%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : HEN010-1 : TPTP v9.2.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n012.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 : Tue May 5 04:28:34 PM UTC 2026
% Result : Unsatisfiable 7.71s 5.30s
% Output : CNFRefutation 7.71s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 13
% Syntax : Number of clauses : 115 ( 57 unt; 0 nHn; 82 RR)
% Number of literals : 213 ( 36 equ; 100 neg)
% Maximal clause size : 6 ( 1 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 6 con; 0-2 aty)
% Number of variables : 204 ( 34 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(divisor_existence,axiom,
( less_equal(X3,X1)
| ~ quotient(X1,X2,X3) ),
file('/export/starexec/sandbox/benchmark/Axioms/HEN001-0.ax',divisor_existence) ).
cnf(closure,axiom,
quotient(X1,X2,divide(X1,X2)),
file('/export/starexec/sandbox/benchmark/Axioms/HEN001-0.ax',closure) ).
cnf(quotient_property,axiom,
( less_equal(X7,X8)
| ~ quotient(X1,X2,X3)
| ~ quotient(X2,X4,X5)
| ~ quotient(X1,X4,X6)
| ~ quotient(X6,X5,X7)
| ~ quotient(X3,X4,X8) ),
file('/export/starexec/sandbox/benchmark/Axioms/HEN001-0.ax',quotient_property) ).
cnf(quotient_less_equal,axiom,
( quotient(X1,X2,zero)
| ~ less_equal(X1,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/HEN001-0.ax',quotient_less_equal) ).
cnf(zero_is_smallest,axiom,
less_equal(zero,X1),
file('/export/starexec/sandbox/benchmark/Axioms/HEN001-0.ax',zero_is_smallest) ).
cnf(identity_is_largest,axiom,
less_equal(X1,identity),
file('/export/starexec/sandbox/benchmark/Axioms/HEN001-0.ax',identity_is_largest) ).
cnf(identity_divide_idQa,hypothesis,
quotient(identity,idQa,idQ_idQa),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',identity_divide_idQa) ).
cnf(less_equal_and_equal,axiom,
( X1 = X2
| ~ less_equal(X1,X2)
| ~ less_equal(X2,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/HEN001-0.ax',less_equal_and_equal) ).
cnf(less_equal_quotient,axiom,
( less_equal(X1,X2)
| ~ quotient(X1,X2,zero) ),
file('/export/starexec/sandbox/benchmark/Axioms/HEN001-0.ax',less_equal_quotient) ).
cnf(identity_divide_idQ_idQa,hypothesis,
quotient(idQa,idQ_idQa,idQa_Q__idQ_idQa),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',identity_divide_idQ_idQa) ).
cnf(well_defined,axiom,
( X3 = X4
| ~ quotient(X1,X2,X3)
| ~ quotient(X1,X2,X4) ),
file('/export/starexec/sandbox/benchmark/Axioms/HEN001-0.ax',well_defined) ).
cnf(identity_divide_a,hypothesis,
quotient(identity,a,idQa),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',identity_divide_a) ).
cnf(prove_idQa_equals_idQa_Q__idQ_idQa,negated_conjecture,
idQa != idQa_Q__idQ_idQa,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_idQa_equals_idQa_Q__idQ_idQa) ).
cnf(c_0_13,axiom,
( less_equal(X3,X1)
| ~ quotient(X1,X2,X3) ),
divisor_existence ).
cnf(c_0_14,axiom,
quotient(X1,X2,divide(X1,X2)),
closure ).
cnf(c_0_15,axiom,
( less_equal(X7,X8)
| ~ quotient(X1,X2,X3)
| ~ quotient(X2,X4,X5)
| ~ quotient(X1,X4,X6)
| ~ quotient(X6,X5,X7)
| ~ quotient(X3,X4,X8) ),
quotient_property ).
cnf(c_0_16,axiom,
( quotient(X1,X2,zero)
| ~ less_equal(X1,X2) ),
quotient_less_equal ).
cnf(c_0_17,axiom,
less_equal(zero,X1),
zero_is_smallest ).
cnf(c_0_18,plain,
less_equal(divide(X1,X2),X1),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_19,plain,
( less_equal(divide(X1,X2),X3)
| ~ quotient(X4,X5,X3)
| ~ quotient(X6,X5,X2)
| ~ quotient(X7,X5,X1)
| ~ quotient(X7,X6,X4) ),
inference(spm,[status(thm)],[c_0_15,c_0_14]) ).
cnf(c_0_20,plain,
quotient(zero,X1,zero),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_21,axiom,
less_equal(X1,identity),
identity_is_largest ).
cnf(c_0_22,plain,
quotient(divide(X1,X2),X1,zero),
inference(spm,[status(thm)],[c_0_16,c_0_18]) ).
cnf(c_0_23,plain,
( less_equal(divide(X1,X2),zero)
| ~ quotient(X3,X4,zero)
| ~ quotient(X4,X5,X2)
| ~ quotient(X3,X5,X1) ),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_24,plain,
quotient(X1,identity,zero),
inference(spm,[status(thm)],[c_0_16,c_0_21]) ).
cnf(c_0_25,plain,
( less_equal(divide(X1,X2),zero)
| ~ quotient(X3,X4,divide(X5,X6))
| ~ quotient(X4,X5,X2)
| ~ quotient(X3,X5,X1) ),
inference(spm,[status(thm)],[c_0_19,c_0_22]) ).
cnf(c_0_26,plain,
( less_equal(divide(X1,X2),zero)
| ~ quotient(identity,X3,X2)
| ~ quotient(X4,X3,X1) ),
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_27,hypothesis,
quotient(identity,idQa,idQ_idQa),
identity_divide_idQa ).
cnf(c_0_28,plain,
( less_equal(divide(X1,X2),zero)
| ~ quotient(X3,X4,X2)
| ~ quotient(X4,X4,X1) ),
inference(spm,[status(thm)],[c_0_25,c_0_14]) ).
cnf(c_0_29,axiom,
( X1 = X2
| ~ less_equal(X1,X2)
| ~ less_equal(X2,X1) ),
less_equal_and_equal ).
cnf(c_0_30,axiom,
( less_equal(X1,X2)
| ~ quotient(X1,X2,zero) ),
less_equal_quotient ).
cnf(c_0_31,hypothesis,
( less_equal(divide(X1,idQ_idQa),zero)
| ~ quotient(X2,idQa,X1) ),
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_32,plain,
( less_equal(divide(X1,zero),zero)
| ~ quotient(X2,X2,X1) ),
inference(spm,[status(thm)],[c_0_28,c_0_22]) ).
cnf(c_0_33,plain,
( X1 = X2
| ~ quotient(X2,X1,zero)
| ~ less_equal(X1,X2) ),
inference(spm,[status(thm)],[c_0_29,c_0_30]) ).
cnf(c_0_34,hypothesis,
less_equal(divide(divide(X1,idQa),idQ_idQa),zero),
inference(spm,[status(thm)],[c_0_31,c_0_14]) ).
cnf(c_0_35,plain,
less_equal(divide(divide(X1,X1),zero),zero),
inference(spm,[status(thm)],[c_0_32,c_0_14]) ).
cnf(c_0_36,hypothesis,
quotient(idQa,idQ_idQa,idQa_Q__idQ_idQa),
identity_divide_idQ_idQa ).
cnf(c_0_37,hypothesis,
divide(divide(X1,idQa),idQ_idQa) = zero,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_34]),c_0_20])]) ).
cnf(c_0_38,plain,
divide(divide(X1,X1),zero) = zero,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_35]),c_0_20])]) ).
cnf(c_0_39,hypothesis,
less_equal(idQa_Q__idQ_idQa,idQa),
inference(spm,[status(thm)],[c_0_13,c_0_36]) ).
cnf(c_0_40,hypothesis,
quotient(divide(X1,idQa),idQ_idQa,zero),
inference(spm,[status(thm)],[c_0_14,c_0_37]) ).
cnf(c_0_41,axiom,
( X3 = X4
| ~ quotient(X1,X2,X3)
| ~ quotient(X1,X2,X4) ),
well_defined ).
cnf(c_0_42,plain,
( X1 = X2
| ~ quotient(X2,X1,zero)
| ~ quotient(X1,X2,zero) ),
inference(spm,[status(thm)],[c_0_33,c_0_30]) ).
cnf(c_0_43,plain,
quotient(divide(X1,X1),zero,zero),
inference(spm,[status(thm)],[c_0_14,c_0_38]) ).
cnf(c_0_44,hypothesis,
quotient(idQa_Q__idQ_idQa,idQa,zero),
inference(spm,[status(thm)],[c_0_16,c_0_39]) ).
cnf(c_0_45,hypothesis,
( less_equal(divide(X1,X2),zero)
| ~ quotient(X3,X4,divide(X5,idQa))
| ~ quotient(X4,idQ_idQa,X2)
| ~ quotient(X3,idQ_idQa,X1) ),
inference(spm,[status(thm)],[c_0_19,c_0_40]) ).
cnf(c_0_46,hypothesis,
( X1 = idQa_Q__idQ_idQa
| ~ quotient(idQa,idQ_idQa,X1) ),
inference(spm,[status(thm)],[c_0_41,c_0_36]) ).
cnf(c_0_47,plain,
divide(X1,X1) = zero,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_43]),c_0_20])]) ).
cnf(c_0_48,hypothesis,
quotient(identity,a,idQa),
identity_divide_a ).
cnf(c_0_49,hypothesis,
( less_equal(divide(X1,X2),zero)
| ~ quotient(X3,idQa,X2)
| ~ quotient(X4,idQa,X1)
| ~ quotient(X4,X3,idQa_Q__idQ_idQa) ),
inference(spm,[status(thm)],[c_0_19,c_0_44]) ).
cnf(c_0_50,plain,
( less_equal(divide(X1,divide(identity,X2)),zero)
| ~ quotient(X3,X2,X1) ),
inference(spm,[status(thm)],[c_0_26,c_0_14]) ).
cnf(c_0_51,hypothesis,
( less_equal(divide(X1,X2),zero)
| ~ quotient(idQa,idQ_idQa,X2)
| ~ quotient(X3,idQ_idQa,X1) ),
inference(spm,[status(thm)],[c_0_45,c_0_14]) ).
cnf(c_0_52,hypothesis,
divide(idQa,idQ_idQa) = idQa_Q__idQ_idQa,
inference(spm,[status(thm)],[c_0_46,c_0_14]) ).
cnf(c_0_53,plain,
quotient(X1,X1,zero),
inference(spm,[status(thm)],[c_0_14,c_0_47]) ).
cnf(c_0_54,hypothesis,
( less_equal(divide(X1,idQa),zero)
| ~ quotient(X2,a,X1) ),
inference(spm,[status(thm)],[c_0_26,c_0_48]) ).
cnf(c_0_55,hypothesis,
( less_equal(divide(X1,divide(X2,idQa)),zero)
| ~ quotient(X3,idQa,X1)
| ~ quotient(X3,X2,idQa_Q__idQ_idQa) ),
inference(spm,[status(thm)],[c_0_49,c_0_14]) ).
cnf(c_0_56,hypothesis,
less_equal(divide(idQa_Q__idQ_idQa,divide(identity,idQ_idQa)),zero),
inference(spm,[status(thm)],[c_0_50,c_0_36]) ).
cnf(c_0_57,hypothesis,
( less_equal(divide(X1,idQa_Q__idQ_idQa),zero)
| ~ quotient(X2,idQ_idQa,X1) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_14]),c_0_52]) ).
cnf(c_0_58,plain,
( less_equal(divide(X1,X2),zero)
| ~ quotient(X3,X4,X2)
| ~ quotient(X5,X4,X1)
| ~ quotient(X5,X3,X4) ),
inference(spm,[status(thm)],[c_0_19,c_0_53]) ).
cnf(c_0_59,hypothesis,
less_equal(divide(divide(X1,a),idQa),zero),
inference(spm,[status(thm)],[c_0_54,c_0_14]) ).
cnf(c_0_60,hypothesis,
( less_equal(divide(idQ_idQa,divide(X1,idQa)),zero)
| ~ quotient(identity,X1,idQa_Q__idQ_idQa) ),
inference(spm,[status(thm)],[c_0_55,c_0_27]) ).
cnf(c_0_61,hypothesis,
divide(idQa_Q__idQ_idQa,divide(identity,idQ_idQa)) = zero,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_56]),c_0_20])]) ).
cnf(c_0_62,hypothesis,
less_equal(divide(divide(X1,idQ_idQa),idQa_Q__idQ_idQa),zero),
inference(spm,[status(thm)],[c_0_57,c_0_14]) ).
cnf(c_0_63,plain,
( less_equal(divide(X1,zero),zero)
| ~ quotient(X2,zero,X3)
| ~ quotient(X2,X3,X1) ),
inference(spm,[status(thm)],[c_0_58,c_0_20]) ).
cnf(c_0_64,hypothesis,
divide(divide(X1,a),idQa) = zero,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_59]),c_0_20])]) ).
cnf(c_0_65,hypothesis,
( divide(idQ_idQa,divide(X1,idQa)) = zero
| ~ quotient(identity,X1,idQa_Q__idQ_idQa) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_60]),c_0_20])]) ).
cnf(c_0_66,hypothesis,
quotient(idQa_Q__idQ_idQa,divide(identity,idQ_idQa),zero),
inference(spm,[status(thm)],[c_0_14,c_0_61]) ).
cnf(c_0_67,hypothesis,
divide(divide(X1,idQ_idQa),idQa_Q__idQ_idQa) = zero,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_62]),c_0_20])]) ).
cnf(c_0_68,plain,
( less_equal(divide(X1,zero),zero)
| ~ quotient(X2,divide(X2,zero),X1) ),
inference(spm,[status(thm)],[c_0_63,c_0_14]) ).
cnf(c_0_69,hypothesis,
quotient(divide(X1,a),idQa,zero),
inference(spm,[status(thm)],[c_0_14,c_0_64]) ).
cnf(c_0_70,hypothesis,
( quotient(idQ_idQa,divide(X1,idQa),zero)
| ~ quotient(identity,X1,idQa_Q__idQ_idQa) ),
inference(spm,[status(thm)],[c_0_14,c_0_65]) ).
cnf(c_0_71,hypothesis,
( divide(identity,idQ_idQa) = idQa_Q__idQ_idQa
| ~ quotient(divide(identity,idQ_idQa),idQa_Q__idQ_idQa,zero) ),
inference(spm,[status(thm)],[c_0_42,c_0_66]) ).
cnf(c_0_72,hypothesis,
quotient(divide(X1,idQ_idQa),idQa_Q__idQ_idQa,zero),
inference(spm,[status(thm)],[c_0_14,c_0_67]) ).
cnf(c_0_73,plain,
less_equal(divide(divide(X1,divide(X1,zero)),zero),zero),
inference(spm,[status(thm)],[c_0_68,c_0_14]) ).
cnf(c_0_74,hypothesis,
( less_equal(divide(X1,X2),zero)
| ~ quotient(X3,X4,divide(X5,a))
| ~ quotient(X4,idQa,X2)
| ~ quotient(X3,idQa,X1) ),
inference(spm,[status(thm)],[c_0_19,c_0_69]) ).
cnf(c_0_75,hypothesis,
( divide(X1,idQa) = idQ_idQa
| ~ quotient(identity,X1,idQa_Q__idQ_idQa) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_70]),c_0_40])]) ).
cnf(c_0_76,hypothesis,
divide(identity,idQ_idQa) = idQa_Q__idQ_idQa,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_71,c_0_72])]) ).
cnf(c_0_77,plain,
divide(divide(X1,divide(X1,zero)),zero) = zero,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_73]),c_0_20])]) ).
cnf(c_0_78,hypothesis,
( less_equal(divide(X1,X2),zero)
| ~ quotient(a,idQa,X2)
| ~ quotient(X3,idQa,X1) ),
inference(spm,[status(thm)],[c_0_74,c_0_14]) ).
cnf(c_0_79,hypothesis,
( quotient(X1,idQa,idQ_idQa)
| ~ quotient(identity,X1,idQa_Q__idQ_idQa) ),
inference(spm,[status(thm)],[c_0_14,c_0_75]) ).
cnf(c_0_80,hypothesis,
quotient(identity,idQ_idQa,idQa_Q__idQ_idQa),
inference(spm,[status(thm)],[c_0_14,c_0_76]) ).
cnf(c_0_81,plain,
quotient(divide(X1,divide(X1,zero)),zero,zero),
inference(spm,[status(thm)],[c_0_14,c_0_77]) ).
cnf(c_0_82,hypothesis,
( less_equal(divide(X1,divide(a,idQa)),zero)
| ~ quotient(X2,idQa,X1) ),
inference(spm,[status(thm)],[c_0_78,c_0_14]) ).
cnf(c_0_83,hypothesis,
quotient(idQ_idQa,idQa,idQ_idQa),
inference(spm,[status(thm)],[c_0_79,c_0_80]) ).
cnf(c_0_84,plain,
( less_equal(divide(X1,X2),divide(X3,X4))
| ~ quotient(X5,X4,X2)
| ~ quotient(X6,X4,X1)
| ~ quotient(X6,X5,X3) ),
inference(spm,[status(thm)],[c_0_19,c_0_14]) ).
cnf(c_0_85,plain,
divide(X1,divide(X1,zero)) = zero,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_81]),c_0_20])]) ).
cnf(c_0_86,hypothesis,
less_equal(divide(idQ_idQa,divide(a,idQa)),zero),
inference(spm,[status(thm)],[c_0_82,c_0_83]) ).
cnf(c_0_87,plain,
( less_equal(divide(X1,zero),divide(X2,X3))
| ~ quotient(X4,X3,X1)
| ~ quotient(X4,X3,X2) ),
inference(spm,[status(thm)],[c_0_84,c_0_53]) ).
cnf(c_0_88,plain,
quotient(X1,divide(X1,zero),zero),
inference(spm,[status(thm)],[c_0_14,c_0_85]) ).
cnf(c_0_89,plain,
( less_equal(divide(X1,X2),zero)
| ~ quotient(divide(X3,X4),X5,X1)
| ~ quotient(X3,X5,X2) ),
inference(spm,[status(thm)],[c_0_23,c_0_22]) ).
cnf(c_0_90,hypothesis,
divide(idQ_idQa,divide(a,idQa)) = zero,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_86]),c_0_20])]) ).
cnf(c_0_91,plain,
( less_equal(divide(divide(X1,X2),zero),divide(X3,X2))
| ~ quotient(X1,X2,X3) ),
inference(spm,[status(thm)],[c_0_87,c_0_14]) ).
cnf(c_0_92,plain,
divide(X1,zero) = X1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_88]),c_0_22])]) ).
cnf(c_0_93,plain,
( less_equal(divide(divide(divide(X1,X2),X3),X4),zero)
| ~ quotient(X1,X3,X4) ),
inference(spm,[status(thm)],[c_0_89,c_0_14]) ).
cnf(c_0_94,hypothesis,
quotient(idQ_idQa,divide(a,idQa),zero),
inference(spm,[status(thm)],[c_0_14,c_0_90]) ).
cnf(c_0_95,plain,
( divide(X1,X2) = X1
| ~ less_equal(X1,divide(X1,X2)) ),
inference(spm,[status(thm)],[c_0_29,c_0_18]) ).
cnf(c_0_96,plain,
( less_equal(divide(X1,X2),divide(X3,X2))
| ~ quotient(X1,X2,X3) ),
inference(rw,[status(thm)],[c_0_91,c_0_92]) ).
cnf(c_0_97,hypothesis,
( X1 = idQa
| ~ quotient(identity,a,X1) ),
inference(spm,[status(thm)],[c_0_41,c_0_48]) ).
cnf(c_0_98,plain,
( divide(divide(divide(X1,X2),X3),X4) = zero
| ~ quotient(X1,X3,X4) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_93]),c_0_20])]) ).
cnf(c_0_99,hypothesis,
divide(a,idQa) = idQ_idQa,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_94]),c_0_40])]) ).
cnf(c_0_100,plain,
divide(divide(X1,X2),X2) = divide(X1,X2),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_95,c_0_96]),c_0_14])]) ).
cnf(c_0_101,hypothesis,
divide(identity,a) = idQa,
inference(spm,[status(thm)],[c_0_97,c_0_14]) ).
cnf(c_0_102,hypothesis,
( divide(divide(idQa_Q__idQ_idQa,X1),X2) = zero
| ~ quotient(idQa,X1,X2) ),
inference(spm,[status(thm)],[c_0_98,c_0_52]) ).
cnf(c_0_103,hypothesis,
quotient(idQ_idQa,a,zero),
inference(spm,[status(thm)],[c_0_22,c_0_99]) ).
cnf(c_0_104,hypothesis,
divide(idQa,a) = idQa,
inference(spm,[status(thm)],[c_0_100,c_0_101]) ).
cnf(c_0_105,hypothesis,
( divide(idQa_Q__idQ_idQa,X1) = zero
| ~ quotient(idQa,X1,zero) ),
inference(spm,[status(thm)],[c_0_92,c_0_102]) ).
cnf(c_0_106,hypothesis,
( less_equal(X1,divide(X2,a))
| ~ quotient(X3,a,X1)
| ~ quotient(X3,idQ_idQa,X2) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_84,c_0_103]),c_0_92]) ).
cnf(c_0_107,hypothesis,
quotient(idQa,a,idQa),
inference(spm,[status(thm)],[c_0_14,c_0_104]) ).
cnf(c_0_108,plain,
( divide(X1,X2) = X1
| ~ quotient(X1,divide(X1,X2),zero) ),
inference(spm,[status(thm)],[c_0_33,c_0_18]) ).
cnf(c_0_109,hypothesis,
( quotient(idQa_Q__idQ_idQa,X1,zero)
| ~ quotient(idQa,X1,zero) ),
inference(spm,[status(thm)],[c_0_14,c_0_105]) ).
cnf(c_0_110,hypothesis,
( less_equal(idQa,divide(X1,a))
| ~ quotient(idQa,idQ_idQa,X1) ),
inference(spm,[status(thm)],[c_0_106,c_0_107]) ).
cnf(c_0_111,hypothesis,
( divide(idQa_Q__idQ_idQa,X1) = idQa_Q__idQ_idQa
| ~ quotient(idQa,divide(idQa_Q__idQ_idQa,X1),zero) ),
inference(spm,[status(thm)],[c_0_108,c_0_109]) ).
cnf(c_0_112,hypothesis,
( divide(X1,a) = idQa
| ~ quotient(idQa,idQ_idQa,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_110]),c_0_69])]) ).
cnf(c_0_113,negated_conjecture,
idQa != idQa_Q__idQ_idQa,
prove_idQa_equals_idQa_Q__idQ_idQa ).
cnf(c_0_114,hypothesis,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_111,c_0_112]),c_0_53]),c_0_36])]),c_0_113]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.06 % Problem : HEN010-1 : TPTP v9.2.1. Released v1.0.0.
% 0.00/0.06 % Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.06/0.24 % Computer : n012.cluster.edu
% 0.06/0.24 % Model : x86_64 x86_64
% 0.06/0.24 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.24 % Memory : 8042.1875MB
% 0.06/0.24 % OS : Linux 3.10.0-693.el7.x86_64
% 0.06/0.24 % CPULimit : 300
% 0.06/0.24 % WCLimit : 300
% 0.06/0.24 % DateTime : Mon May 4 19:09:30 EDT 2026
% 0.06/0.24 % CPUTime :
% 0.06/0.25 % start to proof: theBenchmark
% 7.71/5.30 % Version : CSE_E---1.7
% 7.71/5.30 % Problem : theBenchmark.p
% 7.71/5.30 % SZS status Unsatisfiable for theBenchmark.p
% 7.71/5.30 % SZS output start CNFRefutation
% See solution above
% 7.71/5.34 % Total time : 3.367s
%------------------------------------------------------------------------------