TSTP Solution File: HEN010-7 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : HEN010-7 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n008.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 22:39:55 EDT 2022
% Result : Unsatisfiable 1.04s 0.91s
% Output : Proof 1.09s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : HEN010-7 : TPTP v8.1.0. Released v1.0.0.
% 0.12/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n008.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Wed Aug 31 21:53:10 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.35 Usage: tptp [options] [-file:]file
% 0.13/0.35 -h, -? prints this message.
% 0.13/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.35 -m, -model generate model.
% 0.13/0.35 -p, -proof generate proof.
% 0.13/0.35 -c, -core generate unsat core of named formulas.
% 0.13/0.35 -st, -statistics display statistics.
% 0.13/0.35 -t:timeout set timeout (in second).
% 0.13/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.35 -<param>:<value> configuration parameter and value.
% 0.13/0.35 -o:<output-file> file to place output in.
% 1.04/0.91 % SZS status Unsatisfiable
% 1.04/0.91 % SZS output start Proof
% 1.04/0.91 tff(less_equal_type, type, (
% 1.04/0.91 less_equal: ( $i * $i ) > $o)).
% 1.04/0.91 tff(idQa_Q__idQ_idQa_type, type, (
% 1.04/0.91 idQa_Q__idQ_idQa: $i)).
% 1.04/0.91 tff(idQa_type, type, (
% 1.04/0.91 idQa: $i)).
% 1.04/0.91 tff(quotient_type, type, (
% 1.04/0.91 quotient: ( $i * $i * $i ) > $o)).
% 1.04/0.91 tff(divide_type, type, (
% 1.04/0.91 divide: ( $i * $i ) > $i)).
% 1.04/0.91 tff(identity_type, type, (
% 1.04/0.91 identity: $i)).
% 1.04/0.91 tff(idQ_idQa_type, type, (
% 1.04/0.91 idQ_idQa: $i)).
% 1.04/0.91 tff(a_type, type, (
% 1.04/0.91 a: $i)).
% 1.04/0.91 tff(zero_type, type, (
% 1.04/0.91 zero: $i)).
% 1.04/0.91 tff(1,plain,
% 1.04/0.91 (^[Y: $i, X: $i] : refl(quotient(X, Y, divide(X, Y)) <=> quotient(X, Y, divide(X, Y)))),
% 1.04/0.91 inference(bind,[status(th)],[])).
% 1.04/0.91 tff(2,plain,
% 1.04/0.91 (![Y: $i, X: $i] : quotient(X, Y, divide(X, Y)) <=> ![Y: $i, X: $i] : quotient(X, Y, divide(X, Y))),
% 1.04/0.91 inference(quant_intro,[status(thm)],[1])).
% 1.04/0.91 tff(3,plain,
% 1.04/0.91 (![Y: $i, X: $i] : quotient(X, Y, divide(X, Y)) <=> ![Y: $i, X: $i] : quotient(X, Y, divide(X, Y))),
% 1.04/0.91 inference(rewrite,[status(thm)],[])).
% 1.04/0.91 tff(4,axiom,(![Y: $i, X: $i] : quotient(X, Y, divide(X, Y))), file('/export/starexec/sandbox2/benchmark/Axioms/HEN001-0.ax','closure')).
% 1.04/0.91 tff(5,plain,
% 1.04/0.91 (![Y: $i, X: $i] : quotient(X, Y, divide(X, Y))),
% 1.04/0.91 inference(modus_ponens,[status(thm)],[4, 3])).
% 1.04/0.91 tff(6,plain,(
% 1.04/0.91 ![Y: $i, X: $i] : quotient(X, Y, divide(X, Y))),
% 1.04/0.91 inference(skolemize,[status(sab)],[5])).
% 1.04/0.91 tff(7,plain,
% 1.04/0.91 (![Y: $i, X: $i] : quotient(X, Y, divide(X, Y))),
% 1.04/0.91 inference(modus_ponens,[status(thm)],[6, 2])).
% 1.04/0.91 tff(8,plain,
% 1.04/0.91 ((~![Y: $i, X: $i] : quotient(X, Y, divide(X, Y))) | quotient(identity, divide(idQ_idQa, divide(idQa, identity)), divide(identity, divide(idQ_idQa, divide(idQa, identity))))),
% 1.04/0.91 inference(quant_inst,[status(thm)],[])).
% 1.04/0.91 tff(9,plain,
% 1.04/0.91 (quotient(identity, divide(idQ_idQa, divide(idQa, identity)), divide(identity, divide(idQ_idQa, divide(idQa, identity))))),
% 1.04/0.91 inference(unit_resolution,[status(thm)],[8, 7])).
% 1.04/0.91 tff(10,plain,
% 1.04/0.91 ((~![Y: $i, X: $i] : quotient(X, Y, divide(X, Y))) | quotient(idQ_idQa, divide(idQa, identity), divide(idQ_idQa, divide(idQa, identity)))),
% 1.04/0.91 inference(quant_inst,[status(thm)],[])).
% 1.04/0.91 tff(11,plain,
% 1.04/0.91 (quotient(idQ_idQa, divide(idQa, identity), divide(idQ_idQa, divide(idQa, identity)))),
% 1.04/0.91 inference(unit_resolution,[status(thm)],[10, 7])).
% 1.04/0.91 tff(12,plain,
% 1.04/0.91 (^[Z: $i, Y: $i, X: $i] : refl(((~quotient(X, Y, Z)) | less_equal(Z, X)) <=> ((~quotient(X, Y, Z)) | less_equal(Z, X)))),
% 1.04/0.91 inference(bind,[status(th)],[])).
% 1.04/0.91 tff(13,plain,
% 1.04/0.91 (![Z: $i, Y: $i, X: $i] : ((~quotient(X, Y, Z)) | less_equal(Z, X)) <=> ![Z: $i, Y: $i, X: $i] : ((~quotient(X, Y, Z)) | less_equal(Z, X))),
% 1.04/0.91 inference(quant_intro,[status(thm)],[12])).
% 1.04/0.91 tff(14,plain,
% 1.04/0.91 (![Z: $i, Y: $i, X: $i] : ((~quotient(X, Y, Z)) | less_equal(Z, X)) <=> ![Z: $i, Y: $i, X: $i] : ((~quotient(X, Y, Z)) | less_equal(Z, X))),
% 1.04/0.91 inference(rewrite,[status(thm)],[])).
% 1.04/0.91 tff(15,axiom,(![Z: $i, Y: $i, X: $i] : ((~quotient(X, Y, Z)) | less_equal(Z, X))), file('/export/starexec/sandbox2/benchmark/Axioms/HEN001-0.ax','divisor_existence')).
% 1.04/0.91 tff(16,plain,
% 1.04/0.91 (![Z: $i, Y: $i, X: $i] : ((~quotient(X, Y, Z)) | less_equal(Z, X))),
% 1.04/0.91 inference(modus_ponens,[status(thm)],[15, 14])).
% 1.04/0.91 tff(17,plain,(
% 1.04/0.91 ![Z: $i, Y: $i, X: $i] : ((~quotient(X, Y, Z)) | less_equal(Z, X))),
% 1.04/0.91 inference(skolemize,[status(sab)],[16])).
% 1.04/0.91 tff(18,plain,
% 1.04/0.91 (![Z: $i, Y: $i, X: $i] : ((~quotient(X, Y, Z)) | less_equal(Z, X))),
% 1.04/0.91 inference(modus_ponens,[status(thm)],[17, 13])).
% 1.04/0.91 tff(19,plain,
% 1.04/0.91 (((~![Z: $i, Y: $i, X: $i] : ((~quotient(X, Y, Z)) | less_equal(Z, X))) | ((~quotient(idQ_idQa, divide(idQa, identity), divide(idQ_idQa, divide(idQa, identity)))) | less_equal(divide(idQ_idQa, divide(idQa, identity)), idQ_idQa))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~quotient(X, Y, Z)) | less_equal(Z, X))) | (~quotient(idQ_idQa, divide(idQa, identity), divide(idQ_idQa, divide(idQa, identity)))) | less_equal(divide(idQ_idQa, divide(idQa, identity)), idQ_idQa))),
% 1.04/0.91 inference(rewrite,[status(thm)],[])).
% 1.04/0.91 tff(20,plain,
% 1.04/0.91 ((~![Z: $i, Y: $i, X: $i] : ((~quotient(X, Y, Z)) | less_equal(Z, X))) | ((~quotient(idQ_idQa, divide(idQa, identity), divide(idQ_idQa, divide(idQa, identity)))) | less_equal(divide(idQ_idQa, divide(idQa, identity)), idQ_idQa))),
% 1.04/0.91 inference(quant_inst,[status(thm)],[])).
% 1.04/0.91 tff(21,plain,
% 1.04/0.91 ((~![Z: $i, Y: $i, X: $i] : ((~quotient(X, Y, Z)) | less_equal(Z, X))) | (~quotient(idQ_idQa, divide(idQa, identity), divide(idQ_idQa, divide(idQa, identity)))) | less_equal(divide(idQ_idQa, divide(idQa, identity)), idQ_idQa)),
% 1.04/0.91 inference(modus_ponens,[status(thm)],[20, 19])).
% 1.04/0.91 tff(22,plain,
% 1.04/0.91 (less_equal(divide(idQ_idQa, divide(idQa, identity)), idQ_idQa)),
% 1.04/0.91 inference(unit_resolution,[status(thm)],[21, 18, 11])).
% 1.04/0.91 tff(23,assumption,(~less_equal(identity, identity)), introduced(assumption)).
% 1.04/0.91 tff(24,plain,
% 1.04/0.91 (^[X: $i] : refl(less_equal(X, identity) <=> less_equal(X, identity))),
% 1.04/0.91 inference(bind,[status(th)],[])).
% 1.04/0.91 tff(25,plain,
% 1.04/0.91 (![X: $i] : less_equal(X, identity) <=> ![X: $i] : less_equal(X, identity)),
% 1.04/0.91 inference(quant_intro,[status(thm)],[24])).
% 1.04/0.91 tff(26,plain,
% 1.04/0.91 (![X: $i] : less_equal(X, identity) <=> ![X: $i] : less_equal(X, identity)),
% 1.04/0.91 inference(rewrite,[status(thm)],[])).
% 1.04/0.91 tff(27,axiom,(![X: $i] : less_equal(X, identity)), file('/export/starexec/sandbox2/benchmark/Axioms/HEN001-0.ax','identity_is_largest')).
% 1.04/0.91 tff(28,plain,
% 1.04/0.91 (![X: $i] : less_equal(X, identity)),
% 1.04/0.91 inference(modus_ponens,[status(thm)],[27, 26])).
% 1.04/0.91 tff(29,plain,(
% 1.04/0.91 ![X: $i] : less_equal(X, identity)),
% 1.04/0.91 inference(skolemize,[status(sab)],[28])).
% 1.04/0.91 tff(30,plain,
% 1.04/0.91 (![X: $i] : less_equal(X, identity)),
% 1.04/0.91 inference(modus_ponens,[status(thm)],[29, 25])).
% 1.04/0.91 tff(31,plain,
% 1.04/0.91 ((~![X: $i] : less_equal(X, identity)) | less_equal(identity, identity)),
% 1.04/0.91 inference(quant_inst,[status(thm)],[])).
% 1.04/0.91 tff(32,plain,
% 1.04/0.91 ($false),
% 1.04/0.91 inference(unit_resolution,[status(thm)],[31, 30, 23])).
% 1.04/0.91 tff(33,plain,(less_equal(identity, identity)), inference(lemma,lemma(discharge,[]))).
% 1.04/0.91 tff(34,plain,
% 1.04/0.91 (quotient(identity, a, idQa) <=> quotient(identity, a, idQa)),
% 1.04/0.91 inference(rewrite,[status(thm)],[])).
% 1.04/0.91 tff(35,axiom,(quotient(identity, a, idQa)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','identity_divide_a')).
% 1.04/0.91 tff(36,plain,
% 1.04/0.91 (quotient(identity, a, idQa)),
% 1.04/0.91 inference(modus_ponens,[status(thm)],[35, 34])).
% 1.04/0.91 tff(37,plain,
% 1.04/0.91 (^[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))))),
% 1.04/0.91 inference(bind,[status(th)],[])).
% 1.04/0.91 tff(38,plain,
% 1.04/0.91 (![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)))),
% 1.04/0.91 inference(quant_intro,[status(thm)],[37])).
% 1.04/0.91 tff(39,plain,
% 1.04/0.91 (![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)))),
% 1.04/0.91 inference(rewrite,[status(thm)],[])).
% 1.04/0.91 tff(40,plain,
% 1.04/0.91 (^[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)))))),
% 1.04/0.91 inference(bind,[status(th)],[])).
% 1.04/0.91 tff(41,plain,
% 1.04/0.91 (![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)))),
% 1.04/0.91 inference(quant_intro,[status(thm)],[40])).
% 1.04/0.91 tff(42,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/sandbox2/benchmark/theBenchmark.p','xLEy_implies_xQzLEyQz')).
% 1.04/0.91 tff(43,plain,
% 1.04/0.91 (![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)))),
% 1.04/0.91 inference(modus_ponens,[status(thm)],[42, 41])).
% 1.04/0.91 tff(44,plain,
% 1.04/0.91 (![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)))),
% 1.04/0.91 inference(modus_ponens,[status(thm)],[43, 39])).
% 1.04/0.91 tff(45,plain,(
% 1.04/0.91 ![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)))),
% 1.04/0.91 inference(skolemize,[status(sab)],[44])).
% 1.04/0.91 tff(46,plain,
% 1.04/0.91 (![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)))),
% 1.04/0.91 inference(modus_ponens,[status(thm)],[45, 38])).
% 1.04/0.91 tff(47,plain,
% 1.04/0.91 (((~![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)))),
% 1.04/0.91 inference(rewrite,[status(thm)],[])).
% 1.04/0.91 tff(48,plain,
% 1.04/0.91 ((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)))),
% 1.04/0.91 inference(rewrite,[status(thm)],[])).
% 1.04/0.91 tff(49,plain,
% 1.04/0.91 (((~![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))))),
% 1.04/0.91 inference(monotonicity,[status(thm)],[48])).
% 1.04/0.91 tff(50,plain,
% 1.04/0.91 (((~![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)))),
% 1.04/0.91 inference(transitivity,[status(thm)],[49, 47])).
% 1.04/0.91 tff(51,plain,
% 1.04/0.91 ((~![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)))),
% 1.04/0.91 inference(quant_inst,[status(thm)],[])).
% 1.04/0.91 tff(52,plain,
% 1.04/0.91 ((~![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))),
% 1.04/0.91 inference(modus_ponens,[status(thm)],[51, 50])).
% 1.04/0.91 tff(53,plain,
% 1.04/0.91 (less_equal(idQa, idQa) | (~less_equal(identity, identity))),
% 1.04/0.91 inference(unit_resolution,[status(thm)],[52, 46, 36])).
% 1.04/0.91 tff(54,plain,
% 1.04/0.91 (less_equal(idQa, idQa)),
% 1.04/0.91 inference(unit_resolution,[status(thm)],[53, 33])).
% 1.04/0.91 tff(55,plain,
% 1.04/0.91 (quotient(identity, idQa, idQ_idQa) <=> quotient(identity, idQa, idQ_idQa)),
% 1.04/0.91 inference(rewrite,[status(thm)],[])).
% 1.04/0.91 tff(56,axiom,(quotient(identity, idQa, idQ_idQa)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','identity_divide_idQa')).
% 1.04/0.91 tff(57,plain,
% 1.04/0.91 (quotient(identity, idQa, idQ_idQa)),
% 1.04/0.91 inference(modus_ponens,[status(thm)],[56, 55])).
% 1.04/0.91 tff(58,plain,
% 1.04/0.91 (^[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))))),
% 1.04/0.91 inference(bind,[status(th)],[])).
% 1.04/0.91 tff(59,plain,
% 1.04/0.91 (![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)))),
% 1.04/0.91 inference(quant_intro,[status(thm)],[58])).
% 1.04/0.91 tff(60,plain,
% 1.04/0.91 (![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)))),
% 1.04/0.91 inference(rewrite,[status(thm)],[])).
% 1.04/0.91 tff(61,plain,
% 1.04/0.91 (^[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)))))),
% 1.04/0.91 inference(bind,[status(th)],[])).
% 1.04/0.91 tff(62,plain,
% 1.04/0.91 (![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)))),
% 1.04/0.91 inference(quant_intro,[status(thm)],[61])).
% 1.04/0.91 tff(63,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/sandbox2/benchmark/theBenchmark.p','xQyLEz_implies_xQzLEy')).
% 1.04/0.91 tff(64,plain,
% 1.04/0.91 (![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)))),
% 1.04/0.91 inference(modus_ponens,[status(thm)],[63, 62])).
% 1.04/0.91 tff(65,plain,
% 1.04/0.91 (![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)))),
% 1.04/0.91 inference(modus_ponens,[status(thm)],[64, 60])).
% 1.04/0.91 tff(66,plain,(
% 1.04/0.91 ![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)))),
% 1.04/0.91 inference(skolemize,[status(sab)],[65])).
% 1.04/0.91 tff(67,plain,
% 1.04/0.91 (![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)))),
% 1.04/0.91 inference(modus_ponens,[status(thm)],[66, 59])).
% 1.04/0.91 tff(68,plain,
% 1.04/0.91 (((~![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)))),
% 1.04/0.91 inference(rewrite,[status(thm)],[])).
% 1.04/0.91 tff(69,plain,
% 1.04/0.91 ((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)))),
% 1.04/0.91 inference(rewrite,[status(thm)],[])).
% 1.04/0.91 tff(70,plain,
% 1.04/0.91 (((~![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))))),
% 1.04/0.91 inference(monotonicity,[status(thm)],[69])).
% 1.04/0.91 tff(71,plain,
% 1.04/0.91 (((~![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)))),
% 1.04/0.91 inference(transitivity,[status(thm)],[70, 68])).
% 1.04/0.91 tff(72,plain,
% 1.04/0.91 ((~![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)))),
% 1.04/0.91 inference(quant_inst,[status(thm)],[])).
% 1.04/0.91 tff(73,plain,
% 1.04/0.91 ((~![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))),
% 1.04/0.91 inference(modus_ponens,[status(thm)],[72, 71])).
% 1.04/0.91 tff(74,plain,
% 1.04/0.91 (less_equal(idQ_idQa, a) | (~less_equal(idQa, idQa))),
% 1.04/0.91 inference(unit_resolution,[status(thm)],[73, 67, 36, 57])).
% 1.04/0.91 tff(75,plain,
% 1.04/0.91 (less_equal(idQ_idQa, a)),
% 1.04/0.91 inference(unit_resolution,[status(thm)],[74, 54])).
% 1.04/0.91 tff(76,plain,
% 1.04/0.91 (![Z: $i, Y: $i, X: $i] : ((~less_equal(X, Y)) | less_equal(X, Z) | (~less_equal(Y, Z))) <=> ![Z: $i, Y: $i, X: $i] : ((~less_equal(X, Y)) | less_equal(X, Z) | (~less_equal(Y, Z)))),
% 1.04/0.91 inference(rewrite,[status(thm)],[])).
% 1.04/0.91 tff(77,plain,
% 1.04/0.91 (![Z: $i, Y: $i, X: $i] : ((~less_equal(X, Y)) | less_equal(X, Z) | (~less_equal(Y, Z))) <=> ![Z: $i, Y: $i, X: $i] : ((~less_equal(X, Y)) | less_equal(X, Z) | (~less_equal(Y, Z)))),
% 1.04/0.91 inference(rewrite,[status(thm)],[])).
% 1.04/0.91 tff(78,plain,
% 1.04/0.91 (^[Z: $i, Y: $i, X: $i] : rewrite((((~less_equal(X, Y)) | (~less_equal(Y, Z))) | less_equal(X, Z)) <=> ((~less_equal(X, Y)) | less_equal(X, Z) | (~less_equal(Y, Z))))),
% 1.04/0.91 inference(bind,[status(th)],[])).
% 1.04/0.91 tff(79,plain,
% 1.04/0.91 (![Z: $i, Y: $i, X: $i] : (((~less_equal(X, Y)) | (~less_equal(Y, Z))) | less_equal(X, Z)) <=> ![Z: $i, Y: $i, X: $i] : ((~less_equal(X, Y)) | less_equal(X, Z) | (~less_equal(Y, Z)))),
% 1.04/0.91 inference(quant_intro,[status(thm)],[78])).
% 1.04/0.91 tff(80,axiom,(![Z: $i, Y: $i, X: $i] : (((~less_equal(X, Y)) | (~less_equal(Y, Z))) | less_equal(X, Z))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','transitivity_of_less_equal')).
% 1.04/0.92 tff(81,plain,
% 1.04/0.92 (![Z: $i, Y: $i, X: $i] : ((~less_equal(X, Y)) | less_equal(X, Z) | (~less_equal(Y, Z)))),
% 1.04/0.92 inference(modus_ponens,[status(thm)],[80, 79])).
% 1.04/0.92 tff(82,plain,
% 1.04/0.92 (![Z: $i, Y: $i, X: $i] : ((~less_equal(X, Y)) | less_equal(X, Z) | (~less_equal(Y, Z)))),
% 1.04/0.92 inference(modus_ponens,[status(thm)],[81, 77])).
% 1.04/0.92 tff(83,plain,(
% 1.04/0.92 ![Z: $i, Y: $i, X: $i] : ((~less_equal(X, Y)) | less_equal(X, Z) | (~less_equal(Y, Z)))),
% 1.04/0.92 inference(skolemize,[status(sab)],[82])).
% 1.04/0.92 tff(84,plain,
% 1.04/0.92 (![Z: $i, Y: $i, X: $i] : ((~less_equal(X, Y)) | less_equal(X, Z) | (~less_equal(Y, Z)))),
% 1.04/0.92 inference(modus_ponens,[status(thm)],[83, 76])).
% 1.04/0.92 tff(85,plain,
% 1.04/0.92 (((~![Z: $i, Y: $i, X: $i] : ((~less_equal(X, Y)) | less_equal(X, Z) | (~less_equal(Y, Z)))) | ((~less_equal(idQ_idQa, a)) | (~less_equal(divide(idQ_idQa, divide(idQa, identity)), idQ_idQa)) | less_equal(divide(idQ_idQa, divide(idQa, identity)), a))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~less_equal(X, Y)) | less_equal(X, Z) | (~less_equal(Y, Z)))) | (~less_equal(idQ_idQa, a)) | (~less_equal(divide(idQ_idQa, divide(idQa, identity)), idQ_idQa)) | less_equal(divide(idQ_idQa, divide(idQa, identity)), a))),
% 1.04/0.92 inference(rewrite,[status(thm)],[])).
% 1.04/0.92 tff(86,plain,
% 1.04/0.92 (((~less_equal(divide(idQ_idQa, divide(idQa, identity)), idQ_idQa)) | less_equal(divide(idQ_idQa, divide(idQa, identity)), a) | (~less_equal(idQ_idQa, a))) <=> ((~less_equal(idQ_idQa, a)) | (~less_equal(divide(idQ_idQa, divide(idQa, identity)), idQ_idQa)) | less_equal(divide(idQ_idQa, divide(idQa, identity)), a))),
% 1.04/0.92 inference(rewrite,[status(thm)],[])).
% 1.04/0.92 tff(87,plain,
% 1.04/0.92 (((~![Z: $i, Y: $i, X: $i] : ((~less_equal(X, Y)) | less_equal(X, Z) | (~less_equal(Y, Z)))) | ((~less_equal(divide(idQ_idQa, divide(idQa, identity)), idQ_idQa)) | less_equal(divide(idQ_idQa, divide(idQa, identity)), a) | (~less_equal(idQ_idQa, a)))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~less_equal(X, Y)) | less_equal(X, Z) | (~less_equal(Y, Z)))) | ((~less_equal(idQ_idQa, a)) | (~less_equal(divide(idQ_idQa, divide(idQa, identity)), idQ_idQa)) | less_equal(divide(idQ_idQa, divide(idQa, identity)), a)))),
% 1.04/0.92 inference(monotonicity,[status(thm)],[86])).
% 1.04/0.92 tff(88,plain,
% 1.04/0.92 (((~![Z: $i, Y: $i, X: $i] : ((~less_equal(X, Y)) | less_equal(X, Z) | (~less_equal(Y, Z)))) | ((~less_equal(divide(idQ_idQa, divide(idQa, identity)), idQ_idQa)) | less_equal(divide(idQ_idQa, divide(idQa, identity)), a) | (~less_equal(idQ_idQa, a)))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~less_equal(X, Y)) | less_equal(X, Z) | (~less_equal(Y, Z)))) | (~less_equal(idQ_idQa, a)) | (~less_equal(divide(idQ_idQa, divide(idQa, identity)), idQ_idQa)) | less_equal(divide(idQ_idQa, divide(idQa, identity)), a))),
% 1.04/0.92 inference(transitivity,[status(thm)],[87, 85])).
% 1.04/0.92 tff(89,plain,
% 1.04/0.92 ((~![Z: $i, Y: $i, X: $i] : ((~less_equal(X, Y)) | less_equal(X, Z) | (~less_equal(Y, Z)))) | ((~less_equal(divide(idQ_idQa, divide(idQa, identity)), idQ_idQa)) | less_equal(divide(idQ_idQa, divide(idQa, identity)), a) | (~less_equal(idQ_idQa, a)))),
% 1.04/0.92 inference(quant_inst,[status(thm)],[])).
% 1.04/0.92 tff(90,plain,
% 1.04/0.92 ((~![Z: $i, Y: $i, X: $i] : ((~less_equal(X, Y)) | less_equal(X, Z) | (~less_equal(Y, Z)))) | (~less_equal(idQ_idQa, a)) | (~less_equal(divide(idQ_idQa, divide(idQa, identity)), idQ_idQa)) | less_equal(divide(idQ_idQa, divide(idQa, identity)), a)),
% 1.04/0.92 inference(modus_ponens,[status(thm)],[89, 88])).
% 1.04/0.92 tff(91,plain,
% 1.04/0.92 (less_equal(divide(idQ_idQa, divide(idQa, identity)), a)),
% 1.04/0.92 inference(unit_resolution,[status(thm)],[90, 84, 75, 22])).
% 1.04/0.92 tff(92,plain,
% 1.04/0.92 (^[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))))),
% 1.04/0.92 inference(bind,[status(th)],[])).
% 1.04/0.92 tff(93,plain,
% 1.04/0.92 (![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)))),
% 1.04/0.92 inference(quant_intro,[status(thm)],[92])).
% 1.04/0.92 tff(94,plain,
% 1.04/0.92 (![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)))),
% 1.04/0.92 inference(rewrite,[status(thm)],[])).
% 1.04/0.92 tff(95,plain,
% 1.04/0.92 (^[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)))))),
% 1.04/0.92 inference(bind,[status(th)],[])).
% 1.04/0.92 tff(96,plain,
% 1.04/0.92 (![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)))),
% 1.04/0.92 inference(quant_intro,[status(thm)],[95])).
% 1.04/0.92 tff(97,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/sandbox2/benchmark/theBenchmark.p','xLEy_implies_zQyLEzQx')).
% 1.04/0.92 tff(98,plain,
% 1.04/0.92 (![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)))),
% 1.04/0.92 inference(modus_ponens,[status(thm)],[97, 96])).
% 1.04/0.92 tff(99,plain,
% 1.04/0.92 (![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)))),
% 1.04/0.92 inference(modus_ponens,[status(thm)],[98, 94])).
% 1.04/0.92 tff(100,plain,(
% 1.04/0.92 ![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)))),
% 1.04/0.92 inference(skolemize,[status(sab)],[99])).
% 1.04/0.92 tff(101,plain,
% 1.04/0.92 (![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)))),
% 1.04/0.92 inference(modus_ponens,[status(thm)],[100, 93])).
% 1.04/0.92 tff(102,plain,
% 1.04/0.92 (((~![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)) | less_equal(idQa, divide(identity, divide(idQ_idQa, divide(idQa, identity)))) | (~less_equal(divide(idQ_idQa, divide(idQa, identity)), a)) | (~quotient(identity, divide(idQ_idQa, divide(idQa, identity)), divide(identity, divide(idQ_idQa, divide(idQa, identity))))))) <=> ((~![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)) | less_equal(idQa, divide(identity, divide(idQ_idQa, divide(idQa, identity)))) | (~less_equal(divide(idQ_idQa, divide(idQa, identity)), a)) | (~quotient(identity, divide(idQ_idQa, divide(idQa, identity)), divide(identity, divide(idQ_idQa, divide(idQa, identity))))))),
% 1.04/0.92 inference(rewrite,[status(thm)],[])).
% 1.04/0.92 tff(103,plain,
% 1.04/0.92 ((less_equal(idQa, divide(identity, divide(idQ_idQa, divide(idQa, identity)))) | (~quotient(identity, divide(idQ_idQa, divide(idQa, identity)), divide(identity, divide(idQ_idQa, divide(idQa, identity))))) | (~quotient(identity, a, idQa)) | (~less_equal(divide(idQ_idQa, divide(idQa, identity)), a))) <=> ((~quotient(identity, a, idQa)) | less_equal(idQa, divide(identity, divide(idQ_idQa, divide(idQa, identity)))) | (~less_equal(divide(idQ_idQa, divide(idQa, identity)), a)) | (~quotient(identity, divide(idQ_idQa, divide(idQa, identity)), divide(identity, divide(idQ_idQa, divide(idQa, identity))))))),
% 1.04/0.92 inference(rewrite,[status(thm)],[])).
% 1.04/0.92 tff(104,plain,
% 1.04/0.92 (((~![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, divide(identity, divide(idQ_idQa, divide(idQa, identity)))) | (~quotient(identity, divide(idQ_idQa, divide(idQa, identity)), divide(identity, divide(idQ_idQa, divide(idQa, identity))))) | (~quotient(identity, a, idQa)) | (~less_equal(divide(idQ_idQa, divide(idQa, identity)), 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)) | less_equal(idQa, divide(identity, divide(idQ_idQa, divide(idQa, identity)))) | (~less_equal(divide(idQ_idQa, divide(idQa, identity)), a)) | (~quotient(identity, divide(idQ_idQa, divide(idQa, identity)), divide(identity, divide(idQ_idQa, divide(idQa, identity)))))))),
% 1.04/0.92 inference(monotonicity,[status(thm)],[103])).
% 1.04/0.92 tff(105,plain,
% 1.04/0.92 (((~![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, divide(identity, divide(idQ_idQa, divide(idQa, identity)))) | (~quotient(identity, divide(idQ_idQa, divide(idQa, identity)), divide(identity, divide(idQ_idQa, divide(idQa, identity))))) | (~quotient(identity, a, idQa)) | (~less_equal(divide(idQ_idQa, divide(idQa, identity)), 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)) | less_equal(idQa, divide(identity, divide(idQ_idQa, divide(idQa, identity)))) | (~less_equal(divide(idQ_idQa, divide(idQa, identity)), a)) | (~quotient(identity, divide(idQ_idQa, divide(idQa, identity)), divide(identity, divide(idQ_idQa, divide(idQa, identity))))))),
% 1.04/0.92 inference(transitivity,[status(thm)],[104, 102])).
% 1.04/0.92 tff(106,plain,
% 1.04/0.92 ((~![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, divide(identity, divide(idQ_idQa, divide(idQa, identity)))) | (~quotient(identity, divide(idQ_idQa, divide(idQa, identity)), divide(identity, divide(idQ_idQa, divide(idQa, identity))))) | (~quotient(identity, a, idQa)) | (~less_equal(divide(idQ_idQa, divide(idQa, identity)), a)))),
% 1.04/0.92 inference(quant_inst,[status(thm)],[])).
% 1.04/0.92 tff(107,plain,
% 1.04/0.92 ((~![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)) | less_equal(idQa, divide(identity, divide(idQ_idQa, divide(idQa, identity)))) | (~less_equal(divide(idQ_idQa, divide(idQa, identity)), a)) | (~quotient(identity, divide(idQ_idQa, divide(idQa, identity)), divide(identity, divide(idQ_idQa, divide(idQa, identity)))))),
% 1.04/0.92 inference(modus_ponens,[status(thm)],[106, 105])).
% 1.04/0.92 tff(108,plain,
% 1.04/0.92 (less_equal(idQa, divide(identity, divide(idQ_idQa, divide(idQa, identity))))),
% 1.04/0.92 inference(unit_resolution,[status(thm)],[107, 101, 36, 91, 9])).
% 1.04/0.92 tff(109,plain,
% 1.04/0.92 ((~![Y: $i, X: $i] : quotient(X, Y, divide(X, Y))) | quotient(idQa, identity, divide(idQa, identity))),
% 1.04/0.92 inference(quant_inst,[status(thm)],[])).
% 1.04/0.92 tff(110,plain,
% 1.04/0.92 (quotient(idQa, identity, divide(idQa, identity))),
% 1.04/0.92 inference(unit_resolution,[status(thm)],[109, 7])).
% 1.04/0.92 tff(111,plain,
% 1.04/0.92 (((~![Z: $i, Y: $i, X: $i] : ((~quotient(X, Y, Z)) | less_equal(Z, X))) | ((~quotient(identity, a, idQa)) | less_equal(idQa, identity))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~quotient(X, Y, Z)) | less_equal(Z, X))) | (~quotient(identity, a, idQa)) | less_equal(idQa, identity))),
% 1.04/0.92 inference(rewrite,[status(thm)],[])).
% 1.04/0.92 tff(112,plain,
% 1.04/0.92 ((~![Z: $i, Y: $i, X: $i] : ((~quotient(X, Y, Z)) | less_equal(Z, X))) | ((~quotient(identity, a, idQa)) | less_equal(idQa, identity))),
% 1.04/0.92 inference(quant_inst,[status(thm)],[])).
% 1.04/0.92 tff(113,plain,
% 1.04/0.92 ((~![Z: $i, Y: $i, X: $i] : ((~quotient(X, Y, Z)) | less_equal(Z, X))) | (~quotient(identity, a, idQa)) | less_equal(idQa, identity)),
% 1.04/0.92 inference(modus_ponens,[status(thm)],[112, 111])).
% 1.04/0.92 tff(114,plain,
% 1.04/0.92 (less_equal(idQa, identity)),
% 1.04/0.92 inference(unit_resolution,[status(thm)],[113, 18, 36])).
% 1.04/0.92 tff(115,plain,
% 1.04/0.92 (^[Y: $i, X: $i] : refl(((~less_equal(X, Y)) | quotient(X, Y, zero)) <=> ((~less_equal(X, Y)) | quotient(X, Y, zero)))),
% 1.04/0.92 inference(bind,[status(th)],[])).
% 1.04/0.92 tff(116,plain,
% 1.04/0.92 (![Y: $i, X: $i] : ((~less_equal(X, Y)) | quotient(X, Y, zero)) <=> ![Y: $i, X: $i] : ((~less_equal(X, Y)) | quotient(X, Y, zero))),
% 1.04/0.92 inference(quant_intro,[status(thm)],[115])).
% 1.04/0.92 tff(117,plain,
% 1.04/0.92 (![Y: $i, X: $i] : ((~less_equal(X, Y)) | quotient(X, Y, zero)) <=> ![Y: $i, X: $i] : ((~less_equal(X, Y)) | quotient(X, Y, zero))),
% 1.04/0.92 inference(rewrite,[status(thm)],[])).
% 1.04/0.92 tff(118,axiom,(![Y: $i, X: $i] : ((~less_equal(X, Y)) | quotient(X, Y, zero))), file('/export/starexec/sandbox2/benchmark/Axioms/HEN001-0.ax','quotient_less_equal')).
% 1.04/0.92 tff(119,plain,
% 1.04/0.92 (![Y: $i, X: $i] : ((~less_equal(X, Y)) | quotient(X, Y, zero))),
% 1.04/0.92 inference(modus_ponens,[status(thm)],[118, 117])).
% 1.04/0.92 tff(120,plain,(
% 1.04/0.92 ![Y: $i, X: $i] : ((~less_equal(X, Y)) | quotient(X, Y, zero))),
% 1.04/0.92 inference(skolemize,[status(sab)],[119])).
% 1.04/0.92 tff(121,plain,
% 1.04/0.92 (![Y: $i, X: $i] : ((~less_equal(X, Y)) | quotient(X, Y, zero))),
% 1.04/0.92 inference(modus_ponens,[status(thm)],[120, 116])).
% 1.04/0.92 tff(122,plain,
% 1.04/0.92 (((~![Y: $i, X: $i] : ((~less_equal(X, Y)) | quotient(X, Y, zero))) | ((~less_equal(idQa, identity)) | quotient(idQa, identity, zero))) <=> ((~![Y: $i, X: $i] : ((~less_equal(X, Y)) | quotient(X, Y, zero))) | (~less_equal(idQa, identity)) | quotient(idQa, identity, zero))),
% 1.04/0.92 inference(rewrite,[status(thm)],[])).
% 1.04/0.92 tff(123,plain,
% 1.04/0.92 ((~![Y: $i, X: $i] : ((~less_equal(X, Y)) | quotient(X, Y, zero))) | ((~less_equal(idQa, identity)) | quotient(idQa, identity, zero))),
% 1.04/0.92 inference(quant_inst,[status(thm)],[])).
% 1.04/0.92 tff(124,plain,
% 1.04/0.92 ((~![Y: $i, X: $i] : ((~less_equal(X, Y)) | quotient(X, Y, zero))) | (~less_equal(idQa, identity)) | quotient(idQa, identity, zero)),
% 1.04/0.92 inference(modus_ponens,[status(thm)],[123, 122])).
% 1.04/0.92 tff(125,plain,
% 1.04/0.92 (quotient(idQa, identity, zero)),
% 1.04/0.92 inference(unit_resolution,[status(thm)],[124, 121, 114])).
% 1.04/0.92 tff(126,plain,
% 1.04/0.92 (^[W: $i, Z: $i, Y: $i, X: $i] : refl(((~quotient(X, Y, Z)) | (Z = W) | (~quotient(X, Y, W))) <=> ((~quotient(X, Y, Z)) | (Z = W) | (~quotient(X, Y, W))))),
% 1.04/0.92 inference(bind,[status(th)],[])).
% 1.04/0.92 tff(127,plain,
% 1.04/0.92 (![W: $i, Z: $i, Y: $i, X: $i] : ((~quotient(X, Y, Z)) | (Z = W) | (~quotient(X, Y, W))) <=> ![W: $i, Z: $i, Y: $i, X: $i] : ((~quotient(X, Y, Z)) | (Z = W) | (~quotient(X, Y, W)))),
% 1.04/0.92 inference(quant_intro,[status(thm)],[126])).
% 1.04/0.92 tff(128,plain,
% 1.04/0.92 (![W: $i, Z: $i, Y: $i, X: $i] : ((~quotient(X, Y, Z)) | (Z = W) | (~quotient(X, Y, W))) <=> ![W: $i, Z: $i, Y: $i, X: $i] : ((~quotient(X, Y, Z)) | (Z = W) | (~quotient(X, Y, W)))),
% 1.04/0.92 inference(rewrite,[status(thm)],[])).
% 1.04/0.92 tff(129,plain,
% 1.04/0.92 (^[W: $i, Z: $i, Y: $i, X: $i] : rewrite((((~quotient(X, Y, Z)) | (~quotient(X, Y, W))) | (Z = W)) <=> ((~quotient(X, Y, Z)) | (Z = W) | (~quotient(X, Y, W))))),
% 1.04/0.92 inference(bind,[status(th)],[])).
% 1.04/0.92 tff(130,plain,
% 1.04/0.92 (![W: $i, Z: $i, Y: $i, X: $i] : (((~quotient(X, Y, Z)) | (~quotient(X, Y, W))) | (Z = W)) <=> ![W: $i, Z: $i, Y: $i, X: $i] : ((~quotient(X, Y, Z)) | (Z = W) | (~quotient(X, Y, W)))),
% 1.04/0.92 inference(quant_intro,[status(thm)],[129])).
% 1.04/0.92 tff(131,axiom,(![W: $i, Z: $i, Y: $i, X: $i] : (((~quotient(X, Y, Z)) | (~quotient(X, Y, W))) | (Z = W))), file('/export/starexec/sandbox2/benchmark/Axioms/HEN001-0.ax','well_defined')).
% 1.04/0.92 tff(132,plain,
% 1.04/0.92 (![W: $i, Z: $i, Y: $i, X: $i] : ((~quotient(X, Y, Z)) | (Z = W) | (~quotient(X, Y, W)))),
% 1.04/0.92 inference(modus_ponens,[status(thm)],[131, 130])).
% 1.04/0.92 tff(133,plain,
% 1.04/0.92 (![W: $i, Z: $i, Y: $i, X: $i] : ((~quotient(X, Y, Z)) | (Z = W) | (~quotient(X, Y, W)))),
% 1.04/0.92 inference(modus_ponens,[status(thm)],[132, 128])).
% 1.04/0.92 tff(134,plain,(
% 1.04/0.92 ![W: $i, Z: $i, Y: $i, X: $i] : ((~quotient(X, Y, Z)) | (Z = W) | (~quotient(X, Y, W)))),
% 1.04/0.92 inference(skolemize,[status(sab)],[133])).
% 1.04/0.92 tff(135,plain,
% 1.04/0.92 (![W: $i, Z: $i, Y: $i, X: $i] : ((~quotient(X, Y, Z)) | (Z = W) | (~quotient(X, Y, W)))),
% 1.04/0.92 inference(modus_ponens,[status(thm)],[134, 127])).
% 1.04/0.92 tff(136,plain,
% 1.04/0.92 (((~![W: $i, Z: $i, Y: $i, X: $i] : ((~quotient(X, Y, Z)) | (Z = W) | (~quotient(X, Y, W)))) | ((~quotient(idQa, identity, zero)) | (~quotient(idQa, identity, divide(idQa, identity))) | (zero = divide(idQa, identity)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : ((~quotient(X, Y, Z)) | (Z = W) | (~quotient(X, Y, W)))) | (~quotient(idQa, identity, zero)) | (~quotient(idQa, identity, divide(idQa, identity))) | (zero = divide(idQa, identity)))),
% 1.04/0.92 inference(rewrite,[status(thm)],[])).
% 1.04/0.92 tff(137,plain,
% 1.04/0.92 (((~quotient(idQa, identity, zero)) | (zero = divide(idQa, identity)) | (~quotient(idQa, identity, divide(idQa, identity)))) <=> ((~quotient(idQa, identity, zero)) | (~quotient(idQa, identity, divide(idQa, identity))) | (zero = divide(idQa, identity)))),
% 1.04/0.92 inference(rewrite,[status(thm)],[])).
% 1.04/0.92 tff(138,plain,
% 1.04/0.92 (((~![W: $i, Z: $i, Y: $i, X: $i] : ((~quotient(X, Y, Z)) | (Z = W) | (~quotient(X, Y, W)))) | ((~quotient(idQa, identity, zero)) | (zero = divide(idQa, identity)) | (~quotient(idQa, identity, divide(idQa, identity))))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : ((~quotient(X, Y, Z)) | (Z = W) | (~quotient(X, Y, W)))) | ((~quotient(idQa, identity, zero)) | (~quotient(idQa, identity, divide(idQa, identity))) | (zero = divide(idQa, identity))))),
% 1.04/0.92 inference(monotonicity,[status(thm)],[137])).
% 1.04/0.92 tff(139,plain,
% 1.04/0.92 (((~![W: $i, Z: $i, Y: $i, X: $i] : ((~quotient(X, Y, Z)) | (Z = W) | (~quotient(X, Y, W)))) | ((~quotient(idQa, identity, zero)) | (zero = divide(idQa, identity)) | (~quotient(idQa, identity, divide(idQa, identity))))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : ((~quotient(X, Y, Z)) | (Z = W) | (~quotient(X, Y, W)))) | (~quotient(idQa, identity, zero)) | (~quotient(idQa, identity, divide(idQa, identity))) | (zero = divide(idQa, identity)))),
% 1.04/0.92 inference(transitivity,[status(thm)],[138, 136])).
% 1.04/0.92 tff(140,plain,
% 1.04/0.92 ((~![W: $i, Z: $i, Y: $i, X: $i] : ((~quotient(X, Y, Z)) | (Z = W) | (~quotient(X, Y, W)))) | ((~quotient(idQa, identity, zero)) | (zero = divide(idQa, identity)) | (~quotient(idQa, identity, divide(idQa, identity))))),
% 1.04/0.92 inference(quant_inst,[status(thm)],[])).
% 1.04/0.92 tff(141,plain,
% 1.04/0.92 ((~![W: $i, Z: $i, Y: $i, X: $i] : ((~quotient(X, Y, Z)) | (Z = W) | (~quotient(X, Y, W)))) | (~quotient(idQa, identity, zero)) | (~quotient(idQa, identity, divide(idQa, identity))) | (zero = divide(idQa, identity))),
% 1.04/0.92 inference(modus_ponens,[status(thm)],[140, 139])).
% 1.04/0.92 tff(142,plain,
% 1.04/0.92 (zero = divide(idQa, identity)),
% 1.04/0.92 inference(unit_resolution,[status(thm)],[141, 135, 125, 110])).
% 1.04/0.92 tff(143,plain,
% 1.04/0.92 (divide(idQa, identity) = zero),
% 1.04/0.92 inference(symmetry,[status(thm)],[142])).
% 1.04/0.92 tff(144,plain,
% 1.04/0.92 (quotient(idQ_idQa, divide(idQa, identity), idQ_idQa) <=> quotient(idQ_idQa, zero, idQ_idQa)),
% 1.04/0.92 inference(monotonicity,[status(thm)],[143])).
% 1.04/0.92 tff(145,plain,
% 1.04/0.92 (quotient(idQ_idQa, zero, idQ_idQa) <=> quotient(idQ_idQa, divide(idQa, identity), idQ_idQa)),
% 1.04/0.92 inference(symmetry,[status(thm)],[144])).
% 1.04/0.92 tff(146,plain,
% 1.04/0.92 (^[X: $i] : refl(quotient(X, zero, X) <=> quotient(X, zero, X))),
% 1.04/0.92 inference(bind,[status(th)],[])).
% 1.04/0.92 tff(147,plain,
% 1.04/0.92 (![X: $i] : quotient(X, zero, X) <=> ![X: $i] : quotient(X, zero, X)),
% 1.04/0.92 inference(quant_intro,[status(thm)],[146])).
% 1.04/0.92 tff(148,plain,
% 1.04/0.92 (![X: $i] : quotient(X, zero, X) <=> ![X: $i] : quotient(X, zero, X)),
% 1.04/0.92 inference(rewrite,[status(thm)],[])).
% 1.04/0.92 tff(149,axiom,(![X: $i] : quotient(X, zero, X)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','x_divde_zero_is_x')).
% 1.04/0.92 tff(150,plain,
% 1.04/0.92 (![X: $i] : quotient(X, zero, X)),
% 1.04/0.92 inference(modus_ponens,[status(thm)],[149, 148])).
% 1.04/0.92 tff(151,plain,(
% 1.04/0.92 ![X: $i] : quotient(X, zero, X)),
% 1.04/0.92 inference(skolemize,[status(sab)],[150])).
% 1.04/0.92 tff(152,plain,
% 1.04/0.92 (![X: $i] : quotient(X, zero, X)),
% 1.04/0.92 inference(modus_ponens,[status(thm)],[151, 147])).
% 1.04/0.92 tff(153,plain,
% 1.04/0.92 ((~![X: $i] : quotient(X, zero, X)) | quotient(idQ_idQa, zero, idQ_idQa)),
% 1.04/0.92 inference(quant_inst,[status(thm)],[])).
% 1.04/0.92 tff(154,plain,
% 1.04/0.92 (quotient(idQ_idQa, zero, idQ_idQa)),
% 1.04/0.92 inference(unit_resolution,[status(thm)],[153, 152])).
% 1.04/0.92 tff(155,plain,
% 1.04/0.92 (quotient(idQ_idQa, divide(idQa, identity), idQ_idQa)),
% 1.04/0.92 inference(modus_ponens,[status(thm)],[154, 145])).
% 1.04/0.92 tff(156,plain,
% 1.04/0.92 (((~![W: $i, Z: $i, Y: $i, X: $i] : ((~quotient(X, Y, Z)) | (Z = W) | (~quotient(X, Y, W)))) | ((~quotient(idQ_idQa, divide(idQa, identity), divide(idQ_idQa, divide(idQa, identity)))) | (idQ_idQa = divide(idQ_idQa, divide(idQa, identity))) | (~quotient(idQ_idQa, divide(idQa, identity), idQ_idQa)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : ((~quotient(X, Y, Z)) | (Z = W) | (~quotient(X, Y, W)))) | (~quotient(idQ_idQa, divide(idQa, identity), divide(idQ_idQa, divide(idQa, identity)))) | (idQ_idQa = divide(idQ_idQa, divide(idQa, identity))) | (~quotient(idQ_idQa, divide(idQa, identity), idQ_idQa)))),
% 1.04/0.92 inference(rewrite,[status(thm)],[])).
% 1.04/0.92 tff(157,plain,
% 1.04/0.92 (((~quotient(idQ_idQa, divide(idQa, identity), idQ_idQa)) | (idQ_idQa = divide(idQ_idQa, divide(idQa, identity))) | (~quotient(idQ_idQa, divide(idQa, identity), divide(idQ_idQa, divide(idQa, identity))))) <=> ((~quotient(idQ_idQa, divide(idQa, identity), divide(idQ_idQa, divide(idQa, identity)))) | (idQ_idQa = divide(idQ_idQa, divide(idQa, identity))) | (~quotient(idQ_idQa, divide(idQa, identity), idQ_idQa)))),
% 1.04/0.92 inference(rewrite,[status(thm)],[])).
% 1.04/0.92 tff(158,plain,
% 1.04/0.92 (((~![W: $i, Z: $i, Y: $i, X: $i] : ((~quotient(X, Y, Z)) | (Z = W) | (~quotient(X, Y, W)))) | ((~quotient(idQ_idQa, divide(idQa, identity), idQ_idQa)) | (idQ_idQa = divide(idQ_idQa, divide(idQa, identity))) | (~quotient(idQ_idQa, divide(idQa, identity), divide(idQ_idQa, divide(idQa, identity)))))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : ((~quotient(X, Y, Z)) | (Z = W) | (~quotient(X, Y, W)))) | ((~quotient(idQ_idQa, divide(idQa, identity), divide(idQ_idQa, divide(idQa, identity)))) | (idQ_idQa = divide(idQ_idQa, divide(idQa, identity))) | (~quotient(idQ_idQa, divide(idQa, identity), idQ_idQa))))),
% 1.04/0.92 inference(monotonicity,[status(thm)],[157])).
% 1.04/0.92 tff(159,plain,
% 1.04/0.92 (((~![W: $i, Z: $i, Y: $i, X: $i] : ((~quotient(X, Y, Z)) | (Z = W) | (~quotient(X, Y, W)))) | ((~quotient(idQ_idQa, divide(idQa, identity), idQ_idQa)) | (idQ_idQa = divide(idQ_idQa, divide(idQa, identity))) | (~quotient(idQ_idQa, divide(idQa, identity), divide(idQ_idQa, divide(idQa, identity)))))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : ((~quotient(X, Y, Z)) | (Z = W) | (~quotient(X, Y, W)))) | (~quotient(idQ_idQa, divide(idQa, identity), divide(idQ_idQa, divide(idQa, identity)))) | (idQ_idQa = divide(idQ_idQa, divide(idQa, identity))) | (~quotient(idQ_idQa, divide(idQa, identity), idQ_idQa)))),
% 1.04/0.92 inference(transitivity,[status(thm)],[158, 156])).
% 1.04/0.92 tff(160,plain,
% 1.04/0.92 ((~![W: $i, Z: $i, Y: $i, X: $i] : ((~quotient(X, Y, Z)) | (Z = W) | (~quotient(X, Y, W)))) | ((~quotient(idQ_idQa, divide(idQa, identity), idQ_idQa)) | (idQ_idQa = divide(idQ_idQa, divide(idQa, identity))) | (~quotient(idQ_idQa, divide(idQa, identity), divide(idQ_idQa, divide(idQa, identity)))))),
% 1.04/0.92 inference(quant_inst,[status(thm)],[])).
% 1.04/0.92 tff(161,plain,
% 1.04/0.92 ((~![W: $i, Z: $i, Y: $i, X: $i] : ((~quotient(X, Y, Z)) | (Z = W) | (~quotient(X, Y, W)))) | (~quotient(idQ_idQa, divide(idQa, identity), divide(idQ_idQa, divide(idQa, identity)))) | (idQ_idQa = divide(idQ_idQa, divide(idQa, identity))) | (~quotient(idQ_idQa, divide(idQa, identity), idQ_idQa))),
% 1.04/0.92 inference(modus_ponens,[status(thm)],[160, 159])).
% 1.04/0.92 tff(162,plain,
% 1.04/0.92 ((idQ_idQa = divide(idQ_idQa, divide(idQa, identity))) | (~quotient(idQ_idQa, divide(idQa, identity), idQ_idQa))),
% 1.04/0.92 inference(unit_resolution,[status(thm)],[161, 135, 11])).
% 1.04/0.92 tff(163,plain,
% 1.04/0.92 (idQ_idQa = divide(idQ_idQa, divide(idQa, identity))),
% 1.04/0.92 inference(unit_resolution,[status(thm)],[162, 155])).
% 1.04/0.92 tff(164,plain,
% 1.04/0.92 (divide(idQ_idQa, divide(idQa, identity)) = idQ_idQa),
% 1.04/0.92 inference(symmetry,[status(thm)],[163])).
% 1.04/0.92 tff(165,plain,
% 1.04/0.92 (quotient(identity, idQa, divide(idQ_idQa, divide(idQa, identity))) <=> quotient(identity, idQa, idQ_idQa)),
% 1.04/0.92 inference(monotonicity,[status(thm)],[164])).
% 1.04/0.92 tff(166,plain,
% 1.04/0.92 (quotient(identity, idQa, idQ_idQa) <=> quotient(identity, idQa, divide(idQ_idQa, divide(idQa, identity)))),
% 1.04/0.92 inference(symmetry,[status(thm)],[165])).
% 1.04/0.92 tff(167,plain,
% 1.04/0.92 (quotient(identity, idQa, divide(idQ_idQa, divide(idQa, identity)))),
% 1.04/0.92 inference(modus_ponens,[status(thm)],[57, 166])).
% 1.04/0.92 tff(168,plain,
% 1.04/0.92 (((~![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))),
% 1.04/0.92 inference(rewrite,[status(thm)],[])).
% 1.04/0.92 tff(169,plain,
% 1.04/0.92 ((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))),
% 1.04/0.92 inference(rewrite,[status(thm)],[])).
% 1.04/0.92 tff(170,plain,
% 1.04/0.92 (((~![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)))),
% 1.04/0.92 inference(monotonicity,[status(thm)],[169])).
% 1.04/0.92 tff(171,plain,
% 1.04/0.92 (((~![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))),
% 1.04/0.92 inference(transitivity,[status(thm)],[170, 168])).
% 1.04/0.92 tff(172,plain,
% 1.04/0.92 ((~![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)))),
% 1.04/0.92 inference(quant_inst,[status(thm)],[])).
% 1.04/0.92 tff(173,plain,
% 1.04/0.92 ((~![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)),
% 1.04/0.92 inference(modus_ponens,[status(thm)],[172, 171])).
% 1.04/0.92 tff(174,plain,
% 1.04/0.92 ((~less_equal(identity, identity)) | less_equal(idQ_idQa, idQ_idQa)),
% 1.04/0.92 inference(unit_resolution,[status(thm)],[173, 46, 57])).
% 1.04/0.92 tff(175,plain,
% 1.04/0.92 (less_equal(idQ_idQa, idQ_idQa)),
% 1.04/0.92 inference(unit_resolution,[status(thm)],[174, 33])).
% 1.04/0.92 tff(176,plain,
% 1.04/0.92 (((~![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)) | (~quotient(idQ_idQa, divide(idQa, identity), divide(idQ_idQa, divide(idQa, identity)))) | less_equal(divide(idQ_idQa, divide(idQa, identity)), divide(idQ_idQa, divide(idQa, identity))))) <=> ((~![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)) | (~quotient(idQ_idQa, divide(idQa, identity), divide(idQ_idQa, divide(idQa, identity)))) | less_equal(divide(idQ_idQa, divide(idQa, identity)), divide(idQ_idQa, divide(idQa, identity))))),
% 1.04/0.93 inference(rewrite,[status(thm)],[])).
% 1.04/0.93 tff(177,plain,
% 1.04/0.93 ((less_equal(divide(idQ_idQa, divide(idQa, identity)), divide(idQ_idQa, divide(idQa, identity))) | (~less_equal(idQ_idQa, idQ_idQa)) | (~quotient(idQ_idQa, divide(idQa, identity), divide(idQ_idQa, divide(idQa, identity)))) | (~quotient(idQ_idQa, divide(idQa, identity), divide(idQ_idQa, divide(idQa, identity))))) <=> ((~less_equal(idQ_idQa, idQ_idQa)) | (~quotient(idQ_idQa, divide(idQa, identity), divide(idQ_idQa, divide(idQa, identity)))) | less_equal(divide(idQ_idQa, divide(idQa, identity)), divide(idQ_idQa, divide(idQa, identity))))),
% 1.04/0.93 inference(rewrite,[status(thm)],[])).
% 1.04/0.93 tff(178,plain,
% 1.04/0.93 (((~![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(divide(idQ_idQa, divide(idQa, identity)), divide(idQ_idQa, divide(idQa, identity))) | (~less_equal(idQ_idQa, idQ_idQa)) | (~quotient(idQ_idQa, divide(idQa, identity), divide(idQ_idQa, divide(idQa, identity)))) | (~quotient(idQ_idQa, divide(idQa, identity), divide(idQ_idQa, divide(idQa, identity)))))) <=> ((~![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)) | (~quotient(idQ_idQa, divide(idQa, identity), divide(idQ_idQa, divide(idQa, identity)))) | less_equal(divide(idQ_idQa, divide(idQa, identity)), divide(idQ_idQa, divide(idQa, identity)))))),
% 1.04/0.93 inference(monotonicity,[status(thm)],[177])).
% 1.04/0.93 tff(179,plain,
% 1.04/0.93 (((~![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(divide(idQ_idQa, divide(idQa, identity)), divide(idQ_idQa, divide(idQa, identity))) | (~less_equal(idQ_idQa, idQ_idQa)) | (~quotient(idQ_idQa, divide(idQa, identity), divide(idQ_idQa, divide(idQa, identity)))) | (~quotient(idQ_idQa, divide(idQa, identity), divide(idQ_idQa, divide(idQa, identity)))))) <=> ((~![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)) | (~quotient(idQ_idQa, divide(idQa, identity), divide(idQ_idQa, divide(idQa, identity)))) | less_equal(divide(idQ_idQa, divide(idQa, identity)), divide(idQ_idQa, divide(idQa, identity))))),
% 1.04/0.93 inference(transitivity,[status(thm)],[178, 176])).
% 1.04/0.93 tff(180,plain,
% 1.04/0.93 ((~![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(divide(idQ_idQa, divide(idQa, identity)), divide(idQ_idQa, divide(idQa, identity))) | (~less_equal(idQ_idQa, idQ_idQa)) | (~quotient(idQ_idQa, divide(idQa, identity), divide(idQ_idQa, divide(idQa, identity)))) | (~quotient(idQ_idQa, divide(idQa, identity), divide(idQ_idQa, divide(idQa, identity)))))),
% 1.04/0.93 inference(quant_inst,[status(thm)],[])).
% 1.04/0.93 tff(181,plain,
% 1.04/0.93 ((~![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)) | (~quotient(idQ_idQa, divide(idQa, identity), divide(idQ_idQa, divide(idQa, identity)))) | less_equal(divide(idQ_idQa, divide(idQa, identity)), divide(idQ_idQa, divide(idQa, identity)))),
% 1.04/0.93 inference(modus_ponens,[status(thm)],[180, 179])).
% 1.04/0.93 tff(182,plain,
% 1.04/0.93 (less_equal(divide(idQ_idQa, divide(idQa, identity)), divide(idQ_idQa, divide(idQa, identity)))),
% 1.04/0.93 inference(unit_resolution,[status(thm)],[181, 46, 175, 11])).
% 1.04/0.93 tff(183,plain,
% 1.04/0.93 (((~![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(divide(identity, divide(idQ_idQa, divide(idQa, identity))), idQa) | (~less_equal(divide(idQ_idQa, divide(idQa, identity)), divide(idQ_idQa, divide(idQa, identity)))) | (~quotient(identity, idQa, divide(idQ_idQa, divide(idQa, identity)))) | (~quotient(identity, divide(idQ_idQa, divide(idQa, identity)), divide(identity, divide(idQ_idQa, divide(idQa, identity))))))) <=> ((~![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(divide(identity, divide(idQ_idQa, divide(idQa, identity))), idQa) | (~less_equal(divide(idQ_idQa, divide(idQa, identity)), divide(idQ_idQa, divide(idQa, identity)))) | (~quotient(identity, idQa, divide(idQ_idQa, divide(idQa, identity)))) | (~quotient(identity, divide(idQ_idQa, divide(idQa, identity)), divide(identity, divide(idQ_idQa, divide(idQa, identity))))))),
% 1.04/0.93 inference(rewrite,[status(thm)],[])).
% 1.04/0.93 tff(184,plain,
% 1.04/0.93 ((less_equal(divide(identity, divide(idQ_idQa, divide(idQa, identity))), idQa) | (~quotient(identity, divide(idQ_idQa, divide(idQa, identity)), divide(identity, divide(idQ_idQa, divide(idQa, identity))))) | (~less_equal(divide(idQ_idQa, divide(idQa, identity)), divide(idQ_idQa, divide(idQa, identity)))) | (~quotient(identity, idQa, divide(idQ_idQa, divide(idQa, identity))))) <=> (less_equal(divide(identity, divide(idQ_idQa, divide(idQa, identity))), idQa) | (~less_equal(divide(idQ_idQa, divide(idQa, identity)), divide(idQ_idQa, divide(idQa, identity)))) | (~quotient(identity, idQa, divide(idQ_idQa, divide(idQa, identity)))) | (~quotient(identity, divide(idQ_idQa, divide(idQa, identity)), divide(identity, divide(idQ_idQa, divide(idQa, identity))))))),
% 1.04/0.93 inference(rewrite,[status(thm)],[])).
% 1.04/0.93 tff(185,plain,
% 1.04/0.93 (((~![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(divide(identity, divide(idQ_idQa, divide(idQa, identity))), idQa) | (~quotient(identity, divide(idQ_idQa, divide(idQa, identity)), divide(identity, divide(idQ_idQa, divide(idQa, identity))))) | (~less_equal(divide(idQ_idQa, divide(idQa, identity)), divide(idQ_idQa, divide(idQa, identity)))) | (~quotient(identity, idQa, divide(idQ_idQa, divide(idQa, identity)))))) <=> ((~![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(divide(identity, divide(idQ_idQa, divide(idQa, identity))), idQa) | (~less_equal(divide(idQ_idQa, divide(idQa, identity)), divide(idQ_idQa, divide(idQa, identity)))) | (~quotient(identity, idQa, divide(idQ_idQa, divide(idQa, identity)))) | (~quotient(identity, divide(idQ_idQa, divide(idQa, identity)), divide(identity, divide(idQ_idQa, divide(idQa, identity)))))))),
% 1.04/0.93 inference(monotonicity,[status(thm)],[184])).
% 1.04/0.93 tff(186,plain,
% 1.04/0.93 (((~![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(divide(identity, divide(idQ_idQa, divide(idQa, identity))), idQa) | (~quotient(identity, divide(idQ_idQa, divide(idQa, identity)), divide(identity, divide(idQ_idQa, divide(idQa, identity))))) | (~less_equal(divide(idQ_idQa, divide(idQa, identity)), divide(idQ_idQa, divide(idQa, identity)))) | (~quotient(identity, idQa, divide(idQ_idQa, divide(idQa, identity)))))) <=> ((~![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(divide(identity, divide(idQ_idQa, divide(idQa, identity))), idQa) | (~less_equal(divide(idQ_idQa, divide(idQa, identity)), divide(idQ_idQa, divide(idQa, identity)))) | (~quotient(identity, idQa, divide(idQ_idQa, divide(idQa, identity)))) | (~quotient(identity, divide(idQ_idQa, divide(idQa, identity)), divide(identity, divide(idQ_idQa, divide(idQa, identity))))))),
% 1.04/0.93 inference(transitivity,[status(thm)],[185, 183])).
% 1.04/0.93 tff(187,plain,
% 1.04/0.93 ((~![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(divide(identity, divide(idQ_idQa, divide(idQa, identity))), idQa) | (~quotient(identity, divide(idQ_idQa, divide(idQa, identity)), divide(identity, divide(idQ_idQa, divide(idQa, identity))))) | (~less_equal(divide(idQ_idQa, divide(idQa, identity)), divide(idQ_idQa, divide(idQa, identity)))) | (~quotient(identity, idQa, divide(idQ_idQa, divide(idQa, identity)))))),
% 1.04/0.93 inference(quant_inst,[status(thm)],[])).
% 1.04/0.93 tff(188,plain,
% 1.04/0.93 ((~![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(divide(identity, divide(idQ_idQa, divide(idQa, identity))), idQa) | (~less_equal(divide(idQ_idQa, divide(idQa, identity)), divide(idQ_idQa, divide(idQa, identity)))) | (~quotient(identity, idQa, divide(idQ_idQa, divide(idQa, identity)))) | (~quotient(identity, divide(idQ_idQa, divide(idQa, identity)), divide(identity, divide(idQ_idQa, divide(idQa, identity)))))),
% 1.04/0.93 inference(modus_ponens,[status(thm)],[187, 186])).
% 1.04/0.93 tff(189,plain,
% 1.04/0.93 (less_equal(divide(identity, divide(idQ_idQa, divide(idQa, identity))), idQa)),
% 1.04/0.93 inference(unit_resolution,[status(thm)],[188, 67, 182, 167, 9])).
% 1.04/0.93 tff(190,plain,
% 1.04/0.93 (![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)))),
% 1.04/0.93 inference(rewrite,[status(thm)],[])).
% 1.04/0.93 tff(191,plain,
% 1.04/0.93 (![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)))),
% 1.04/0.93 inference(rewrite,[status(thm)],[])).
% 1.04/0.93 tff(192,plain,
% 1.04/0.93 (^[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))))),
% 1.04/0.93 inference(bind,[status(th)],[])).
% 1.04/0.93 tff(193,plain,
% 1.04/0.93 (![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)))),
% 1.04/0.93 inference(quant_intro,[status(thm)],[192])).
% 1.04/0.93 tff(194,axiom,(![Y: $i, X: $i] : (((~less_equal(X, Y)) | (~less_equal(Y, X))) | (X = Y))), file('/export/starexec/sandbox2/benchmark/Axioms/HEN001-0.ax','less_equal_and_equal')).
% 1.04/0.93 tff(195,plain,
% 1.04/0.93 (![Y: $i, X: $i] : ((~less_equal(X, Y)) | (X = Y) | (~less_equal(Y, X)))),
% 1.04/0.93 inference(modus_ponens,[status(thm)],[194, 193])).
% 1.04/0.93 tff(196,plain,
% 1.04/0.93 (![Y: $i, X: $i] : ((~less_equal(X, Y)) | (X = Y) | (~less_equal(Y, X)))),
% 1.04/0.93 inference(modus_ponens,[status(thm)],[195, 191])).
% 1.04/0.93 tff(197,plain,(
% 1.04/0.93 ![Y: $i, X: $i] : ((~less_equal(X, Y)) | (X = Y) | (~less_equal(Y, X)))),
% 1.04/0.93 inference(skolemize,[status(sab)],[196])).
% 1.04/0.93 tff(198,plain,
% 1.04/0.93 (![Y: $i, X: $i] : ((~less_equal(X, Y)) | (X = Y) | (~less_equal(Y, X)))),
% 1.04/0.93 inference(modus_ponens,[status(thm)],[197, 190])).
% 1.04/0.93 tff(199,plain,
% 1.04/0.93 (((~![Y: $i, X: $i] : ((~less_equal(X, Y)) | (X = Y) | (~less_equal(Y, X)))) | ((~less_equal(divide(identity, divide(idQ_idQa, divide(idQa, identity))), idQa)) | (~less_equal(idQa, divide(identity, divide(idQ_idQa, divide(idQa, identity))))) | (divide(identity, divide(idQ_idQa, divide(idQa, identity))) = idQa))) <=> ((~![Y: $i, X: $i] : ((~less_equal(X, Y)) | (X = Y) | (~less_equal(Y, X)))) | (~less_equal(divide(identity, divide(idQ_idQa, divide(idQa, identity))), idQa)) | (~less_equal(idQa, divide(identity, divide(idQ_idQa, divide(idQa, identity))))) | (divide(identity, divide(idQ_idQa, divide(idQa, identity))) = idQa))),
% 1.04/0.93 inference(rewrite,[status(thm)],[])).
% 1.04/0.93 tff(200,plain,
% 1.04/0.93 (((~less_equal(divide(identity, divide(idQ_idQa, divide(idQa, identity))), idQa)) | (divide(identity, divide(idQ_idQa, divide(idQa, identity))) = idQa) | (~less_equal(idQa, divide(identity, divide(idQ_idQa, divide(idQa, identity)))))) <=> ((~less_equal(divide(identity, divide(idQ_idQa, divide(idQa, identity))), idQa)) | (~less_equal(idQa, divide(identity, divide(idQ_idQa, divide(idQa, identity))))) | (divide(identity, divide(idQ_idQa, divide(idQa, identity))) = idQa))),
% 1.04/0.93 inference(rewrite,[status(thm)],[])).
% 1.04/0.93 tff(201,plain,
% 1.04/0.93 (((~![Y: $i, X: $i] : ((~less_equal(X, Y)) | (X = Y) | (~less_equal(Y, X)))) | ((~less_equal(divide(identity, divide(idQ_idQa, divide(idQa, identity))), idQa)) | (divide(identity, divide(idQ_idQa, divide(idQa, identity))) = idQa) | (~less_equal(idQa, divide(identity, divide(idQ_idQa, divide(idQa, identity))))))) <=> ((~![Y: $i, X: $i] : ((~less_equal(X, Y)) | (X = Y) | (~less_equal(Y, X)))) | ((~less_equal(divide(identity, divide(idQ_idQa, divide(idQa, identity))), idQa)) | (~less_equal(idQa, divide(identity, divide(idQ_idQa, divide(idQa, identity))))) | (divide(identity, divide(idQ_idQa, divide(idQa, identity))) = idQa)))),
% 1.04/0.93 inference(monotonicity,[status(thm)],[200])).
% 1.04/0.93 tff(202,plain,
% 1.04/0.93 (((~![Y: $i, X: $i] : ((~less_equal(X, Y)) | (X = Y) | (~less_equal(Y, X)))) | ((~less_equal(divide(identity, divide(idQ_idQa, divide(idQa, identity))), idQa)) | (divide(identity, divide(idQ_idQa, divide(idQa, identity))) = idQa) | (~less_equal(idQa, divide(identity, divide(idQ_idQa, divide(idQa, identity))))))) <=> ((~![Y: $i, X: $i] : ((~less_equal(X, Y)) | (X = Y) | (~less_equal(Y, X)))) | (~less_equal(divide(identity, divide(idQ_idQa, divide(idQa, identity))), idQa)) | (~less_equal(idQa, divide(identity, divide(idQ_idQa, divide(idQa, identity))))) | (divide(identity, divide(idQ_idQa, divide(idQa, identity))) = idQa))),
% 1.04/0.93 inference(transitivity,[status(thm)],[201, 199])).
% 1.04/0.93 tff(203,plain,
% 1.04/0.93 ((~![Y: $i, X: $i] : ((~less_equal(X, Y)) | (X = Y) | (~less_equal(Y, X)))) | ((~less_equal(divide(identity, divide(idQ_idQa, divide(idQa, identity))), idQa)) | (divide(identity, divide(idQ_idQa, divide(idQa, identity))) = idQa) | (~less_equal(idQa, divide(identity, divide(idQ_idQa, divide(idQa, identity))))))),
% 1.04/0.93 inference(quant_inst,[status(thm)],[])).
% 1.04/0.93 tff(204,plain,
% 1.04/0.93 ((~![Y: $i, X: $i] : ((~less_equal(X, Y)) | (X = Y) | (~less_equal(Y, X)))) | (~less_equal(divide(identity, divide(idQ_idQa, divide(idQa, identity))), idQa)) | (~less_equal(idQa, divide(identity, divide(idQ_idQa, divide(idQa, identity))))) | (divide(identity, divide(idQ_idQa, divide(idQa, identity))) = idQa)),
% 1.04/0.93 inference(modus_ponens,[status(thm)],[203, 202])).
% 1.04/0.93 tff(205,plain,
% 1.04/0.93 (divide(identity, divide(idQ_idQa, divide(idQa, identity))) = idQa),
% 1.04/0.93 inference(unit_resolution,[status(thm)],[204, 198, 189, 108])).
% 1.04/0.93 tff(206,plain,
% 1.04/0.93 (idQa = divide(identity, divide(idQ_idQa, divide(idQa, identity)))),
% 1.04/0.93 inference(symmetry,[status(thm)],[205])).
% 1.04/0.93 tff(207,plain,
% 1.04/0.93 (quotient(identity, divide(idQ_idQa, divide(idQa, identity)), idQa) <=> quotient(identity, divide(idQ_idQa, divide(idQa, identity)), divide(identity, divide(idQ_idQa, divide(idQa, identity))))),
% 1.04/0.93 inference(monotonicity,[status(thm)],[206])).
% 1.04/0.93 tff(208,plain,
% 1.04/0.93 (quotient(identity, divide(idQ_idQa, divide(idQa, identity)), divide(identity, divide(idQ_idQa, divide(idQa, identity)))) <=> quotient(identity, divide(idQ_idQa, divide(idQa, identity)), idQa)),
% 1.04/0.93 inference(symmetry,[status(thm)],[207])).
% 1.04/0.93 tff(209,plain,
% 1.04/0.93 (quotient(identity, divide(idQ_idQa, divide(idQa, identity)), idQa)),
% 1.04/0.93 inference(modus_ponens,[status(thm)],[9, 208])).
% 1.04/0.93 tff(210,plain,
% 1.04/0.93 (quotient(divide(idQ_idQa, divide(idQa, identity)), divide(idQ_idQa, divide(idQa, identity)), divide(idQa, identity)) <=> quotient(divide(idQ_idQa, divide(idQa, identity)), divide(idQ_idQa, divide(idQa, identity)), zero)),
% 1.04/0.93 inference(monotonicity,[status(thm)],[143])).
% 1.04/0.93 tff(211,plain,
% 1.04/0.93 (quotient(divide(idQ_idQa, divide(idQa, identity)), divide(idQ_idQa, divide(idQa, identity)), zero) <=> quotient(divide(idQ_idQa, divide(idQa, identity)), divide(idQ_idQa, divide(idQa, identity)), divide(idQa, identity))),
% 1.04/0.93 inference(symmetry,[status(thm)],[210])).
% 1.04/0.93 tff(212,plain,
% 1.04/0.93 (((~![Y: $i, X: $i] : ((~less_equal(X, Y)) | quotient(X, Y, zero))) | ((~less_equal(divide(idQ_idQa, divide(idQa, identity)), divide(idQ_idQa, divide(idQa, identity)))) | quotient(divide(idQ_idQa, divide(idQa, identity)), divide(idQ_idQa, divide(idQa, identity)), zero))) <=> ((~![Y: $i, X: $i] : ((~less_equal(X, Y)) | quotient(X, Y, zero))) | (~less_equal(divide(idQ_idQa, divide(idQa, identity)), divide(idQ_idQa, divide(idQa, identity)))) | quotient(divide(idQ_idQa, divide(idQa, identity)), divide(idQ_idQa, divide(idQa, identity)), zero))),
% 1.04/0.93 inference(rewrite,[status(thm)],[])).
% 1.04/0.93 tff(213,plain,
% 1.04/0.93 ((~![Y: $i, X: $i] : ((~less_equal(X, Y)) | quotient(X, Y, zero))) | ((~less_equal(divide(idQ_idQa, divide(idQa, identity)), divide(idQ_idQa, divide(idQa, identity)))) | quotient(divide(idQ_idQa, divide(idQa, identity)), divide(idQ_idQa, divide(idQa, identity)), zero))),
% 1.04/0.93 inference(quant_inst,[status(thm)],[])).
% 1.04/0.93 tff(214,plain,
% 1.04/0.93 ((~![Y: $i, X: $i] : ((~less_equal(X, Y)) | quotient(X, Y, zero))) | (~less_equal(divide(idQ_idQa, divide(idQa, identity)), divide(idQ_idQa, divide(idQa, identity)))) | quotient(divide(idQ_idQa, divide(idQa, identity)), divide(idQ_idQa, divide(idQa, identity)), zero)),
% 1.04/0.93 inference(modus_ponens,[status(thm)],[213, 212])).
% 1.04/0.93 tff(215,plain,
% 1.04/0.93 (quotient(divide(idQ_idQa, divide(idQa, identity)), divide(idQ_idQa, divide(idQa, identity)), zero)),
% 1.04/0.93 inference(unit_resolution,[status(thm)],[214, 121, 182])).
% 1.04/0.93 tff(216,plain,
% 1.04/0.93 (quotient(divide(idQ_idQa, divide(idQa, identity)), divide(idQ_idQa, divide(idQa, identity)), divide(idQa, identity))),
% 1.04/0.93 inference(modus_ponens,[status(thm)],[215, 211])).
% 1.04/0.93 tff(217,plain,
% 1.04/0.93 (quotient(idQa, divide(idQ_idQa, divide(idQa, identity)), idQa_Q__idQ_idQa) <=> quotient(idQa, idQ_idQa, idQa_Q__idQ_idQa)),
% 1.04/0.93 inference(monotonicity,[status(thm)],[164])).
% 1.04/0.93 tff(218,plain,
% 1.04/0.93 (quotient(idQa, idQ_idQa, idQa_Q__idQ_idQa) <=> quotient(idQa, divide(idQ_idQa, divide(idQa, identity)), idQa_Q__idQ_idQa)),
% 1.04/0.93 inference(symmetry,[status(thm)],[217])).
% 1.04/0.93 tff(219,plain,
% 1.04/0.93 (quotient(idQa, idQ_idQa, idQa_Q__idQ_idQa) <=> quotient(idQa, idQ_idQa, idQa_Q__idQ_idQa)),
% 1.04/0.93 inference(rewrite,[status(thm)],[])).
% 1.04/0.93 tff(220,axiom,(quotient(idQa, idQ_idQa, idQa_Q__idQ_idQa)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','identity_divide_idQ_idQa')).
% 1.04/0.93 tff(221,plain,
% 1.04/0.93 (quotient(idQa, idQ_idQa, idQa_Q__idQ_idQa)),
% 1.04/0.93 inference(modus_ponens,[status(thm)],[220, 219])).
% 1.04/0.93 tff(222,plain,
% 1.04/0.93 (quotient(idQa, divide(idQ_idQa, divide(idQa, identity)), idQa_Q__idQ_idQa)),
% 1.04/0.93 inference(modus_ponens,[status(thm)],[221, 218])).
% 1.04/0.93 tff(223,plain,
% 1.04/0.93 (quotient(idQa, divide(idQa, identity), idQa) <=> quotient(idQa, zero, idQa)),
% 1.04/0.93 inference(monotonicity,[status(thm)],[143])).
% 1.04/0.93 tff(224,plain,
% 1.04/0.93 (quotient(idQa, zero, idQa) <=> quotient(idQa, divide(idQa, identity), idQa)),
% 1.04/0.93 inference(symmetry,[status(thm)],[223])).
% 1.04/0.93 tff(225,plain,
% 1.04/0.93 ((~![X: $i] : quotient(X, zero, X)) | quotient(idQa, zero, idQa)),
% 1.04/0.93 inference(quant_inst,[status(thm)],[])).
% 1.04/0.93 tff(226,plain,
% 1.04/0.93 (quotient(idQa, zero, idQa)),
% 1.04/0.93 inference(unit_resolution,[status(thm)],[225, 152])).
% 1.04/0.93 tff(227,plain,
% 1.04/0.93 (quotient(idQa, divide(idQa, identity), idQa)),
% 1.04/0.93 inference(modus_ponens,[status(thm)],[226, 224])).
% 1.04/0.93 tff(228,plain,
% 1.04/0.93 (^[Z: $i, Y: $i, V1: $i, V5: $i, X: $i, V2: $i, V3: $i, V4: $i] : refl((less_equal(V4, V5) | (~quotient(V1, Z, V5)) | (~quotient(V3, V2, V4)) | (~quotient(X, Z, V3)) | (~quotient(Y, Z, V2)) | (~quotient(X, Y, V1))) <=> (less_equal(V4, V5) | (~quotient(V1, Z, V5)) | (~quotient(V3, V2, V4)) | (~quotient(X, Z, V3)) | (~quotient(Y, Z, V2)) | (~quotient(X, Y, V1))))),
% 1.04/0.93 inference(bind,[status(th)],[])).
% 1.04/0.93 tff(229,plain,
% 1.04/0.93 (![Z: $i, Y: $i, V1: $i, V5: $i, X: $i, V2: $i, V3: $i, V4: $i] : (less_equal(V4, V5) | (~quotient(V1, Z, V5)) | (~quotient(V3, V2, V4)) | (~quotient(X, Z, V3)) | (~quotient(Y, Z, V2)) | (~quotient(X, Y, V1))) <=> ![Z: $i, Y: $i, V1: $i, V5: $i, X: $i, V2: $i, V3: $i, V4: $i] : (less_equal(V4, V5) | (~quotient(V1, Z, V5)) | (~quotient(V3, V2, V4)) | (~quotient(X, Z, V3)) | (~quotient(Y, Z, V2)) | (~quotient(X, Y, V1)))),
% 1.04/0.93 inference(quant_intro,[status(thm)],[228])).
% 1.04/0.93 tff(230,plain,
% 1.04/0.93 (![Z: $i, Y: $i, V1: $i, V5: $i, X: $i, V2: $i, V3: $i, V4: $i] : (less_equal(V4, V5) | (~quotient(V1, Z, V5)) | (~quotient(V3, V2, V4)) | (~quotient(X, Z, V3)) | (~quotient(Y, Z, V2)) | (~quotient(X, Y, V1))) <=> ![Z: $i, Y: $i, V1: $i, V5: $i, X: $i, V2: $i, V3: $i, V4: $i] : (less_equal(V4, V5) | (~quotient(V1, Z, V5)) | (~quotient(V3, V2, V4)) | (~quotient(X, Z, V3)) | (~quotient(Y, Z, V2)) | (~quotient(X, Y, V1)))),
% 1.04/0.93 inference(rewrite,[status(thm)],[])).
% 1.04/0.93 tff(231,plain,
% 1.04/0.93 (^[Z: $i, Y: $i, V1: $i, V5: $i, X: $i, V2: $i, V3: $i, V4: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~quotient(X, Y, V1)) | (~quotient(Y, Z, V2))) | (~quotient(X, Z, V3))) <=> ((~quotient(X, Z, V3)) | (~quotient(Y, Z, V2)) | (~quotient(X, Y, V1)))), (((((~quotient(X, Y, V1)) | (~quotient(Y, Z, V2))) | (~quotient(X, Z, V3))) | (~quotient(V3, V2, V4))) <=> (((~quotient(X, Z, V3)) | (~quotient(Y, Z, V2)) | (~quotient(X, Y, V1))) | (~quotient(V3, V2, V4))))), rewrite((((~quotient(X, Z, V3)) | (~quotient(Y, Z, V2)) | (~quotient(X, Y, V1))) | (~quotient(V3, V2, V4))) <=> ((~quotient(V3, V2, V4)) | (~quotient(X, Z, V3)) | (~quotient(Y, Z, V2)) | (~quotient(X, Y, V1)))), (((((~quotient(X, Y, V1)) | (~quotient(Y, Z, V2))) | (~quotient(X, Z, V3))) | (~quotient(V3, V2, V4))) <=> ((~quotient(V3, V2, V4)) | (~quotient(X, Z, V3)) | (~quotient(Y, Z, V2)) | (~quotient(X, Y, V1))))), ((((((~quotient(X, Y, V1)) | (~quotient(Y, Z, V2))) | (~quotient(X, Z, V3))) | (~quotient(V3, V2, V4))) | (~quotient(V1, Z, V5))) <=> (((~quotient(V3, V2, V4)) | (~quotient(X, Z, V3)) | (~quotient(Y, Z, V2)) | (~quotient(X, Y, V1))) | (~quotient(V1, Z, V5))))), rewrite((((~quotient(V3, V2, V4)) | (~quotient(X, Z, V3)) | (~quotient(Y, Z, V2)) | (~quotient(X, Y, V1))) | (~quotient(V1, Z, V5))) <=> ((~quotient(V1, Z, V5)) | (~quotient(V3, V2, V4)) | (~quotient(X, Z, V3)) | (~quotient(Y, Z, V2)) | (~quotient(X, Y, V1)))), ((((((~quotient(X, Y, V1)) | (~quotient(Y, Z, V2))) | (~quotient(X, Z, V3))) | (~quotient(V3, V2, V4))) | (~quotient(V1, Z, V5))) <=> ((~quotient(V1, Z, V5)) | (~quotient(V3, V2, V4)) | (~quotient(X, Z, V3)) | (~quotient(Y, Z, V2)) | (~quotient(X, Y, V1))))), (((((((~quotient(X, Y, V1)) | (~quotient(Y, Z, V2))) | (~quotient(X, Z, V3))) | (~quotient(V3, V2, V4))) | (~quotient(V1, Z, V5))) | less_equal(V4, V5)) <=> (((~quotient(V1, Z, V5)) | (~quotient(V3, V2, V4)) | (~quotient(X, Z, V3)) | (~quotient(Y, Z, V2)) | (~quotient(X, Y, V1))) | less_equal(V4, V5)))), rewrite((((~quotient(V1, Z, V5)) | (~quotient(V3, V2, V4)) | (~quotient(X, Z, V3)) | (~quotient(Y, Z, V2)) | (~quotient(X, Y, V1))) | less_equal(V4, V5)) <=> (less_equal(V4, V5) | (~quotient(V1, Z, V5)) | (~quotient(V3, V2, V4)) | (~quotient(X, Z, V3)) | (~quotient(Y, Z, V2)) | (~quotient(X, Y, V1)))), (((((((~quotient(X, Y, V1)) | (~quotient(Y, Z, V2))) | (~quotient(X, Z, V3))) | (~quotient(V3, V2, V4))) | (~quotient(V1, Z, V5))) | less_equal(V4, V5)) <=> (less_equal(V4, V5) | (~quotient(V1, Z, V5)) | (~quotient(V3, V2, V4)) | (~quotient(X, Z, V3)) | (~quotient(Y, Z, V2)) | (~quotient(X, Y, V1)))))),
% 1.04/0.93 inference(bind,[status(th)],[])).
% 1.04/0.93 tff(232,plain,
% 1.04/0.93 (![Z: $i, Y: $i, V1: $i, V5: $i, X: $i, V2: $i, V3: $i, V4: $i] : ((((((~quotient(X, Y, V1)) | (~quotient(Y, Z, V2))) | (~quotient(X, Z, V3))) | (~quotient(V3, V2, V4))) | (~quotient(V1, Z, V5))) | less_equal(V4, V5)) <=> ![Z: $i, Y: $i, V1: $i, V5: $i, X: $i, V2: $i, V3: $i, V4: $i] : (less_equal(V4, V5) | (~quotient(V1, Z, V5)) | (~quotient(V3, V2, V4)) | (~quotient(X, Z, V3)) | (~quotient(Y, Z, V2)) | (~quotient(X, Y, V1)))),
% 1.04/0.93 inference(quant_intro,[status(thm)],[231])).
% 1.04/0.93 tff(233,axiom,(![Z: $i, Y: $i, V1: $i, V5: $i, X: $i, V2: $i, V3: $i, V4: $i] : ((((((~quotient(X, Y, V1)) | (~quotient(Y, Z, V2))) | (~quotient(X, Z, V3))) | (~quotient(V3, V2, V4))) | (~quotient(V1, Z, V5))) | less_equal(V4, V5))), file('/export/starexec/sandbox2/benchmark/Axioms/HEN001-0.ax','quotient_property')).
% 1.04/0.93 tff(234,plain,
% 1.04/0.93 (![Z: $i, Y: $i, V1: $i, V5: $i, X: $i, V2: $i, V3: $i, V4: $i] : (less_equal(V4, V5) | (~quotient(V1, Z, V5)) | (~quotient(V3, V2, V4)) | (~quotient(X, Z, V3)) | (~quotient(Y, Z, V2)) | (~quotient(X, Y, V1)))),
% 1.04/0.93 inference(modus_ponens,[status(thm)],[233, 232])).
% 1.04/0.93 tff(235,plain,
% 1.04/0.93 (![Z: $i, Y: $i, V1: $i, V5: $i, X: $i, V2: $i, V3: $i, V4: $i] : (less_equal(V4, V5) | (~quotient(V1, Z, V5)) | (~quotient(V3, V2, V4)) | (~quotient(X, Z, V3)) | (~quotient(Y, Z, V2)) | (~quotient(X, Y, V1)))),
% 1.04/0.93 inference(modus_ponens,[status(thm)],[234, 230])).
% 1.04/0.93 tff(236,plain,(
% 1.04/0.93 ![Z: $i, Y: $i, V1: $i, V5: $i, X: $i, V2: $i, V3: $i, V4: $i] : (less_equal(V4, V5) | (~quotient(V1, Z, V5)) | (~quotient(V3, V2, V4)) | (~quotient(X, Z, V3)) | (~quotient(Y, Z, V2)) | (~quotient(X, Y, V1)))),
% 1.04/0.93 inference(skolemize,[status(sab)],[235])).
% 1.04/0.93 tff(237,plain,
% 1.04/0.93 (![Z: $i, Y: $i, V1: $i, V5: $i, X: $i, V2: $i, V3: $i, V4: $i] : (less_equal(V4, V5) | (~quotient(V1, Z, V5)) | (~quotient(V3, V2, V4)) | (~quotient(X, Z, V3)) | (~quotient(Y, Z, V2)) | (~quotient(X, Y, V1)))),
% 1.04/0.93 inference(modus_ponens,[status(thm)],[236, 229])).
% 1.04/0.93 tff(238,plain,
% 1.04/0.93 (((~![Z: $i, Y: $i, V1: $i, V5: $i, X: $i, V2: $i, V3: $i, V4: $i] : (less_equal(V4, V5) | (~quotient(V1, Z, V5)) | (~quotient(V3, V2, V4)) | (~quotient(X, Z, V3)) | (~quotient(Y, Z, V2)) | (~quotient(X, Y, V1)))) | (less_equal(idQa, idQa_Q__idQ_idQa) | (~quotient(divide(idQ_idQa, divide(idQa, identity)), divide(idQ_idQa, divide(idQa, identity)), divide(idQa, identity))) | (~quotient(idQa, divide(idQ_idQa, divide(idQa, identity)), idQa_Q__idQ_idQa)) | (~quotient(idQa, divide(idQa, identity), idQa)) | (~quotient(identity, divide(idQ_idQa, divide(idQa, identity)), idQa)))) <=> ((~![Z: $i, Y: $i, V1: $i, V5: $i, X: $i, V2: $i, V3: $i, V4: $i] : (less_equal(V4, V5) | (~quotient(V1, Z, V5)) | (~quotient(V3, V2, V4)) | (~quotient(X, Z, V3)) | (~quotient(Y, Z, V2)) | (~quotient(X, Y, V1)))) | less_equal(idQa, idQa_Q__idQ_idQa) | (~quotient(divide(idQ_idQa, divide(idQa, identity)), divide(idQ_idQa, divide(idQa, identity)), divide(idQa, identity))) | (~quotient(idQa, divide(idQ_idQa, divide(idQa, identity)), idQa_Q__idQ_idQa)) | (~quotient(idQa, divide(idQa, identity), idQa)) | (~quotient(identity, divide(idQ_idQa, divide(idQa, identity)), idQa)))),
% 1.04/0.94 inference(rewrite,[status(thm)],[])).
% 1.04/0.94 tff(239,plain,
% 1.04/0.94 ((less_equal(idQa, idQa_Q__idQ_idQa) | (~quotient(idQa, divide(idQ_idQa, divide(idQa, identity)), idQa_Q__idQ_idQa)) | (~quotient(idQa, divide(idQa, identity), idQa)) | (~quotient(identity, divide(idQ_idQa, divide(idQa, identity)), idQa)) | (~quotient(divide(idQ_idQa, divide(idQa, identity)), divide(idQ_idQa, divide(idQa, identity)), divide(idQa, identity))) | (~quotient(identity, divide(idQ_idQa, divide(idQa, identity)), idQa))) <=> (less_equal(idQa, idQa_Q__idQ_idQa) | (~quotient(divide(idQ_idQa, divide(idQa, identity)), divide(idQ_idQa, divide(idQa, identity)), divide(idQa, identity))) | (~quotient(idQa, divide(idQ_idQa, divide(idQa, identity)), idQa_Q__idQ_idQa)) | (~quotient(idQa, divide(idQa, identity), idQa)) | (~quotient(identity, divide(idQ_idQa, divide(idQa, identity)), idQa)))),
% 1.04/0.94 inference(rewrite,[status(thm)],[])).
% 1.04/0.94 tff(240,plain,
% 1.04/0.94 (((~![Z: $i, Y: $i, V1: $i, V5: $i, X: $i, V2: $i, V3: $i, V4: $i] : (less_equal(V4, V5) | (~quotient(V1, Z, V5)) | (~quotient(V3, V2, V4)) | (~quotient(X, Z, V3)) | (~quotient(Y, Z, V2)) | (~quotient(X, Y, V1)))) | (less_equal(idQa, idQa_Q__idQ_idQa) | (~quotient(idQa, divide(idQ_idQa, divide(idQa, identity)), idQa_Q__idQ_idQa)) | (~quotient(idQa, divide(idQa, identity), idQa)) | (~quotient(identity, divide(idQ_idQa, divide(idQa, identity)), idQa)) | (~quotient(divide(idQ_idQa, divide(idQa, identity)), divide(idQ_idQa, divide(idQa, identity)), divide(idQa, identity))) | (~quotient(identity, divide(idQ_idQa, divide(idQa, identity)), idQa)))) <=> ((~![Z: $i, Y: $i, V1: $i, V5: $i, X: $i, V2: $i, V3: $i, V4: $i] : (less_equal(V4, V5) | (~quotient(V1, Z, V5)) | (~quotient(V3, V2, V4)) | (~quotient(X, Z, V3)) | (~quotient(Y, Z, V2)) | (~quotient(X, Y, V1)))) | (less_equal(idQa, idQa_Q__idQ_idQa) | (~quotient(divide(idQ_idQa, divide(idQa, identity)), divide(idQ_idQa, divide(idQa, identity)), divide(idQa, identity))) | (~quotient(idQa, divide(idQ_idQa, divide(idQa, identity)), idQa_Q__idQ_idQa)) | (~quotient(idQa, divide(idQa, identity), idQa)) | (~quotient(identity, divide(idQ_idQa, divide(idQa, identity)), idQa))))),
% 1.04/0.94 inference(monotonicity,[status(thm)],[239])).
% 1.04/0.94 tff(241,plain,
% 1.04/0.94 (((~![Z: $i, Y: $i, V1: $i, V5: $i, X: $i, V2: $i, V3: $i, V4: $i] : (less_equal(V4, V5) | (~quotient(V1, Z, V5)) | (~quotient(V3, V2, V4)) | (~quotient(X, Z, V3)) | (~quotient(Y, Z, V2)) | (~quotient(X, Y, V1)))) | (less_equal(idQa, idQa_Q__idQ_idQa) | (~quotient(idQa, divide(idQ_idQa, divide(idQa, identity)), idQa_Q__idQ_idQa)) | (~quotient(idQa, divide(idQa, identity), idQa)) | (~quotient(identity, divide(idQ_idQa, divide(idQa, identity)), idQa)) | (~quotient(divide(idQ_idQa, divide(idQa, identity)), divide(idQ_idQa, divide(idQa, identity)), divide(idQa, identity))) | (~quotient(identity, divide(idQ_idQa, divide(idQa, identity)), idQa)))) <=> ((~![Z: $i, Y: $i, V1: $i, V5: $i, X: $i, V2: $i, V3: $i, V4: $i] : (less_equal(V4, V5) | (~quotient(V1, Z, V5)) | (~quotient(V3, V2, V4)) | (~quotient(X, Z, V3)) | (~quotient(Y, Z, V2)) | (~quotient(X, Y, V1)))) | less_equal(idQa, idQa_Q__idQ_idQa) | (~quotient(divide(idQ_idQa, divide(idQa, identity)), divide(idQ_idQa, divide(idQa, identity)), divide(idQa, identity))) | (~quotient(idQa, divide(idQ_idQa, divide(idQa, identity)), idQa_Q__idQ_idQa)) | (~quotient(idQa, divide(idQa, identity), idQa)) | (~quotient(identity, divide(idQ_idQa, divide(idQa, identity)), idQa)))),
% 1.04/0.94 inference(transitivity,[status(thm)],[240, 238])).
% 1.04/0.94 tff(242,plain,
% 1.04/0.94 ((~![Z: $i, Y: $i, V1: $i, V5: $i, X: $i, V2: $i, V3: $i, V4: $i] : (less_equal(V4, V5) | (~quotient(V1, Z, V5)) | (~quotient(V3, V2, V4)) | (~quotient(X, Z, V3)) | (~quotient(Y, Z, V2)) | (~quotient(X, Y, V1)))) | (less_equal(idQa, idQa_Q__idQ_idQa) | (~quotient(idQa, divide(idQ_idQa, divide(idQa, identity)), idQa_Q__idQ_idQa)) | (~quotient(idQa, divide(idQa, identity), idQa)) | (~quotient(identity, divide(idQ_idQa, divide(idQa, identity)), idQa)) | (~quotient(divide(idQ_idQa, divide(idQa, identity)), divide(idQ_idQa, divide(idQa, identity)), divide(idQa, identity))) | (~quotient(identity, divide(idQ_idQa, divide(idQa, identity)), idQa)))),
% 1.04/0.94 inference(quant_inst,[status(thm)],[])).
% 1.04/0.94 tff(243,plain,
% 1.04/0.94 ((~![Z: $i, Y: $i, V1: $i, V5: $i, X: $i, V2: $i, V3: $i, V4: $i] : (less_equal(V4, V5) | (~quotient(V1, Z, V5)) | (~quotient(V3, V2, V4)) | (~quotient(X, Z, V3)) | (~quotient(Y, Z, V2)) | (~quotient(X, Y, V1)))) | less_equal(idQa, idQa_Q__idQ_idQa) | (~quotient(divide(idQ_idQa, divide(idQa, identity)), divide(idQ_idQa, divide(idQa, identity)), divide(idQa, identity))) | (~quotient(idQa, divide(idQ_idQa, divide(idQa, identity)), idQa_Q__idQ_idQa)) | (~quotient(idQa, divide(idQa, identity), idQa)) | (~quotient(identity, divide(idQ_idQa, divide(idQa, identity)), idQa))),
% 1.04/0.94 inference(modus_ponens,[status(thm)],[242, 241])).
% 1.04/0.94 tff(244,plain,
% 1.04/0.94 (less_equal(idQa, idQa_Q__idQ_idQa) | (~quotient(identity, divide(idQ_idQa, divide(idQa, identity)), idQa))),
% 1.04/0.94 inference(unit_resolution,[status(thm)],[243, 237, 227, 222, 216])).
% 1.04/0.94 tff(245,plain,
% 1.04/0.94 (less_equal(idQa, idQa_Q__idQ_idQa)),
% 1.04/0.94 inference(unit_resolution,[status(thm)],[244, 209])).
% 1.04/0.94 tff(246,plain,
% 1.04/0.94 (((~![Z: $i, Y: $i, X: $i] : ((~quotient(X, Y, Z)) | less_equal(Z, X))) | ((~quotient(idQa, idQ_idQa, idQa_Q__idQ_idQa)) | less_equal(idQa_Q__idQ_idQa, idQa))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~quotient(X, Y, Z)) | less_equal(Z, X))) | (~quotient(idQa, idQ_idQa, idQa_Q__idQ_idQa)) | less_equal(idQa_Q__idQ_idQa, idQa))),
% 1.04/0.94 inference(rewrite,[status(thm)],[])).
% 1.04/0.94 tff(247,plain,
% 1.04/0.94 ((~![Z: $i, Y: $i, X: $i] : ((~quotient(X, Y, Z)) | less_equal(Z, X))) | ((~quotient(idQa, idQ_idQa, idQa_Q__idQ_idQa)) | less_equal(idQa_Q__idQ_idQa, idQa))),
% 1.04/0.94 inference(quant_inst,[status(thm)],[])).
% 1.04/0.94 tff(248,plain,
% 1.04/0.94 ((~![Z: $i, Y: $i, X: $i] : ((~quotient(X, Y, Z)) | less_equal(Z, X))) | (~quotient(idQa, idQ_idQa, idQa_Q__idQ_idQa)) | less_equal(idQa_Q__idQ_idQa, idQa)),
% 1.04/0.94 inference(modus_ponens,[status(thm)],[247, 246])).
% 1.04/0.94 tff(249,plain,
% 1.04/0.94 (less_equal(idQa_Q__idQ_idQa, idQa)),
% 1.04/0.94 inference(unit_resolution,[status(thm)],[248, 18, 221])).
% 1.04/0.94 tff(250,plain,
% 1.04/0.94 ((~(idQa = idQa_Q__idQ_idQa)) <=> (~(idQa = idQa_Q__idQ_idQa))),
% 1.04/0.94 inference(rewrite,[status(thm)],[])).
% 1.04/0.94 tff(251,axiom,(~(idQa = idQa_Q__idQ_idQa)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_idQa_equals_idQa_Q__idQ_idQa')).
% 1.04/0.94 tff(252,plain,
% 1.04/0.94 (~(idQa = idQa_Q__idQ_idQa)),
% 1.04/0.94 inference(modus_ponens,[status(thm)],[251, 250])).
% 1.09/0.94 tff(253,plain,
% 1.09/0.94 (((~![Y: $i, X: $i] : ((~less_equal(X, Y)) | (X = Y) | (~less_equal(Y, X)))) | ((idQa = idQa_Q__idQ_idQa) | (~less_equal(idQa_Q__idQ_idQa, idQa)) | (~less_equal(idQa, idQa_Q__idQ_idQa)))) <=> ((~![Y: $i, X: $i] : ((~less_equal(X, Y)) | (X = Y) | (~less_equal(Y, X)))) | (idQa = idQa_Q__idQ_idQa) | (~less_equal(idQa_Q__idQ_idQa, idQa)) | (~less_equal(idQa, idQa_Q__idQ_idQa)))),
% 1.09/0.94 inference(rewrite,[status(thm)],[])).
% 1.09/0.94 tff(254,plain,
% 1.09/0.94 (((~less_equal(idQa, idQa_Q__idQ_idQa)) | (idQa = idQa_Q__idQ_idQa) | (~less_equal(idQa_Q__idQ_idQa, idQa))) <=> ((idQa = idQa_Q__idQ_idQa) | (~less_equal(idQa_Q__idQ_idQa, idQa)) | (~less_equal(idQa, idQa_Q__idQ_idQa)))),
% 1.09/0.94 inference(rewrite,[status(thm)],[])).
% 1.09/0.94 tff(255,plain,
% 1.09/0.94 (((~![Y: $i, X: $i] : ((~less_equal(X, Y)) | (X = Y) | (~less_equal(Y, X)))) | ((~less_equal(idQa, idQa_Q__idQ_idQa)) | (idQa = idQa_Q__idQ_idQa) | (~less_equal(idQa_Q__idQ_idQa, idQa)))) <=> ((~![Y: $i, X: $i] : ((~less_equal(X, Y)) | (X = Y) | (~less_equal(Y, X)))) | ((idQa = idQa_Q__idQ_idQa) | (~less_equal(idQa_Q__idQ_idQa, idQa)) | (~less_equal(idQa, idQa_Q__idQ_idQa))))),
% 1.09/0.94 inference(monotonicity,[status(thm)],[254])).
% 1.09/0.94 tff(256,plain,
% 1.09/0.94 (((~![Y: $i, X: $i] : ((~less_equal(X, Y)) | (X = Y) | (~less_equal(Y, X)))) | ((~less_equal(idQa, idQa_Q__idQ_idQa)) | (idQa = idQa_Q__idQ_idQa) | (~less_equal(idQa_Q__idQ_idQa, idQa)))) <=> ((~![Y: $i, X: $i] : ((~less_equal(X, Y)) | (X = Y) | (~less_equal(Y, X)))) | (idQa = idQa_Q__idQ_idQa) | (~less_equal(idQa_Q__idQ_idQa, idQa)) | (~less_equal(idQa, idQa_Q__idQ_idQa)))),
% 1.09/0.94 inference(transitivity,[status(thm)],[255, 253])).
% 1.09/0.94 tff(257,plain,
% 1.09/0.94 ((~![Y: $i, X: $i] : ((~less_equal(X, Y)) | (X = Y) | (~less_equal(Y, X)))) | ((~less_equal(idQa, idQa_Q__idQ_idQa)) | (idQa = idQa_Q__idQ_idQa) | (~less_equal(idQa_Q__idQ_idQa, idQa)))),
% 1.09/0.94 inference(quant_inst,[status(thm)],[])).
% 1.09/0.94 tff(258,plain,
% 1.09/0.94 ((~![Y: $i, X: $i] : ((~less_equal(X, Y)) | (X = Y) | (~less_equal(Y, X)))) | (idQa = idQa_Q__idQ_idQa) | (~less_equal(idQa_Q__idQ_idQa, idQa)) | (~less_equal(idQa, idQa_Q__idQ_idQa))),
% 1.09/0.94 inference(modus_ponens,[status(thm)],[257, 256])).
% 1.09/0.94 tff(259,plain,
% 1.09/0.94 ($false),
% 1.09/0.94 inference(unit_resolution,[status(thm)],[258, 198, 252, 249, 245])).
% 1.09/0.94 % SZS output end Proof
%------------------------------------------------------------------------------