TSTP Solution File: HEN010-2 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : HEN010-2 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n007.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 22:39:54 EDT 2022
% Result : Unsatisfiable 0.98s 0.90s
% Output : Proof 0.98s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.14 % Problem : HEN010-2 : TPTP v8.1.0. Released v1.0.0.
% 0.04/0.15 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.16/0.37 % Computer : n007.cluster.edu
% 0.16/0.37 % Model : x86_64 x86_64
% 0.16/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.37 % Memory : 8042.1875MB
% 0.16/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.37 % CPULimit : 300
% 0.16/0.37 % WCLimit : 300
% 0.16/0.37 % DateTime : Wed Aug 31 21:34:17 EDT 2022
% 0.16/0.37 % CPUTime :
% 0.16/0.38 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.16/0.38 Usage: tptp [options] [-file:]file
% 0.16/0.38 -h, -? prints this message.
% 0.16/0.38 -smt2 print SMT-LIB2 benchmark.
% 0.16/0.38 -m, -model generate model.
% 0.16/0.38 -p, -proof generate proof.
% 0.16/0.38 -c, -core generate unsat core of named formulas.
% 0.16/0.38 -st, -statistics display statistics.
% 0.16/0.38 -t:timeout set timeout (in second).
% 0.16/0.38 -smt2status display status in smt2 format instead of SZS.
% 0.16/0.38 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.16/0.38 -<param>:<value> configuration parameter and value.
% 0.16/0.38 -o:<output-file> file to place output in.
% 0.98/0.90 % SZS status Unsatisfiable
% 0.98/0.90 % SZS output start Proof
% 0.98/0.90 tff(idQa_Q__idQ_idQa_type, type, (
% 0.98/0.90 idQa_Q__idQ_idQa: $i)).
% 0.98/0.90 tff(idQa_type, type, (
% 0.98/0.90 idQa: $i)).
% 0.98/0.90 tff(divide_type, type, (
% 0.98/0.90 divide: ( $i * $i ) > $i)).
% 0.98/0.90 tff(identity_type, type, (
% 0.98/0.90 identity: $i)).
% 0.98/0.90 tff(less_equal_type, type, (
% 0.98/0.90 less_equal: ( $i * $i ) > $o)).
% 0.98/0.90 tff(quotient_type, type, (
% 0.98/0.90 quotient: ( $i * $i * $i ) > $o)).
% 0.98/0.90 tff(idQ_idQa_type, type, (
% 0.98/0.90 idQ_idQa: $i)).
% 0.98/0.90 tff(a_type, type, (
% 0.98/0.90 a: $i)).
% 0.98/0.90 tff(zero_type, type, (
% 0.98/0.90 zero: $i)).
% 0.98/0.90 tff(1,plain,
% 0.98/0.90 (^[Y: $i, X: $i] : refl(quotient(X, Y, divide(X, Y)) <=> quotient(X, Y, divide(X, Y)))),
% 0.98/0.90 inference(bind,[status(th)],[])).
% 0.98/0.90 tff(2,plain,
% 0.98/0.90 (![Y: $i, X: $i] : quotient(X, Y, divide(X, Y)) <=> ![Y: $i, X: $i] : quotient(X, Y, divide(X, Y))),
% 0.98/0.90 inference(quant_intro,[status(thm)],[1])).
% 0.98/0.90 tff(3,plain,
% 0.98/0.90 (![Y: $i, X: $i] : quotient(X, Y, divide(X, Y)) <=> ![Y: $i, X: $i] : quotient(X, Y, divide(X, Y))),
% 0.98/0.90 inference(rewrite,[status(thm)],[])).
% 0.98/0.90 tff(4,axiom,(![Y: $i, X: $i] : quotient(X, Y, divide(X, Y))), file('/export/starexec/sandbox2/benchmark/Axioms/HEN001-0.ax','closure')).
% 0.98/0.90 tff(5,plain,
% 0.98/0.90 (![Y: $i, X: $i] : quotient(X, Y, divide(X, Y))),
% 0.98/0.90 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.98/0.90 tff(6,plain,(
% 0.98/0.90 ![Y: $i, X: $i] : quotient(X, Y, divide(X, Y))),
% 0.98/0.90 inference(skolemize,[status(sab)],[5])).
% 0.98/0.90 tff(7,plain,
% 0.98/0.90 (![Y: $i, X: $i] : quotient(X, Y, divide(X, Y))),
% 0.98/0.90 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.98/0.90 tff(8,plain,
% 0.98/0.90 ((~![Y: $i, X: $i] : quotient(X, Y, divide(X, Y))) | quotient(idQa, divide(idQa, identity), divide(idQa, divide(idQa, identity)))),
% 0.98/0.90 inference(quant_inst,[status(thm)],[])).
% 0.98/0.90 tff(9,plain,
% 0.98/0.90 (quotient(idQa, divide(idQa, identity), divide(idQa, divide(idQa, identity)))),
% 0.98/0.90 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.98/0.90 tff(10,plain,
% 0.98/0.90 ((~![Y: $i, X: $i] : quotient(X, Y, divide(X, Y))) | quotient(idQa, identity, divide(idQa, identity))),
% 0.98/0.90 inference(quant_inst,[status(thm)],[])).
% 0.98/0.90 tff(11,plain,
% 0.98/0.90 (quotient(idQa, identity, divide(idQa, identity))),
% 0.98/0.90 inference(unit_resolution,[status(thm)],[10, 7])).
% 0.98/0.90 tff(12,plain,
% 0.98/0.90 (quotient(idQa, idQ_idQa, idQa_Q__idQ_idQa) <=> quotient(idQa, idQ_idQa, idQa_Q__idQ_idQa)),
% 0.98/0.90 inference(rewrite,[status(thm)],[])).
% 0.98/0.90 tff(13,axiom,(quotient(idQa, idQ_idQa, idQa_Q__idQ_idQa)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','identity_divide_idQ_idQa')).
% 0.98/0.90 tff(14,plain,
% 0.98/0.90 (quotient(idQa, idQ_idQa, idQa_Q__idQ_idQa)),
% 0.98/0.90 inference(modus_ponens,[status(thm)],[13, 12])).
% 0.98/0.90 tff(15,plain,
% 0.98/0.90 (^[Z: $i, Y: $i, X: $i] : refl(((~quotient(X, Y, Z)) | less_equal(Z, X)) <=> ((~quotient(X, Y, Z)) | less_equal(Z, X)))),
% 0.98/0.90 inference(bind,[status(th)],[])).
% 0.98/0.90 tff(16,plain,
% 0.98/0.90 (![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))),
% 0.98/0.90 inference(quant_intro,[status(thm)],[15])).
% 0.98/0.90 tff(17,plain,
% 0.98/0.90 (![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))),
% 0.98/0.90 inference(rewrite,[status(thm)],[])).
% 0.98/0.90 tff(18,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')).
% 0.98/0.90 tff(19,plain,
% 0.98/0.90 (![Z: $i, Y: $i, X: $i] : ((~quotient(X, Y, Z)) | less_equal(Z, X))),
% 0.98/0.90 inference(modus_ponens,[status(thm)],[18, 17])).
% 0.98/0.90 tff(20,plain,(
% 0.98/0.90 ![Z: $i, Y: $i, X: $i] : ((~quotient(X, Y, Z)) | less_equal(Z, X))),
% 0.98/0.90 inference(skolemize,[status(sab)],[19])).
% 0.98/0.90 tff(21,plain,
% 0.98/0.90 (![Z: $i, Y: $i, X: $i] : ((~quotient(X, Y, Z)) | less_equal(Z, X))),
% 0.98/0.90 inference(modus_ponens,[status(thm)],[20, 16])).
% 0.98/0.90 tff(22,plain,
% 0.98/0.90 (((~![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))),
% 0.98/0.90 inference(rewrite,[status(thm)],[])).
% 0.98/0.90 tff(23,plain,
% 0.98/0.90 ((~![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))),
% 0.98/0.90 inference(quant_inst,[status(thm)],[])).
% 0.98/0.90 tff(24,plain,
% 0.98/0.90 ((~![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)),
% 0.98/0.90 inference(modus_ponens,[status(thm)],[23, 22])).
% 0.98/0.90 tff(25,plain,
% 0.98/0.90 (less_equal(idQa_Q__idQ_idQa, idQa)),
% 0.98/0.90 inference(unit_resolution,[status(thm)],[24, 21, 14])).
% 0.98/0.90 tff(26,plain,
% 0.98/0.90 (quotient(identity, a, idQa) <=> quotient(identity, a, idQa)),
% 0.98/0.90 inference(rewrite,[status(thm)],[])).
% 0.98/0.90 tff(27,axiom,(quotient(identity, a, idQa)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','identity_divide_a')).
% 0.98/0.90 tff(28,plain,
% 0.98/0.90 (quotient(identity, a, idQa)),
% 0.98/0.90 inference(modus_ponens,[status(thm)],[27, 26])).
% 0.98/0.90 tff(29,plain,
% 0.98/0.90 (((~![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))),
% 0.98/0.90 inference(rewrite,[status(thm)],[])).
% 0.98/0.90 tff(30,plain,
% 0.98/0.90 ((~![Z: $i, Y: $i, X: $i] : ((~quotient(X, Y, Z)) | less_equal(Z, X))) | ((~quotient(identity, a, idQa)) | less_equal(idQa, identity))),
% 0.98/0.90 inference(quant_inst,[status(thm)],[])).
% 0.98/0.90 tff(31,plain,
% 0.98/0.90 ((~![Z: $i, Y: $i, X: $i] : ((~quotient(X, Y, Z)) | less_equal(Z, X))) | (~quotient(identity, a, idQa)) | less_equal(idQa, identity)),
% 0.98/0.90 inference(modus_ponens,[status(thm)],[30, 29])).
% 0.98/0.90 tff(32,plain,
% 0.98/0.90 (less_equal(idQa, identity)),
% 0.98/0.90 inference(unit_resolution,[status(thm)],[31, 21, 28])).
% 0.98/0.90 tff(33,plain,
% 0.98/0.90 (![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)))),
% 0.98/0.90 inference(rewrite,[status(thm)],[])).
% 0.98/0.90 tff(34,plain,
% 0.98/0.90 (![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)))),
% 0.98/0.90 inference(rewrite,[status(thm)],[])).
% 0.98/0.90 tff(35,plain,
% 0.98/0.90 (^[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))))),
% 0.98/0.90 inference(bind,[status(th)],[])).
% 0.98/0.90 tff(36,plain,
% 0.98/0.90 (![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)))),
% 0.98/0.90 inference(quant_intro,[status(thm)],[35])).
% 0.98/0.90 tff(37,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')).
% 0.98/0.90 tff(38,plain,
% 0.98/0.90 (![Z: $i, Y: $i, X: $i] : ((~less_equal(X, Y)) | less_equal(X, Z) | (~less_equal(Y, Z)))),
% 0.98/0.90 inference(modus_ponens,[status(thm)],[37, 36])).
% 0.98/0.90 tff(39,plain,
% 0.98/0.90 (![Z: $i, Y: $i, X: $i] : ((~less_equal(X, Y)) | less_equal(X, Z) | (~less_equal(Y, Z)))),
% 0.98/0.90 inference(modus_ponens,[status(thm)],[38, 34])).
% 0.98/0.90 tff(40,plain,(
% 0.98/0.90 ![Z: $i, Y: $i, X: $i] : ((~less_equal(X, Y)) | less_equal(X, Z) | (~less_equal(Y, Z)))),
% 0.98/0.90 inference(skolemize,[status(sab)],[39])).
% 0.98/0.90 tff(41,plain,
% 0.98/0.90 (![Z: $i, Y: $i, X: $i] : ((~less_equal(X, Y)) | less_equal(X, Z) | (~less_equal(Y, Z)))),
% 0.98/0.90 inference(modus_ponens,[status(thm)],[40, 33])).
% 0.98/0.90 tff(42,plain,
% 0.98/0.90 (((~![Z: $i, Y: $i, X: $i] : ((~less_equal(X, Y)) | less_equal(X, Z) | (~less_equal(Y, Z)))) | ((~less_equal(idQa_Q__idQ_idQa, idQa)) | less_equal(idQa_Q__idQ_idQa, identity) | (~less_equal(idQa, identity)))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~less_equal(X, Y)) | less_equal(X, Z) | (~less_equal(Y, Z)))) | (~less_equal(idQa_Q__idQ_idQa, idQa)) | less_equal(idQa_Q__idQ_idQa, identity) | (~less_equal(idQa, identity)))),
% 0.98/0.90 inference(rewrite,[status(thm)],[])).
% 0.98/0.90 tff(43,plain,
% 0.98/0.90 ((~![Z: $i, Y: $i, X: $i] : ((~less_equal(X, Y)) | less_equal(X, Z) | (~less_equal(Y, Z)))) | ((~less_equal(idQa_Q__idQ_idQa, idQa)) | less_equal(idQa_Q__idQ_idQa, identity) | (~less_equal(idQa, identity)))),
% 0.98/0.90 inference(quant_inst,[status(thm)],[])).
% 0.98/0.90 tff(44,plain,
% 0.98/0.90 ((~![Z: $i, Y: $i, X: $i] : ((~less_equal(X, Y)) | less_equal(X, Z) | (~less_equal(Y, Z)))) | (~less_equal(idQa_Q__idQ_idQa, idQa)) | less_equal(idQa_Q__idQ_idQa, identity) | (~less_equal(idQa, identity))),
% 0.98/0.90 inference(modus_ponens,[status(thm)],[43, 42])).
% 0.98/0.90 tff(45,plain,
% 0.98/0.90 (less_equal(idQa_Q__idQ_idQa, identity)),
% 0.98/0.90 inference(unit_resolution,[status(thm)],[44, 41, 32, 25])).
% 0.98/0.90 tff(46,plain,
% 0.98/0.90 (^[Z: $i, Y: $i, W2: $i, W1: $i, X: $i] : refl((less_equal(W2, Y) | (~quotient(X, Z, W2)) | (~less_equal(W1, Z)) | (~quotient(X, Y, W1))) <=> (less_equal(W2, Y) | (~quotient(X, Z, W2)) | (~less_equal(W1, Z)) | (~quotient(X, Y, W1))))),
% 0.98/0.90 inference(bind,[status(th)],[])).
% 0.98/0.90 tff(47,plain,
% 0.98/0.90 (![Z: $i, Y: $i, W2: $i, W1: $i, X: $i] : (less_equal(W2, Y) | (~quotient(X, Z, W2)) | (~less_equal(W1, Z)) | (~quotient(X, Y, W1))) <=> ![Z: $i, Y: $i, W2: $i, W1: $i, X: $i] : (less_equal(W2, Y) | (~quotient(X, Z, W2)) | (~less_equal(W1, Z)) | (~quotient(X, Y, W1)))),
% 0.98/0.90 inference(quant_intro,[status(thm)],[46])).
% 0.98/0.90 tff(48,plain,
% 0.98/0.90 (![Z: $i, Y: $i, W2: $i, W1: $i, X: $i] : (less_equal(W2, Y) | (~quotient(X, Z, W2)) | (~less_equal(W1, Z)) | (~quotient(X, Y, W1))) <=> ![Z: $i, Y: $i, W2: $i, W1: $i, X: $i] : (less_equal(W2, Y) | (~quotient(X, Z, W2)) | (~less_equal(W1, Z)) | (~quotient(X, Y, W1)))),
% 0.98/0.90 inference(rewrite,[status(thm)],[])).
% 0.98/0.90 tff(49,plain,
% 0.98/0.90 (^[Z: $i, Y: $i, W2: $i, W1: $i, X: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~quotient(X, Y, W1)) | (~less_equal(W1, Z))) <=> ((~less_equal(W1, Z)) | (~quotient(X, Y, W1)))), ((((~quotient(X, Y, W1)) | (~less_equal(W1, Z))) | (~quotient(X, Z, W2))) <=> (((~less_equal(W1, Z)) | (~quotient(X, Y, W1))) | (~quotient(X, Z, W2))))), rewrite((((~less_equal(W1, Z)) | (~quotient(X, Y, W1))) | (~quotient(X, Z, W2))) <=> ((~quotient(X, Z, W2)) | (~less_equal(W1, Z)) | (~quotient(X, Y, W1)))), ((((~quotient(X, Y, W1)) | (~less_equal(W1, Z))) | (~quotient(X, Z, W2))) <=> ((~quotient(X, Z, W2)) | (~less_equal(W1, Z)) | (~quotient(X, Y, W1))))), (((((~quotient(X, Y, W1)) | (~less_equal(W1, Z))) | (~quotient(X, Z, W2))) | less_equal(W2, Y)) <=> (((~quotient(X, Z, W2)) | (~less_equal(W1, Z)) | (~quotient(X, Y, W1))) | less_equal(W2, Y)))), rewrite((((~quotient(X, Z, W2)) | (~less_equal(W1, Z)) | (~quotient(X, Y, W1))) | less_equal(W2, Y)) <=> (less_equal(W2, Y) | (~quotient(X, Z, W2)) | (~less_equal(W1, Z)) | (~quotient(X, Y, W1)))), (((((~quotient(X, Y, W1)) | (~less_equal(W1, Z))) | (~quotient(X, Z, W2))) | less_equal(W2, Y)) <=> (less_equal(W2, Y) | (~quotient(X, Z, W2)) | (~less_equal(W1, Z)) | (~quotient(X, Y, W1)))))),
% 0.98/0.90 inference(bind,[status(th)],[])).
% 0.98/0.90 tff(50,plain,
% 0.98/0.90 (![Z: $i, Y: $i, W2: $i, W1: $i, X: $i] : ((((~quotient(X, Y, W1)) | (~less_equal(W1, Z))) | (~quotient(X, Z, W2))) | less_equal(W2, Y)) <=> ![Z: $i, Y: $i, W2: $i, W1: $i, X: $i] : (less_equal(W2, Y) | (~quotient(X, Z, W2)) | (~less_equal(W1, Z)) | (~quotient(X, Y, W1)))),
% 0.98/0.90 inference(quant_intro,[status(thm)],[49])).
% 0.98/0.90 tff(51,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')).
% 0.98/0.90 tff(52,plain,
% 0.98/0.90 (![Z: $i, Y: $i, W2: $i, W1: $i, X: $i] : (less_equal(W2, Y) | (~quotient(X, Z, W2)) | (~less_equal(W1, Z)) | (~quotient(X, Y, W1)))),
% 0.98/0.90 inference(modus_ponens,[status(thm)],[51, 50])).
% 0.98/0.90 tff(53,plain,
% 0.98/0.90 (![Z: $i, Y: $i, W2: $i, W1: $i, X: $i] : (less_equal(W2, Y) | (~quotient(X, Z, W2)) | (~less_equal(W1, Z)) | (~quotient(X, Y, W1)))),
% 0.98/0.90 inference(modus_ponens,[status(thm)],[52, 48])).
% 0.98/0.90 tff(54,plain,(
% 0.98/0.90 ![Z: $i, Y: $i, W2: $i, W1: $i, X: $i] : (less_equal(W2, Y) | (~quotient(X, Z, W2)) | (~less_equal(W1, Z)) | (~quotient(X, Y, W1)))),
% 0.98/0.90 inference(skolemize,[status(sab)],[53])).
% 0.98/0.90 tff(55,plain,
% 0.98/0.90 (![Z: $i, Y: $i, W2: $i, W1: $i, X: $i] : (less_equal(W2, Y) | (~quotient(X, Z, W2)) | (~less_equal(W1, Z)) | (~quotient(X, Y, W1)))),
% 0.98/0.90 inference(modus_ponens,[status(thm)],[54, 47])).
% 0.98/0.90 tff(56,plain,
% 0.98/0.90 (((~![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(idQa, idQ_idQa, idQa_Q__idQ_idQa)) | (~less_equal(idQa_Q__idQ_idQa, identity)) | (~quotient(idQa, identity, divide(idQa, identity))) | less_equal(divide(idQa, identity), idQ_idQa))) <=> ((~![Z: $i, Y: $i, W2: $i, W1: $i, X: $i] : (less_equal(W2, Y) | (~quotient(X, Z, W2)) | (~less_equal(W1, Z)) | (~quotient(X, Y, W1)))) | (~quotient(idQa, idQ_idQa, idQa_Q__idQ_idQa)) | (~less_equal(idQa_Q__idQ_idQa, identity)) | (~quotient(idQa, identity, divide(idQa, identity))) | less_equal(divide(idQa, identity), idQ_idQa))),
% 0.98/0.90 inference(rewrite,[status(thm)],[])).
% 0.98/0.90 tff(57,plain,
% 0.98/0.90 ((less_equal(divide(idQa, identity), idQ_idQa) | (~quotient(idQa, identity, divide(idQa, identity))) | (~less_equal(idQa_Q__idQ_idQa, identity)) | (~quotient(idQa, idQ_idQa, idQa_Q__idQ_idQa))) <=> ((~quotient(idQa, idQ_idQa, idQa_Q__idQ_idQa)) | (~less_equal(idQa_Q__idQ_idQa, identity)) | (~quotient(idQa, identity, divide(idQa, identity))) | less_equal(divide(idQa, identity), idQ_idQa))),
% 0.98/0.90 inference(rewrite,[status(thm)],[])).
% 0.98/0.90 tff(58,plain,
% 0.98/0.90 (((~![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(idQa, identity), idQ_idQa) | (~quotient(idQa, identity, divide(idQa, identity))) | (~less_equal(idQa_Q__idQ_idQa, identity)) | (~quotient(idQa, idQ_idQa, idQa_Q__idQ_idQa)))) <=> ((~![Z: $i, Y: $i, W2: $i, W1: $i, X: $i] : (less_equal(W2, Y) | (~quotient(X, Z, W2)) | (~less_equal(W1, Z)) | (~quotient(X, Y, W1)))) | ((~quotient(idQa, idQ_idQa, idQa_Q__idQ_idQa)) | (~less_equal(idQa_Q__idQ_idQa, identity)) | (~quotient(idQa, identity, divide(idQa, identity))) | less_equal(divide(idQa, identity), idQ_idQa)))),
% 0.98/0.90 inference(monotonicity,[status(thm)],[57])).
% 0.98/0.90 tff(59,plain,
% 0.98/0.90 (((~![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(idQa, identity), idQ_idQa) | (~quotient(idQa, identity, divide(idQa, identity))) | (~less_equal(idQa_Q__idQ_idQa, identity)) | (~quotient(idQa, idQ_idQa, idQa_Q__idQ_idQa)))) <=> ((~![Z: $i, Y: $i, W2: $i, W1: $i, X: $i] : (less_equal(W2, Y) | (~quotient(X, Z, W2)) | (~less_equal(W1, Z)) | (~quotient(X, Y, W1)))) | (~quotient(idQa, idQ_idQa, idQa_Q__idQ_idQa)) | (~less_equal(idQa_Q__idQ_idQa, identity)) | (~quotient(idQa, identity, divide(idQa, identity))) | less_equal(divide(idQa, identity), idQ_idQa))),
% 0.98/0.90 inference(transitivity,[status(thm)],[58, 56])).
% 0.98/0.90 tff(60,plain,
% 0.98/0.90 ((~![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(idQa, identity), idQ_idQa) | (~quotient(idQa, identity, divide(idQa, identity))) | (~less_equal(idQa_Q__idQ_idQa, identity)) | (~quotient(idQa, idQ_idQa, idQa_Q__idQ_idQa)))),
% 0.98/0.90 inference(quant_inst,[status(thm)],[])).
% 0.98/0.90 tff(61,plain,
% 0.98/0.90 ((~![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(idQa, idQ_idQa, idQa_Q__idQ_idQa)) | (~less_equal(idQa_Q__idQ_idQa, identity)) | (~quotient(idQa, identity, divide(idQa, identity))) | less_equal(divide(idQa, identity), idQ_idQa)),
% 0.98/0.90 inference(modus_ponens,[status(thm)],[60, 59])).
% 0.98/0.90 tff(62,plain,
% 0.98/0.90 (less_equal(divide(idQa, identity), idQ_idQa)),
% 0.98/0.90 inference(unit_resolution,[status(thm)],[61, 55, 14, 45, 11])).
% 0.98/0.90 tff(63,plain,
% 0.98/0.90 (^[Z: $i, Y: $i, W2: $i, W1: $i, X: $i] : refl((less_equal(W1, W2) | (~quotient(Z, X, W2)) | (~quotient(Z, Y, W1)) | (~less_equal(X, Y))) <=> (less_equal(W1, W2) | (~quotient(Z, X, W2)) | (~quotient(Z, Y, W1)) | (~less_equal(X, Y))))),
% 0.98/0.90 inference(bind,[status(th)],[])).
% 0.98/0.90 tff(64,plain,
% 0.98/0.90 (![Z: $i, Y: $i, W2: $i, W1: $i, X: $i] : (less_equal(W1, W2) | (~quotient(Z, X, W2)) | (~quotient(Z, Y, W1)) | (~less_equal(X, Y))) <=> ![Z: $i, Y: $i, W2: $i, W1: $i, X: $i] : (less_equal(W1, W2) | (~quotient(Z, X, W2)) | (~quotient(Z, Y, W1)) | (~less_equal(X, Y)))),
% 0.98/0.90 inference(quant_intro,[status(thm)],[63])).
% 0.98/0.90 tff(65,plain,
% 0.98/0.90 (![Z: $i, Y: $i, W2: $i, W1: $i, X: $i] : (less_equal(W1, W2) | (~quotient(Z, X, W2)) | (~quotient(Z, Y, W1)) | (~less_equal(X, Y))) <=> ![Z: $i, Y: $i, W2: $i, W1: $i, X: $i] : (less_equal(W1, W2) | (~quotient(Z, X, W2)) | (~quotient(Z, Y, W1)) | (~less_equal(X, Y)))),
% 0.98/0.90 inference(rewrite,[status(thm)],[])).
% 0.98/0.90 tff(66,plain,
% 0.98/0.90 (^[Z: $i, Y: $i, W2: $i, W1: $i, X: $i] : trans(monotonicity(rewrite((((~less_equal(X, Y)) | (~quotient(Z, Y, W1))) | (~quotient(Z, X, W2))) <=> ((~quotient(Z, X, W2)) | (~quotient(Z, Y, W1)) | (~less_equal(X, Y)))), (((((~less_equal(X, Y)) | (~quotient(Z, Y, W1))) | (~quotient(Z, X, W2))) | less_equal(W1, W2)) <=> (((~quotient(Z, X, W2)) | (~quotient(Z, Y, W1)) | (~less_equal(X, Y))) | less_equal(W1, W2)))), rewrite((((~quotient(Z, X, W2)) | (~quotient(Z, Y, W1)) | (~less_equal(X, Y))) | less_equal(W1, W2)) <=> (less_equal(W1, W2) | (~quotient(Z, X, W2)) | (~quotient(Z, Y, W1)) | (~less_equal(X, Y)))), (((((~less_equal(X, Y)) | (~quotient(Z, Y, W1))) | (~quotient(Z, X, W2))) | less_equal(W1, W2)) <=> (less_equal(W1, W2) | (~quotient(Z, X, W2)) | (~quotient(Z, Y, W1)) | (~less_equal(X, Y)))))),
% 0.98/0.90 inference(bind,[status(th)],[])).
% 0.98/0.90 tff(67,plain,
% 0.98/0.90 (![Z: $i, Y: $i, W2: $i, W1: $i, X: $i] : ((((~less_equal(X, Y)) | (~quotient(Z, Y, W1))) | (~quotient(Z, X, W2))) | less_equal(W1, W2)) <=> ![Z: $i, Y: $i, W2: $i, W1: $i, X: $i] : (less_equal(W1, W2) | (~quotient(Z, X, W2)) | (~quotient(Z, Y, W1)) | (~less_equal(X, Y)))),
% 0.98/0.90 inference(quant_intro,[status(thm)],[66])).
% 0.98/0.90 tff(68,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')).
% 0.98/0.90 tff(69,plain,
% 0.98/0.90 (![Z: $i, Y: $i, W2: $i, W1: $i, X: $i] : (less_equal(W1, W2) | (~quotient(Z, X, W2)) | (~quotient(Z, Y, W1)) | (~less_equal(X, Y)))),
% 0.98/0.90 inference(modus_ponens,[status(thm)],[68, 67])).
% 0.98/0.90 tff(70,plain,
% 0.98/0.90 (![Z: $i, Y: $i, W2: $i, W1: $i, X: $i] : (less_equal(W1, W2) | (~quotient(Z, X, W2)) | (~quotient(Z, Y, W1)) | (~less_equal(X, Y)))),
% 0.98/0.90 inference(modus_ponens,[status(thm)],[69, 65])).
% 0.98/0.90 tff(71,plain,(
% 0.98/0.90 ![Z: $i, Y: $i, W2: $i, W1: $i, X: $i] : (less_equal(W1, W2) | (~quotient(Z, X, W2)) | (~quotient(Z, Y, W1)) | (~less_equal(X, Y)))),
% 0.98/0.90 inference(skolemize,[status(sab)],[70])).
% 0.98/0.90 tff(72,plain,
% 0.98/0.90 (![Z: $i, Y: $i, W2: $i, W1: $i, X: $i] : (less_equal(W1, W2) | (~quotient(Z, X, W2)) | (~quotient(Z, Y, W1)) | (~less_equal(X, Y)))),
% 0.98/0.90 inference(modus_ponens,[status(thm)],[71, 64])).
% 0.98/0.90 tff(73,plain,
% 0.98/0.90 (((~![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(idQa, idQ_idQa, idQa_Q__idQ_idQa)) | (~less_equal(divide(idQa, identity), idQ_idQa)) | (~quotient(idQa, divide(idQa, identity), divide(idQa, divide(idQa, identity)))) | less_equal(idQa_Q__idQ_idQa, divide(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(idQa, idQ_idQa, idQa_Q__idQ_idQa)) | (~less_equal(divide(idQa, identity), idQ_idQa)) | (~quotient(idQa, divide(idQa, identity), divide(idQa, divide(idQa, identity)))) | less_equal(idQa_Q__idQ_idQa, divide(idQa, divide(idQa, identity))))),
% 0.98/0.90 inference(rewrite,[status(thm)],[])).
% 0.98/0.90 tff(74,plain,
% 0.98/0.90 ((less_equal(idQa_Q__idQ_idQa, divide(idQa, divide(idQa, identity))) | (~quotient(idQa, divide(idQa, identity), divide(idQa, divide(idQa, identity)))) | (~quotient(idQa, idQ_idQa, idQa_Q__idQ_idQa)) | (~less_equal(divide(idQa, identity), idQ_idQa))) <=> ((~quotient(idQa, idQ_idQa, idQa_Q__idQ_idQa)) | (~less_equal(divide(idQa, identity), idQ_idQa)) | (~quotient(idQa, divide(idQa, identity), divide(idQa, divide(idQa, identity)))) | less_equal(idQa_Q__idQ_idQa, divide(idQa, divide(idQa, identity))))),
% 0.98/0.90 inference(rewrite,[status(thm)],[])).
% 0.98/0.90 tff(75,plain,
% 0.98/0.90 (((~![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_Q__idQ_idQa, divide(idQa, divide(idQa, identity))) | (~quotient(idQa, divide(idQa, identity), divide(idQa, divide(idQa, identity)))) | (~quotient(idQa, idQ_idQa, idQa_Q__idQ_idQa)) | (~less_equal(divide(idQa, identity), idQ_idQa)))) <=> ((~![Z: $i, Y: $i, W2: $i, W1: $i, X: $i] : (less_equal(W1, W2) | (~quotient(Z, X, W2)) | (~quotient(Z, Y, W1)) | (~less_equal(X, Y)))) | ((~quotient(idQa, idQ_idQa, idQa_Q__idQ_idQa)) | (~less_equal(divide(idQa, identity), idQ_idQa)) | (~quotient(idQa, divide(idQa, identity), divide(idQa, divide(idQa, identity)))) | less_equal(idQa_Q__idQ_idQa, divide(idQa, divide(idQa, identity)))))),
% 0.98/0.90 inference(monotonicity,[status(thm)],[74])).
% 0.98/0.90 tff(76,plain,
% 0.98/0.90 (((~![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_Q__idQ_idQa, divide(idQa, divide(idQa, identity))) | (~quotient(idQa, divide(idQa, identity), divide(idQa, divide(idQa, identity)))) | (~quotient(idQa, idQ_idQa, idQa_Q__idQ_idQa)) | (~less_equal(divide(idQa, identity), idQ_idQa)))) <=> ((~![Z: $i, Y: $i, W2: $i, W1: $i, X: $i] : (less_equal(W1, W2) | (~quotient(Z, X, W2)) | (~quotient(Z, Y, W1)) | (~less_equal(X, Y)))) | (~quotient(idQa, idQ_idQa, idQa_Q__idQ_idQa)) | (~less_equal(divide(idQa, identity), idQ_idQa)) | (~quotient(idQa, divide(idQa, identity), divide(idQa, divide(idQa, identity)))) | less_equal(idQa_Q__idQ_idQa, divide(idQa, divide(idQa, identity))))),
% 0.98/0.90 inference(transitivity,[status(thm)],[75, 73])).
% 0.98/0.90 tff(77,plain,
% 0.98/0.90 ((~![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_Q__idQ_idQa, divide(idQa, divide(idQa, identity))) | (~quotient(idQa, divide(idQa, identity), divide(idQa, divide(idQa, identity)))) | (~quotient(idQa, idQ_idQa, idQa_Q__idQ_idQa)) | (~less_equal(divide(idQa, identity), idQ_idQa)))),
% 0.98/0.90 inference(quant_inst,[status(thm)],[])).
% 0.98/0.90 tff(78,plain,
% 0.98/0.90 ((~![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(idQa, idQ_idQa, idQa_Q__idQ_idQa)) | (~less_equal(divide(idQa, identity), idQ_idQa)) | (~quotient(idQa, divide(idQa, identity), divide(idQa, divide(idQa, identity)))) | less_equal(idQa_Q__idQ_idQa, divide(idQa, divide(idQa, identity)))),
% 0.98/0.90 inference(modus_ponens,[status(thm)],[77, 76])).
% 0.98/0.90 tff(79,plain,
% 0.98/0.90 (less_equal(idQa_Q__idQ_idQa, divide(idQa, divide(idQa, identity)))),
% 0.98/0.90 inference(unit_resolution,[status(thm)],[78, 72, 14, 62, 9])).
% 0.98/0.90 tff(80,plain,
% 0.98/0.90 (^[Y: $i, X: $i] : refl(((~less_equal(X, Y)) | quotient(X, Y, zero)) <=> ((~less_equal(X, Y)) | quotient(X, Y, zero)))),
% 0.98/0.90 inference(bind,[status(th)],[])).
% 0.98/0.90 tff(81,plain,
% 0.98/0.90 (![Y: $i, X: $i] : ((~less_equal(X, Y)) | quotient(X, Y, zero)) <=> ![Y: $i, X: $i] : ((~less_equal(X, Y)) | quotient(X, Y, zero))),
% 0.98/0.90 inference(quant_intro,[status(thm)],[80])).
% 0.98/0.90 tff(82,plain,
% 0.98/0.90 (![Y: $i, X: $i] : ((~less_equal(X, Y)) | quotient(X, Y, zero)) <=> ![Y: $i, X: $i] : ((~less_equal(X, Y)) | quotient(X, Y, zero))),
% 0.98/0.90 inference(rewrite,[status(thm)],[])).
% 0.98/0.90 tff(83,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')).
% 0.98/0.90 tff(84,plain,
% 0.98/0.90 (![Y: $i, X: $i] : ((~less_equal(X, Y)) | quotient(X, Y, zero))),
% 0.98/0.90 inference(modus_ponens,[status(thm)],[83, 82])).
% 0.98/0.90 tff(85,plain,(
% 0.98/0.90 ![Y: $i, X: $i] : ((~less_equal(X, Y)) | quotient(X, Y, zero))),
% 0.98/0.90 inference(skolemize,[status(sab)],[84])).
% 0.98/0.90 tff(86,plain,
% 0.98/0.90 (![Y: $i, X: $i] : ((~less_equal(X, Y)) | quotient(X, Y, zero))),
% 0.98/0.90 inference(modus_ponens,[status(thm)],[85, 81])).
% 0.98/0.90 tff(87,plain,
% 0.98/0.90 (((~![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))),
% 0.98/0.91 inference(rewrite,[status(thm)],[])).
% 0.98/0.91 tff(88,plain,
% 0.98/0.91 ((~![Y: $i, X: $i] : ((~less_equal(X, Y)) | quotient(X, Y, zero))) | ((~less_equal(idQa, identity)) | quotient(idQa, identity, zero))),
% 0.98/0.91 inference(quant_inst,[status(thm)],[])).
% 0.98/0.91 tff(89,plain,
% 0.98/0.91 ((~![Y: $i, X: $i] : ((~less_equal(X, Y)) | quotient(X, Y, zero))) | (~less_equal(idQa, identity)) | quotient(idQa, identity, zero)),
% 0.98/0.91 inference(modus_ponens,[status(thm)],[88, 87])).
% 0.98/0.91 tff(90,plain,
% 0.98/0.91 (quotient(idQa, identity, zero)),
% 0.98/0.91 inference(unit_resolution,[status(thm)],[89, 86, 32])).
% 0.98/0.91 tff(91,plain,
% 0.98/0.91 (^[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))))),
% 0.98/0.91 inference(bind,[status(th)],[])).
% 0.98/0.91 tff(92,plain,
% 0.98/0.91 (![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)))),
% 0.98/0.91 inference(quant_intro,[status(thm)],[91])).
% 0.98/0.91 tff(93,plain,
% 0.98/0.91 (![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)))),
% 0.98/0.91 inference(rewrite,[status(thm)],[])).
% 0.98/0.91 tff(94,plain,
% 0.98/0.91 (^[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))))),
% 0.98/0.91 inference(bind,[status(th)],[])).
% 0.98/0.91 tff(95,plain,
% 0.98/0.91 (![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)))),
% 0.98/0.91 inference(quant_intro,[status(thm)],[94])).
% 0.98/0.91 tff(96,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')).
% 0.98/0.91 tff(97,plain,
% 0.98/0.91 (![W: $i, Z: $i, Y: $i, X: $i] : ((~quotient(X, Y, Z)) | (Z = W) | (~quotient(X, Y, W)))),
% 0.98/0.91 inference(modus_ponens,[status(thm)],[96, 95])).
% 0.98/0.91 tff(98,plain,
% 0.98/0.91 (![W: $i, Z: $i, Y: $i, X: $i] : ((~quotient(X, Y, Z)) | (Z = W) | (~quotient(X, Y, W)))),
% 0.98/0.91 inference(modus_ponens,[status(thm)],[97, 93])).
% 0.98/0.91 tff(99,plain,(
% 0.98/0.91 ![W: $i, Z: $i, Y: $i, X: $i] : ((~quotient(X, Y, Z)) | (Z = W) | (~quotient(X, Y, W)))),
% 0.98/0.91 inference(skolemize,[status(sab)],[98])).
% 0.98/0.91 tff(100,plain,
% 0.98/0.91 (![W: $i, Z: $i, Y: $i, X: $i] : ((~quotient(X, Y, Z)) | (Z = W) | (~quotient(X, Y, W)))),
% 0.98/0.91 inference(modus_ponens,[status(thm)],[99, 92])).
% 0.98/0.91 tff(101,plain,
% 0.98/0.91 (((~![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)))),
% 0.98/0.91 inference(rewrite,[status(thm)],[])).
% 0.98/0.91 tff(102,plain,
% 0.98/0.91 (((~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)))),
% 0.98/0.91 inference(rewrite,[status(thm)],[])).
% 0.98/0.91 tff(103,plain,
% 0.98/0.91 (((~![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))))),
% 0.98/0.91 inference(monotonicity,[status(thm)],[102])).
% 0.98/0.91 tff(104,plain,
% 0.98/0.91 (((~![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)))),
% 0.98/0.91 inference(transitivity,[status(thm)],[103, 101])).
% 0.98/0.91 tff(105,plain,
% 0.98/0.91 ((~![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))))),
% 0.98/0.91 inference(quant_inst,[status(thm)],[])).
% 0.98/0.91 tff(106,plain,
% 0.98/0.91 ((~![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))),
% 0.98/0.91 inference(modus_ponens,[status(thm)],[105, 104])).
% 0.98/0.91 tff(107,plain,
% 0.98/0.91 (zero = divide(idQa, identity)),
% 0.98/0.91 inference(unit_resolution,[status(thm)],[106, 100, 90, 11])).
% 0.98/0.91 tff(108,plain,
% 0.98/0.91 (divide(idQa, identity) = zero),
% 0.98/0.91 inference(symmetry,[status(thm)],[107])).
% 0.98/0.91 tff(109,plain,
% 0.98/0.91 (quotient(idQa, divide(idQa, identity), idQa) <=> quotient(idQa, zero, idQa)),
% 0.98/0.91 inference(monotonicity,[status(thm)],[108])).
% 0.98/0.91 tff(110,plain,
% 0.98/0.91 (quotient(idQa, zero, idQa) <=> quotient(idQa, divide(idQa, identity), idQa)),
% 0.98/0.91 inference(symmetry,[status(thm)],[109])).
% 0.98/0.91 tff(111,plain,
% 0.98/0.91 (^[X: $i] : refl(quotient(X, zero, X) <=> quotient(X, zero, X))),
% 0.98/0.91 inference(bind,[status(th)],[])).
% 0.98/0.91 tff(112,plain,
% 0.98/0.91 (![X: $i] : quotient(X, zero, X) <=> ![X: $i] : quotient(X, zero, X)),
% 0.98/0.91 inference(quant_intro,[status(thm)],[111])).
% 0.98/0.91 tff(113,plain,
% 0.98/0.91 (![X: $i] : quotient(X, zero, X) <=> ![X: $i] : quotient(X, zero, X)),
% 0.98/0.91 inference(rewrite,[status(thm)],[])).
% 0.98/0.91 tff(114,axiom,(![X: $i] : quotient(X, zero, X)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','x_divde_zero_is_x')).
% 0.98/0.91 tff(115,plain,
% 0.98/0.91 (![X: $i] : quotient(X, zero, X)),
% 0.98/0.91 inference(modus_ponens,[status(thm)],[114, 113])).
% 0.98/0.91 tff(116,plain,(
% 0.98/0.91 ![X: $i] : quotient(X, zero, X)),
% 0.98/0.91 inference(skolemize,[status(sab)],[115])).
% 0.98/0.91 tff(117,plain,
% 0.98/0.91 (![X: $i] : quotient(X, zero, X)),
% 0.98/0.91 inference(modus_ponens,[status(thm)],[116, 112])).
% 0.98/0.91 tff(118,plain,
% 0.98/0.91 ((~![X: $i] : quotient(X, zero, X)) | quotient(idQa, zero, idQa)),
% 0.98/0.91 inference(quant_inst,[status(thm)],[])).
% 0.98/0.91 tff(119,plain,
% 0.98/0.91 (quotient(idQa, zero, idQa)),
% 0.98/0.91 inference(unit_resolution,[status(thm)],[118, 117])).
% 0.98/0.91 tff(120,plain,
% 0.98/0.91 (quotient(idQa, divide(idQa, identity), idQa)),
% 0.98/0.91 inference(modus_ponens,[status(thm)],[119, 110])).
% 0.98/0.91 tff(121,plain,
% 0.98/0.91 (((~![W: $i, Z: $i, Y: $i, X: $i] : ((~quotient(X, Y, Z)) | (Z = W) | (~quotient(X, Y, W)))) | ((~quotient(idQa, divide(idQa, identity), idQa)) | (~quotient(idQa, divide(idQa, identity), divide(idQa, divide(idQa, identity)))) | (idQa = divide(idQa, divide(idQa, identity))))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : ((~quotient(X, Y, Z)) | (Z = W) | (~quotient(X, Y, W)))) | (~quotient(idQa, divide(idQa, identity), idQa)) | (~quotient(idQa, divide(idQa, identity), divide(idQa, divide(idQa, identity)))) | (idQa = divide(idQa, divide(idQa, identity))))),
% 0.98/0.91 inference(rewrite,[status(thm)],[])).
% 0.98/0.91 tff(122,plain,
% 0.98/0.91 (((~quotient(idQa, divide(idQa, identity), idQa)) | (idQa = divide(idQa, divide(idQa, identity))) | (~quotient(idQa, divide(idQa, identity), divide(idQa, divide(idQa, identity))))) <=> ((~quotient(idQa, divide(idQa, identity), idQa)) | (~quotient(idQa, divide(idQa, identity), divide(idQa, divide(idQa, identity)))) | (idQa = divide(idQa, divide(idQa, identity))))),
% 0.98/0.91 inference(rewrite,[status(thm)],[])).
% 0.98/0.91 tff(123,plain,
% 0.98/0.91 (((~![W: $i, Z: $i, Y: $i, X: $i] : ((~quotient(X, Y, Z)) | (Z = W) | (~quotient(X, Y, W)))) | ((~quotient(idQa, divide(idQa, identity), idQa)) | (idQa = divide(idQa, divide(idQa, identity))) | (~quotient(idQa, divide(idQa, identity), divide(idQa, divide(idQa, identity)))))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : ((~quotient(X, Y, Z)) | (Z = W) | (~quotient(X, Y, W)))) | ((~quotient(idQa, divide(idQa, identity), idQa)) | (~quotient(idQa, divide(idQa, identity), divide(idQa, divide(idQa, identity)))) | (idQa = divide(idQa, divide(idQa, identity)))))),
% 0.98/0.91 inference(monotonicity,[status(thm)],[122])).
% 0.98/0.91 tff(124,plain,
% 0.98/0.91 (((~![W: $i, Z: $i, Y: $i, X: $i] : ((~quotient(X, Y, Z)) | (Z = W) | (~quotient(X, Y, W)))) | ((~quotient(idQa, divide(idQa, identity), idQa)) | (idQa = divide(idQa, divide(idQa, identity))) | (~quotient(idQa, divide(idQa, identity), divide(idQa, divide(idQa, identity)))))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : ((~quotient(X, Y, Z)) | (Z = W) | (~quotient(X, Y, W)))) | (~quotient(idQa, divide(idQa, identity), idQa)) | (~quotient(idQa, divide(idQa, identity), divide(idQa, divide(idQa, identity)))) | (idQa = divide(idQa, divide(idQa, identity))))),
% 0.98/0.91 inference(transitivity,[status(thm)],[123, 121])).
% 0.98/0.91 tff(125,plain,
% 0.98/0.91 ((~![W: $i, Z: $i, Y: $i, X: $i] : ((~quotient(X, Y, Z)) | (Z = W) | (~quotient(X, Y, W)))) | ((~quotient(idQa, divide(idQa, identity), idQa)) | (idQa = divide(idQa, divide(idQa, identity))) | (~quotient(idQa, divide(idQa, identity), divide(idQa, divide(idQa, identity)))))),
% 0.98/0.91 inference(quant_inst,[status(thm)],[])).
% 0.98/0.91 tff(126,plain,
% 0.98/0.91 ((~![W: $i, Z: $i, Y: $i, X: $i] : ((~quotient(X, Y, Z)) | (Z = W) | (~quotient(X, Y, W)))) | (~quotient(idQa, divide(idQa, identity), idQa)) | (~quotient(idQa, divide(idQa, identity), divide(idQa, divide(idQa, identity)))) | (idQa = divide(idQa, divide(idQa, identity)))),
% 0.98/0.91 inference(modus_ponens,[status(thm)],[125, 124])).
% 0.98/0.91 tff(127,plain,
% 0.98/0.91 (idQa = divide(idQa, divide(idQa, identity))),
% 0.98/0.91 inference(unit_resolution,[status(thm)],[126, 100, 120, 9])).
% 0.98/0.91 tff(128,plain,
% 0.98/0.91 (divide(idQa, divide(idQa, identity)) = idQa),
% 0.98/0.91 inference(symmetry,[status(thm)],[127])).
% 0.98/0.91 tff(129,plain,
% 0.98/0.91 (quotient(identity, a, divide(idQa, divide(idQa, identity))) <=> quotient(identity, a, idQa)),
% 0.98/0.91 inference(monotonicity,[status(thm)],[128])).
% 0.98/0.91 tff(130,plain,
% 0.98/0.91 (quotient(identity, a, idQa) <=> quotient(identity, a, divide(idQa, divide(idQa, identity)))),
% 0.98/0.91 inference(symmetry,[status(thm)],[129])).
% 0.98/0.91 tff(131,plain,
% 0.98/0.91 (quotient(identity, a, divide(idQa, divide(idQa, identity)))),
% 0.98/0.91 inference(modus_ponens,[status(thm)],[28, 130])).
% 0.98/0.91 tff(132,plain,
% 0.98/0.91 (quotient(identity, divide(idQa, identity), identity) <=> quotient(identity, zero, identity)),
% 0.98/0.91 inference(monotonicity,[status(thm)],[108])).
% 0.98/0.91 tff(133,plain,
% 0.98/0.91 (quotient(identity, zero, identity) <=> quotient(identity, divide(idQa, identity), identity)),
% 0.98/0.91 inference(symmetry,[status(thm)],[132])).
% 0.98/0.91 tff(134,plain,
% 0.98/0.91 ((~![X: $i] : quotient(X, zero, X)) | quotient(identity, zero, identity)),
% 0.98/0.91 inference(quant_inst,[status(thm)],[])).
% 0.98/0.91 tff(135,plain,
% 0.98/0.91 (quotient(identity, zero, identity)),
% 0.98/0.91 inference(unit_resolution,[status(thm)],[134, 117])).
% 0.98/0.91 tff(136,plain,
% 0.98/0.91 (quotient(identity, divide(idQa, identity), identity)),
% 0.98/0.91 inference(modus_ponens,[status(thm)],[135, 133])).
% 0.98/0.91 tff(137,plain,
% 0.98/0.91 (quotient(identity, identity, divide(idQa, identity)) <=> quotient(identity, identity, zero)),
% 0.98/0.91 inference(monotonicity,[status(thm)],[108])).
% 0.98/0.91 tff(138,plain,
% 0.98/0.91 (quotient(identity, identity, zero) <=> quotient(identity, identity, divide(idQa, identity))),
% 0.98/0.91 inference(symmetry,[status(thm)],[137])).
% 0.98/0.91 tff(139,assumption,(~less_equal(identity, identity)), introduced(assumption)).
% 0.98/0.91 tff(140,plain,
% 0.98/0.91 (^[X: $i] : refl(less_equal(X, identity) <=> less_equal(X, identity))),
% 0.98/0.91 inference(bind,[status(th)],[])).
% 0.98/0.91 tff(141,plain,
% 0.98/0.91 (![X: $i] : less_equal(X, identity) <=> ![X: $i] : less_equal(X, identity)),
% 0.98/0.91 inference(quant_intro,[status(thm)],[140])).
% 0.98/0.91 tff(142,plain,
% 0.98/0.91 (![X: $i] : less_equal(X, identity) <=> ![X: $i] : less_equal(X, identity)),
% 0.98/0.91 inference(rewrite,[status(thm)],[])).
% 0.98/0.91 tff(143,axiom,(![X: $i] : less_equal(X, identity)), file('/export/starexec/sandbox2/benchmark/Axioms/HEN001-0.ax','identity_is_largest')).
% 0.98/0.91 tff(144,plain,
% 0.98/0.91 (![X: $i] : less_equal(X, identity)),
% 0.98/0.91 inference(modus_ponens,[status(thm)],[143, 142])).
% 0.98/0.91 tff(145,plain,(
% 0.98/0.91 ![X: $i] : less_equal(X, identity)),
% 0.98/0.91 inference(skolemize,[status(sab)],[144])).
% 0.98/0.91 tff(146,plain,
% 0.98/0.91 (![X: $i] : less_equal(X, identity)),
% 0.98/0.91 inference(modus_ponens,[status(thm)],[145, 141])).
% 0.98/0.91 tff(147,plain,
% 0.98/0.91 ((~![X: $i] : less_equal(X, identity)) | less_equal(identity, identity)),
% 0.98/0.91 inference(quant_inst,[status(thm)],[])).
% 0.98/0.91 tff(148,plain,
% 0.98/0.91 ($false),
% 0.98/0.91 inference(unit_resolution,[status(thm)],[147, 146, 139])).
% 0.98/0.91 tff(149,plain,(less_equal(identity, identity)), inference(lemma,lemma(discharge,[]))).
% 0.98/0.91 tff(150,plain,
% 0.98/0.91 (((~![Y: $i, X: $i] : ((~less_equal(X, Y)) | quotient(X, Y, zero))) | ((~less_equal(identity, identity)) | quotient(identity, identity, zero))) <=> ((~![Y: $i, X: $i] : ((~less_equal(X, Y)) | quotient(X, Y, zero))) | (~less_equal(identity, identity)) | quotient(identity, identity, zero))),
% 0.98/0.91 inference(rewrite,[status(thm)],[])).
% 0.98/0.91 tff(151,plain,
% 0.98/0.91 ((~![Y: $i, X: $i] : ((~less_equal(X, Y)) | quotient(X, Y, zero))) | ((~less_equal(identity, identity)) | quotient(identity, identity, zero))),
% 0.98/0.91 inference(quant_inst,[status(thm)],[])).
% 0.98/0.91 tff(152,plain,
% 0.98/0.91 ((~![Y: $i, X: $i] : ((~less_equal(X, Y)) | quotient(X, Y, zero))) | (~less_equal(identity, identity)) | quotient(identity, identity, zero)),
% 0.98/0.91 inference(modus_ponens,[status(thm)],[151, 150])).
% 0.98/0.91 tff(153,plain,
% 0.98/0.91 (quotient(identity, identity, zero)),
% 0.98/0.91 inference(unit_resolution,[status(thm)],[152, 86, 149])).
% 0.98/0.91 tff(154,plain,
% 0.98/0.91 (quotient(identity, identity, divide(idQa, identity))),
% 0.98/0.91 inference(modus_ponens,[status(thm)],[153, 138])).
% 0.98/0.91 tff(155,plain,
% 0.98/0.91 ((~![Y: $i, X: $i] : quotient(X, Y, divide(X, Y))) | quotient(identity, divide(idQa, identity), divide(identity, divide(idQa, identity)))),
% 0.98/0.91 inference(quant_inst,[status(thm)],[])).
% 0.98/0.91 tff(156,plain,
% 0.98/0.91 (quotient(identity, divide(idQa, identity), divide(identity, divide(idQa, identity)))),
% 0.98/0.91 inference(unit_resolution,[status(thm)],[155, 7])).
% 0.98/0.91 tff(157,plain,
% 0.98/0.91 (^[Y2: $i, Y1: $i, Y3: $i, X: $i] : refl(((Y1 = Y3) | (~quotient(identity, Y2, Y3)) | (~quotient(identity, Y1, Y2)) | (~quotient(identity, X, Y1))) <=> ((Y1 = Y3) | (~quotient(identity, Y2, Y3)) | (~quotient(identity, Y1, Y2)) | (~quotient(identity, X, Y1))))),
% 0.98/0.91 inference(bind,[status(th)],[])).
% 0.98/0.91 tff(158,plain,
% 0.98/0.91 (![Y2: $i, Y1: $i, Y3: $i, X: $i] : ((Y1 = Y3) | (~quotient(identity, Y2, Y3)) | (~quotient(identity, Y1, Y2)) | (~quotient(identity, X, Y1))) <=> ![Y2: $i, Y1: $i, Y3: $i, X: $i] : ((Y1 = Y3) | (~quotient(identity, Y2, Y3)) | (~quotient(identity, Y1, Y2)) | (~quotient(identity, X, Y1)))),
% 0.98/0.91 inference(quant_intro,[status(thm)],[157])).
% 0.98/0.91 tff(159,plain,
% 0.98/0.91 (![Y2: $i, Y1: $i, Y3: $i, X: $i] : ((Y1 = Y3) | (~quotient(identity, Y2, Y3)) | (~quotient(identity, Y1, Y2)) | (~quotient(identity, X, Y1))) <=> ![Y2: $i, Y1: $i, Y3: $i, X: $i] : ((Y1 = Y3) | (~quotient(identity, Y2, Y3)) | (~quotient(identity, Y1, Y2)) | (~quotient(identity, X, Y1)))),
% 0.98/0.91 inference(rewrite,[status(thm)],[])).
% 0.98/0.91 tff(160,plain,
% 0.98/0.91 (^[Y2: $i, Y1: $i, Y3: $i, X: $i] : trans(monotonicity(rewrite((((~quotient(identity, X, Y1)) | (~quotient(identity, Y1, Y2))) | (~quotient(identity, Y2, Y3))) <=> ((~quotient(identity, Y2, Y3)) | (~quotient(identity, Y1, Y2)) | (~quotient(identity, X, Y1)))), (((((~quotient(identity, X, Y1)) | (~quotient(identity, Y1, Y2))) | (~quotient(identity, Y2, Y3))) | (Y1 = Y3)) <=> (((~quotient(identity, Y2, Y3)) | (~quotient(identity, Y1, Y2)) | (~quotient(identity, X, Y1))) | (Y1 = Y3)))), rewrite((((~quotient(identity, Y2, Y3)) | (~quotient(identity, Y1, Y2)) | (~quotient(identity, X, Y1))) | (Y1 = Y3)) <=> ((Y1 = Y3) | (~quotient(identity, Y2, Y3)) | (~quotient(identity, Y1, Y2)) | (~quotient(identity, X, Y1)))), (((((~quotient(identity, X, Y1)) | (~quotient(identity, Y1, Y2))) | (~quotient(identity, Y2, Y3))) | (Y1 = Y3)) <=> ((Y1 = Y3) | (~quotient(identity, Y2, Y3)) | (~quotient(identity, Y1, Y2)) | (~quotient(identity, X, Y1)))))),
% 0.98/0.91 inference(bind,[status(th)],[])).
% 0.98/0.91 tff(161,plain,
% 0.98/0.91 (![Y2: $i, Y1: $i, Y3: $i, X: $i] : ((((~quotient(identity, X, Y1)) | (~quotient(identity, Y1, Y2))) | (~quotient(identity, Y2, Y3))) | (Y1 = Y3)) <=> ![Y2: $i, Y1: $i, Y3: $i, X: $i] : ((Y1 = Y3) | (~quotient(identity, Y2, Y3)) | (~quotient(identity, Y1, Y2)) | (~quotient(identity, X, Y1)))),
% 0.98/0.91 inference(quant_intro,[status(thm)],[160])).
% 0.98/0.91 tff(162,axiom,(![Y2: $i, Y1: $i, Y3: $i, X: $i] : ((((~quotient(identity, X, Y1)) | (~quotient(identity, Y1, Y2))) | (~quotient(identity, Y2, Y3))) | (Y1 = Y3))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','one_inversion_equals_three')).
% 0.98/0.91 tff(163,plain,
% 0.98/0.91 (![Y2: $i, Y1: $i, Y3: $i, X: $i] : ((Y1 = Y3) | (~quotient(identity, Y2, Y3)) | (~quotient(identity, Y1, Y2)) | (~quotient(identity, X, Y1)))),
% 0.98/0.91 inference(modus_ponens,[status(thm)],[162, 161])).
% 0.98/0.91 tff(164,plain,
% 0.98/0.91 (![Y2: $i, Y1: $i, Y3: $i, X: $i] : ((Y1 = Y3) | (~quotient(identity, Y2, Y3)) | (~quotient(identity, Y1, Y2)) | (~quotient(identity, X, Y1)))),
% 0.98/0.91 inference(modus_ponens,[status(thm)],[163, 159])).
% 0.98/0.91 tff(165,plain,(
% 0.98/0.91 ![Y2: $i, Y1: $i, Y3: $i, X: $i] : ((Y1 = Y3) | (~quotient(identity, Y2, Y3)) | (~quotient(identity, Y1, Y2)) | (~quotient(identity, X, Y1)))),
% 0.98/0.91 inference(skolemize,[status(sab)],[164])).
% 0.98/0.91 tff(166,plain,
% 0.98/0.91 (![Y2: $i, Y1: $i, Y3: $i, X: $i] : ((Y1 = Y3) | (~quotient(identity, Y2, Y3)) | (~quotient(identity, Y1, Y2)) | (~quotient(identity, X, Y1)))),
% 0.98/0.91 inference(modus_ponens,[status(thm)],[165, 158])).
% 0.98/0.91 tff(167,plain,
% 0.98/0.91 (((~![Y2: $i, Y1: $i, Y3: $i, X: $i] : ((Y1 = Y3) | (~quotient(identity, Y2, Y3)) | (~quotient(identity, Y1, Y2)) | (~quotient(identity, X, Y1)))) | ((identity = divide(identity, divide(idQa, identity))) | (~quotient(identity, divide(idQa, identity), divide(identity, divide(idQa, identity)))) | (~quotient(identity, identity, divide(idQa, identity))) | (~quotient(identity, divide(idQa, identity), identity)))) <=> ((~![Y2: $i, Y1: $i, Y3: $i, X: $i] : ((Y1 = Y3) | (~quotient(identity, Y2, Y3)) | (~quotient(identity, Y1, Y2)) | (~quotient(identity, X, Y1)))) | (identity = divide(identity, divide(idQa, identity))) | (~quotient(identity, divide(idQa, identity), divide(identity, divide(idQa, identity)))) | (~quotient(identity, identity, divide(idQa, identity))) | (~quotient(identity, divide(idQa, identity), identity)))),
% 0.98/0.91 inference(rewrite,[status(thm)],[])).
% 0.98/0.91 tff(168,plain,
% 0.98/0.91 ((~![Y2: $i, Y1: $i, Y3: $i, X: $i] : ((Y1 = Y3) | (~quotient(identity, Y2, Y3)) | (~quotient(identity, Y1, Y2)) | (~quotient(identity, X, Y1)))) | ((identity = divide(identity, divide(idQa, identity))) | (~quotient(identity, divide(idQa, identity), divide(identity, divide(idQa, identity)))) | (~quotient(identity, identity, divide(idQa, identity))) | (~quotient(identity, divide(idQa, identity), identity)))),
% 0.98/0.91 inference(quant_inst,[status(thm)],[])).
% 0.98/0.91 tff(169,plain,
% 0.98/0.91 ((~![Y2: $i, Y1: $i, Y3: $i, X: $i] : ((Y1 = Y3) | (~quotient(identity, Y2, Y3)) | (~quotient(identity, Y1, Y2)) | (~quotient(identity, X, Y1)))) | (identity = divide(identity, divide(idQa, identity))) | (~quotient(identity, divide(idQa, identity), divide(identity, divide(idQa, identity)))) | (~quotient(identity, identity, divide(idQa, identity))) | (~quotient(identity, divide(idQa, identity), identity))),
% 0.98/0.91 inference(modus_ponens,[status(thm)],[168, 167])).
% 0.98/0.91 tff(170,plain,
% 0.98/0.91 ((identity = divide(identity, divide(idQa, identity))) | (~quotient(identity, identity, divide(idQa, identity))) | (~quotient(identity, divide(idQa, identity), identity))),
% 0.98/0.91 inference(unit_resolution,[status(thm)],[169, 166, 156])).
% 0.98/0.91 tff(171,plain,
% 0.98/0.91 (identity = divide(identity, divide(idQa, identity))),
% 0.98/0.91 inference(unit_resolution,[status(thm)],[170, 154, 136])).
% 0.98/0.91 tff(172,plain,
% 0.98/0.91 (quotient(identity, idQ_idQa, divide(divide(identity, divide(idQa, identity)), idQ_idQa)) <=> quotient(divide(identity, divide(idQa, identity)), idQ_idQa, divide(divide(identity, divide(idQa, identity)), idQ_idQa))),
% 0.98/0.91 inference(monotonicity,[status(thm)],[171])).
% 0.98/0.91 tff(173,plain,
% 0.98/0.91 (quotient(divide(identity, divide(idQa, identity)), idQ_idQa, divide(divide(identity, divide(idQa, identity)), idQ_idQa)) <=> quotient(identity, idQ_idQa, divide(divide(identity, divide(idQa, identity)), idQ_idQa))),
% 0.98/0.92 inference(symmetry,[status(thm)],[172])).
% 0.98/0.92 tff(174,plain,
% 0.98/0.92 ((~![Y: $i, X: $i] : quotient(X, Y, divide(X, Y))) | quotient(divide(identity, divide(idQa, identity)), idQ_idQa, divide(divide(identity, divide(idQa, identity)), idQ_idQa))),
% 0.98/0.92 inference(quant_inst,[status(thm)],[])).
% 0.98/0.92 tff(175,plain,
% 0.98/0.92 (quotient(divide(identity, divide(idQa, identity)), idQ_idQa, divide(divide(identity, divide(idQa, identity)), idQ_idQa))),
% 0.98/0.92 inference(unit_resolution,[status(thm)],[174, 7])).
% 0.98/0.92 tff(176,plain,
% 0.98/0.92 (quotient(identity, idQ_idQa, divide(divide(identity, divide(idQa, identity)), idQ_idQa))),
% 0.98/0.92 inference(modus_ponens,[status(thm)],[175, 173])).
% 0.98/0.92 tff(177,plain,
% 0.98/0.92 (quotient(identity, divide(idQa, divide(idQa, identity)), idQ_idQa) <=> quotient(identity, idQa, idQ_idQa)),
% 0.98/0.92 inference(monotonicity,[status(thm)],[128])).
% 0.98/0.92 tff(178,plain,
% 0.98/0.92 (quotient(identity, idQa, idQ_idQa) <=> quotient(identity, divide(idQa, divide(idQa, identity)), idQ_idQa)),
% 0.98/0.92 inference(symmetry,[status(thm)],[177])).
% 0.98/0.92 tff(179,plain,
% 0.98/0.92 (quotient(identity, idQa, idQ_idQa) <=> quotient(identity, idQa, idQ_idQa)),
% 0.98/0.92 inference(rewrite,[status(thm)],[])).
% 0.98/0.92 tff(180,axiom,(quotient(identity, idQa, idQ_idQa)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','identity_divide_idQa')).
% 0.98/0.92 tff(181,plain,
% 0.98/0.92 (quotient(identity, idQa, idQ_idQa)),
% 0.98/0.92 inference(modus_ponens,[status(thm)],[180, 179])).
% 0.98/0.92 tff(182,plain,
% 0.98/0.92 (quotient(identity, divide(idQa, divide(idQa, identity)), idQ_idQa)),
% 0.98/0.92 inference(modus_ponens,[status(thm)],[181, 178])).
% 0.98/0.92 tff(183,plain,
% 0.98/0.92 (((~![Y2: $i, Y1: $i, Y3: $i, X: $i] : ((Y1 = Y3) | (~quotient(identity, Y2, Y3)) | (~quotient(identity, Y1, Y2)) | (~quotient(identity, X, Y1)))) | ((divide(idQa, divide(idQa, identity)) = divide(divide(identity, divide(idQa, identity)), idQ_idQa)) | (~quotient(identity, divide(idQa, divide(idQa, identity)), idQ_idQa)) | (~quotient(identity, idQ_idQa, divide(divide(identity, divide(idQa, identity)), idQ_idQa))) | (~quotient(identity, a, divide(idQa, divide(idQa, identity)))))) <=> ((~![Y2: $i, Y1: $i, Y3: $i, X: $i] : ((Y1 = Y3) | (~quotient(identity, Y2, Y3)) | (~quotient(identity, Y1, Y2)) | (~quotient(identity, X, Y1)))) | (divide(idQa, divide(idQa, identity)) = divide(divide(identity, divide(idQa, identity)), idQ_idQa)) | (~quotient(identity, divide(idQa, divide(idQa, identity)), idQ_idQa)) | (~quotient(identity, idQ_idQa, divide(divide(identity, divide(idQa, identity)), idQ_idQa))) | (~quotient(identity, a, divide(idQa, divide(idQa, identity)))))),
% 0.98/0.92 inference(rewrite,[status(thm)],[])).
% 0.98/0.92 tff(184,plain,
% 0.98/0.92 (((divide(idQa, divide(idQa, identity)) = divide(divide(identity, divide(idQa, identity)), idQ_idQa)) | (~quotient(identity, idQ_idQa, divide(divide(identity, divide(idQa, identity)), idQ_idQa))) | (~quotient(identity, divide(idQa, divide(idQa, identity)), idQ_idQa)) | (~quotient(identity, a, divide(idQa, divide(idQa, identity))))) <=> ((divide(idQa, divide(idQa, identity)) = divide(divide(identity, divide(idQa, identity)), idQ_idQa)) | (~quotient(identity, divide(idQa, divide(idQa, identity)), idQ_idQa)) | (~quotient(identity, idQ_idQa, divide(divide(identity, divide(idQa, identity)), idQ_idQa))) | (~quotient(identity, a, divide(idQa, divide(idQa, identity)))))),
% 0.98/0.92 inference(rewrite,[status(thm)],[])).
% 0.98/0.92 tff(185,plain,
% 0.98/0.92 (((~![Y2: $i, Y1: $i, Y3: $i, X: $i] : ((Y1 = Y3) | (~quotient(identity, Y2, Y3)) | (~quotient(identity, Y1, Y2)) | (~quotient(identity, X, Y1)))) | ((divide(idQa, divide(idQa, identity)) = divide(divide(identity, divide(idQa, identity)), idQ_idQa)) | (~quotient(identity, idQ_idQa, divide(divide(identity, divide(idQa, identity)), idQ_idQa))) | (~quotient(identity, divide(idQa, divide(idQa, identity)), idQ_idQa)) | (~quotient(identity, a, divide(idQa, divide(idQa, identity)))))) <=> ((~![Y2: $i, Y1: $i, Y3: $i, X: $i] : ((Y1 = Y3) | (~quotient(identity, Y2, Y3)) | (~quotient(identity, Y1, Y2)) | (~quotient(identity, X, Y1)))) | ((divide(idQa, divide(idQa, identity)) = divide(divide(identity, divide(idQa, identity)), idQ_idQa)) | (~quotient(identity, divide(idQa, divide(idQa, identity)), idQ_idQa)) | (~quotient(identity, idQ_idQa, divide(divide(identity, divide(idQa, identity)), idQ_idQa))) | (~quotient(identity, a, divide(idQa, divide(idQa, identity))))))),
% 0.98/0.92 inference(monotonicity,[status(thm)],[184])).
% 0.98/0.92 tff(186,plain,
% 0.98/0.92 (((~![Y2: $i, Y1: $i, Y3: $i, X: $i] : ((Y1 = Y3) | (~quotient(identity, Y2, Y3)) | (~quotient(identity, Y1, Y2)) | (~quotient(identity, X, Y1)))) | ((divide(idQa, divide(idQa, identity)) = divide(divide(identity, divide(idQa, identity)), idQ_idQa)) | (~quotient(identity, idQ_idQa, divide(divide(identity, divide(idQa, identity)), idQ_idQa))) | (~quotient(identity, divide(idQa, divide(idQa, identity)), idQ_idQa)) | (~quotient(identity, a, divide(idQa, divide(idQa, identity)))))) <=> ((~![Y2: $i, Y1: $i, Y3: $i, X: $i] : ((Y1 = Y3) | (~quotient(identity, Y2, Y3)) | (~quotient(identity, Y1, Y2)) | (~quotient(identity, X, Y1)))) | (divide(idQa, divide(idQa, identity)) = divide(divide(identity, divide(idQa, identity)), idQ_idQa)) | (~quotient(identity, divide(idQa, divide(idQa, identity)), idQ_idQa)) | (~quotient(identity, idQ_idQa, divide(divide(identity, divide(idQa, identity)), idQ_idQa))) | (~quotient(identity, a, divide(idQa, divide(idQa, identity)))))),
% 0.98/0.92 inference(transitivity,[status(thm)],[185, 183])).
% 0.98/0.92 tff(187,plain,
% 0.98/0.92 ((~![Y2: $i, Y1: $i, Y3: $i, X: $i] : ((Y1 = Y3) | (~quotient(identity, Y2, Y3)) | (~quotient(identity, Y1, Y2)) | (~quotient(identity, X, Y1)))) | ((divide(idQa, divide(idQa, identity)) = divide(divide(identity, divide(idQa, identity)), idQ_idQa)) | (~quotient(identity, idQ_idQa, divide(divide(identity, divide(idQa, identity)), idQ_idQa))) | (~quotient(identity, divide(idQa, divide(idQa, identity)), idQ_idQa)) | (~quotient(identity, a, divide(idQa, divide(idQa, identity)))))),
% 0.98/0.92 inference(quant_inst,[status(thm)],[])).
% 0.98/0.92 tff(188,plain,
% 0.98/0.92 ((~![Y2: $i, Y1: $i, Y3: $i, X: $i] : ((Y1 = Y3) | (~quotient(identity, Y2, Y3)) | (~quotient(identity, Y1, Y2)) | (~quotient(identity, X, Y1)))) | (divide(idQa, divide(idQa, identity)) = divide(divide(identity, divide(idQa, identity)), idQ_idQa)) | (~quotient(identity, divide(idQa, divide(idQa, identity)), idQ_idQa)) | (~quotient(identity, idQ_idQa, divide(divide(identity, divide(idQa, identity)), idQ_idQa))) | (~quotient(identity, a, divide(idQa, divide(idQa, identity))))),
% 0.98/0.92 inference(modus_ponens,[status(thm)],[187, 186])).
% 0.98/0.92 tff(189,plain,
% 0.98/0.92 ((divide(idQa, divide(idQa, identity)) = divide(divide(identity, divide(idQa, identity)), idQ_idQa)) | (~quotient(identity, divide(idQa, divide(idQa, identity)), idQ_idQa)) | (~quotient(identity, idQ_idQa, divide(divide(identity, divide(idQa, identity)), idQ_idQa))) | (~quotient(identity, a, divide(idQa, divide(idQa, identity))))),
% 0.98/0.92 inference(unit_resolution,[status(thm)],[188, 166])).
% 0.98/0.92 tff(190,plain,
% 0.98/0.92 (divide(idQa, divide(idQa, identity)) = divide(divide(identity, divide(idQa, identity)), idQ_idQa)),
% 0.98/0.92 inference(unit_resolution,[status(thm)],[189, 182, 176, 131])).
% 0.98/0.92 tff(191,plain,
% 0.98/0.92 (quotient(divide(identity, divide(idQa, identity)), idQ_idQa, divide(idQa, divide(idQa, identity))) <=> quotient(divide(identity, divide(idQa, identity)), idQ_idQa, divide(divide(identity, divide(idQa, identity)), idQ_idQa))),
% 0.98/0.92 inference(monotonicity,[status(thm)],[190])).
% 0.98/0.92 tff(192,plain,
% 0.98/0.92 (quotient(divide(identity, divide(idQa, identity)), idQ_idQa, divide(divide(identity, divide(idQa, identity)), idQ_idQa)) <=> quotient(divide(identity, divide(idQa, identity)), idQ_idQa, divide(idQa, divide(idQa, identity)))),
% 0.98/0.92 inference(symmetry,[status(thm)],[191])).
% 0.98/0.92 tff(193,plain,
% 0.98/0.92 (quotient(divide(identity, divide(idQa, identity)), idQ_idQa, divide(idQa, divide(idQa, identity)))),
% 0.98/0.92 inference(modus_ponens,[status(thm)],[175, 192])).
% 0.98/0.92 tff(194,plain,
% 0.98/0.92 (quotient(divide(idQa, divide(idQa, identity)), divide(idQa, identity), divide(idQa, divide(idQa, identity))) <=> quotient(idQa, zero, idQa)),
% 0.98/0.92 inference(monotonicity,[status(thm)],[128, 108, 128])).
% 0.98/0.92 tff(195,plain,
% 0.98/0.92 (quotient(idQa, zero, idQa) <=> quotient(divide(idQa, divide(idQa, identity)), divide(idQa, identity), divide(idQa, divide(idQa, identity)))),
% 0.98/0.92 inference(symmetry,[status(thm)],[194])).
% 0.98/0.92 tff(196,plain,
% 0.98/0.92 (quotient(divide(idQa, divide(idQa, identity)), divide(idQa, identity), divide(idQa, divide(idQa, identity)))),
% 0.98/0.92 inference(modus_ponens,[status(thm)],[119, 195])).
% 0.98/0.92 tff(197,plain,
% 0.98/0.92 (quotient(divide(idQa, divide(idQa, identity)), idQ_idQa, idQa_Q__idQ_idQa) <=> quotient(idQa, idQ_idQa, idQa_Q__idQ_idQa)),
% 0.98/0.92 inference(monotonicity,[status(thm)],[128])).
% 0.98/0.92 tff(198,plain,
% 0.98/0.92 (quotient(idQa, idQ_idQa, idQa_Q__idQ_idQa) <=> quotient(divide(idQa, divide(idQa, identity)), idQ_idQa, idQa_Q__idQ_idQa)),
% 0.98/0.92 inference(symmetry,[status(thm)],[197])).
% 0.98/0.92 tff(199,plain,
% 0.98/0.92 (quotient(divide(idQa, divide(idQa, identity)), idQ_idQa, idQa_Q__idQ_idQa)),
% 0.98/0.92 inference(modus_ponens,[status(thm)],[14, 198])).
% 0.98/0.92 tff(200,plain,
% 0.98/0.92 (quotient(idQ_idQa, idQ_idQa, divide(idQa, identity)) <=> quotient(idQ_idQa, idQ_idQa, zero)),
% 0.98/0.92 inference(monotonicity,[status(thm)],[108])).
% 0.98/0.92 tff(201,plain,
% 0.98/0.92 (quotient(idQ_idQa, idQ_idQa, zero) <=> quotient(idQ_idQa, idQ_idQa, divide(idQa, identity))),
% 0.98/0.92 inference(symmetry,[status(thm)],[200])).
% 0.98/0.92 tff(202,plain,
% 0.98/0.92 (^[Z: $i, Y: $i, W2: $i, W1: $i, X: $i] : refl((less_equal(W1, W2) | (~less_equal(X, Y)) | (~quotient(Y, Z, W2)) | (~quotient(X, Z, W1))) <=> (less_equal(W1, W2) | (~less_equal(X, Y)) | (~quotient(Y, Z, W2)) | (~quotient(X, Z, W1))))),
% 0.98/0.92 inference(bind,[status(th)],[])).
% 0.98/0.92 tff(203,plain,
% 0.98/0.92 (![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))) <=> ![Z: $i, Y: $i, W2: $i, W1: $i, X: $i] : (less_equal(W1, W2) | (~less_equal(X, Y)) | (~quotient(Y, Z, W2)) | (~quotient(X, Z, W1)))),
% 0.98/0.92 inference(quant_intro,[status(thm)],[202])).
% 0.98/0.92 tff(204,plain,
% 0.98/0.92 (![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))) <=> ![Z: $i, Y: $i, W2: $i, W1: $i, X: $i] : (less_equal(W1, W2) | (~less_equal(X, Y)) | (~quotient(Y, Z, W2)) | (~quotient(X, Z, W1)))),
% 0.98/0.92 inference(rewrite,[status(thm)],[])).
% 0.98/0.92 tff(205,plain,
% 0.98/0.92 (^[Z: $i, Y: $i, W2: $i, W1: $i, X: $i] : trans(monotonicity(rewrite((((~less_equal(X, Y)) | (~quotient(X, Z, W1))) | (~quotient(Y, Z, W2))) <=> ((~less_equal(X, Y)) | (~quotient(Y, Z, W2)) | (~quotient(X, Z, W1)))), (((((~less_equal(X, Y)) | (~quotient(X, Z, W1))) | (~quotient(Y, Z, W2))) | less_equal(W1, W2)) <=> (((~less_equal(X, Y)) | (~quotient(Y, Z, W2)) | (~quotient(X, Z, W1))) | less_equal(W1, W2)))), rewrite((((~less_equal(X, Y)) | (~quotient(Y, Z, W2)) | (~quotient(X, Z, W1))) | less_equal(W1, W2)) <=> (less_equal(W1, W2) | (~less_equal(X, Y)) | (~quotient(Y, Z, W2)) | (~quotient(X, Z, W1)))), (((((~less_equal(X, Y)) | (~quotient(X, Z, W1))) | (~quotient(Y, Z, W2))) | less_equal(W1, W2)) <=> (less_equal(W1, W2) | (~less_equal(X, Y)) | (~quotient(Y, Z, W2)) | (~quotient(X, Z, W1)))))),
% 0.98/0.92 inference(bind,[status(th)],[])).
% 0.98/0.92 tff(206,plain,
% 0.98/0.92 (![Z: $i, Y: $i, W2: $i, W1: $i, X: $i] : ((((~less_equal(X, Y)) | (~quotient(X, Z, W1))) | (~quotient(Y, Z, W2))) | less_equal(W1, W2)) <=> ![Z: $i, Y: $i, W2: $i, W1: $i, X: $i] : (less_equal(W1, W2) | (~less_equal(X, Y)) | (~quotient(Y, Z, W2)) | (~quotient(X, Z, W1)))),
% 0.98/0.92 inference(quant_intro,[status(thm)],[205])).
% 0.98/0.92 tff(207,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')).
% 0.98/0.92 tff(208,plain,
% 0.98/0.92 (![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)))),
% 0.98/0.92 inference(modus_ponens,[status(thm)],[207, 206])).
% 0.98/0.92 tff(209,plain,
% 0.98/0.92 (![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)))),
% 0.98/0.92 inference(modus_ponens,[status(thm)],[208, 204])).
% 0.98/0.92 tff(210,plain,(
% 0.98/0.92 ![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)))),
% 0.98/0.92 inference(skolemize,[status(sab)],[209])).
% 0.98/0.92 tff(211,plain,
% 0.98/0.92 (![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)))),
% 0.98/0.92 inference(modus_ponens,[status(thm)],[210, 203])).
% 0.98/0.92 tff(212,plain,
% 0.98/0.92 (((~![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))),
% 0.98/0.92 inference(rewrite,[status(thm)],[])).
% 0.98/0.92 tff(213,plain,
% 0.98/0.92 ((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))),
% 0.98/0.92 inference(rewrite,[status(thm)],[])).
% 0.98/0.92 tff(214,plain,
% 0.98/0.92 (((~![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)))),
% 0.98/0.92 inference(monotonicity,[status(thm)],[213])).
% 0.98/0.92 tff(215,plain,
% 0.98/0.92 (((~![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))),
% 0.98/0.92 inference(transitivity,[status(thm)],[214, 212])).
% 0.98/0.92 tff(216,plain,
% 0.98/0.92 ((~![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)))),
% 0.98/0.92 inference(quant_inst,[status(thm)],[])).
% 0.98/0.92 tff(217,plain,
% 0.98/0.92 ((~![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)),
% 0.98/0.92 inference(modus_ponens,[status(thm)],[216, 215])).
% 0.98/0.92 tff(218,plain,
% 0.98/0.92 ((~less_equal(identity, identity)) | less_equal(idQ_idQa, idQ_idQa)),
% 0.98/0.92 inference(unit_resolution,[status(thm)],[217, 211, 181])).
% 0.98/0.92 tff(219,plain,
% 0.98/0.92 (less_equal(idQ_idQa, idQ_idQa)),
% 0.98/0.92 inference(unit_resolution,[status(thm)],[218, 149])).
% 0.98/0.92 tff(220,plain,
% 0.98/0.92 (((~![Y: $i, X: $i] : ((~less_equal(X, Y)) | quotient(X, Y, zero))) | ((~less_equal(idQ_idQa, idQ_idQa)) | quotient(idQ_idQa, idQ_idQa, zero))) <=> ((~![Y: $i, X: $i] : ((~less_equal(X, Y)) | quotient(X, Y, zero))) | (~less_equal(idQ_idQa, idQ_idQa)) | quotient(idQ_idQa, idQ_idQa, zero))),
% 0.98/0.92 inference(rewrite,[status(thm)],[])).
% 0.98/0.92 tff(221,plain,
% 0.98/0.92 ((~![Y: $i, X: $i] : ((~less_equal(X, Y)) | quotient(X, Y, zero))) | ((~less_equal(idQ_idQa, idQ_idQa)) | quotient(idQ_idQa, idQ_idQa, zero))),
% 0.98/0.92 inference(quant_inst,[status(thm)],[])).
% 0.98/0.92 tff(222,plain,
% 0.98/0.92 ((~![Y: $i, X: $i] : ((~less_equal(X, Y)) | quotient(X, Y, zero))) | (~less_equal(idQ_idQa, idQ_idQa)) | quotient(idQ_idQa, idQ_idQa, zero)),
% 0.98/0.92 inference(modus_ponens,[status(thm)],[221, 220])).
% 0.98/0.92 tff(223,plain,
% 0.98/0.92 (quotient(idQ_idQa, idQ_idQa, zero)),
% 0.98/0.92 inference(unit_resolution,[status(thm)],[222, 86, 219])).
% 0.98/0.92 tff(224,plain,
% 0.98/0.92 (quotient(idQ_idQa, idQ_idQa, divide(idQa, identity))),
% 0.98/0.92 inference(modus_ponens,[status(thm)],[223, 201])).
% 0.98/0.92 tff(225,plain,
% 0.98/0.92 (^[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))))),
% 0.98/0.92 inference(bind,[status(th)],[])).
% 0.98/0.92 tff(226,plain,
% 0.98/0.92 (![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)))),
% 0.98/0.92 inference(quant_intro,[status(thm)],[225])).
% 0.98/0.92 tff(227,plain,
% 0.98/0.92 (![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)))),
% 0.98/0.92 inference(rewrite,[status(thm)],[])).
% 0.98/0.92 tff(228,plain,
% 0.98/0.92 (^[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)))))),
% 0.98/0.92 inference(bind,[status(th)],[])).
% 0.98/0.92 tff(229,plain,
% 0.98/0.92 (![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)))),
% 0.98/0.92 inference(quant_intro,[status(thm)],[228])).
% 0.98/0.92 tff(230,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')).
% 0.98/0.92 tff(231,plain,
% 0.98/0.92 (![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)))),
% 0.98/0.92 inference(modus_ponens,[status(thm)],[230, 229])).
% 0.98/0.92 tff(232,plain,
% 0.98/0.92 (![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)))),
% 0.98/0.92 inference(modus_ponens,[status(thm)],[231, 227])).
% 0.98/0.92 tff(233,plain,(
% 0.98/0.92 ![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)))),
% 0.98/0.92 inference(skolemize,[status(sab)],[232])).
% 0.98/0.92 tff(234,plain,
% 0.98/0.92 (![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)))),
% 0.98/0.92 inference(modus_ponens,[status(thm)],[233, 226])).
% 0.98/0.92 tff(235,plain,
% 0.98/0.92 (((~![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)))) | ((~quotient(idQ_idQa, idQ_idQa, divide(idQa, identity))) | (~quotient(divide(idQa, divide(idQa, identity)), idQ_idQa, idQa_Q__idQ_idQa)) | less_equal(divide(idQa, divide(idQa, identity)), idQa_Q__idQ_idQa) | (~quotient(divide(identity, divide(idQa, identity)), idQ_idQa, divide(idQa, divide(idQa, identity)))) | (~quotient(divide(idQa, divide(idQa, identity)), divide(idQa, identity), divide(idQa, divide(idQa, identity)))))) <=> ((~![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)))) | (~quotient(idQ_idQa, idQ_idQa, divide(idQa, identity))) | (~quotient(divide(idQa, divide(idQa, identity)), idQ_idQa, idQa_Q__idQ_idQa)) | less_equal(divide(idQa, divide(idQa, identity)), idQa_Q__idQ_idQa) | (~quotient(divide(identity, divide(idQa, identity)), idQ_idQa, divide(idQa, divide(idQa, identity)))) | (~quotient(divide(idQa, divide(idQa, identity)), divide(idQa, identity), divide(idQa, divide(idQa, identity)))))),
% 0.98/0.92 inference(rewrite,[status(thm)],[])).
% 0.98/0.92 tff(236,plain,
% 0.98/0.92 ((less_equal(divide(idQa, divide(idQa, identity)), idQa_Q__idQ_idQa) | (~quotient(divide(idQa, divide(idQa, identity)), idQ_idQa, idQa_Q__idQ_idQa)) | (~quotient(divide(idQa, divide(idQa, identity)), divide(idQa, identity), divide(idQa, divide(idQa, identity)))) | (~quotient(divide(identity, divide(idQa, identity)), idQ_idQa, divide(idQa, divide(idQa, identity)))) | (~quotient(idQ_idQa, idQ_idQa, divide(idQa, identity))) | (~quotient(divide(identity, divide(idQa, identity)), idQ_idQa, divide(idQa, divide(idQa, identity))))) <=> ((~quotient(idQ_idQa, idQ_idQa, divide(idQa, identity))) | (~quotient(divide(idQa, divide(idQa, identity)), idQ_idQa, idQa_Q__idQ_idQa)) | less_equal(divide(idQa, divide(idQa, identity)), idQa_Q__idQ_idQa) | (~quotient(divide(identity, divide(idQa, identity)), idQ_idQa, divide(idQa, divide(idQa, identity)))) | (~quotient(divide(idQa, divide(idQa, identity)), divide(idQa, identity), divide(idQa, divide(idQa, identity)))))),
% 0.98/0.92 inference(rewrite,[status(thm)],[])).
% 0.98/0.92 tff(237,plain,
% 0.98/0.92 (((~![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(divide(idQa, divide(idQa, identity)), idQa_Q__idQ_idQa) | (~quotient(divide(idQa, divide(idQa, identity)), idQ_idQa, idQa_Q__idQ_idQa)) | (~quotient(divide(idQa, divide(idQa, identity)), divide(idQa, identity), divide(idQa, divide(idQa, identity)))) | (~quotient(divide(identity, divide(idQa, identity)), idQ_idQa, divide(idQa, divide(idQa, identity)))) | (~quotient(idQ_idQa, idQ_idQa, divide(idQa, identity))) | (~quotient(divide(identity, divide(idQa, identity)), idQ_idQa, divide(idQa, divide(idQa, identity)))))) <=> ((~![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)))) | ((~quotient(idQ_idQa, idQ_idQa, divide(idQa, identity))) | (~quotient(divide(idQa, divide(idQa, identity)), idQ_idQa, idQa_Q__idQ_idQa)) | less_equal(divide(idQa, divide(idQa, identity)), idQa_Q__idQ_idQa) | (~quotient(divide(identity, divide(idQa, identity)), idQ_idQa, divide(idQa, divide(idQa, identity)))) | (~quotient(divide(idQa, divide(idQa, identity)), divide(idQa, identity), divide(idQa, divide(idQa, identity))))))),
% 0.98/0.92 inference(monotonicity,[status(thm)],[236])).
% 0.98/0.92 tff(238,plain,
% 0.98/0.92 (((~![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(divide(idQa, divide(idQa, identity)), idQa_Q__idQ_idQa) | (~quotient(divide(idQa, divide(idQa, identity)), idQ_idQa, idQa_Q__idQ_idQa)) | (~quotient(divide(idQa, divide(idQa, identity)), divide(idQa, identity), divide(idQa, divide(idQa, identity)))) | (~quotient(divide(identity, divide(idQa, identity)), idQ_idQa, divide(idQa, divide(idQa, identity)))) | (~quotient(idQ_idQa, idQ_idQa, divide(idQa, identity))) | (~quotient(divide(identity, divide(idQa, identity)), idQ_idQa, divide(idQa, divide(idQa, identity)))))) <=> ((~![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)))) | (~quotient(idQ_idQa, idQ_idQa, divide(idQa, identity))) | (~quotient(divide(idQa, divide(idQa, identity)), idQ_idQa, idQa_Q__idQ_idQa)) | less_equal(divide(idQa, divide(idQa, identity)), idQa_Q__idQ_idQa) | (~quotient(divide(identity, divide(idQa, identity)), idQ_idQa, divide(idQa, divide(idQa, identity)))) | (~quotient(divide(idQa, divide(idQa, identity)), divide(idQa, identity), divide(idQa, divide(idQa, identity)))))),
% 0.98/0.93 inference(transitivity,[status(thm)],[237, 235])).
% 0.98/0.93 tff(239,plain,
% 0.98/0.93 ((~![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(divide(idQa, divide(idQa, identity)), idQa_Q__idQ_idQa) | (~quotient(divide(idQa, divide(idQa, identity)), idQ_idQa, idQa_Q__idQ_idQa)) | (~quotient(divide(idQa, divide(idQa, identity)), divide(idQa, identity), divide(idQa, divide(idQa, identity)))) | (~quotient(divide(identity, divide(idQa, identity)), idQ_idQa, divide(idQa, divide(idQa, identity)))) | (~quotient(idQ_idQa, idQ_idQa, divide(idQa, identity))) | (~quotient(divide(identity, divide(idQa, identity)), idQ_idQa, divide(idQa, divide(idQa, identity)))))),
% 0.98/0.93 inference(quant_inst,[status(thm)],[])).
% 0.98/0.93 tff(240,plain,
% 0.98/0.93 ((~![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)))) | (~quotient(idQ_idQa, idQ_idQa, divide(idQa, identity))) | (~quotient(divide(idQa, divide(idQa, identity)), idQ_idQa, idQa_Q__idQ_idQa)) | less_equal(divide(idQa, divide(idQa, identity)), idQa_Q__idQ_idQa) | (~quotient(divide(identity, divide(idQa, identity)), idQ_idQa, divide(idQa, divide(idQa, identity)))) | (~quotient(divide(idQa, divide(idQa, identity)), divide(idQa, identity), divide(idQa, divide(idQa, identity))))),
% 0.98/0.93 inference(modus_ponens,[status(thm)],[239, 238])).
% 0.98/0.93 tff(241,plain,
% 0.98/0.93 (less_equal(divide(idQa, divide(idQa, identity)), idQa_Q__idQ_idQa) | (~quotient(divide(identity, divide(idQa, identity)), idQ_idQa, divide(idQa, divide(idQa, identity))))),
% 0.98/0.93 inference(unit_resolution,[status(thm)],[240, 234, 224, 199, 196])).
% 0.98/0.93 tff(242,plain,
% 0.98/0.93 (less_equal(divide(idQa, divide(idQa, identity)), idQa_Q__idQ_idQa)),
% 0.98/0.93 inference(unit_resolution,[status(thm)],[241, 193])).
% 0.98/0.93 tff(243,plain,
% 0.98/0.93 (![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)))),
% 0.98/0.93 inference(rewrite,[status(thm)],[])).
% 0.98/0.93 tff(244,plain,
% 0.98/0.93 (![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)))),
% 0.98/0.93 inference(rewrite,[status(thm)],[])).
% 0.98/0.93 tff(245,plain,
% 0.98/0.93 (^[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))))),
% 0.98/0.93 inference(bind,[status(th)],[])).
% 0.98/0.93 tff(246,plain,
% 0.98/0.93 (![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)))),
% 0.98/0.93 inference(quant_intro,[status(thm)],[245])).
% 0.98/0.93 tff(247,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')).
% 0.98/0.93 tff(248,plain,
% 0.98/0.93 (![Y: $i, X: $i] : ((~less_equal(X, Y)) | (X = Y) | (~less_equal(Y, X)))),
% 0.98/0.93 inference(modus_ponens,[status(thm)],[247, 246])).
% 0.98/0.93 tff(249,plain,
% 0.98/0.93 (![Y: $i, X: $i] : ((~less_equal(X, Y)) | (X = Y) | (~less_equal(Y, X)))),
% 0.98/0.93 inference(modus_ponens,[status(thm)],[248, 244])).
% 0.98/0.93 tff(250,plain,(
% 0.98/0.93 ![Y: $i, X: $i] : ((~less_equal(X, Y)) | (X = Y) | (~less_equal(Y, X)))),
% 0.98/0.93 inference(skolemize,[status(sab)],[249])).
% 0.98/0.93 tff(251,plain,
% 0.98/0.93 (![Y: $i, X: $i] : ((~less_equal(X, Y)) | (X = Y) | (~less_equal(Y, X)))),
% 0.98/0.93 inference(modus_ponens,[status(thm)],[250, 243])).
% 0.98/0.93 tff(252,plain,
% 0.98/0.93 (((~![Y: $i, X: $i] : ((~less_equal(X, Y)) | (X = Y) | (~less_equal(Y, X)))) | ((idQa_Q__idQ_idQa = divide(idQa, divide(idQa, identity))) | (~less_equal(divide(idQa, divide(idQa, identity)), idQa_Q__idQ_idQa)) | (~less_equal(idQa_Q__idQ_idQa, divide(idQa, divide(idQa, identity)))))) <=> ((~![Y: $i, X: $i] : ((~less_equal(X, Y)) | (X = Y) | (~less_equal(Y, X)))) | (idQa_Q__idQ_idQa = divide(idQa, divide(idQa, identity))) | (~less_equal(divide(idQa, divide(idQa, identity)), idQa_Q__idQ_idQa)) | (~less_equal(idQa_Q__idQ_idQa, divide(idQa, divide(idQa, identity)))))),
% 0.98/0.93 inference(rewrite,[status(thm)],[])).
% 0.98/0.93 tff(253,plain,
% 0.98/0.93 (((~less_equal(idQa_Q__idQ_idQa, divide(idQa, divide(idQa, identity)))) | (idQa_Q__idQ_idQa = divide(idQa, divide(idQa, identity))) | (~less_equal(divide(idQa, divide(idQa, identity)), idQa_Q__idQ_idQa))) <=> ((idQa_Q__idQ_idQa = divide(idQa, divide(idQa, identity))) | (~less_equal(divide(idQa, divide(idQa, identity)), idQa_Q__idQ_idQa)) | (~less_equal(idQa_Q__idQ_idQa, divide(idQa, divide(idQa, identity)))))),
% 0.98/0.93 inference(rewrite,[status(thm)],[])).
% 0.98/0.93 tff(254,plain,
% 0.98/0.93 (((~![Y: $i, X: $i] : ((~less_equal(X, Y)) | (X = Y) | (~less_equal(Y, X)))) | ((~less_equal(idQa_Q__idQ_idQa, divide(idQa, divide(idQa, identity)))) | (idQa_Q__idQ_idQa = divide(idQa, divide(idQa, identity))) | (~less_equal(divide(idQa, divide(idQa, identity)), idQa_Q__idQ_idQa)))) <=> ((~![Y: $i, X: $i] : ((~less_equal(X, Y)) | (X = Y) | (~less_equal(Y, X)))) | ((idQa_Q__idQ_idQa = divide(idQa, divide(idQa, identity))) | (~less_equal(divide(idQa, divide(idQa, identity)), idQa_Q__idQ_idQa)) | (~less_equal(idQa_Q__idQ_idQa, divide(idQa, divide(idQa, identity))))))),
% 0.98/0.93 inference(monotonicity,[status(thm)],[253])).
% 0.98/0.93 tff(255,plain,
% 0.98/0.93 (((~![Y: $i, X: $i] : ((~less_equal(X, Y)) | (X = Y) | (~less_equal(Y, X)))) | ((~less_equal(idQa_Q__idQ_idQa, divide(idQa, divide(idQa, identity)))) | (idQa_Q__idQ_idQa = divide(idQa, divide(idQa, identity))) | (~less_equal(divide(idQa, divide(idQa, identity)), idQa_Q__idQ_idQa)))) <=> ((~![Y: $i, X: $i] : ((~less_equal(X, Y)) | (X = Y) | (~less_equal(Y, X)))) | (idQa_Q__idQ_idQa = divide(idQa, divide(idQa, identity))) | (~less_equal(divide(idQa, divide(idQa, identity)), idQa_Q__idQ_idQa)) | (~less_equal(idQa_Q__idQ_idQa, divide(idQa, divide(idQa, identity)))))),
% 0.98/0.93 inference(transitivity,[status(thm)],[254, 252])).
% 0.98/0.93 tff(256,plain,
% 0.98/0.93 ((~![Y: $i, X: $i] : ((~less_equal(X, Y)) | (X = Y) | (~less_equal(Y, X)))) | ((~less_equal(idQa_Q__idQ_idQa, divide(idQa, divide(idQa, identity)))) | (idQa_Q__idQ_idQa = divide(idQa, divide(idQa, identity))) | (~less_equal(divide(idQa, divide(idQa, identity)), idQa_Q__idQ_idQa)))),
% 0.98/0.93 inference(quant_inst,[status(thm)],[])).
% 0.98/0.93 tff(257,plain,
% 0.98/0.93 ((~![Y: $i, X: $i] : ((~less_equal(X, Y)) | (X = Y) | (~less_equal(Y, X)))) | (idQa_Q__idQ_idQa = divide(idQa, divide(idQa, identity))) | (~less_equal(divide(idQa, divide(idQa, identity)), idQa_Q__idQ_idQa)) | (~less_equal(idQa_Q__idQ_idQa, divide(idQa, divide(idQa, identity))))),
% 0.98/0.93 inference(modus_ponens,[status(thm)],[256, 255])).
% 0.98/0.93 tff(258,plain,
% 0.98/0.93 (idQa_Q__idQ_idQa = divide(idQa, divide(idQa, identity))),
% 0.98/0.93 inference(unit_resolution,[status(thm)],[257, 251, 242, 79])).
% 0.98/0.93 tff(259,plain,
% 0.98/0.93 (divide(idQa, divide(idQa, identity)) = idQa_Q__idQ_idQa),
% 0.98/0.93 inference(symmetry,[status(thm)],[258])).
% 0.98/0.93 tff(260,plain,
% 0.98/0.93 (idQa = idQa_Q__idQ_idQa),
% 0.98/0.93 inference(transitivity,[status(thm)],[127, 259])).
% 0.98/0.93 tff(261,plain,
% 0.98/0.93 ((~(idQa = idQa_Q__idQ_idQa)) <=> (~(idQa = idQa_Q__idQ_idQa))),
% 0.98/0.93 inference(rewrite,[status(thm)],[])).
% 0.98/0.93 tff(262,axiom,(~(idQa = idQa_Q__idQ_idQa)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_idQa_equals_idQa_Q__idQ_idQa')).
% 0.98/0.93 tff(263,plain,
% 0.98/0.93 (~(idQa = idQa_Q__idQ_idQa)),
% 0.98/0.93 inference(modus_ponens,[status(thm)],[262, 261])).
% 0.98/0.93 tff(264,plain,
% 0.98/0.93 ($false),
% 0.98/0.93 inference(unit_resolution,[status(thm)],[263, 260])).
% 0.98/0.93 % SZS output end Proof
%------------------------------------------------------------------------------