TSTP Solution File: HEN009-2 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : HEN009-2 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n025.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri Sep 16 22:39:52 EDT 2022
% Result : Unsatisfiable 0.14s 0.41s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : HEN009-2 : TPTP v8.1.0. Released v1.0.0.
% 0.12/0.14 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.14/0.35 % Computer : n025.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Wed Aug 31 21:56:01 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.14/0.36 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.14/0.36 Usage: tptp [options] [-file:]file
% 0.14/0.36 -h, -? prints this message.
% 0.14/0.36 -smt2 print SMT-LIB2 benchmark.
% 0.14/0.36 -m, -model generate model.
% 0.14/0.36 -p, -proof generate proof.
% 0.14/0.36 -c, -core generate unsat core of named formulas.
% 0.14/0.36 -st, -statistics display statistics.
% 0.14/0.36 -t:timeout set timeout (in second).
% 0.14/0.36 -smt2status display status in smt2 format instead of SZS.
% 0.14/0.36 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.14/0.36 -<param>:<value> configuration parameter and value.
% 0.14/0.36 -o:<output-file> file to place output in.
% 0.14/0.41 % SZS status Unsatisfiable
% 0.14/0.41 % SZS output start Proof
% 0.14/0.41 tff(less_equal_type, type, (
% 0.14/0.41 less_equal: ( $i * $i ) > $o)).
% 0.14/0.41 tff(idQ__idQ_idQa_type, type, (
% 0.14/0.41 idQ__idQ_idQa: $i)).
% 0.14/0.41 tff(idQa_type, type, (
% 0.14/0.41 idQa: $i)).
% 0.14/0.41 tff(a_type, type, (
% 0.14/0.41 a: $i)).
% 0.14/0.41 tff(idQ_idQa_type, type, (
% 0.14/0.41 idQ_idQa: $i)).
% 0.14/0.41 tff(identity_type, type, (
% 0.14/0.41 identity: $i)).
% 0.14/0.41 tff(quotient_type, type, (
% 0.14/0.41 quotient: ( $i * $i * $i ) > $o)).
% 0.14/0.41 tff(1,assumption,(~less_equal(identity, identity)), introduced(assumption)).
% 0.14/0.41 tff(2,plain,
% 0.14/0.41 (^[X: $i] : refl(less_equal(X, identity) <=> less_equal(X, identity))),
% 0.14/0.41 inference(bind,[status(th)],[])).
% 0.14/0.41 tff(3,plain,
% 0.14/0.41 (![X: $i] : less_equal(X, identity) <=> ![X: $i] : less_equal(X, identity)),
% 0.14/0.41 inference(quant_intro,[status(thm)],[2])).
% 0.14/0.41 tff(4,plain,
% 0.14/0.41 (![X: $i] : less_equal(X, identity) <=> ![X: $i] : less_equal(X, identity)),
% 0.14/0.41 inference(rewrite,[status(thm)],[])).
% 0.14/0.41 tff(5,axiom,(![X: $i] : less_equal(X, identity)), file('/export/starexec/sandbox/benchmark/Axioms/HEN001-0.ax','identity_is_largest')).
% 0.14/0.41 tff(6,plain,
% 0.14/0.41 (![X: $i] : less_equal(X, identity)),
% 0.14/0.41 inference(modus_ponens,[status(thm)],[5, 4])).
% 0.14/0.41 tff(7,plain,(
% 0.14/0.41 ![X: $i] : less_equal(X, identity)),
% 0.14/0.41 inference(skolemize,[status(sab)],[6])).
% 0.14/0.41 tff(8,plain,
% 0.14/0.41 (![X: $i] : less_equal(X, identity)),
% 0.14/0.41 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.14/0.41 tff(9,plain,
% 0.14/0.41 ((~![X: $i] : less_equal(X, identity)) | less_equal(identity, identity)),
% 0.14/0.41 inference(quant_inst,[status(thm)],[])).
% 0.14/0.41 tff(10,plain,
% 0.14/0.41 ($false),
% 0.14/0.41 inference(unit_resolution,[status(thm)],[9, 8, 1])).
% 0.14/0.41 tff(11,plain,(less_equal(identity, identity)), inference(lemma,lemma(discharge,[]))).
% 0.14/0.41 tff(12,plain,
% 0.14/0.41 (quotient(identity, a, idQa) <=> quotient(identity, a, idQa)),
% 0.14/0.41 inference(rewrite,[status(thm)],[])).
% 0.14/0.41 tff(13,axiom,(quotient(identity, a, idQa)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','identity_divide_a')).
% 0.14/0.41 tff(14,plain,
% 0.14/0.41 (quotient(identity, a, idQa)),
% 0.14/0.41 inference(modus_ponens,[status(thm)],[13, 12])).
% 0.14/0.41 tff(15,plain,
% 0.14/0.41 (^[Z: $i, Y: $i, W2: $i, W1: $i, X: $i] : refl((less_equal(W1, W2) | (~less_equal(X, Y)) | (~quotient(Y, Z, W2)) | (~quotient(X, Z, W1))) <=> (less_equal(W1, W2) | (~less_equal(X, Y)) | (~quotient(Y, Z, W2)) | (~quotient(X, Z, W1))))),
% 0.14/0.41 inference(bind,[status(th)],[])).
% 0.14/0.41 tff(16,plain,
% 0.14/0.41 (![Z: $i, Y: $i, W2: $i, W1: $i, X: $i] : (less_equal(W1, W2) | (~less_equal(X, Y)) | (~quotient(Y, Z, W2)) | (~quotient(X, Z, W1))) <=> ![Z: $i, Y: $i, W2: $i, W1: $i, X: $i] : (less_equal(W1, W2) | (~less_equal(X, Y)) | (~quotient(Y, Z, W2)) | (~quotient(X, Z, W1)))),
% 0.14/0.41 inference(quant_intro,[status(thm)],[15])).
% 0.14/0.41 tff(17,plain,
% 0.14/0.41 (![Z: $i, Y: $i, W2: $i, W1: $i, X: $i] : (less_equal(W1, W2) | (~less_equal(X, Y)) | (~quotient(Y, Z, W2)) | (~quotient(X, Z, W1))) <=> ![Z: $i, Y: $i, W2: $i, W1: $i, X: $i] : (less_equal(W1, W2) | (~less_equal(X, Y)) | (~quotient(Y, Z, W2)) | (~quotient(X, Z, W1)))),
% 0.14/0.41 inference(rewrite,[status(thm)],[])).
% 0.14/0.41 tff(18,plain,
% 0.14/0.41 (^[Z: $i, Y: $i, W2: $i, W1: $i, X: $i] : trans(monotonicity(rewrite((((~less_equal(X, Y)) | (~quotient(X, Z, W1))) | (~quotient(Y, Z, W2))) <=> ((~less_equal(X, Y)) | (~quotient(Y, Z, W2)) | (~quotient(X, Z, W1)))), (((((~less_equal(X, Y)) | (~quotient(X, Z, W1))) | (~quotient(Y, Z, W2))) | less_equal(W1, W2)) <=> (((~less_equal(X, Y)) | (~quotient(Y, Z, W2)) | (~quotient(X, Z, W1))) | less_equal(W1, W2)))), rewrite((((~less_equal(X, Y)) | (~quotient(Y, Z, W2)) | (~quotient(X, Z, W1))) | less_equal(W1, W2)) <=> (less_equal(W1, W2) | (~less_equal(X, Y)) | (~quotient(Y, Z, W2)) | (~quotient(X, Z, W1)))), (((((~less_equal(X, Y)) | (~quotient(X, Z, W1))) | (~quotient(Y, Z, W2))) | less_equal(W1, W2)) <=> (less_equal(W1, W2) | (~less_equal(X, Y)) | (~quotient(Y, Z, W2)) | (~quotient(X, Z, W1)))))),
% 0.14/0.41 inference(bind,[status(th)],[])).
% 0.14/0.41 tff(19,plain,
% 0.14/0.41 (![Z: $i, Y: $i, W2: $i, W1: $i, X: $i] : ((((~less_equal(X, Y)) | (~quotient(X, Z, W1))) | (~quotient(Y, Z, W2))) | less_equal(W1, W2)) <=> ![Z: $i, Y: $i, W2: $i, W1: $i, X: $i] : (less_equal(W1, W2) | (~less_equal(X, Y)) | (~quotient(Y, Z, W2)) | (~quotient(X, Z, W1)))),
% 0.14/0.41 inference(quant_intro,[status(thm)],[18])).
% 0.14/0.41 tff(20,axiom,(![Z: $i, Y: $i, W2: $i, W1: $i, X: $i] : ((((~less_equal(X, Y)) | (~quotient(X, Z, W1))) | (~quotient(Y, Z, W2))) | less_equal(W1, W2))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','xLEy_implies_xQzLEyQz')).
% 0.14/0.41 tff(21,plain,
% 0.14/0.41 (![Z: $i, Y: $i, W2: $i, W1: $i, X: $i] : (less_equal(W1, W2) | (~less_equal(X, Y)) | (~quotient(Y, Z, W2)) | (~quotient(X, Z, W1)))),
% 0.14/0.41 inference(modus_ponens,[status(thm)],[20, 19])).
% 0.14/0.41 tff(22,plain,
% 0.14/0.41 (![Z: $i, Y: $i, W2: $i, W1: $i, X: $i] : (less_equal(W1, W2) | (~less_equal(X, Y)) | (~quotient(Y, Z, W2)) | (~quotient(X, Z, W1)))),
% 0.14/0.41 inference(modus_ponens,[status(thm)],[21, 17])).
% 0.14/0.41 tff(23,plain,(
% 0.14/0.41 ![Z: $i, Y: $i, W2: $i, W1: $i, X: $i] : (less_equal(W1, W2) | (~less_equal(X, Y)) | (~quotient(Y, Z, W2)) | (~quotient(X, Z, W1)))),
% 0.14/0.41 inference(skolemize,[status(sab)],[22])).
% 0.14/0.41 tff(24,plain,
% 0.14/0.41 (![Z: $i, Y: $i, W2: $i, W1: $i, X: $i] : (less_equal(W1, W2) | (~less_equal(X, Y)) | (~quotient(Y, Z, W2)) | (~quotient(X, Z, W1)))),
% 0.14/0.41 inference(modus_ponens,[status(thm)],[23, 16])).
% 0.14/0.41 tff(25,plain,
% 0.14/0.41 (((~![Z: $i, Y: $i, W2: $i, W1: $i, X: $i] : (less_equal(W1, W2) | (~less_equal(X, Y)) | (~quotient(Y, Z, W2)) | (~quotient(X, Z, W1)))) | (less_equal(idQa, idQa) | (~less_equal(identity, identity)) | (~quotient(identity, a, idQa)))) <=> ((~![Z: $i, Y: $i, W2: $i, W1: $i, X: $i] : (less_equal(W1, W2) | (~less_equal(X, Y)) | (~quotient(Y, Z, W2)) | (~quotient(X, Z, W1)))) | less_equal(idQa, idQa) | (~less_equal(identity, identity)) | (~quotient(identity, a, idQa)))),
% 0.14/0.41 inference(rewrite,[status(thm)],[])).
% 0.14/0.41 tff(26,plain,
% 0.14/0.41 ((less_equal(idQa, idQa) | (~less_equal(identity, identity)) | (~quotient(identity, a, idQa)) | (~quotient(identity, a, idQa))) <=> (less_equal(idQa, idQa) | (~less_equal(identity, identity)) | (~quotient(identity, a, idQa)))),
% 0.14/0.41 inference(rewrite,[status(thm)],[])).
% 0.14/0.41 tff(27,plain,
% 0.14/0.41 (((~![Z: $i, Y: $i, W2: $i, W1: $i, X: $i] : (less_equal(W1, W2) | (~less_equal(X, Y)) | (~quotient(Y, Z, W2)) | (~quotient(X, Z, W1)))) | (less_equal(idQa, idQa) | (~less_equal(identity, identity)) | (~quotient(identity, a, idQa)) | (~quotient(identity, a, idQa)))) <=> ((~![Z: $i, Y: $i, W2: $i, W1: $i, X: $i] : (less_equal(W1, W2) | (~less_equal(X, Y)) | (~quotient(Y, Z, W2)) | (~quotient(X, Z, W1)))) | (less_equal(idQa, idQa) | (~less_equal(identity, identity)) | (~quotient(identity, a, idQa))))),
% 0.14/0.41 inference(monotonicity,[status(thm)],[26])).
% 0.14/0.41 tff(28,plain,
% 0.14/0.41 (((~![Z: $i, Y: $i, W2: $i, W1: $i, X: $i] : (less_equal(W1, W2) | (~less_equal(X, Y)) | (~quotient(Y, Z, W2)) | (~quotient(X, Z, W1)))) | (less_equal(idQa, idQa) | (~less_equal(identity, identity)) | (~quotient(identity, a, idQa)) | (~quotient(identity, a, idQa)))) <=> ((~![Z: $i, Y: $i, W2: $i, W1: $i, X: $i] : (less_equal(W1, W2) | (~less_equal(X, Y)) | (~quotient(Y, Z, W2)) | (~quotient(X, Z, W1)))) | less_equal(idQa, idQa) | (~less_equal(identity, identity)) | (~quotient(identity, a, idQa)))),
% 0.14/0.41 inference(transitivity,[status(thm)],[27, 25])).
% 0.14/0.41 tff(29,plain,
% 0.14/0.41 ((~![Z: $i, Y: $i, W2: $i, W1: $i, X: $i] : (less_equal(W1, W2) | (~less_equal(X, Y)) | (~quotient(Y, Z, W2)) | (~quotient(X, Z, W1)))) | (less_equal(idQa, idQa) | (~less_equal(identity, identity)) | (~quotient(identity, a, idQa)) | (~quotient(identity, a, idQa)))),
% 0.14/0.41 inference(quant_inst,[status(thm)],[])).
% 0.14/0.41 tff(30,plain,
% 0.14/0.41 ((~![Z: $i, Y: $i, W2: $i, W1: $i, X: $i] : (less_equal(W1, W2) | (~less_equal(X, Y)) | (~quotient(Y, Z, W2)) | (~quotient(X, Z, W1)))) | less_equal(idQa, idQa) | (~less_equal(identity, identity)) | (~quotient(identity, a, idQa))),
% 0.14/0.41 inference(modus_ponens,[status(thm)],[29, 28])).
% 0.14/0.41 tff(31,plain,
% 0.14/0.41 (less_equal(idQa, idQa) | (~less_equal(identity, identity))),
% 0.14/0.41 inference(unit_resolution,[status(thm)],[30, 24, 14])).
% 0.14/0.41 tff(32,plain,
% 0.14/0.41 (less_equal(idQa, idQa)),
% 0.14/0.41 inference(unit_resolution,[status(thm)],[31, 11])).
% 0.14/0.41 tff(33,plain,
% 0.14/0.41 (quotient(identity, idQa, idQ_idQa) <=> quotient(identity, idQa, idQ_idQa)),
% 0.14/0.41 inference(rewrite,[status(thm)],[])).
% 0.14/0.41 tff(34,axiom,(quotient(identity, idQa, idQ_idQa)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','identity_divide_idQa')).
% 0.14/0.41 tff(35,plain,
% 0.14/0.41 (quotient(identity, idQa, idQ_idQa)),
% 0.14/0.41 inference(modus_ponens,[status(thm)],[34, 33])).
% 0.14/0.41 tff(36,plain,
% 0.14/0.41 (^[Z: $i, Y: $i, W2: $i, W1: $i, X: $i] : refl((less_equal(W2, Y) | (~quotient(X, Z, W2)) | (~less_equal(W1, Z)) | (~quotient(X, Y, W1))) <=> (less_equal(W2, Y) | (~quotient(X, Z, W2)) | (~less_equal(W1, Z)) | (~quotient(X, Y, W1))))),
% 0.14/0.41 inference(bind,[status(th)],[])).
% 0.14/0.41 tff(37,plain,
% 0.14/0.41 (![Z: $i, Y: $i, W2: $i, W1: $i, X: $i] : (less_equal(W2, Y) | (~quotient(X, Z, W2)) | (~less_equal(W1, Z)) | (~quotient(X, Y, W1))) <=> ![Z: $i, Y: $i, W2: $i, W1: $i, X: $i] : (less_equal(W2, Y) | (~quotient(X, Z, W2)) | (~less_equal(W1, Z)) | (~quotient(X, Y, W1)))),
% 0.14/0.41 inference(quant_intro,[status(thm)],[36])).
% 0.14/0.41 tff(38,plain,
% 0.14/0.41 (![Z: $i, Y: $i, W2: $i, W1: $i, X: $i] : (less_equal(W2, Y) | (~quotient(X, Z, W2)) | (~less_equal(W1, Z)) | (~quotient(X, Y, W1))) <=> ![Z: $i, Y: $i, W2: $i, W1: $i, X: $i] : (less_equal(W2, Y) | (~quotient(X, Z, W2)) | (~less_equal(W1, Z)) | (~quotient(X, Y, W1)))),
% 0.14/0.41 inference(rewrite,[status(thm)],[])).
% 0.14/0.41 tff(39,plain,
% 0.14/0.41 (^[Z: $i, Y: $i, W2: $i, W1: $i, X: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~quotient(X, Y, W1)) | (~less_equal(W1, Z))) <=> ((~less_equal(W1, Z)) | (~quotient(X, Y, W1)))), ((((~quotient(X, Y, W1)) | (~less_equal(W1, Z))) | (~quotient(X, Z, W2))) <=> (((~less_equal(W1, Z)) | (~quotient(X, Y, W1))) | (~quotient(X, Z, W2))))), rewrite((((~less_equal(W1, Z)) | (~quotient(X, Y, W1))) | (~quotient(X, Z, W2))) <=> ((~quotient(X, Z, W2)) | (~less_equal(W1, Z)) | (~quotient(X, Y, W1)))), ((((~quotient(X, Y, W1)) | (~less_equal(W1, Z))) | (~quotient(X, Z, W2))) <=> ((~quotient(X, Z, W2)) | (~less_equal(W1, Z)) | (~quotient(X, Y, W1))))), (((((~quotient(X, Y, W1)) | (~less_equal(W1, Z))) | (~quotient(X, Z, W2))) | less_equal(W2, Y)) <=> (((~quotient(X, Z, W2)) | (~less_equal(W1, Z)) | (~quotient(X, Y, W1))) | less_equal(W2, Y)))), rewrite((((~quotient(X, Z, W2)) | (~less_equal(W1, Z)) | (~quotient(X, Y, W1))) | less_equal(W2, Y)) <=> (less_equal(W2, Y) | (~quotient(X, Z, W2)) | (~less_equal(W1, Z)) | (~quotient(X, Y, W1)))), (((((~quotient(X, Y, W1)) | (~less_equal(W1, Z))) | (~quotient(X, Z, W2))) | less_equal(W2, Y)) <=> (less_equal(W2, Y) | (~quotient(X, Z, W2)) | (~less_equal(W1, Z)) | (~quotient(X, Y, W1)))))),
% 0.14/0.41 inference(bind,[status(th)],[])).
% 0.14/0.41 tff(40,plain,
% 0.14/0.41 (![Z: $i, Y: $i, W2: $i, W1: $i, X: $i] : ((((~quotient(X, Y, W1)) | (~less_equal(W1, Z))) | (~quotient(X, Z, W2))) | less_equal(W2, Y)) <=> ![Z: $i, Y: $i, W2: $i, W1: $i, X: $i] : (less_equal(W2, Y) | (~quotient(X, Z, W2)) | (~less_equal(W1, Z)) | (~quotient(X, Y, W1)))),
% 0.14/0.41 inference(quant_intro,[status(thm)],[39])).
% 0.14/0.41 tff(41,axiom,(![Z: $i, Y: $i, W2: $i, W1: $i, X: $i] : ((((~quotient(X, Y, W1)) | (~less_equal(W1, Z))) | (~quotient(X, Z, W2))) | less_equal(W2, Y))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','xQyLEz_implies_xQzLEy')).
% 0.14/0.41 tff(42,plain,
% 0.14/0.41 (![Z: $i, Y: $i, W2: $i, W1: $i, X: $i] : (less_equal(W2, Y) | (~quotient(X, Z, W2)) | (~less_equal(W1, Z)) | (~quotient(X, Y, W1)))),
% 0.14/0.41 inference(modus_ponens,[status(thm)],[41, 40])).
% 0.14/0.41 tff(43,plain,
% 0.14/0.41 (![Z: $i, Y: $i, W2: $i, W1: $i, X: $i] : (less_equal(W2, Y) | (~quotient(X, Z, W2)) | (~less_equal(W1, Z)) | (~quotient(X, Y, W1)))),
% 0.14/0.41 inference(modus_ponens,[status(thm)],[42, 38])).
% 0.14/0.41 tff(44,plain,(
% 0.14/0.41 ![Z: $i, Y: $i, W2: $i, W1: $i, X: $i] : (less_equal(W2, Y) | (~quotient(X, Z, W2)) | (~less_equal(W1, Z)) | (~quotient(X, Y, W1)))),
% 0.14/0.41 inference(skolemize,[status(sab)],[43])).
% 0.14/0.41 tff(45,plain,
% 0.14/0.41 (![Z: $i, Y: $i, W2: $i, W1: $i, X: $i] : (less_equal(W2, Y) | (~quotient(X, Z, W2)) | (~less_equal(W1, Z)) | (~quotient(X, Y, W1)))),
% 0.14/0.41 inference(modus_ponens,[status(thm)],[44, 37])).
% 0.14/0.41 tff(46,plain,
% 0.14/0.41 (((~![Z: $i, Y: $i, W2: $i, W1: $i, X: $i] : (less_equal(W2, Y) | (~quotient(X, Z, W2)) | (~less_equal(W1, Z)) | (~quotient(X, Y, W1)))) | ((~quotient(identity, a, idQa)) | (~quotient(identity, idQa, idQ_idQa)) | less_equal(idQ_idQa, a) | (~less_equal(idQa, idQa)))) <=> ((~![Z: $i, Y: $i, W2: $i, W1: $i, X: $i] : (less_equal(W2, Y) | (~quotient(X, Z, W2)) | (~less_equal(W1, Z)) | (~quotient(X, Y, W1)))) | (~quotient(identity, a, idQa)) | (~quotient(identity, idQa, idQ_idQa)) | less_equal(idQ_idQa, a) | (~less_equal(idQa, idQa)))),
% 0.14/0.42 inference(rewrite,[status(thm)],[])).
% 0.14/0.42 tff(47,plain,
% 0.14/0.42 ((less_equal(idQ_idQa, a) | (~quotient(identity, idQa, idQ_idQa)) | (~less_equal(idQa, idQa)) | (~quotient(identity, a, idQa))) <=> ((~quotient(identity, a, idQa)) | (~quotient(identity, idQa, idQ_idQa)) | less_equal(idQ_idQa, a) | (~less_equal(idQa, idQa)))),
% 0.14/0.42 inference(rewrite,[status(thm)],[])).
% 0.14/0.42 tff(48,plain,
% 0.14/0.42 (((~![Z: $i, Y: $i, W2: $i, W1: $i, X: $i] : (less_equal(W2, Y) | (~quotient(X, Z, W2)) | (~less_equal(W1, Z)) | (~quotient(X, Y, W1)))) | (less_equal(idQ_idQa, a) | (~quotient(identity, idQa, idQ_idQa)) | (~less_equal(idQa, idQa)) | (~quotient(identity, a, idQa)))) <=> ((~![Z: $i, Y: $i, W2: $i, W1: $i, X: $i] : (less_equal(W2, Y) | (~quotient(X, Z, W2)) | (~less_equal(W1, Z)) | (~quotient(X, Y, W1)))) | ((~quotient(identity, a, idQa)) | (~quotient(identity, idQa, idQ_idQa)) | less_equal(idQ_idQa, a) | (~less_equal(idQa, idQa))))),
% 0.14/0.42 inference(monotonicity,[status(thm)],[47])).
% 0.14/0.42 tff(49,plain,
% 0.14/0.42 (((~![Z: $i, Y: $i, W2: $i, W1: $i, X: $i] : (less_equal(W2, Y) | (~quotient(X, Z, W2)) | (~less_equal(W1, Z)) | (~quotient(X, Y, W1)))) | (less_equal(idQ_idQa, a) | (~quotient(identity, idQa, idQ_idQa)) | (~less_equal(idQa, idQa)) | (~quotient(identity, a, idQa)))) <=> ((~![Z: $i, Y: $i, W2: $i, W1: $i, X: $i] : (less_equal(W2, Y) | (~quotient(X, Z, W2)) | (~less_equal(W1, Z)) | (~quotient(X, Y, W1)))) | (~quotient(identity, a, idQa)) | (~quotient(identity, idQa, idQ_idQa)) | less_equal(idQ_idQa, a) | (~less_equal(idQa, idQa)))),
% 0.14/0.42 inference(transitivity,[status(thm)],[48, 46])).
% 0.14/0.42 tff(50,plain,
% 0.14/0.42 ((~![Z: $i, Y: $i, W2: $i, W1: $i, X: $i] : (less_equal(W2, Y) | (~quotient(X, Z, W2)) | (~less_equal(W1, Z)) | (~quotient(X, Y, W1)))) | (less_equal(idQ_idQa, a) | (~quotient(identity, idQa, idQ_idQa)) | (~less_equal(idQa, idQa)) | (~quotient(identity, a, idQa)))),
% 0.14/0.42 inference(quant_inst,[status(thm)],[])).
% 0.14/0.42 tff(51,plain,
% 0.14/0.42 ((~![Z: $i, Y: $i, W2: $i, W1: $i, X: $i] : (less_equal(W2, Y) | (~quotient(X, Z, W2)) | (~less_equal(W1, Z)) | (~quotient(X, Y, W1)))) | (~quotient(identity, a, idQa)) | (~quotient(identity, idQa, idQ_idQa)) | less_equal(idQ_idQa, a) | (~less_equal(idQa, idQa))),
% 0.14/0.42 inference(modus_ponens,[status(thm)],[50, 49])).
% 0.14/0.42 tff(52,plain,
% 0.14/0.42 (less_equal(idQ_idQa, a) | (~less_equal(idQa, idQa))),
% 0.14/0.42 inference(unit_resolution,[status(thm)],[51, 45, 14, 35])).
% 0.14/0.42 tff(53,plain,
% 0.14/0.42 (less_equal(idQ_idQa, a)),
% 0.14/0.42 inference(unit_resolution,[status(thm)],[52, 32])).
% 0.14/0.42 tff(54,plain,
% 0.14/0.42 (quotient(identity, idQ_idQa, idQ__idQ_idQa) <=> quotient(identity, idQ_idQa, idQ__idQ_idQa)),
% 0.14/0.42 inference(rewrite,[status(thm)],[])).
% 0.14/0.42 tff(55,axiom,(quotient(identity, idQ_idQa, idQ__idQ_idQa)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','identity_divide_idQ_idQa')).
% 0.14/0.42 tff(56,plain,
% 0.14/0.42 (quotient(identity, idQ_idQa, idQ__idQ_idQa)),
% 0.14/0.42 inference(modus_ponens,[status(thm)],[55, 54])).
% 0.14/0.42 tff(57,plain,
% 0.14/0.42 (^[Z: $i, Y: $i, W2: $i, W1: $i, X: $i] : refl((less_equal(W1, W2) | (~quotient(Z, X, W2)) | (~quotient(Z, Y, W1)) | (~less_equal(X, Y))) <=> (less_equal(W1, W2) | (~quotient(Z, X, W2)) | (~quotient(Z, Y, W1)) | (~less_equal(X, Y))))),
% 0.14/0.42 inference(bind,[status(th)],[])).
% 0.14/0.42 tff(58,plain,
% 0.14/0.42 (![Z: $i, Y: $i, W2: $i, W1: $i, X: $i] : (less_equal(W1, W2) | (~quotient(Z, X, W2)) | (~quotient(Z, Y, W1)) | (~less_equal(X, Y))) <=> ![Z: $i, Y: $i, W2: $i, W1: $i, X: $i] : (less_equal(W1, W2) | (~quotient(Z, X, W2)) | (~quotient(Z, Y, W1)) | (~less_equal(X, Y)))),
% 0.14/0.42 inference(quant_intro,[status(thm)],[57])).
% 0.14/0.42 tff(59,plain,
% 0.14/0.42 (![Z: $i, Y: $i, W2: $i, W1: $i, X: $i] : (less_equal(W1, W2) | (~quotient(Z, X, W2)) | (~quotient(Z, Y, W1)) | (~less_equal(X, Y))) <=> ![Z: $i, Y: $i, W2: $i, W1: $i, X: $i] : (less_equal(W1, W2) | (~quotient(Z, X, W2)) | (~quotient(Z, Y, W1)) | (~less_equal(X, Y)))),
% 0.14/0.42 inference(rewrite,[status(thm)],[])).
% 0.14/0.42 tff(60,plain,
% 0.14/0.42 (^[Z: $i, Y: $i, W2: $i, W1: $i, X: $i] : trans(monotonicity(rewrite((((~less_equal(X, Y)) | (~quotient(Z, Y, W1))) | (~quotient(Z, X, W2))) <=> ((~quotient(Z, X, W2)) | (~quotient(Z, Y, W1)) | (~less_equal(X, Y)))), (((((~less_equal(X, Y)) | (~quotient(Z, Y, W1))) | (~quotient(Z, X, W2))) | less_equal(W1, W2)) <=> (((~quotient(Z, X, W2)) | (~quotient(Z, Y, W1)) | (~less_equal(X, Y))) | less_equal(W1, W2)))), rewrite((((~quotient(Z, X, W2)) | (~quotient(Z, Y, W1)) | (~less_equal(X, Y))) | less_equal(W1, W2)) <=> (less_equal(W1, W2) | (~quotient(Z, X, W2)) | (~quotient(Z, Y, W1)) | (~less_equal(X, Y)))), (((((~less_equal(X, Y)) | (~quotient(Z, Y, W1))) | (~quotient(Z, X, W2))) | less_equal(W1, W2)) <=> (less_equal(W1, W2) | (~quotient(Z, X, W2)) | (~quotient(Z, Y, W1)) | (~less_equal(X, Y)))))),
% 0.14/0.42 inference(bind,[status(th)],[])).
% 0.14/0.42 tff(61,plain,
% 0.14/0.42 (![Z: $i, Y: $i, W2: $i, W1: $i, X: $i] : ((((~less_equal(X, Y)) | (~quotient(Z, Y, W1))) | (~quotient(Z, X, W2))) | less_equal(W1, W2)) <=> ![Z: $i, Y: $i, W2: $i, W1: $i, X: $i] : (less_equal(W1, W2) | (~quotient(Z, X, W2)) | (~quotient(Z, Y, W1)) | (~less_equal(X, Y)))),
% 0.14/0.42 inference(quant_intro,[status(thm)],[60])).
% 0.14/0.42 tff(62,axiom,(![Z: $i, Y: $i, W2: $i, W1: $i, X: $i] : ((((~less_equal(X, Y)) | (~quotient(Z, Y, W1))) | (~quotient(Z, X, W2))) | less_equal(W1, W2))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','xLEy_implies_zQyLEzQx')).
% 0.14/0.42 tff(63,plain,
% 0.14/0.42 (![Z: $i, Y: $i, W2: $i, W1: $i, X: $i] : (less_equal(W1, W2) | (~quotient(Z, X, W2)) | (~quotient(Z, Y, W1)) | (~less_equal(X, Y)))),
% 0.14/0.42 inference(modus_ponens,[status(thm)],[62, 61])).
% 0.14/0.42 tff(64,plain,
% 0.14/0.42 (![Z: $i, Y: $i, W2: $i, W1: $i, X: $i] : (less_equal(W1, W2) | (~quotient(Z, X, W2)) | (~quotient(Z, Y, W1)) | (~less_equal(X, Y)))),
% 0.14/0.42 inference(modus_ponens,[status(thm)],[63, 59])).
% 0.14/0.42 tff(65,plain,(
% 0.14/0.42 ![Z: $i, Y: $i, W2: $i, W1: $i, X: $i] : (less_equal(W1, W2) | (~quotient(Z, X, W2)) | (~quotient(Z, Y, W1)) | (~less_equal(X, Y)))),
% 0.14/0.42 inference(skolemize,[status(sab)],[64])).
% 0.14/0.42 tff(66,plain,
% 0.14/0.42 (![Z: $i, Y: $i, W2: $i, W1: $i, X: $i] : (less_equal(W1, W2) | (~quotient(Z, X, W2)) | (~quotient(Z, Y, W1)) | (~less_equal(X, Y)))),
% 0.14/0.42 inference(modus_ponens,[status(thm)],[65, 58])).
% 0.14/0.42 tff(67,plain,
% 0.14/0.42 (((~![Z: $i, Y: $i, W2: $i, W1: $i, X: $i] : (less_equal(W1, W2) | (~quotient(Z, X, W2)) | (~quotient(Z, Y, W1)) | (~less_equal(X, Y)))) | ((~quotient(identity, a, idQa)) | (~quotient(identity, idQ_idQa, idQ__idQ_idQa)) | (~less_equal(idQ_idQa, a)) | less_equal(idQa, idQ__idQ_idQa))) <=> ((~![Z: $i, Y: $i, W2: $i, W1: $i, X: $i] : (less_equal(W1, W2) | (~quotient(Z, X, W2)) | (~quotient(Z, Y, W1)) | (~less_equal(X, Y)))) | (~quotient(identity, a, idQa)) | (~quotient(identity, idQ_idQa, idQ__idQ_idQa)) | (~less_equal(idQ_idQa, a)) | less_equal(idQa, idQ__idQ_idQa))),
% 0.14/0.42 inference(rewrite,[status(thm)],[])).
% 0.14/0.42 tff(68,plain,
% 0.14/0.42 ((less_equal(idQa, idQ__idQ_idQa) | (~quotient(identity, idQ_idQa, idQ__idQ_idQa)) | (~quotient(identity, a, idQa)) | (~less_equal(idQ_idQa, a))) <=> ((~quotient(identity, a, idQa)) | (~quotient(identity, idQ_idQa, idQ__idQ_idQa)) | (~less_equal(idQ_idQa, a)) | less_equal(idQa, idQ__idQ_idQa))),
% 0.14/0.42 inference(rewrite,[status(thm)],[])).
% 0.14/0.42 tff(69,plain,
% 0.14/0.42 (((~![Z: $i, Y: $i, W2: $i, W1: $i, X: $i] : (less_equal(W1, W2) | (~quotient(Z, X, W2)) | (~quotient(Z, Y, W1)) | (~less_equal(X, Y)))) | (less_equal(idQa, idQ__idQ_idQa) | (~quotient(identity, idQ_idQa, idQ__idQ_idQa)) | (~quotient(identity, a, idQa)) | (~less_equal(idQ_idQa, a)))) <=> ((~![Z: $i, Y: $i, W2: $i, W1: $i, X: $i] : (less_equal(W1, W2) | (~quotient(Z, X, W2)) | (~quotient(Z, Y, W1)) | (~less_equal(X, Y)))) | ((~quotient(identity, a, idQa)) | (~quotient(identity, idQ_idQa, idQ__idQ_idQa)) | (~less_equal(idQ_idQa, a)) | less_equal(idQa, idQ__idQ_idQa)))),
% 0.14/0.42 inference(monotonicity,[status(thm)],[68])).
% 0.14/0.42 tff(70,plain,
% 0.14/0.42 (((~![Z: $i, Y: $i, W2: $i, W1: $i, X: $i] : (less_equal(W1, W2) | (~quotient(Z, X, W2)) | (~quotient(Z, Y, W1)) | (~less_equal(X, Y)))) | (less_equal(idQa, idQ__idQ_idQa) | (~quotient(identity, idQ_idQa, idQ__idQ_idQa)) | (~quotient(identity, a, idQa)) | (~less_equal(idQ_idQa, a)))) <=> ((~![Z: $i, Y: $i, W2: $i, W1: $i, X: $i] : (less_equal(W1, W2) | (~quotient(Z, X, W2)) | (~quotient(Z, Y, W1)) | (~less_equal(X, Y)))) | (~quotient(identity, a, idQa)) | (~quotient(identity, idQ_idQa, idQ__idQ_idQa)) | (~less_equal(idQ_idQa, a)) | less_equal(idQa, idQ__idQ_idQa))),
% 0.20/0.42 inference(transitivity,[status(thm)],[69, 67])).
% 0.20/0.42 tff(71,plain,
% 0.20/0.42 ((~![Z: $i, Y: $i, W2: $i, W1: $i, X: $i] : (less_equal(W1, W2) | (~quotient(Z, X, W2)) | (~quotient(Z, Y, W1)) | (~less_equal(X, Y)))) | (less_equal(idQa, idQ__idQ_idQa) | (~quotient(identity, idQ_idQa, idQ__idQ_idQa)) | (~quotient(identity, a, idQa)) | (~less_equal(idQ_idQa, a)))),
% 0.20/0.42 inference(quant_inst,[status(thm)],[])).
% 0.20/0.42 tff(72,plain,
% 0.20/0.42 ((~![Z: $i, Y: $i, W2: $i, W1: $i, X: $i] : (less_equal(W1, W2) | (~quotient(Z, X, W2)) | (~quotient(Z, Y, W1)) | (~less_equal(X, Y)))) | (~quotient(identity, a, idQa)) | (~quotient(identity, idQ_idQa, idQ__idQ_idQa)) | (~less_equal(idQ_idQa, a)) | less_equal(idQa, idQ__idQ_idQa)),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[71, 70])).
% 0.20/0.42 tff(73,plain,
% 0.20/0.42 ((~less_equal(idQ_idQa, a)) | less_equal(idQa, idQ__idQ_idQa)),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[72, 66, 14, 56])).
% 0.20/0.42 tff(74,plain,
% 0.20/0.42 (less_equal(idQa, idQ__idQ_idQa)),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[73, 53])).
% 0.20/0.42 tff(75,plain,
% 0.20/0.42 (((~![Z: $i, Y: $i, W2: $i, W1: $i, X: $i] : (less_equal(W1, W2) | (~less_equal(X, Y)) | (~quotient(Y, Z, W2)) | (~quotient(X, Z, W1)))) | ((~less_equal(identity, identity)) | (~quotient(identity, idQa, idQ_idQa)) | less_equal(idQ_idQa, idQ_idQa))) <=> ((~![Z: $i, Y: $i, W2: $i, W1: $i, X: $i] : (less_equal(W1, W2) | (~less_equal(X, Y)) | (~quotient(Y, Z, W2)) | (~quotient(X, Z, W1)))) | (~less_equal(identity, identity)) | (~quotient(identity, idQa, idQ_idQa)) | less_equal(idQ_idQa, idQ_idQa))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(76,plain,
% 0.20/0.42 ((less_equal(idQ_idQa, idQ_idQa) | (~less_equal(identity, identity)) | (~quotient(identity, idQa, idQ_idQa)) | (~quotient(identity, idQa, idQ_idQa))) <=> ((~less_equal(identity, identity)) | (~quotient(identity, idQa, idQ_idQa)) | less_equal(idQ_idQa, idQ_idQa))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(77,plain,
% 0.20/0.42 (((~![Z: $i, Y: $i, W2: $i, W1: $i, X: $i] : (less_equal(W1, W2) | (~less_equal(X, Y)) | (~quotient(Y, Z, W2)) | (~quotient(X, Z, W1)))) | (less_equal(idQ_idQa, idQ_idQa) | (~less_equal(identity, identity)) | (~quotient(identity, idQa, idQ_idQa)) | (~quotient(identity, idQa, idQ_idQa)))) <=> ((~![Z: $i, Y: $i, W2: $i, W1: $i, X: $i] : (less_equal(W1, W2) | (~less_equal(X, Y)) | (~quotient(Y, Z, W2)) | (~quotient(X, Z, W1)))) | ((~less_equal(identity, identity)) | (~quotient(identity, idQa, idQ_idQa)) | less_equal(idQ_idQa, idQ_idQa)))),
% 0.20/0.42 inference(monotonicity,[status(thm)],[76])).
% 0.20/0.42 tff(78,plain,
% 0.20/0.42 (((~![Z: $i, Y: $i, W2: $i, W1: $i, X: $i] : (less_equal(W1, W2) | (~less_equal(X, Y)) | (~quotient(Y, Z, W2)) | (~quotient(X, Z, W1)))) | (less_equal(idQ_idQa, idQ_idQa) | (~less_equal(identity, identity)) | (~quotient(identity, idQa, idQ_idQa)) | (~quotient(identity, idQa, idQ_idQa)))) <=> ((~![Z: $i, Y: $i, W2: $i, W1: $i, X: $i] : (less_equal(W1, W2) | (~less_equal(X, Y)) | (~quotient(Y, Z, W2)) | (~quotient(X, Z, W1)))) | (~less_equal(identity, identity)) | (~quotient(identity, idQa, idQ_idQa)) | less_equal(idQ_idQa, idQ_idQa))),
% 0.20/0.42 inference(transitivity,[status(thm)],[77, 75])).
% 0.20/0.42 tff(79,plain,
% 0.20/0.42 ((~![Z: $i, Y: $i, W2: $i, W1: $i, X: $i] : (less_equal(W1, W2) | (~less_equal(X, Y)) | (~quotient(Y, Z, W2)) | (~quotient(X, Z, W1)))) | (less_equal(idQ_idQa, idQ_idQa) | (~less_equal(identity, identity)) | (~quotient(identity, idQa, idQ_idQa)) | (~quotient(identity, idQa, idQ_idQa)))),
% 0.20/0.42 inference(quant_inst,[status(thm)],[])).
% 0.20/0.42 tff(80,plain,
% 0.20/0.42 ((~![Z: $i, Y: $i, W2: $i, W1: $i, X: $i] : (less_equal(W1, W2) | (~less_equal(X, Y)) | (~quotient(Y, Z, W2)) | (~quotient(X, Z, W1)))) | (~less_equal(identity, identity)) | (~quotient(identity, idQa, idQ_idQa)) | less_equal(idQ_idQa, idQ_idQa)),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[79, 78])).
% 0.20/0.43 tff(81,plain,
% 0.20/0.43 ((~less_equal(identity, identity)) | less_equal(idQ_idQa, idQ_idQa)),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[80, 24, 35])).
% 0.20/0.43 tff(82,plain,
% 0.20/0.43 (less_equal(idQ_idQa, idQ_idQa)),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[81, 11])).
% 0.20/0.43 tff(83,plain,
% 0.20/0.43 (((~![Z: $i, Y: $i, W2: $i, W1: $i, X: $i] : (less_equal(W2, Y) | (~quotient(X, Z, W2)) | (~less_equal(W1, Z)) | (~quotient(X, Y, W1)))) | ((~quotient(identity, idQa, idQ_idQa)) | less_equal(idQ__idQ_idQa, idQa) | (~quotient(identity, idQ_idQa, idQ__idQ_idQa)) | (~less_equal(idQ_idQa, idQ_idQa)))) <=> ((~![Z: $i, Y: $i, W2: $i, W1: $i, X: $i] : (less_equal(W2, Y) | (~quotient(X, Z, W2)) | (~less_equal(W1, Z)) | (~quotient(X, Y, W1)))) | (~quotient(identity, idQa, idQ_idQa)) | less_equal(idQ__idQ_idQa, idQa) | (~quotient(identity, idQ_idQa, idQ__idQ_idQa)) | (~less_equal(idQ_idQa, idQ_idQa)))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(84,plain,
% 0.20/0.43 ((less_equal(idQ__idQ_idQa, idQa) | (~quotient(identity, idQ_idQa, idQ__idQ_idQa)) | (~less_equal(idQ_idQa, idQ_idQa)) | (~quotient(identity, idQa, idQ_idQa))) <=> ((~quotient(identity, idQa, idQ_idQa)) | less_equal(idQ__idQ_idQa, idQa) | (~quotient(identity, idQ_idQa, idQ__idQ_idQa)) | (~less_equal(idQ_idQa, idQ_idQa)))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(85,plain,
% 0.20/0.43 (((~![Z: $i, Y: $i, W2: $i, W1: $i, X: $i] : (less_equal(W2, Y) | (~quotient(X, Z, W2)) | (~less_equal(W1, Z)) | (~quotient(X, Y, W1)))) | (less_equal(idQ__idQ_idQa, idQa) | (~quotient(identity, idQ_idQa, idQ__idQ_idQa)) | (~less_equal(idQ_idQa, idQ_idQa)) | (~quotient(identity, idQa, idQ_idQa)))) <=> ((~![Z: $i, Y: $i, W2: $i, W1: $i, X: $i] : (less_equal(W2, Y) | (~quotient(X, Z, W2)) | (~less_equal(W1, Z)) | (~quotient(X, Y, W1)))) | ((~quotient(identity, idQa, idQ_idQa)) | less_equal(idQ__idQ_idQa, idQa) | (~quotient(identity, idQ_idQa, idQ__idQ_idQa)) | (~less_equal(idQ_idQa, idQ_idQa))))),
% 0.20/0.43 inference(monotonicity,[status(thm)],[84])).
% 0.20/0.43 tff(86,plain,
% 0.20/0.43 (((~![Z: $i, Y: $i, W2: $i, W1: $i, X: $i] : (less_equal(W2, Y) | (~quotient(X, Z, W2)) | (~less_equal(W1, Z)) | (~quotient(X, Y, W1)))) | (less_equal(idQ__idQ_idQa, idQa) | (~quotient(identity, idQ_idQa, idQ__idQ_idQa)) | (~less_equal(idQ_idQa, idQ_idQa)) | (~quotient(identity, idQa, idQ_idQa)))) <=> ((~![Z: $i, Y: $i, W2: $i, W1: $i, X: $i] : (less_equal(W2, Y) | (~quotient(X, Z, W2)) | (~less_equal(W1, Z)) | (~quotient(X, Y, W1)))) | (~quotient(identity, idQa, idQ_idQa)) | less_equal(idQ__idQ_idQa, idQa) | (~quotient(identity, idQ_idQa, idQ__idQ_idQa)) | (~less_equal(idQ_idQa, idQ_idQa)))),
% 0.20/0.43 inference(transitivity,[status(thm)],[85, 83])).
% 0.20/0.43 tff(87,plain,
% 0.20/0.43 ((~![Z: $i, Y: $i, W2: $i, W1: $i, X: $i] : (less_equal(W2, Y) | (~quotient(X, Z, W2)) | (~less_equal(W1, Z)) | (~quotient(X, Y, W1)))) | (less_equal(idQ__idQ_idQa, idQa) | (~quotient(identity, idQ_idQa, idQ__idQ_idQa)) | (~less_equal(idQ_idQa, idQ_idQa)) | (~quotient(identity, idQa, idQ_idQa)))),
% 0.20/0.43 inference(quant_inst,[status(thm)],[])).
% 0.20/0.43 tff(88,plain,
% 0.20/0.43 ((~![Z: $i, Y: $i, W2: $i, W1: $i, X: $i] : (less_equal(W2, Y) | (~quotient(X, Z, W2)) | (~less_equal(W1, Z)) | (~quotient(X, Y, W1)))) | (~quotient(identity, idQa, idQ_idQa)) | less_equal(idQ__idQ_idQa, idQa) | (~quotient(identity, idQ_idQa, idQ__idQ_idQa)) | (~less_equal(idQ_idQa, idQ_idQa))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[87, 86])).
% 0.20/0.43 tff(89,plain,
% 0.20/0.43 (less_equal(idQ__idQ_idQa, idQa) | (~less_equal(idQ_idQa, idQ_idQa))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[88, 45, 35, 56])).
% 0.20/0.43 tff(90,plain,
% 0.20/0.43 (less_equal(idQ__idQ_idQa, idQa)),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[89, 82])).
% 0.20/0.43 tff(91,plain,
% 0.20/0.43 ((~(idQa = idQ__idQ_idQa)) <=> (~(idQa = idQ__idQ_idQa))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(92,axiom,(~(idQa = idQ__idQ_idQa)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_one_inversion_equals_three')).
% 0.20/0.43 tff(93,plain,
% 0.20/0.43 (~(idQa = idQ__idQ_idQa)),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[92, 91])).
% 0.20/0.43 tff(94,plain,
% 0.20/0.43 (![Y: $i, X: $i] : ((~less_equal(X, Y)) | (X = Y) | (~less_equal(Y, X))) <=> ![Y: $i, X: $i] : ((~less_equal(X, Y)) | (X = Y) | (~less_equal(Y, X)))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(95,plain,
% 0.20/0.43 (![Y: $i, X: $i] : ((~less_equal(X, Y)) | (X = Y) | (~less_equal(Y, X))) <=> ![Y: $i, X: $i] : ((~less_equal(X, Y)) | (X = Y) | (~less_equal(Y, X)))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(96,plain,
% 0.20/0.43 (^[Y: $i, X: $i] : rewrite((((~less_equal(X, Y)) | (~less_equal(Y, X))) | (X = Y)) <=> ((~less_equal(X, Y)) | (X = Y) | (~less_equal(Y, X))))),
% 0.20/0.43 inference(bind,[status(th)],[])).
% 0.20/0.43 tff(97,plain,
% 0.20/0.43 (![Y: $i, X: $i] : (((~less_equal(X, Y)) | (~less_equal(Y, X))) | (X = Y)) <=> ![Y: $i, X: $i] : ((~less_equal(X, Y)) | (X = Y) | (~less_equal(Y, X)))),
% 0.20/0.43 inference(quant_intro,[status(thm)],[96])).
% 0.20/0.43 tff(98,axiom,(![Y: $i, X: $i] : (((~less_equal(X, Y)) | (~less_equal(Y, X))) | (X = Y))), file('/export/starexec/sandbox/benchmark/Axioms/HEN001-0.ax','less_equal_and_equal')).
% 0.20/0.43 tff(99,plain,
% 0.20/0.43 (![Y: $i, X: $i] : ((~less_equal(X, Y)) | (X = Y) | (~less_equal(Y, X)))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[98, 97])).
% 0.20/0.43 tff(100,plain,
% 0.20/0.43 (![Y: $i, X: $i] : ((~less_equal(X, Y)) | (X = Y) | (~less_equal(Y, X)))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[99, 95])).
% 0.20/0.43 tff(101,plain,(
% 0.20/0.43 ![Y: $i, X: $i] : ((~less_equal(X, Y)) | (X = Y) | (~less_equal(Y, X)))),
% 0.20/0.43 inference(skolemize,[status(sab)],[100])).
% 0.20/0.43 tff(102,plain,
% 0.20/0.43 (![Y: $i, X: $i] : ((~less_equal(X, Y)) | (X = Y) | (~less_equal(Y, X)))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[101, 94])).
% 0.20/0.43 tff(103,plain,
% 0.20/0.43 (((~![Y: $i, X: $i] : ((~less_equal(X, Y)) | (X = Y) | (~less_equal(Y, X)))) | ((idQa = idQ__idQ_idQa) | (~less_equal(idQ__idQ_idQa, idQa)) | (~less_equal(idQa, idQ__idQ_idQa)))) <=> ((~![Y: $i, X: $i] : ((~less_equal(X, Y)) | (X = Y) | (~less_equal(Y, X)))) | (idQa = idQ__idQ_idQa) | (~less_equal(idQ__idQ_idQa, idQa)) | (~less_equal(idQa, idQ__idQ_idQa)))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(104,plain,
% 0.20/0.43 (((~less_equal(idQa, idQ__idQ_idQa)) | (idQa = idQ__idQ_idQa) | (~less_equal(idQ__idQ_idQa, idQa))) <=> ((idQa = idQ__idQ_idQa) | (~less_equal(idQ__idQ_idQa, idQa)) | (~less_equal(idQa, idQ__idQ_idQa)))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(105,plain,
% 0.20/0.43 (((~![Y: $i, X: $i] : ((~less_equal(X, Y)) | (X = Y) | (~less_equal(Y, X)))) | ((~less_equal(idQa, idQ__idQ_idQa)) | (idQa = idQ__idQ_idQa) | (~less_equal(idQ__idQ_idQa, idQa)))) <=> ((~![Y: $i, X: $i] : ((~less_equal(X, Y)) | (X = Y) | (~less_equal(Y, X)))) | ((idQa = idQ__idQ_idQa) | (~less_equal(idQ__idQ_idQa, idQa)) | (~less_equal(idQa, idQ__idQ_idQa))))),
% 0.20/0.43 inference(monotonicity,[status(thm)],[104])).
% 0.20/0.43 tff(106,plain,
% 0.20/0.43 (((~![Y: $i, X: $i] : ((~less_equal(X, Y)) | (X = Y) | (~less_equal(Y, X)))) | ((~less_equal(idQa, idQ__idQ_idQa)) | (idQa = idQ__idQ_idQa) | (~less_equal(idQ__idQ_idQa, idQa)))) <=> ((~![Y: $i, X: $i] : ((~less_equal(X, Y)) | (X = Y) | (~less_equal(Y, X)))) | (idQa = idQ__idQ_idQa) | (~less_equal(idQ__idQ_idQa, idQa)) | (~less_equal(idQa, idQ__idQ_idQa)))),
% 0.20/0.43 inference(transitivity,[status(thm)],[105, 103])).
% 0.20/0.43 tff(107,plain,
% 0.20/0.43 ((~![Y: $i, X: $i] : ((~less_equal(X, Y)) | (X = Y) | (~less_equal(Y, X)))) | ((~less_equal(idQa, idQ__idQ_idQa)) | (idQa = idQ__idQ_idQa) | (~less_equal(idQ__idQ_idQa, idQa)))),
% 0.20/0.43 inference(quant_inst,[status(thm)],[])).
% 0.20/0.43 tff(108,plain,
% 0.20/0.43 ((~![Y: $i, X: $i] : ((~less_equal(X, Y)) | (X = Y) | (~less_equal(Y, X)))) | (idQa = idQ__idQ_idQa) | (~less_equal(idQ__idQ_idQa, idQa)) | (~less_equal(idQa, idQ__idQ_idQa))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[107, 106])).
% 0.20/0.43 tff(109,plain,
% 0.20/0.43 ($false),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[108, 102, 93, 90, 74])).
% 0.20/0.43 % SZS output end Proof
%------------------------------------------------------------------------------