%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : HEN011-3 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n003.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 12:45:40 PM UTC 2026
% Result : Unsatisfiable 1.61s 0.78s
% Output : CNFRefutation 1.61s
% Verified :
% SZS Type : Refutation
% Derivation depth : 28
% Number of leaves : 12
% Syntax : Number of clauses : 126 ( 112 unt; 0 nHn; 72 RR)
% Number of literals : 143 ( 86 equ; 21 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 : 101 ( 33 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(quotient_less_equal1,axiom,
( ~ less_equal(X1,X2)
| divide(X1,X2) = zero ),
file('/export/starexec/sandbox/benchmark/Axioms/HEN002-0.ax',quotient_less_equal1) ).
cnf(identity_is_largest,axiom,
less_equal(X1,identity),
file('/export/starexec/sandbox/benchmark/Axioms/HEN002-0.ax',identity_is_largest) ).
cnf(zero_is_smallest,axiom,
less_equal(zero,X1),
file('/export/starexec/sandbox/benchmark/Axioms/HEN002-0.ax',zero_is_smallest) ).
cnf(less_equal_and_equal,axiom,
( ~ less_equal(X2,X1)
| ~ less_equal(X1,X2)
| X1 = X2 ),
file('/export/starexec/sandbox/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/sandbox/benchmark/Axioms/HEN002-0.ax',quotient_property) ).
cnf(identity_divide_a,hypothesis,
divide(identity,a) = c,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',identity_divide_a) ).
cnf(identity_divide_d,hypothesis,
divide(identity,d) = g,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',identity_divide_d) ).
cnf(quotient_less_equal2,axiom,
( divide(X1,X2) != zero
| less_equal(X1,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/HEN002-0.ax',quotient_less_equal2) ).
cnf(identity_divide_c,hypothesis,
divide(identity,c) = e,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',identity_divide_c) ).
cnf(quotient_smaller_than_numerator,axiom,
less_equal(divide(X1,X2),X1),
file('/export/starexec/sandbox/benchmark/Axioms/HEN002-0.ax',quotient_smaller_than_numerator) ).
cnf(identity_divide_b,hypothesis,
divide(identity,b) = d,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',identity_divide_b) ).
cnf(prove_commutativity,negated_conjecture,
divide(c,g) != divide(d,e),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_commutativity) ).
cnf(c_0_12,plain,
( ~ less_equal(X1,X2)
| divide(X1,X2) = zero ),
inference(fof_simplification,[status(thm)],[quotient_less_equal1]) ).
cnf(c_0_13,plain,
( ~ less_equal(X1,X2)
| divide(X1,X2) = zero ),
c_0_12 ).
cnf(c_0_14,axiom,
less_equal(X1,identity),
identity_is_largest ).
cnf(c_0_15,axiom,
less_equal(zero,X1),
zero_is_smallest ).
cnf(c_0_16,plain,
( ~ less_equal(X2,X1)
| ~ less_equal(X1,X2)
| X1 = X2 ),
inference(fof_simplification,[status(thm)],[less_equal_and_equal]) ).
cnf(c_0_17,axiom,
less_equal(divide(divide(X1,X2),divide(X3,X2)),divide(divide(X1,X3),X2)),
quotient_property ).
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_13,c_0_14]) ).
cnf(c_0_20,plain,
divide(zero,X1) = zero,
inference(spm,[status(thm)],[c_0_13,c_0_15]) ).
cnf(c_0_21,hypothesis,
divide(identity,d) = g,
identity_divide_d ).
cnf(c_0_22,plain,
( ~ less_equal(X2,X1)
| ~ less_equal(X1,X2)
| X1 = X2 ),
c_0_16 ).
cnf(c_0_23,hypothesis,
less_equal(divide(divide(X1,a),c),zero),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_18]),c_0_19]),c_0_20]) ).
cnf(c_0_24,plain,
( divide(X1,X2) != zero
| less_equal(X1,X2) ),
inference(fof_simplification,[status(thm)],[quotient_less_equal2]) ).
cnf(c_0_25,plain,
less_equal(divide(divide(X1,X2),divide(identity,X2)),zero),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_19]),c_0_20]) ).
cnf(c_0_26,hypothesis,
less_equal(divide(divide(X1,d),g),zero),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_21]),c_0_19]),c_0_20]) ).
cnf(c_0_27,plain,
( ~ less_equal(divide(divide(X1,X3),X2),divide(divide(X1,X2),divide(X3,X2)))
| divide(divide(X1,X2),divide(X3,X2)) = divide(divide(X1,X3),X2) ),
inference(spm,[status(thm)],[c_0_22,c_0_17]) ).
cnf(c_0_28,hypothesis,
divide(divide(X1,a),c) = zero,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_23]),c_0_15])]) ).
cnf(c_0_29,hypothesis,
divide(identity,c) = e,
identity_divide_c ).
cnf(c_0_30,plain,
( divide(X1,X2) != zero
| less_equal(X1,X2) ),
c_0_24 ).
cnf(c_0_31,plain,
divide(divide(X1,X2),divide(identity,X2)) = zero,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_25]),c_0_15])]) ).
cnf(c_0_32,hypothesis,
divide(divide(X1,d),g) = zero,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_26]),c_0_15])]) ).
cnf(c_0_33,hypothesis,
divide(divide(X1,c),divide(a,c)) = zero,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_28]),c_0_15])]) ).
cnf(c_0_34,hypothesis,
less_equal(divide(divide(X1,c),e),zero),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_29]),c_0_19]),c_0_20]) ).
cnf(c_0_35,plain,
less_equal(divide(X1,X2),divide(identity,X2)),
inference(spm,[status(thm)],[c_0_30,c_0_31]) ).
cnf(c_0_36,hypothesis,
divide(divide(X1,g),divide(d,g)) = zero,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_32]),c_0_15])]) ).
cnf(c_0_37,hypothesis,
divide(e,divide(a,c)) = zero,
inference(spm,[status(thm)],[c_0_33,c_0_29]) ).
cnf(c_0_38,hypothesis,
divide(divide(X1,c),e) = zero,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_34]),c_0_15])]) ).
cnf(c_0_39,axiom,
less_equal(divide(X1,X2),X1),
quotient_smaller_than_numerator ).
cnf(c_0_40,plain,
( ~ less_equal(divide(identity,X1),divide(X2,X1))
| divide(identity,X1) = divide(X2,X1) ),
inference(spm,[status(thm)],[c_0_22,c_0_35]) ).
cnf(c_0_41,hypothesis,
less_equal(divide(X1,g),divide(d,g)),
inference(spm,[status(thm)],[c_0_30,c_0_36]) ).
cnf(c_0_42,hypothesis,
less_equal(e,divide(a,c)),
inference(spm,[status(thm)],[c_0_30,c_0_37]) ).
cnf(c_0_43,hypothesis,
less_equal(divide(X1,c),e),
inference(spm,[status(thm)],[c_0_30,c_0_38]) ).
cnf(c_0_44,plain,
divide(divide(X1,X2),X1) = zero,
inference(spm,[status(thm)],[c_0_13,c_0_39]) ).
cnf(c_0_45,hypothesis,
divide(d,g) = divide(identity,g),
inference(spm,[status(thm)],[c_0_40,c_0_41]) ).
cnf(c_0_46,hypothesis,
divide(a,c) = e,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_42]),c_0_43])]) ).
cnf(c_0_47,hypothesis,
divide(divide(X1,e),divide(c,e)) = zero,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_38]),c_0_15])]) ).
cnf(c_0_48,hypothesis,
divide(divide(identity,g),d) = zero,
inference(spm,[status(thm)],[c_0_44,c_0_45]) ).
cnf(c_0_49,plain,
less_equal(divide(divide(X1,X2),zero),divide(divide(X1,zero),X2)),
inference(spm,[status(thm)],[c_0_17,c_0_20]) ).
cnf(c_0_50,hypothesis,
divide(e,a) = zero,
inference(spm,[status(thm)],[c_0_44,c_0_46]) ).
cnf(c_0_51,hypothesis,
less_equal(divide(X1,e),divide(c,e)),
inference(spm,[status(thm)],[c_0_30,c_0_47]) ).
cnf(c_0_52,hypothesis,
divide(g,divide(g,d)) = zero,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_48]),c_0_21]),c_0_21]),c_0_15])]) ).
cnf(c_0_53,plain,
less_equal(divide(divide(X1,X1),zero),zero),
inference(spm,[status(thm)],[c_0_49,c_0_44]) ).
cnf(c_0_54,hypothesis,
divide(divide(e,X1),divide(a,X1)) = zero,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_50]),c_0_20]),c_0_20]),c_0_15])]) ).
cnf(c_0_55,hypothesis,
divide(divide(X1,divide(c,e)),divide(e,divide(c,e))) = zero,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_47]),c_0_15])]) ).
cnf(c_0_56,hypothesis,
divide(c,e) = divide(identity,e),
inference(spm,[status(thm)],[c_0_40,c_0_51]) ).
cnf(c_0_57,hypothesis,
less_equal(g,divide(g,d)),
inference(spm,[status(thm)],[c_0_30,c_0_52]) ).
cnf(c_0_58,plain,
divide(divide(X1,X1),zero) = zero,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_53]),c_0_15])]) ).
cnf(c_0_59,hypothesis,
less_equal(divide(e,X1),divide(a,X1)),
inference(spm,[status(thm)],[c_0_30,c_0_54]) ).
cnf(c_0_60,hypothesis,
less_equal(divide(X1,divide(identity,e)),divide(e,divide(identity,e))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_55]),c_0_56]),c_0_56]) ).
cnf(c_0_61,plain,
divide(divide(divide(X1,X2),divide(X3,X2)),divide(divide(X1,X3),X2)) = zero,
inference(spm,[status(thm)],[c_0_13,c_0_17]) ).
cnf(c_0_62,hypothesis,
divide(g,d) = g,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_57]),c_0_39])]) ).
cnf(c_0_63,plain,
less_equal(divide(X1,X1),zero),
inference(spm,[status(thm)],[c_0_30,c_0_58]) ).
cnf(c_0_64,hypothesis,
( ~ less_equal(divide(a,X1),divide(e,X1))
| divide(e,X1) = divide(a,X1) ),
inference(spm,[status(thm)],[c_0_22,c_0_59]) ).
cnf(c_0_65,hypothesis,
divide(e,divide(identity,e)) = divide(identity,divide(identity,e)),
inference(spm,[status(thm)],[c_0_40,c_0_60]) ).
cnf(c_0_66,hypothesis,
divide(divide(g,divide(X1,d)),divide(divide(g,X1),d)) = zero,
inference(spm,[status(thm)],[c_0_61,c_0_62]) ).
cnf(c_0_67,hypothesis,
divide(identity,b) = d,
identity_divide_b ).
cnf(c_0_68,plain,
( ~ less_equal(divide(divide(X1,zero),X2),divide(divide(X1,X2),zero))
| divide(divide(X1,zero),X2) = divide(divide(X1,X2),zero) ),
inference(spm,[status(thm)],[c_0_22,c_0_49]) ).
cnf(c_0_69,plain,
divide(X1,X1) = zero,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_63]),c_0_15])]) ).
cnf(c_0_70,hypothesis,
divide(a,divide(identity,e)) = divide(identity,divide(identity,e)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_65]),c_0_35])]) ).
cnf(c_0_71,hypothesis,
divide(divide(g,zero),divide(divide(g,zero),d)) = zero,
inference(spm,[status(thm)],[c_0_66,c_0_20]) ).
cnf(c_0_72,hypothesis,
less_equal(divide(g,zero),divide(divide(g,zero),d)),
inference(spm,[status(thm)],[c_0_49,c_0_62]) ).
cnf(c_0_73,hypothesis,
less_equal(divide(divide(identity,X1),divide(b,X1)),divide(d,X1)),
inference(spm,[status(thm)],[c_0_17,c_0_67]) ).
cnf(c_0_74,plain,
divide(divide(X1,divide(X1,zero)),zero) = zero,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_69]),c_0_15])]) ).
cnf(c_0_75,hypothesis,
divide(divide(identity,divide(identity,e)),a) = zero,
inference(spm,[status(thm)],[c_0_44,c_0_70]) ).
cnf(c_0_76,hypothesis,
divide(divide(g,divide(divide(g,zero),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_27,c_0_71]),c_0_20]),c_0_20]),c_0_15])]) ).
cnf(c_0_77,hypothesis,
divide(divide(g,zero),d) = divide(g,zero),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_72]),c_0_39])]) ).
cnf(c_0_78,hypothesis,
less_equal(divide(g,divide(b,d)),zero),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_21]),c_0_69]) ).
cnf(c_0_79,plain,
less_equal(divide(X1,divide(X1,zero)),zero),
inference(spm,[status(thm)],[c_0_30,c_0_74]) ).
cnf(c_0_80,hypothesis,
divide(c,divide(divide(identity,e),a)) = zero,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_75]),c_0_18]),c_0_18]),c_0_15])]) ).
cnf(c_0_81,hypothesis,
divide(divide(g,divide(g,zero)),zero) = zero,
inference(spm,[status(thm)],[c_0_76,c_0_77]) ).
cnf(c_0_82,hypothesis,
divide(g,divide(b,d)) = zero,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_78]),c_0_15])]) ).
cnf(c_0_83,plain,
divide(X1,divide(X1,zero)) = zero,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_79]),c_0_15])]) ).
cnf(c_0_84,hypothesis,
less_equal(c,divide(divide(identity,e),a)),
inference(spm,[status(thm)],[c_0_30,c_0_80]) ).
cnf(c_0_85,hypothesis,
less_equal(divide(X1,a),c),
inference(spm,[status(thm)],[c_0_30,c_0_28]) ).
cnf(c_0_86,hypothesis,
less_equal(divide(g,divide(g,zero)),zero),
inference(spm,[status(thm)],[c_0_30,c_0_81]) ).
cnf(c_0_87,hypothesis,
less_equal(g,divide(b,d)),
inference(spm,[status(thm)],[c_0_30,c_0_82]) ).
cnf(c_0_88,hypothesis,
less_equal(divide(X1,d),g),
inference(spm,[status(thm)],[c_0_30,c_0_32]) ).
cnf(c_0_89,plain,
less_equal(X1,divide(X1,zero)),
inference(spm,[status(thm)],[c_0_30,c_0_83]) ).
cnf(c_0_90,plain,
( ~ less_equal(X1,divide(X1,X2))
| divide(X1,X2) = X1 ),
inference(spm,[status(thm)],[c_0_22,c_0_39]) ).
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_22,c_0_84]),c_0_85])]) ).
cnf(c_0_92,hypothesis,
less_equal(divide(identity,e),c),
inference(spm,[status(thm)],[c_0_39,c_0_56]) ).
cnf(c_0_93,hypothesis,
divide(g,divide(g,zero)) = zero,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_86]),c_0_15])]) ).
cnf(c_0_94,hypothesis,
divide(b,d) = g,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_87]),c_0_88])]) ).
cnf(c_0_95,plain,
divide(X1,zero) = X1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_89]),c_0_39])]) ).
cnf(c_0_96,hypothesis,
divide(divide(divide(identity,X1),divide(d,X1)),divide(g,X1)) = zero,
inference(spm,[status(thm)],[c_0_61,c_0_21]) ).
cnf(c_0_97,hypothesis,
divide(identity,e) = c,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_90,c_0_91]),c_0_92])]) ).
cnf(c_0_98,hypothesis,
less_equal(g,divide(g,zero)),
inference(spm,[status(thm)],[c_0_30,c_0_93]) ).
cnf(c_0_99,hypothesis,
divide(g,b) = zero,
inference(spm,[status(thm)],[c_0_44,c_0_94]) ).
cnf(c_0_100,plain,
divide(divide(divide(X1,X2),X3),divide(divide(identity,X2),X3)) = zero,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_31]),c_0_20]),c_0_95]) ).
cnf(c_0_101,plain,
divide(divide(divide(X1,X2),zero),divide(divide(X1,divide(X2,X3)),X2)) = zero,
inference(spm,[status(thm)],[c_0_61,c_0_44]) ).
cnf(c_0_102,hypothesis,
divide(divide(c,divide(d,e)),divide(g,e)) = zero,
inference(spm,[status(thm)],[c_0_96,c_0_97]) ).
cnf(c_0_103,hypothesis,
divide(g,zero) = g,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_98]),c_0_39])]) ).
cnf(c_0_104,hypothesis,
less_equal(divide(X1,b),divide(divide(X1,g),b)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_99]),c_0_95]) ).
cnf(c_0_105,hypothesis,
divide(divide(X1,g),d) = zero,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_100,c_0_48]),c_0_95]) ).
cnf(c_0_106,hypothesis,
divide(divide(divide(divide(c,divide(d,e)),g),zero),zero) = zero,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_101,c_0_102]),c_0_20]) ).
cnf(c_0_107,hypothesis,
divide(divide(X1,g),zero) = divide(divide(X1,zero),g),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_103]),c_0_49])]) ).
cnf(c_0_108,hypothesis,
divide(divide(identity,g),b) = d,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_104]),c_0_67]) ).
cnf(c_0_109,hypothesis,
less_equal(divide(X1,g),d),
inference(spm,[status(thm)],[c_0_30,c_0_105]) ).
cnf(c_0_110,hypothesis,
divide(divide(divide(divide(c,divide(d,e)),zero),zero),g) = zero,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_106,c_0_107]),c_0_107]) ).
cnf(c_0_111,hypothesis,
divide(divide(divide(identity,X1),divide(c,X1)),divide(e,X1)) = zero,
inference(spm,[status(thm)],[c_0_61,c_0_29]) ).
cnf(c_0_112,hypothesis,
divide(identity,g) = d,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_90,c_0_108]),c_0_109])]) ).
cnf(c_0_113,hypothesis,
divide(divide(c,divide(d,e)),g) = zero,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_110,c_0_95]),c_0_95]) ).
cnf(c_0_114,plain,
divide(divide(X1,X2),divide(divide(X1,divide(X2,X3)),X2)) = zero,
inference(rw,[status(thm)],[c_0_101,c_0_95]) ).
cnf(c_0_115,hypothesis,
divide(divide(d,divide(c,g)),divide(e,g)) = zero,
inference(spm,[status(thm)],[c_0_111,c_0_112]) ).
cnf(c_0_116,hypothesis,
divide(divide(c,g),divide(divide(d,e),g)) = zero,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_113]),c_0_95]) ).
cnf(c_0_117,hypothesis,
divide(divide(d,divide(c,g)),e) = zero,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_114,c_0_115]),c_0_20]),c_0_95]) ).
cnf(c_0_118,hypothesis,
divide(divide(c,g),divide(d,e)) = zero,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_114,c_0_116]),c_0_20]),c_0_95]) ).
cnf(c_0_119,negated_conjecture,
divide(c,g) != divide(d,e),
inference(fof_simplification,[status(thm)],[prove_commutativity]) ).
cnf(c_0_120,hypothesis,
divide(divide(d,e),divide(divide(c,g),e)) = zero,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_117]),c_0_95]) ).
cnf(c_0_121,hypothesis,
less_equal(divide(c,g),divide(d,e)),
inference(spm,[status(thm)],[c_0_30,c_0_118]) ).
cnf(c_0_122,negated_conjecture,
divide(c,g) != divide(d,e),
c_0_119 ).
cnf(c_0_123,hypothesis,
divide(divide(d,e),divide(c,g)) = zero,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_114,c_0_120]),c_0_20]),c_0_95]) ).
cnf(c_0_124,hypothesis,
~ less_equal(divide(d,e),divide(c,g)),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_121]),c_0_122]) ).
cnf(c_0_125,hypothesis,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_123]),c_0_124]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : HEN011-3 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.06 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.20/0.44 % Computer : n003.cluster.edu
% 0.20/0.44 % Model : x86_64 x86_64
% 0.20/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.20/0.44 % Memory : 8046.5625MB
% 0.20/0.44 % OS : Linux 6.8.0-71-generic
% 0.20/0.44 % CPULimit : 300
% 0.20/0.44 % WCLimit : 300
% 0.20/0.44 % DateTime : Sun Sep 20 20:48:16 UTC 2026
% 0.20/0.44 % CPUTime :
% 0.20/0.44 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.24/0.49 Running first-order theorem proving
% 0.24/0.49 Running: /export/starexec/sandbox/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 1.61/0.78 % Version: 3.5.1
% 1.61/0.78 % Preprocessing class: FSMSSMSMSSSNFFN.
% 1.61/0.78 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.61/0.78 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with 1500s (5) cores
% 1.61/0.78 % Starting new_bool_3 with 300s (1) cores
% 1.61/0.78 % Starting new_bool_1 with 300s (1) cores
% 1.61/0.78 % Starting sh5l with 300s (1) cores
% 1.61/0.78 % new_bool_1 with pid 2580470 completed with status 9
% 1.61/0.78 % new_bool_3 with pid 2580469 completed with status 9
% 1.61/0.78 % G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with pid 2580468 completed with status 0
% 1.61/0.78 % Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI
% 1.61/0.78 % Preprocessing class: FSMSSMSMSSSNFFN.
% 1.61/0.78 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.61/0.78 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with 1500s (5) cores
% 1.61/0.78 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 1.61/0.78 % No SInE strategy applied
% 1.61/0.78 % Search class: FHUSM-FFSS22-MFFFFFNN
% 1.61/0.78 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 1.61/0.78 % Starting SubtermCWHack with 136s (1) cores
% 1.61/0.78 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with 151s (1) cores
% 1.61/0.78 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S0Y with 136s (1) cores
% 1.61/0.78 % Starting new_bool_3 with 136s (1) cores
% 1.61/0.78 % Starting new_bool_1 with 136s (1) cores
% 1.61/0.78 % new_bool_1 with pid 2580476 completed with status 0
% 1.61/0.78 % Result found by new_bool_1
% 1.61/0.78 % Preprocessing class: FSMSSMSMSSSNFFN.
% 1.61/0.78 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.61/0.78 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with 1500s (5) cores
% 1.61/0.78 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 1.61/0.78 % No SInE strategy applied
% 1.61/0.78 % Search class: FHUSM-FFSS22-MFFFFFNN
% 1.61/0.78 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 1.61/0.78 % Starting SubtermCWHack with 136s (1) cores
% 1.61/0.78 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with 151s (1) cores
% 1.61/0.78 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S0Y with 136s (1) cores
% 1.61/0.78 % Starting new_bool_3 with 136s (1) cores
% 1.61/0.78 % Starting new_bool_1 with 136s (1) cores
% 1.61/0.78 % Preprocessing time : 0.001 s
% 1.61/0.78 % Presaturation interreduction done
% 1.61/0.78
% 1.61/0.78 % Proof found!
% 1.61/0.78 % SZS status Unsatisfiable
% 1.61/0.78 % SZS output start CNFRefutation
% See solution above
% 1.61/0.78 % Parsed axioms : 13
% 1.61/0.78 % Removed by relevancy pruning/SinE : 0
% 1.61/0.78 % Initial clauses : 13
% 1.61/0.78 % Removed in clause preprocessing : 0
% 1.61/0.78 % Initial clauses in saturation : 13
% 1.61/0.78 % Processed clauses : 1882
% 1.61/0.78 % ...of these trivial : 194
% 1.61/0.78 % ...subsumed : 810
% 1.61/0.78 % ...remaining for further processing : 877
% 1.61/0.78 % Other redundant clauses eliminated : 1
% 1.61/0.78 % Clauses deleted for lack of memory : 0
% 1.61/0.78 % Backward-subsumed : 7
% 1.61/0.78 % Backward-rewritten : 389
% 1.61/0.78 % Generated clauses : 43640
% 1.61/0.78 % ...of the previous two non-redundant : 19848
% 1.61/0.78 % ...aggressively subsumed : 0
% 1.61/0.78 % Contextual simplify-reflections : 0
% 1.61/0.78 % Paramodulations : 43639
% 1.61/0.78 % Factorizations : 0
% 1.61/0.78 % NegExts : 0
% 1.61/0.78 % Equation resolutions : 1
% 1.61/0.78 % Disequality decompositions : 0
% 1.61/0.78 % Total rewrite steps : 88341
% 1.61/0.78 % ...of those cached : 74728
% 1.61/0.78 % Propositional unsat checks : 0
% 1.61/0.78 % Propositional check models : 0
% 1.61/0.78 % Propositional check unsatisfiable : 0
% 1.61/0.78 % Propositional clauses : 0
% 1.61/0.78 % Propositional clauses after purity: 0
% 1.61/0.78 % Propositional unsat core size : 0
% 1.61/0.78 % Propositional preprocessing time : 0.000
% 1.61/0.78 % Propositional encoding time : 0.000
% 1.61/0.78 % Propositional solver time : 0.000
% 1.61/0.78 % Success case prop preproc time : 0.000
% 1.61/0.78 % Success case prop encoding time : 0.000
% 1.61/0.78 % Success case prop solver time : 0.000
% 1.61/0.78 % Current number of processed clauses : 469
% 1.61/0.78 % Positive orientable unit clauses : 383
% 1.61/0.78 % Positive unorientable unit clauses: 0
% 1.61/0.78 % Negative unit clauses : 2
% 1.61/0.78 % Non-unit-clauses : 84
% 1.61/0.78 % Current number of unprocessed clauses: 17708
% 1.61/0.78 % ...number of literals in the above : 19516
% 1.61/0.78 % Current number of archived formulas : 0
% 1.61/0.78 % Current number of archived clauses : 408
% 1.61/0.78 % Clause-clause subsumption calls (NU) : 2934
% 1.61/0.78 % Rec. Clause-clause subsumption calls : 2884
% 1.61/0.78 % Non-unit clause-clause subsumptions : 816
% 1.61/0.78 % Unit Clause-clause subsumption calls : 458
% 1.61/0.78 % Rewrite failures with RHS unbound : 0
% 1.61/0.78 % BW rewrite match attempts : 1572
% 1.61/0.78 % BW rewrite match successes : 158
% 1.61/0.78 % Condensation attempts : 0
% 1.61/0.78 % Condensation successes : 0
% 1.61/0.78 % Termbank termtop insertions : 824753
% 1.61/0.78 % Search garbage collected termcells : 12
% 1.61/0.78
% 1.61/0.78 % -------------------------------------------------
% 1.61/0.78 % User time : 0.254 s
% 1.61/0.78 % System time : 0.016 s
% 1.61/0.78 % Total time : 0.270 s
% 1.61/0.78 % Maximum resident set size: 3588 pages
% 1.61/0.78
% 1.61/0.78 % -------------------------------------------------
% 1.61/0.78 % User time : 1.410 s
% 1.61/0.78 % System time : 0.151 s
% 1.61/0.78 % Total time : 1.561 s
% 1.61/0.78 % Maximum resident set size: 4864 pages
% 1.61/0.78 % E exiting
%------------------------------------------------------------------------------