%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : HEN011-3 : TPTP v9.2.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n022.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 04:28:36 PM UTC 2026
% Result : Unsatisfiable 21.35s 13.03s
% Output : CNFRefutation 21.35s
% Verified :
% SZS Type : Refutation
% Derivation depth : 30
% Number of leaves : 12
% Syntax : Number of clauses : 168 ( 145 unt; 0 nHn; 112 RR)
% Number of literals : 195 ( 150 equ; 30 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 8 con; 0-2 aty)
% Number of variables : 117 ( 36 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(less_equal_and_equal,axiom,
( X1 = X2
| ~ less_equal(X1,X2)
| ~ less_equal(X2,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/HEN002-0.ax',less_equal_and_equal) ).
cnf(quotient_property,axiom,
less_equal(divide(divide(X1,X2),divide(X3,X2)),divide(divide(X1,X3),X2)),
file('/export/starexec/sandbox2/benchmark/Axioms/HEN002-0.ax',quotient_property) ).
cnf(quotient_less_equal1,axiom,
( divide(X1,X2) = zero
| ~ less_equal(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/HEN002-0.ax',quotient_less_equal1) ).
cnf(identity_is_largest,axiom,
less_equal(X1,identity),
file('/export/starexec/sandbox2/benchmark/Axioms/HEN002-0.ax',identity_is_largest) ).
cnf(zero_is_smallest,axiom,
less_equal(zero,X1),
file('/export/starexec/sandbox2/benchmark/Axioms/HEN002-0.ax',zero_is_smallest) ).
cnf(identity_divide_a,hypothesis,
divide(identity,a) = c,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',identity_divide_a) ).
cnf(quotient_less_equal2,axiom,
( less_equal(X1,X2)
| divide(X1,X2) != zero ),
file('/export/starexec/sandbox2/benchmark/Axioms/HEN002-0.ax',quotient_less_equal2) ).
cnf(identity_divide_c,hypothesis,
divide(identity,c) = e,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',identity_divide_c) ).
cnf(quotient_smaller_than_numerator,axiom,
less_equal(divide(X1,X2),X1),
file('/export/starexec/sandbox2/benchmark/Axioms/HEN002-0.ax',quotient_smaller_than_numerator) ).
cnf(identity_divide_b,hypothesis,
divide(identity,b) = d,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',identity_divide_b) ).
cnf(identity_divide_d,hypothesis,
divide(identity,d) = g,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',identity_divide_d) ).
cnf(prove_commutativity,negated_conjecture,
divide(c,g) != divide(d,e),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_commutativity) ).
cnf(c_0_12,axiom,
( X1 = X2
| ~ less_equal(X1,X2)
| ~ less_equal(X2,X1) ),
less_equal_and_equal ).
cnf(c_0_13,axiom,
less_equal(divide(divide(X1,X2),divide(X3,X2)),divide(divide(X1,X3),X2)),
quotient_property ).
cnf(c_0_14,axiom,
( divide(X1,X2) = zero
| ~ less_equal(X1,X2) ),
quotient_less_equal1 ).
cnf(c_0_15,axiom,
less_equal(X1,identity),
identity_is_largest ).
cnf(c_0_16,axiom,
less_equal(zero,X1),
zero_is_smallest ).
cnf(c_0_17,plain,
( divide(divide(X1,X2),divide(X3,X2)) = divide(divide(X1,X3),X2)
| ~ less_equal(divide(divide(X1,X3),X2),divide(divide(X1,X2),divide(X3,X2))) ),
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
cnf(c_0_18,hypothesis,
divide(identity,a) = c,
identity_divide_a ).
cnf(c_0_19,plain,
divide(X1,identity) = zero,
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_20,plain,
divide(zero,X1) = zero,
inference(spm,[status(thm)],[c_0_14,c_0_16]) ).
cnf(c_0_21,axiom,
( less_equal(X1,X2)
| divide(X1,X2) != zero ),
quotient_less_equal2 ).
cnf(c_0_22,hypothesis,
divide(divide(X1,a),c) = zero,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_18]),c_0_19]),c_0_20]),c_0_19]),c_0_20]),c_0_16])]) ).
cnf(c_0_23,hypothesis,
divide(identity,c) = e,
identity_divide_c ).
cnf(c_0_24,plain,
( X1 = X2
| divide(X2,X1) != zero
| ~ less_equal(X1,X2) ),
inference(spm,[status(thm)],[c_0_12,c_0_21]) ).
cnf(c_0_25,hypothesis,
divide(divide(X1,c),divide(a,c)) = zero,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_22]),c_0_16])]) ).
cnf(c_0_26,hypothesis,
less_equal(divide(divide(X1,c),e),zero),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_23]),c_0_19]),c_0_20]) ).
cnf(c_0_27,hypothesis,
less_equal(divide(divide(identity,X1),divide(c,X1)),divide(e,X1)),
inference(spm,[status(thm)],[c_0_13,c_0_23]) ).
cnf(c_0_28,hypothesis,
divide(c,c) = zero,
inference(spm,[status(thm)],[c_0_22,c_0_18]) ).
cnf(c_0_29,axiom,
less_equal(divide(X1,X2),X1),
quotient_smaller_than_numerator ).
cnf(c_0_30,plain,
( X1 = X2
| divide(X2,X1) != zero
| divide(X1,X2) != zero ),
inference(spm,[status(thm)],[c_0_24,c_0_21]) ).
cnf(c_0_31,hypothesis,
divide(e,divide(a,c)) = zero,
inference(spm,[status(thm)],[c_0_25,c_0_23]) ).
cnf(c_0_32,hypothesis,
divide(divide(X1,c),e) = zero,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_26]),c_0_16])]) ).
cnf(c_0_33,hypothesis,
less_equal(divide(e,zero),divide(e,c)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_28]),c_0_23]) ).
cnf(c_0_34,plain,
divide(divide(X1,X2),X1) = zero,
inference(spm,[status(thm)],[c_0_14,c_0_29]) ).
cnf(c_0_35,hypothesis,
divide(a,c) = e,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_31]),c_0_32])]) ).
cnf(c_0_36,plain,
( divide(X1,X2) = X1
| ~ less_equal(X1,divide(X1,X2)) ),
inference(spm,[status(thm)],[c_0_12,c_0_29]) ).
cnf(c_0_37,hypothesis,
divide(divide(e,zero),divide(e,c)) = zero,
inference(spm,[status(thm)],[c_0_14,c_0_33]) ).
cnf(c_0_38,hypothesis,
divide(identity,b) = d,
identity_divide_b ).
cnf(c_0_39,hypothesis,
divide(e,a) = zero,
inference(spm,[status(thm)],[c_0_34,c_0_35]) ).
cnf(c_0_40,plain,
( divide(X1,X2) = X1
| divide(X1,divide(X1,X2)) != zero ),
inference(spm,[status(thm)],[c_0_36,c_0_21]) ).
cnf(c_0_41,hypothesis,
divide(divide(e,divide(e,c)),zero) = zero,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_37]),c_0_20]),c_0_20]),c_0_16])]) ).
cnf(c_0_42,hypothesis,
divide(divide(X1,b),d) = zero,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_38]),c_0_19]),c_0_20]),c_0_19]),c_0_20]),c_0_16])]) ).
cnf(c_0_43,hypothesis,
divide(identity,d) = g,
identity_divide_d ).
cnf(c_0_44,hypothesis,
less_equal(divide(c,divide(c,a)),zero),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_39]),c_0_18]) ).
cnf(c_0_45,hypothesis,
divide(e,divide(e,c)) = zero,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_41]),c_0_41])]) ).
cnf(c_0_46,hypothesis,
divide(divide(X1,d),divide(b,d)) = zero,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_42]),c_0_16])]) ).
cnf(c_0_47,hypothesis,
less_equal(divide(divide(X1,d),g),zero),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_43]),c_0_19]),c_0_20]) ).
cnf(c_0_48,hypothesis,
divide(c,divide(c,a)) = zero,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_44]),c_0_20])]) ).
cnf(c_0_49,hypothesis,
less_equal(divide(g,divide(c,d)),divide(e,d)),
inference(spm,[status(thm)],[c_0_27,c_0_43]) ).
cnf(c_0_50,plain,
less_equal(divide(divide(X1,X2),zero),divide(divide(X1,zero),X2)),
inference(spm,[status(thm)],[c_0_13,c_0_20]) ).
cnf(c_0_51,hypothesis,
divide(e,c) = e,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_45]),c_0_32])]) ).
cnf(c_0_52,hypothesis,
divide(g,divide(b,d)) = zero,
inference(spm,[status(thm)],[c_0_46,c_0_43]) ).
cnf(c_0_53,hypothesis,
divide(divide(X1,d),g) = zero,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_47]),c_0_16])]) ).
cnf(c_0_54,plain,
divide(divide(divide(X1,X2),divide(X3,X2)),divide(divide(X1,X3),X2)) = zero,
inference(spm,[status(thm)],[c_0_14,c_0_13]) ).
cnf(c_0_55,plain,
( divide(divide(X1,X2),zero) = divide(divide(X1,zero),X2)
| ~ less_equal(divide(divide(X1,zero),X2),divide(divide(X1,X2),zero)) ),
inference(spm,[status(thm)],[c_0_17,c_0_20]) ).
cnf(c_0_56,hypothesis,
divide(c,a) = c,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_48]),c_0_22])]) ).
cnf(c_0_57,hypothesis,
divide(divide(g,divide(c,d)),divide(e,d)) = zero,
inference(spm,[status(thm)],[c_0_14,c_0_49]) ).
cnf(c_0_58,hypothesis,
less_equal(divide(e,zero),divide(divide(e,zero),c)),
inference(spm,[status(thm)],[c_0_50,c_0_51]) ).
cnf(c_0_59,hypothesis,
divide(b,d) = g,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_52]),c_0_53])]) ).
cnf(c_0_60,plain,
divide(divide(divide(X1,X2),divide(divide(X1,X3),X2)),divide(divide(X3,X2),divide(divide(X1,X3),X2))) = zero,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_54]),c_0_16])]) ).
cnf(c_0_61,hypothesis,
divide(divide(c,zero),a) = divide(c,zero),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_56]),c_0_29])]) ).
cnf(c_0_62,hypothesis,
divide(divide(g,divide(e,d)),divide(divide(c,d),divide(e,d))) = zero,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_57]),c_0_16])]) ).
cnf(c_0_63,hypothesis,
divide(divide(e,zero),c) = divide(e,zero),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_58]),c_0_34])]) ).
cnf(c_0_64,hypothesis,
less_equal(divide(divide(identity,X1),divide(d,X1)),divide(g,X1)),
inference(spm,[status(thm)],[c_0_13,c_0_43]) ).
cnf(c_0_65,hypothesis,
divide(g,b) = zero,
inference(spm,[status(thm)],[c_0_34,c_0_59]) ).
cnf(c_0_66,hypothesis,
divide(divide(c,divide(c,zero)),zero) = zero,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_61]),c_0_56]),c_0_20]),c_0_20]) ).
cnf(c_0_67,hypothesis,
( divide(divide(c,d),divide(e,d)) = divide(g,divide(e,d))
| divide(divide(divide(c,d),divide(e,d)),divide(g,divide(e,d))) != zero ),
inference(spm,[status(thm)],[c_0_30,c_0_62]) ).
cnf(c_0_68,hypothesis,
divide(divide(divide(X1,d),X2),divide(g,X2)) = zero,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_53]),c_0_20]),c_0_20]),c_0_16])]) ).
cnf(c_0_69,hypothesis,
divide(divide(e,divide(e,zero)),zero) = zero,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_63]),c_0_51]),c_0_20]),c_0_20]) ).
cnf(c_0_70,hypothesis,
less_equal(divide(d,divide(d,b)),zero),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_65]),c_0_38]) ).
cnf(c_0_71,hypothesis,
less_equal(divide(c,divide(X1,a)),divide(divide(identity,X1),a)),
inference(spm,[status(thm)],[c_0_13,c_0_18]) ).
cnf(c_0_72,hypothesis,
divide(c,divide(c,zero)) = zero,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_66]),c_0_66])]) ).
cnf(c_0_73,hypothesis,
divide(divide(X1,e),divide(c,e)) = zero,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_32]),c_0_16])]) ).
cnf(c_0_74,hypothesis,
divide(divide(c,d),divide(e,d)) = divide(g,divide(e,d)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_67,c_0_68])]) ).
cnf(c_0_75,plain,
less_equal(divide(divide(X1,X2),zero),divide(divide(X1,divide(X2,X3)),X2)),
inference(spm,[status(thm)],[c_0_13,c_0_34]) ).
cnf(c_0_76,hypothesis,
divide(e,divide(e,zero)) = zero,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_69]),c_0_69])]) ).
cnf(c_0_77,hypothesis,
divide(d,divide(d,b)) = zero,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_70]),c_0_20])]) ).
cnf(c_0_78,hypothesis,
less_equal(divide(c,zero),divide(divide(identity,e),a)),
inference(spm,[status(thm)],[c_0_71,c_0_39]) ).
cnf(c_0_79,hypothesis,
divide(c,zero) = c,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_72]),c_0_34])]) ).
cnf(c_0_80,hypothesis,
( divide(c,e) = divide(X1,e)
| divide(divide(c,e),divide(X1,e)) != zero ),
inference(spm,[status(thm)],[c_0_30,c_0_73]) ).
cnf(c_0_81,plain,
divide(divide(X1,X2),divide(identity,X2)) = zero,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_19]),c_0_20]),c_0_20]),c_0_16])]) ).
cnf(c_0_82,hypothesis,
divide(divide(g,divide(e,d)),divide(c,d)) = zero,
inference(spm,[status(thm)],[c_0_34,c_0_74]) ).
cnf(c_0_83,hypothesis,
less_equal(divide(e,zero),divide(divide(e,divide(c,X1)),c)),
inference(spm,[status(thm)],[c_0_75,c_0_51]) ).
cnf(c_0_84,hypothesis,
divide(e,zero) = e,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_76]),c_0_34])]) ).
cnf(c_0_85,hypothesis,
divide(d,b) = d,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_77]),c_0_42])]) ).
cnf(c_0_86,hypothesis,
less_equal(c,divide(divide(identity,e),a)),
inference(rw,[status(thm)],[c_0_78,c_0_79]) ).
cnf(c_0_87,hypothesis,
divide(c,e) = divide(identity,e),
inference(spm,[status(thm)],[c_0_80,c_0_81]) ).
cnf(c_0_88,hypothesis,
divide(divide(g,divide(c,d)),divide(divide(e,d),divide(c,d))) = zero,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_82]),c_0_16])]) ).
cnf(c_0_89,hypothesis,
less_equal(e,divide(divide(e,divide(c,X1)),c)),
inference(rw,[status(thm)],[c_0_83,c_0_84]) ).
cnf(c_0_90,hypothesis,
divide(divide(d,zero),b) = divide(d,zero),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_85]),c_0_29])]) ).
cnf(c_0_91,hypothesis,
divide(divide(identity,e),a) = c,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_86]),c_0_22])]) ).
cnf(c_0_92,hypothesis,
less_equal(divide(identity,e),c),
inference(spm,[status(thm)],[c_0_29,c_0_87]) ).
cnf(c_0_93,plain,
divide(divide(divide(X1,X2),X3),divide(X1,X3)) = zero,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_34]),c_0_20]),c_0_20]),c_0_16])]) ).
cnf(c_0_94,hypothesis,
divide(divide(e,d),divide(c,d)) = divide(g,divide(c,d)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_88]),c_0_68])]) ).
cnf(c_0_95,hypothesis,
divide(divide(e,divide(c,X1)),c) = e,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_89]),c_0_32])]) ).
cnf(c_0_96,hypothesis,
divide(divide(divide(X1,d),b),zero) = zero,
inference(spm,[status(thm)],[c_0_68,c_0_65]) ).
cnf(c_0_97,hypothesis,
divide(divide(d,divide(d,zero)),zero) = zero,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_90]),c_0_85]),c_0_20]),c_0_20]) ).
cnf(c_0_98,plain,
less_equal(divide(divide(X1,X1),divide(X2,X1)),zero),
inference(spm,[status(thm)],[c_0_13,c_0_34]) ).
cnf(c_0_99,hypothesis,
divide(d,d) = zero,
inference(spm,[status(thm)],[c_0_42,c_0_38]) ).
cnf(c_0_100,hypothesis,
divide(divide(divide(identity,e),divide(X1,e)),divide(divide(c,X1),e)) = zero,
inference(spm,[status(thm)],[c_0_54,c_0_87]) ).
cnf(c_0_101,hypothesis,
divide(identity,e) = c,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_91]),c_0_92])]) ).
cnf(c_0_102,hypothesis,
divide(divide(g,divide(c,d)),divide(e,divide(c,d))) = zero,
inference(spm,[status(thm)],[c_0_93,c_0_94]) ).
cnf(c_0_103,hypothesis,
divide(e,divide(c,X1)) = e,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_95]),c_0_29])]) ).
cnf(c_0_104,plain,
( divide(divide(X1,X2),divide(X3,X2)) = divide(divide(X1,X3),X2)
| divide(divide(divide(X1,X3),X2),divide(divide(X1,X2),divide(X3,X2))) != zero ),
inference(spm,[status(thm)],[c_0_24,c_0_13]) ).
cnf(c_0_105,hypothesis,
divide(divide(X1,d),b) = zero,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_96]),c_0_96])]) ).
cnf(c_0_106,hypothesis,
divide(d,divide(d,zero)) = zero,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_97]),c_0_97])]) ).
cnf(c_0_107,plain,
less_equal(divide(divide(X1,X1),zero),zero),
inference(spm,[status(thm)],[c_0_98,c_0_20]) ).
cnf(c_0_108,hypothesis,
less_equal(divide(g,zero),divide(g,d)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_99]),c_0_43]) ).
cnf(c_0_109,hypothesis,
divide(divide(c,divide(X1,e)),divide(divide(c,X1),e)) = zero,
inference(rw,[status(thm)],[c_0_100,c_0_101]) ).
cnf(c_0_110,hypothesis,
divide(divide(g,divide(c,d)),e) = zero,
inference(rw,[status(thm)],[c_0_102,c_0_103]) ).
cnf(c_0_111,hypothesis,
( divide(divide(X1,divide(X2,d)),b) = divide(divide(X1,b),zero)
| divide(divide(divide(X1,divide(X2,d)),b),divide(divide(X1,b),zero)) != zero ),
inference(spm,[status(thm)],[c_0_104,c_0_105]) ).
cnf(c_0_112,hypothesis,
divide(d,zero) = d,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_106]),c_0_34])]) ).
cnf(c_0_113,plain,
divide(divide(X1,X1),zero) = zero,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_107]),c_0_20])]) ).
cnf(c_0_114,hypothesis,
divide(divide(g,zero),divide(g,d)) = zero,
inference(spm,[status(thm)],[c_0_14,c_0_108]) ).
cnf(c_0_115,hypothesis,
divide(c,divide(divide(c,divide(g,divide(c,d))),e)) = zero,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_109,c_0_110]),c_0_79]) ).
cnf(c_0_116,hypothesis,
divide(divide(X1,e),c) = zero,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_101]),c_0_19]),c_0_20]),c_0_19]),c_0_20]),c_0_16])]) ).
cnf(c_0_117,hypothesis,
( divide(divide(e,divide(c,d)),divide(d,divide(c,d))) = divide(g,divide(c,d))
| divide(divide(g,divide(c,d)),divide(divide(e,divide(c,d)),divide(d,divide(c,d)))) != zero ),
inference(spm,[status(thm)],[c_0_104,c_0_94]) ).
cnf(c_0_118,hypothesis,
divide(divide(d,divide(X1,d)),b) = d,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_111,c_0_85]),c_0_112]),c_0_112]),c_0_42])]) ).
cnf(c_0_119,hypothesis,
divide(divide(divide(X1,g),divide(d,g)),zero) = zero,
inference(spm,[status(thm)],[c_0_54,c_0_53]) ).
cnf(c_0_120,plain,
divide(X1,X1) = zero,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_113]),c_0_113])]) ).
cnf(c_0_121,hypothesis,
divide(divide(g,divide(g,d)),zero) = zero,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_114]),c_0_20]),c_0_20]),c_0_16])]) ).
cnf(c_0_122,hypothesis,
divide(divide(c,divide(g,divide(c,d))),e) = c,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_115]),c_0_116])]) ).
cnf(c_0_123,hypothesis,
( divide(e,divide(d,divide(c,d))) = divide(g,divide(c,d))
| divide(divide(g,divide(c,d)),divide(e,divide(d,divide(c,d)))) != zero ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_117,c_0_103]),c_0_103]) ).
cnf(c_0_124,hypothesis,
divide(d,divide(X1,d)) = d,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_118]),c_0_29])]) ).
cnf(c_0_125,hypothesis,
less_equal(divide(d,divide(X1,b)),divide(divide(identity,X1),b)),
inference(spm,[status(thm)],[c_0_13,c_0_38]) ).
cnf(c_0_126,hypothesis,
divide(divide(X1,g),divide(d,g)) = zero,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_119]),c_0_20])]) ).
cnf(c_0_127,plain,
divide(divide(X1,divide(X1,zero)),zero) = zero,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_120]),c_0_16])]) ).
cnf(c_0_128,hypothesis,
divide(g,divide(g,d)) = zero,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_121]),c_0_121])]) ).
cnf(c_0_129,hypothesis,
divide(c,divide(g,divide(c,d))) = c,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_122]),c_0_29])]) ).
cnf(c_0_130,hypothesis,
divide(g,divide(c,d)) = divide(e,d),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_123,c_0_124]),c_0_124]),c_0_57])]) ).
cnf(c_0_131,hypothesis,
less_equal(divide(d,zero),divide(divide(identity,g),b)),
inference(spm,[status(thm)],[c_0_125,c_0_65]) ).
cnf(c_0_132,hypothesis,
( divide(d,g) = divide(X1,g)
| divide(divide(d,g),divide(X1,g)) != zero ),
inference(spm,[status(thm)],[c_0_30,c_0_126]) ).
cnf(c_0_133,plain,
divide(X1,divide(X1,zero)) = zero,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_127]),c_0_127])]) ).
cnf(c_0_134,hypothesis,
divide(g,d) = g,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_128]),c_0_53])]) ).
cnf(c_0_135,hypothesis,
( divide(divide(c,divide(e,d)),divide(d,divide(e,d))) = divide(g,divide(e,d))
| divide(divide(g,divide(e,d)),divide(divide(c,divide(e,d)),divide(d,divide(e,d)))) != zero ),
inference(spm,[status(thm)],[c_0_104,c_0_74]) ).
cnf(c_0_136,hypothesis,
divide(c,divide(e,d)) = c,
inference(rw,[status(thm)],[c_0_129,c_0_130]) ).
cnf(c_0_137,hypothesis,
less_equal(d,divide(divide(identity,g),b)),
inference(rw,[status(thm)],[c_0_131,c_0_112]) ).
cnf(c_0_138,hypothesis,
divide(d,g) = divide(identity,g),
inference(spm,[status(thm)],[c_0_132,c_0_81]) ).
cnf(c_0_139,hypothesis,
divide(divide(g,e),divide(divide(c,d),e)) = zero,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_110]),c_0_16])]) ).
cnf(c_0_140,plain,
( divide(divide(X1,divide(X2,X3)),X2) = divide(divide(X1,X2),zero)
| divide(divide(divide(X1,divide(X2,X3)),X2),divide(divide(X1,X2),zero)) != zero ),
inference(spm,[status(thm)],[c_0_24,c_0_75]) ).
cnf(c_0_141,plain,
divide(X1,zero) = X1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_133]),c_0_34])]) ).
cnf(c_0_142,hypothesis,
divide(divide(g,divide(X1,d)),divide(divide(g,X1),d)) = zero,
inference(spm,[status(thm)],[c_0_54,c_0_134]) ).
cnf(c_0_143,hypothesis,
divide(g,divide(e,d)) = divide(c,d),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_135,c_0_124]),c_0_124]),c_0_136]),c_0_136]),c_0_82])]) ).
cnf(c_0_144,hypothesis,
divide(divide(identity,g),b) = d,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_137]),c_0_42])]) ).
cnf(c_0_145,hypothesis,
less_equal(divide(identity,g),d),
inference(spm,[status(thm)],[c_0_29,c_0_138]) ).
cnf(c_0_146,hypothesis,
divide(divide(c,d),e) = divide(g,e),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_139]),c_0_68])]) ).
cnf(c_0_147,plain,
divide(divide(X1,divide(X2,X3)),X2) = divide(X1,X2),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_140,c_0_141]),c_0_141]),c_0_93])]) ).
cnf(c_0_148,hypothesis,
divide(divide(c,d),divide(divide(g,e),d)) = zero,
inference(spm,[status(thm)],[c_0_142,c_0_143]) ).
cnf(c_0_149,hypothesis,
divide(divide(divide(identity,X1),divide(c,X1)),divide(e,X1)) = zero,
inference(spm,[status(thm)],[c_0_54,c_0_23]) ).
cnf(c_0_150,hypothesis,
divide(identity,g) = d,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_144]),c_0_145])]) ).
cnf(c_0_151,hypothesis,
divide(divide(divide(identity,X1),divide(d,X1)),divide(g,X1)) = zero,
inference(spm,[status(thm)],[c_0_54,c_0_43]) ).
cnf(c_0_152,hypothesis,
( divide(g,e) = divide(c,d)
| divide(divide(c,d),divide(g,e)) != zero ),
inference(spm,[status(thm)],[c_0_40,c_0_146]) ).
cnf(c_0_153,hypothesis,
divide(divide(c,d),divide(g,e)) = zero,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_147,c_0_148]),c_0_20]) ).
cnf(c_0_154,hypothesis,
divide(divide(d,divide(c,g)),divide(e,g)) = zero,
inference(spm,[status(thm)],[c_0_149,c_0_150]) ).
cnf(c_0_155,plain,
( divide(divide(X1,divide(X2,X3)),divide(identity,X3)) = divide(divide(X1,divide(identity,X3)),zero)
| divide(divide(divide(X1,divide(X2,X3)),divide(identity,X3)),divide(divide(X1,divide(identity,X3)),zero)) != zero ),
inference(spm,[status(thm)],[c_0_104,c_0_81]) ).
cnf(c_0_156,hypothesis,
divide(divide(c,divide(d,e)),divide(g,e)) = zero,
inference(spm,[status(thm)],[c_0_151,c_0_101]) ).
cnf(c_0_157,hypothesis,
divide(g,e) = divide(c,d),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_152,c_0_153])]) ).
cnf(c_0_158,hypothesis,
divide(divide(d,divide(c,g)),e) = zero,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_147,c_0_154]),c_0_20]) ).
cnf(c_0_159,plain,
divide(divide(X1,divide(X2,X3)),divide(identity,X3)) = divide(X1,divide(identity,X3)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_155,c_0_141]),c_0_141]),c_0_93])]) ).
cnf(c_0_160,hypothesis,
divide(divide(c,divide(d,e)),divide(c,d)) = zero,
inference(rw,[status(thm)],[c_0_156,c_0_157]) ).
cnf(c_0_161,hypothesis,
divide(divide(d,e),divide(divide(c,g),e)) = zero,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_158]),c_0_16])]) ).
cnf(c_0_162,hypothesis,
divide(divide(c,divide(d,e)),g) = zero,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_159,c_0_160]),c_0_43]),c_0_20]),c_0_43]) ).
cnf(c_0_163,hypothesis,
divide(divide(d,e),divide(c,g)) = zero,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_147,c_0_161]),c_0_20]) ).
cnf(c_0_164,negated_conjecture,
divide(c,g) != divide(d,e),
prove_commutativity ).
cnf(c_0_165,hypothesis,
divide(divide(c,g),divide(divide(d,e),g)) = zero,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_162]),c_0_16])]) ).
cnf(c_0_166,hypothesis,
divide(divide(c,g),divide(d,e)) != zero,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_163]),c_0_164]) ).
cnf(c_0_167,hypothesis,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_147,c_0_165]),c_0_20]),c_0_166]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : HEN011-3 : TPTP v9.2.1. Released v1.0.0.
% 0.00/0.12 % Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.15/0.33 % Computer : n022.cluster.edu
% 0.15/0.33 % Model : x86_64 x86_64
% 0.15/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.33 % Memory : 8042.1875MB
% 0.15/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.33 % CPULimit : 300
% 0.15/0.33 % WCLimit : 300
% 0.15/0.33 % DateTime : Mon May 4 19:09:21 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.35 % start to proof: theBenchmark
% 21.35/13.03 % Version : CSE_E---1.7
% 21.35/13.03 % Problem : theBenchmark.p
% 21.35/13.03 % SZS status Unsatisfiable for theBenchmark.p
% 21.35/13.03 % SZS output start CNFRefutation
% See solution above
% 21.35/13.12 % Total time : 9.384s
%------------------------------------------------------------------------------