: $i] : (((~q1(X, Y, Z)) | (~less_or_equalish(X, Y))) | q2(X, Y, Z)) <=> ![Z: $i, Y: $i, X: $i] : (q2(X, Y, Z) | (~less_or_equalish(X, Y)) | (~q1(X, Y, Z)))),
% 0.18/0.39 inference(quant_intro,[status(thm)],[79])).
% 0.18/0.39 tff(81,axiom,(![Z: $i, Y: $i, X: $i] : (((~q1(X, Y, Z)) | (~less_or_equalish(X, Y))) | q2(X, Y, Z))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause_1')).
% 0.18/0.39 tff(82,plain,
% 0.18/0.39 (![Z: $i, Y: $i, X: $i] : (q2(X, Y, Z) | (~less_or_equalish(X, Y)) | (~q1(X, Y, Z)))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[81, 80])).
% 0.18/0.39 tff(83,plain,
% 0.18/0.39 (![Z: $i, Y: $i, X: $i] : (q2(X, Y, Z) | (~less_or_equalish(X, Y)) | (~q1(X, Y, Z)))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[82, 78])).
% 0.18/0.39 tff(84,plain,(
% 0.18/0.39 ![Z: $i, Y: $i, X: $i] : (q2(X, Y, Z) | (~less_or_equalish(X, Y)) | (~q1(X, Y, Z)))),
% 0.18/0.39 inference(skolemize,[status(sab)],[83])).
% 0.18/0.39 tff(85,plain,
% 0.18/0.39 (![Z: $i, Y: $i, X: $i] : (q2(X, Y, Z) | (~less_or_equalish(X, Y)) | (~q1(X, Y, Z)))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[84, 77])).
% 0.18/0.39 tff(86,plain,
% 0.18/0.39 (((~![Z: $i, Y: $i, X: $i] : (q2(X, Y, Z) | (~less_or_equalish(X, Y)) | (~q1(X, Y, Z)))) | (q2(a, b, c) | (~less_or_equalish(a, b)) | (~q1(a, b, c)))) <=> ((~![Z: $i, Y: $i, X: $i] : (q2(X, Y, Z) | (~less_or_equalish(X, Y)) | (~q1(X, Y, Z)))) | q2(a, b, c) | (~less_or_equalish(a, b)) | (~q1(a, b, c)))),
% 0.18/0.39 inference(rewrite,[status(thm)],[])).
% 0.18/0.39 tff(87,plain,
% 0.18/0.39 ((~![Z: $i, Y: $i, X: $i] : (q2(X, Y, Z) | (~less_or_equalish(X, Y)) | (~q1(X, Y, Z)))) | (q2(a, b, c) | (~less_or_equalish(a, b)) | (~q1(a, b, c)))),
% 0.18/0.39 inference(quant_inst,[status(thm)],[])).
% 0.18/0.39 tff(88,plain,
% 0.18/0.39 ((~![Z: $i, Y: $i, X: $i] : (q2(X, Y, Z) | (~less_or_equalish(X, Y)) | (~q1(X, Y, Z)))) | q2(a, b, c) | (~less_or_equalish(a, b)) | (~q1(a, b, c))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[87, 86])).
% 0.18/0.39 tff(89,plain,
% 0.18/0.39 (q2(a, b, c) | (~less_or_equalish(a, b))),
% 0.18/0.39 inference(unit_resolution,[status(thm)],[88, 85, 4])).
% 0.18/0.39 tff(90,plain,
% 0.18/0.39 (q2(a, b, c)),
% 0.18/0.39 inference(unit_resolution,[status(thm)],[89, 75])).
% 0.18/0.39 tff(91,plain,
% 0.18/0.39 (^[Z: $i, Y: $i, X: $i] : refl(((~q2(X, Y, Z)) | q4(X, Y, Y)) <=> ((~q2(X, Y, Z)) | q4(X, Y, Y)))),
% 0.18/0.39 inference(bind,[status(th)],[])).
% 0.18/0.39 tff(92,plain,
% 0.18/0.39 (![Z: $i, Y: $i, X: $i] : ((~q2(X, Y, Z)) | q4(X, Y, Y)) <=> ![Z: $i, Y: $i, X: $i] : ((~q2(X, Y, Z)) | q4(X, Y, Y))),
% 0.18/0.39 inference(quant_intro,[status(thm)],[91])).
% 0.18/0.39 tff(93,plain,
% 0.18/0.39 (![Z: $i, Y: $i, X: $i] : ((~q2(X, Y, Z)) | q4(X, Y, Y)) <=> ![Z: $i, Y: $i, X: $i] : ((~q2(X, Y, Z)) | q4(X, Y, Y))),
% 0.18/0.39 inference(rewrite,[status(thm)],[])).
% 0.18/0.39 tff(94,axiom,(![Z: $i, Y: $i, X: $i] : ((~q2(X, Y, Z)) | q4(X, Y, Y))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause_3')).
% 0.18/0.40 tff(95,plain,
% 0.18/0.40 (![Z: $i, Y: $i, X: $i] : ((~q2(X, Y, Z)) | q4(X, Y, Y))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[94, 93])).
% 0.18/0.40 tff(96,plain,(
% 0.18/0.40 ![Z: $i, Y: $i, X: $i] : ((~q2(X, Y, Z)) | q4(X, Y, Y))),
% 0.18/0.40 inference(skolemize,[status(sab)],[95])).
% 0.18/0.40 tff(97,plain,
% 0.18/0.40 (![Z: $i, Y: $i, X: $i] : ((~q2(X, Y, Z)) | q4(X, Y, Y))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[96, 92])).
% 0.18/0.40 tff(98,plain,
% 0.18/0.40 (((~![Z: $i, Y: $i, X: $i] : ((~q2(X, Y, Z)) | q4(X, Y, Y))) | ((~q2(a, b, c)) | q4(a, b, b))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~q2(X, Y, Z)) | q4(X, Y, Y))) | (~q2(a, b, c)) | q4(a, b, b))),
% 0.18/0.40 inference(rewrite,[status(thm)],[])).
% 0.18/0.40 tff(99,plain,
% 0.18/0.40 ((~![Z: $i, Y: $i, X: $i] : ((~q2(X, Y, Z)) | q4(X, Y, Y))) | ((~q2(a, b, c)) | q4(a, b, b))),
% 0.18/0.40 inference(quant_inst,[status(thm)],[])).
% 0.18/0.40 tff(100,plain,
% 0.18/0.40 ((~![Z: $i, Y: $i, X: $i] : ((~q2(X, Y, Z)) | q4(X, Y, Y))) | (~q2(a, b, c)) | q4(a, b, b)),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[99, 98])).
% 0.18/0.40 tff(101,plain,
% 0.18/0.40 (q4(a, b, b)),
% 0.18/0.40 inference(unit_resolution,[status(thm)],[100, 97, 90])).
% 0.18/0.40 tff(102,plain,
% 0.18/0.40 (^[W: $i] : refl(((~less_or_equalish(b, W)) | (~less_or_equalish(a, W)) | (~q4(a, b, W)) | (~less_or_equalish(W, b))) <=> ((~less_or_equalish(b, W)) | (~less_or_equalish(a, W)) | (~q4(a, b, W)) | (~less_or_equalish(W, b))))),
% 0.18/0.40 inference(bind,[status(th)],[])).
% 0.18/0.40 tff(103,plain,
% 0.18/0.40 (![W: $i] : ((~less_or_equalish(b, W)) | (~less_or_equalish(a, W)) | (~q4(a, b, W)) | (~less_or_equalish(W, b))) <=> ![W: $i] : ((~less_or_equalish(b, W)) | (~less_or_equalish(a, W)) | (~q4(a, b, W)) | (~less_or_equalish(W, b)))),
% 0.18/0.40 inference(quant_intro,[status(thm)],[102])).
% 0.18/0.40 tff(104,plain,
% 0.18/0.40 (![W: $i] : ((~less_or_equalish(b, W)) | (~less_or_equalish(a, W)) | (~q4(a, b, W)) | (~less_or_equalish(W, b))) <=> ![W: $i] : ((~less_or_equalish(b, W)) | (~less_or_equalish(a, W)) | (~q4(a, b, W)) | (~less_or_equalish(W, b)))),
% 0.18/0.40 inference(rewrite,[status(thm)],[])).
% 0.18/0.40 tff(105,plain,
% 0.18/0.40 (^[W: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~q4(a, b, W)) | (~less_or_equalish(a, W))) <=> ((~less_or_equalish(a, W)) | (~q4(a, b, W)))), ((((~q4(a, b, W)) | (~less_or_equalish(a, W))) | (~less_or_equalish(b, W))) <=> (((~less_or_equalish(a, W)) | (~q4(a, b, W))) | (~less_or_equalish(b, W))))), rewrite((((~less_or_equalish(a, W)) | (~q4(a, b, W))) | (~less_or_equalish(b, W))) <=> ((~less_or_equalish(b, W)) | (~less_or_equalish(a, W)) | (~q4(a, b, W)))), ((((~q4(a, b, W)) | (~less_or_equalish(a, W))) | (~less_or_equalish(b, W))) <=> ((~less_or_equalish(b, W)) | (~less_or_equalish(a, W)) | (~q4(a, b, W))))), (((((~q4(a, b, W)) | (~less_or_equalish(a, W))) | (~less_or_equalish(b, W))) | (~less_or_equalish(W, b))) <=> (((~less_or_equalish(b, W)) | (~less_or_equalish(a, W)) | (~q4(a, b, W))) | (~less_or_equalish(W, b))))), rewrite((((~less_or_equalish(b, W)) | (~less_or_equalish(a, W)) | (~q4(a, b, W))) | (~less_or_equalish(W, b))) <=> ((~less_or_equalish(b, W)) | (~less_or_equalish(a, W)) | (~q4(a, b, W)) | (~less_or_equalish(W, b)))), (((((~q4(a, b, W)) | (~less_or_equalish(a, W))) | (~less_or_equalish(b, W))) | (~less_or_equalish(W, b))) <=> ((~less_or_equalish(b, W)) | (~less_or_equalish(a, W)) | (~q4(a, b, W)) | (~less_or_equalish(W, b)))))),
% 0.18/0.40 inference(bind,[status(th)],[])).
% 0.18/0.40 tff(106,plain,
% 0.18/0.40 (![W: $i] : ((((~q4(a, b, W)) | (~less_or_equalish(a, W))) | (~less_or_equalish(b, W))) | (~less_or_equalish(W, b))) <=> ![W: $i] : ((~less_or_equalish(b, W)) | (~less_or_equalish(a, W)) | (~q4(a, b, W)) | (~less_or_equalish(W, b)))),
% 0.18/0.40 inference(quant_intro,[status(thm)],[105])).
% 0.18/0.40 tff(107,axiom,(![W: $i] : ((((~q4(a, b, W)) | (~less_or_equalish(a, W))) | (~less_or_equalish(b, W))) | (~less_or_equalish(W, b)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause_7')).
% 0.18/0.40 tff(108,plain,
% 0.18/0.40 (![W: $i] : ((~less_or_equalish(b, W)) | (~less_or_equalish(a, W)) | (~q4(a, b, W)) | (~less_or_equalish(W, b)))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[107, 106])).
% 0.18/0.40 tff(109,plain,
% 0.18/0.40 (![W: $i] : ((~less_or_equalish(b, W)) | (~less_or_equalish(a, W)) | (~q4(a, b, W)) | (~less_or_equalish(W, b)))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[108, 104])).
% 0.18/0.40 tff(110,plain,(
% 0.18/0.40 ![W: $i] : ((~less_or_equalish(b, W)) | (~less_or_equalish(a, W)) | (~q4(a, b, W)) | (~less_or_equalish(W, b)))),
% 0.18/0.40 inference(skolemize,[status(sab)],[109])).
% 0.18/0.40 tff(111,plain,
% 0.18/0.40 (![W: $i] : ((~less_or_equalish(b, W)) | (~less_or_equalish(a, W)) | (~q4(a, b, W)) | (~less_or_equalish(W, b)))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[110, 103])).
% 0.18/0.40 tff(112,plain,
% 0.18/0.40 (((~![W: $i] : ((~less_or_equalish(b, W)) | (~less_or_equalish(a, W)) | (~q4(a, b, W)) | (~less_or_equalish(W, b)))) | ((~less_or_equalish(a, b)) | (~q4(a, b, b)) | (~less_or_equalish(b, b)))) <=> ((~![W: $i] : ((~less_or_equalish(b, W)) | (~less_or_equalish(a, W)) | (~q4(a, b, W)) | (~less_or_equalish(W, b)))) | (~less_or_equalish(a, b)) | (~q4(a, b, b)) | (~less_or_equalish(b, b)))),
% 0.18/0.40 inference(rewrite,[status(thm)],[])).
% 0.18/0.40 tff(113,plain,
% 0.18/0.40 (((~less_or_equalish(b, b)) | (~less_or_equalish(a, b)) | (~q4(a, b, b)) | (~less_or_equalish(b, b))) <=> ((~less_or_equalish(a, b)) | (~q4(a, b, b)) | (~less_or_equalish(b, b)))),
% 0.18/0.40 inference(rewrite,[status(thm)],[])).
% 0.18/0.40 tff(114,plain,
% 0.18/0.40 (((~![W: $i] : ((~less_or_equalish(b, W)) | (~less_or_equalish(a, W)) | (~q4(a, b, W)) | (~less_or_equalish(W, b)))) | ((~less_or_equalish(b, b)) | (~less_or_equalish(a, b)) | (~q4(a, b, b)) | (~less_or_equalish(b, b)))) <=> ((~![W: $i] : ((~less_or_equalish(b, W)) | (~less_or_equalish(a, W)) | (~q4(a, b, W)) | (~less_or_equalish(W, b)))) | ((~less_or_equalish(a, b)) | (~q4(a, b, b)) | (~less_or_equalish(b, b))))),
% 0.18/0.40 inference(monotonicity,[status(thm)],[113])).
% 0.18/0.40 tff(115,plain,
% 0.18/0.40 (((~![W: $i] : ((~less_or_equalish(b, W)) | (~less_or_equalish(a, W)) | (~q4(a, b, W)) | (~less_or_equalish(W, b)))) | ((~less_or_equalish(b, b)) | (~less_or_equalish(a, b)) | (~q4(a, b, b)) | (~less_or_equalish(b, b)))) <=> ((~![W: $i] : ((~less_or_equalish(b, W)) | (~less_or_equalish(a, W)) | (~q4(a, b, W)) | (~less_or_equalish(W, b)))) | (~less_or_equalish(a, b)) | (~q4(a, b, b)) | (~less_or_equalish(b, b)))),
% 0.18/0.40 inference(transitivity,[status(thm)],[114, 112])).
% 0.18/0.40 tff(116,plain,
% 0.18/0.40 ((~![W: $i] : ((~less_or_equalish(b, W)) | (~less_or_equalish(a, W)) | (~q4(a, b, W)) | (~less_or_equalish(W, b)))) | ((~less_or_equalish(b, b)) | (~less_or_equalish(a, b)) | (~q4(a, b, b)) | (~less_or_equalish(b, b)))),
% 0.18/0.40 inference(quant_inst,[status(thm)],[])).
% 0.18/0.40 tff(117,plain,
% 0.18/0.40 ((~![W: $i] : ((~less_or_equalish(b, W)) | (~less_or_equalish(a, W)) | (~q4(a, b, W)) | (~less_or_equalish(W, b)))) | (~less_or_equalish(a, b)) | (~q4(a, b, b)) | (~less_or_equalish(b, b))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[116, 115])).
% 0.18/0.40 tff(118,plain,
% 0.18/0.40 ((~q4(a, b, b)) | (~less_or_equalish(b, b))),
% 0.18/0.40 inference(unit_resolution,[status(thm)],[117, 111, 75])).
% 0.18/0.40 tff(119,plain,
% 0.18/0.40 (~less_or_equalish(b, b)),
% 0.18/0.40 inference(unit_resolution,[status(thm)],[118, 101])).
% 0.18/0.40 tff(120,plain,
% 0.18/0.40 (((~![Y: $i, X: $i] : (less_or_equalish(X, Y) | less_or_equalish(Y, X))) | less_or_equalish(b, b)) <=> ((~![Y: $i, X: $i] : (less_or_equalish(X, Y) | less_or_equalish(Y, X))) | less_or_equalish(b, b))),
% 0.18/0.40 inference(rewrite,[status(thm)],[])).
% 0.18/0.40 tff(121,plain,
% 0.18/0.40 ((less_or_equalish(b, b) | less_or_equalish(b, b)) <=> less_or_equalish(b, b)),
% 0.18/0.40 inference(rewrite,[status(thm)],[])).
% 0.18/0.40 tff(122,plain,
% 0.18/0.40 (((~![Y: $i, X: $i] : (less_or_equalish(X, Y) | less_or_equalish(Y, X))) | (less_or_equalish(b, b) | less_or_equalish(b, b))) <=> ((~![Y: $i, X: $i] : (less_or_equalish(X, Y) | less_or_equalish(Y, X))) | less_or_equalish(b, b))),
% 0.18/0.40 inference(monotonicity,[status(thm)],[121])).
% 0.18/0.40 tff(123,plain,
% 0.18/0.40 (((~![Y: $i, X: $i] : (less_or_equalish(X, Y) | less_or_equalish(Y, X))) | (less_or_equalish(b, b) | less_or_equalish(b, b))) <=> ((~![Y: $i, X: $i] : (less_or_equalish(X, Y) | less_or_equalish(Y, X))) | less_or_equalish(b, b))),
% 0.18/0.40 inference(transitivity,[status(thm)],[122, 120])).
% 0.18/0.40 tff(124,plain,
% 0.18/0.40 ((~![Y: $i, X: $i] : (less_or_equalish(X, Y) | less_or_equalish(Y, X))) | (less_or_equalish(b, b) | less_or_equalish(b, b))),
% 0.18/0.40 inference(quant_inst,[status(thm)],[])).
% 0.18/0.40 tff(125,plain,
% 0.18/0.40 ((~![Y: $i, X: $i] : (less_or_equalish(X, Y) | less_or_equalish(Y, X))) | less_or_equalish(b, b)),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[124, 123])).
% 0.18/0.40 tff(126,plain,
% 0.18/0.40 ($false),
% 0.18/0.40 inference(unit_resolution,[status(thm)],[125, 40, 119])).
% 0.18/0.40 % SZS output end Proof
%------------------------------------------------------------------------------