%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : KLE028+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n026.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 12:58:40 PM UTC 2026
% Result : Theorem 148.66s 22.48s
% Output : CNFRefutation 148.66s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 15
% Syntax : Number of formulae : 98 ( 79 unt; 0 def)
% Number of atoms : 140 ( 94 equ)
% Maximal formula atoms : 10 ( 1 avg)
% Number of connectives : 71 ( 29 ~; 23 |; 12 &)
% ( 4 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 2 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 8 con; 0-2 aty)
% Number of variables : 128 ( 4 sgn 66 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(additive_associativity,axiom,
! [X3,X2,X1] : addition(X1,addition(X2,X3)) = addition(addition(X1,X2),X3),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',additive_associativity) ).
fof(additive_idempotence,axiom,
! [X1] : addition(X1,X1) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',additive_idempotence) ).
fof(test_3,axiom,
! [X4,X5] :
( test(X4)
=> ( c(X4) = X5
<=> complement(X4,X5) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+1.ax',test_3) ).
fof(goals,conjecture,
! [X4,X5,X6,X7,X8,X9] :
( ( test(X9)
& test(X8) )
=> addition(multiplication(X8,addition(multiplication(X9,X4),multiplication(c(X9),X5))),multiplication(c(X8),addition(multiplication(X9,X6),multiplication(c(X9),X7)))) = addition(multiplication(X9,addition(multiplication(X8,X4),multiplication(c(X8),X6))),multiplication(c(X9),addition(multiplication(X8,X5),multiplication(c(X8),X7)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
fof(order,axiom,
! [X1,X2] :
( leq(X1,X2)
<=> addition(X1,X2) = X2 ),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',order) ).
fof(test_1,axiom,
! [X4] :
( test(X4)
<=> ? [X5] : complement(X5,X4) ),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+1.ax',test_1) ).
fof(additive_commutativity,axiom,
! [X1,X2] : addition(X1,X2) = addition(X2,X1),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',additive_commutativity) ).
fof(test_2,axiom,
! [X4,X5] :
( complement(X5,X4)
<=> ( addition(X4,X5) = one
& multiplication(X5,X4) = zero
& multiplication(X4,X5) = zero ) ),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+1.ax',test_2) ).
fof(left_distributivity,axiom,
! [X1,X2,X3] : multiplication(addition(X1,X2),X3) = addition(multiplication(X1,X3),multiplication(X2,X3)),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',left_distributivity) ).
fof(multiplicative_left_identity,axiom,
! [X1] : multiplication(one,X1) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',multiplicative_left_identity) ).
fof(right_distributivity,axiom,
! [X1,X2,X3] : multiplication(X1,addition(X2,X3)) = addition(multiplication(X1,X2),multiplication(X1,X3)),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',right_distributivity) ).
fof(additive_identity,axiom,
! [X1] : addition(X1,zero) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',additive_identity) ).
fof(multiplicative_right_identity,axiom,
! [X1] : multiplication(X1,one) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',multiplicative_right_identity) ).
fof(multiplicative_associativity,axiom,
! [X1,X2,X3] : multiplication(X1,multiplication(X2,X3)) = multiplication(multiplication(X1,X2),X3),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',multiplicative_associativity) ).
fof(left_annihilation,axiom,
! [X1] : multiplication(zero,X1) = zero,
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',left_annihilation) ).
fof(c_0_15,plain,
! [X12,X13,X14] : addition(X14,addition(X13,X12)) = addition(addition(X14,X13),X12),
inference(variable_rename,[status(thm)],[additive_associativity]) ).
fof(c_0_16,plain,
! [X16] : addition(X16,X16) = X16,
inference(variable_rename,[status(thm)],[additive_idempotence]) ).
fof(c_0_17,plain,
! [X38,X39] :
( ( ~ test(X38)
| c(X38) = X39
| ~ complement(X38,X39) )
& ( ~ test(X38)
| complement(X38,X39)
| c(X38) != X39 ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[test_3])])])]) ).
fof(c_0_18,negated_conjecture,
~ ! [X4,X5,X6,X7,X8,X9] :
( ( test(X9)
& test(X8) )
=> addition(multiplication(X8,addition(multiplication(X9,X4),multiplication(c(X9),X5))),multiplication(c(X8),addition(multiplication(X9,X6),multiplication(c(X9),X7)))) = addition(multiplication(X9,addition(multiplication(X8,X4),multiplication(c(X8),X6))),multiplication(c(X9),addition(multiplication(X8,X5),multiplication(c(X8),X7)))) ),
inference(assume_negation,[status(cth)],[goals]) ).
fof(c_0_19,plain,
! [X30,X31] :
( ( leq(X30,X31)
| addition(X30,X31) != X31 )
& ( addition(X30,X31) = X31
| ~ leq(X30,X31) ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[order])])]) ).
cnf(c_0_20,plain,
addition(X1,addition(X2,X3)) = addition(addition(X1,X2),X3),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_21,plain,
addition(X1,X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_22,plain,
( ~ test(X1)
| c(X1) != X2
| complement(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
fof(c_0_23,negated_conjecture,
( addition(multiplication(esk6_0,addition(multiplication(esk7_0,esk2_0),multiplication(c(esk7_0),esk3_0))),multiplication(c(esk6_0),addition(multiplication(esk7_0,esk4_0),multiplication(c(esk7_0),esk5_0)))) != addition(multiplication(esk7_0,addition(multiplication(esk6_0,esk2_0),multiplication(c(esk6_0),esk4_0))),multiplication(c(esk7_0),addition(multiplication(esk6_0,esk3_0),multiplication(c(esk6_0),esk5_0))))
& test(esk7_0)
& test(esk6_0) ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_18])])])]) ).
fof(c_0_24,plain,
! [X32,X34,X35] :
( ( test(X34)
| ~ complement(X35,X34) )
& ( complement(esk1_1(X32),X32)
| ~ test(X32) ) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[test_1])])])])])]) ).
cnf(c_0_25,plain,
( addition(X1,X2) != X2
| leq(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_26,plain,
addition(X1,addition(X1,X2)) = addition(X1,X2),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
fof(c_0_27,plain,
! [X10,X11] : addition(X10,X11) = addition(X11,X10),
inference(variable_rename,[status(thm)],[additive_commutativity]) ).
fof(c_0_28,plain,
! [X36,X37] :
( ( complement(X37,X36)
| addition(X36,X37) != one
| multiplication(X37,X36) != zero
| multiplication(X36,X37) != zero )
& ( ~ complement(X37,X36)
| addition(X36,X37) = one )
& ( ~ complement(X37,X36)
| multiplication(X37,X36) = zero )
& ( ~ complement(X37,X36)
| multiplication(X36,X37) = zero ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[test_2])])])]) ).
cnf(c_0_29,plain,
( ~ test(X1)
| complement(X1,c(X1)) ),
inference(er,[status(thm)],[c_0_22]) ).
cnf(c_0_30,negated_conjecture,
test(esk6_0),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_31,plain,
( ~ test(X1)
| complement(esk1_1(X1),X1) ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_32,plain,
leq(X1,addition(X1,X2)),
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_33,plain,
addition(X1,X2) = addition(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_34,plain,
( ~ complement(X2,X1)
| addition(X1,X2) = one ),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_35,negated_conjecture,
complement(esk6_0,c(esk6_0)),
inference(spm,[status(thm)],[c_0_29,c_0_30]) ).
cnf(c_0_36,negated_conjecture,
complement(esk1_1(esk6_0),esk6_0),
inference(spm,[status(thm)],[c_0_31,c_0_30]) ).
cnf(c_0_37,plain,
leq(X1,addition(X2,X1)),
inference(spm,[status(thm)],[c_0_32,c_0_33]) ).
cnf(c_0_38,negated_conjecture,
addition(esk6_0,c(esk6_0)) = one,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_35]),c_0_33]) ).
cnf(c_0_39,negated_conjecture,
test(esk7_0),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
fof(c_0_40,plain,
! [X25,X26,X27] : multiplication(addition(X25,X26),X27) = addition(multiplication(X25,X27),multiplication(X26,X27)),
inference(variable_rename,[status(thm)],[left_distributivity]) ).
cnf(c_0_41,negated_conjecture,
addition(esk6_0,esk1_1(esk6_0)) = one,
inference(spm,[status(thm)],[c_0_34,c_0_36]) ).
fof(c_0_42,plain,
! [X21] : multiplication(one,X21) = X21,
inference(variable_rename,[status(thm)],[multiplicative_left_identity]) ).
cnf(c_0_43,plain,
( ~ leq(X1,X2)
| addition(X1,X2) = X2 ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_44,negated_conjecture,
leq(c(esk6_0),one),
inference(spm,[status(thm)],[c_0_37,c_0_38]) ).
cnf(c_0_45,negated_conjecture,
complement(esk7_0,c(esk7_0)),
inference(spm,[status(thm)],[c_0_29,c_0_39]) ).
fof(c_0_46,plain,
! [X22,X23,X24] : multiplication(X22,addition(X23,X24)) = addition(multiplication(X22,X23),multiplication(X22,X24)),
inference(variable_rename,[status(thm)],[right_distributivity]) ).
cnf(c_0_47,plain,
multiplication(addition(X1,X2),X3) = addition(multiplication(X1,X3),multiplication(X2,X3)),
inference(split_conjunct,[status(thm)],[c_0_40]) ).
cnf(c_0_48,negated_conjecture,
addition(one,esk6_0) = one,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_41]),c_0_33]) ).
cnf(c_0_49,plain,
multiplication(one,X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_42]) ).
fof(c_0_50,plain,
! [X15] : addition(X15,zero) = X15,
inference(variable_rename,[status(thm)],[additive_identity]) ).
fof(c_0_51,plain,
! [X20] : multiplication(X20,one) = X20,
inference(variable_rename,[status(thm)],[multiplicative_right_identity]) ).
cnf(c_0_52,negated_conjecture,
addition(one,c(esk6_0)) = one,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_44]),c_0_33]) ).
cnf(c_0_53,negated_conjecture,
addition(esk7_0,c(esk7_0)) = one,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_45]),c_0_33]) ).
cnf(c_0_54,plain,
multiplication(X1,addition(X2,X3)) = addition(multiplication(X1,X2),multiplication(X1,X3)),
inference(split_conjunct,[status(thm)],[c_0_46]) ).
cnf(c_0_55,negated_conjecture,
addition(X1,multiplication(esk6_0,X1)) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_48]),c_0_49]),c_0_49]) ).
cnf(c_0_56,plain,
( ~ complement(X2,X1)
| multiplication(X1,X2) = zero ),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_57,plain,
addition(X1,zero) = X1,
inference(split_conjunct,[status(thm)],[c_0_50]) ).
cnf(c_0_58,plain,
multiplication(X1,one) = X1,
inference(split_conjunct,[status(thm)],[c_0_51]) ).
cnf(c_0_59,negated_conjecture,
addition(X1,multiplication(c(esk6_0),X1)) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_52]),c_0_49]),c_0_49]) ).
cnf(c_0_60,plain,
( ~ complement(X1,X2)
| multiplication(X1,X2) = zero ),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_61,negated_conjecture,
addition(esk7_0,addition(c(esk7_0),X1)) = addition(one,X1),
inference(spm,[status(thm)],[c_0_20,c_0_53]) ).
cnf(c_0_62,negated_conjecture,
addition(multiplication(X1,X2),multiplication(X1,multiplication(esk6_0,X2))) = multiplication(X1,X2),
inference(spm,[status(thm)],[c_0_54,c_0_55]) ).
cnf(c_0_63,negated_conjecture,
multiplication(c(esk7_0),esk7_0) = zero,
inference(spm,[status(thm)],[c_0_56,c_0_45]) ).
cnf(c_0_64,plain,
addition(zero,X1) = X1,
inference(spm,[status(thm)],[c_0_57,c_0_33]) ).
cnf(c_0_65,negated_conjecture,
addition(multiplication(X1,esk7_0),multiplication(X1,c(esk7_0))) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_53]),c_0_58]) ).
cnf(c_0_66,negated_conjecture,
addition(multiplication(X1,X2),multiplication(X1,multiplication(c(esk6_0),X2))) = multiplication(X1,X2),
inference(spm,[status(thm)],[c_0_54,c_0_59]) ).
cnf(c_0_67,negated_conjecture,
multiplication(esk7_0,c(esk7_0)) = zero,
inference(spm,[status(thm)],[c_0_60,c_0_45]) ).
cnf(c_0_68,negated_conjecture,
addition(multiplication(esk7_0,X1),addition(multiplication(c(esk7_0),X1),multiplication(X2,X1))) = addition(X1,multiplication(X2,X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_61]),c_0_47]),c_0_49]),c_0_47]) ).
cnf(c_0_69,negated_conjecture,
multiplication(c(esk7_0),multiplication(esk6_0,esk7_0)) = zero,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_63]),c_0_64]) ).
cnf(c_0_70,negated_conjecture,
addition(multiplication(X1,multiplication(X2,esk7_0)),multiplication(X1,multiplication(X2,c(esk7_0)))) = multiplication(X1,X2),
inference(spm,[status(thm)],[c_0_54,c_0_65]) ).
cnf(c_0_71,negated_conjecture,
multiplication(esk7_0,multiplication(c(esk6_0),c(esk7_0))) = zero,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_67]),c_0_64]) ).
fof(c_0_72,plain,
! [X17,X18,X19] : multiplication(X17,multiplication(X18,X19)) = multiplication(multiplication(X17,X18),X19),
inference(variable_rename,[status(thm)],[multiplicative_associativity]) ).
fof(c_0_73,plain,
! [X29] : multiplication(zero,X29) = zero,
inference(variable_rename,[status(thm)],[left_annihilation]) ).
cnf(c_0_74,negated_conjecture,
addition(multiplication(esk6_0,addition(multiplication(esk7_0,esk2_0),multiplication(c(esk7_0),esk3_0))),multiplication(c(esk6_0),addition(multiplication(esk7_0,esk4_0),multiplication(c(esk7_0),esk5_0)))) != addition(multiplication(esk7_0,addition(multiplication(esk6_0,esk2_0),multiplication(c(esk6_0),esk4_0))),multiplication(c(esk7_0),addition(multiplication(esk6_0,esk3_0),multiplication(c(esk6_0),esk5_0)))),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_75,negated_conjecture,
multiplication(esk7_0,multiplication(esk6_0,c(esk7_0))) = zero,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_67]),c_0_64]) ).
cnf(c_0_76,negated_conjecture,
multiplication(esk7_0,multiplication(esk6_0,esk7_0)) = multiplication(esk6_0,esk7_0),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_69]),c_0_69]),c_0_21]),c_0_57]),c_0_57]) ).
cnf(c_0_77,negated_conjecture,
addition(multiplication(esk7_0,X1),multiplication(c(esk7_0),X1)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_53]),c_0_49]) ).
cnf(c_0_78,negated_conjecture,
multiplication(c(esk7_0),multiplication(c(esk6_0),esk7_0)) = zero,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_63]),c_0_64]) ).
cnf(c_0_79,negated_conjecture,
multiplication(esk7_0,multiplication(c(esk6_0),esk7_0)) = multiplication(esk7_0,c(esk6_0)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_71]),c_0_57]) ).
cnf(c_0_80,plain,
multiplication(X1,multiplication(X2,X3)) = multiplication(multiplication(X1,X2),X3),
inference(split_conjunct,[status(thm)],[c_0_72]) ).
cnf(c_0_81,plain,
multiplication(zero,X1) = zero,
inference(split_conjunct,[status(thm)],[c_0_73]) ).
cnf(c_0_82,negated_conjecture,
addition(multiplication(esk7_0,multiplication(esk6_0,esk2_0)),addition(multiplication(esk7_0,multiplication(c(esk6_0),esk4_0)),addition(multiplication(c(esk7_0),multiplication(esk6_0,esk3_0)),multiplication(c(esk7_0),multiplication(c(esk6_0),esk5_0))))) != addition(multiplication(esk6_0,multiplication(esk7_0,esk2_0)),addition(multiplication(esk6_0,multiplication(c(esk7_0),esk3_0)),addition(multiplication(c(esk6_0),multiplication(esk7_0,esk4_0)),multiplication(c(esk6_0),multiplication(c(esk7_0),esk5_0))))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_74,c_0_54]),c_0_54]),c_0_20]),c_0_54]),c_0_54]),c_0_20]) ).
cnf(c_0_83,plain,
addition(X1,addition(X2,X3)) = addition(X2,addition(X1,X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_33]),c_0_20]) ).
cnf(c_0_84,negated_conjecture,
multiplication(esk7_0,esk6_0) = multiplication(esk6_0,esk7_0),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_75]),c_0_57]),c_0_76]) ).
cnf(c_0_85,negated_conjecture,
multiplication(c(esk7_0),multiplication(c(esk6_0),c(esk7_0))) = multiplication(c(esk6_0),c(esk7_0)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_71]),c_0_64]) ).
cnf(c_0_86,negated_conjecture,
multiplication(c(esk6_0),esk7_0) = multiplication(esk7_0,c(esk6_0)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_78]),c_0_57]),c_0_79]) ).
cnf(c_0_87,negated_conjecture,
multiplication(c(esk7_0),multiplication(esk7_0,X1)) = zero,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_80,c_0_63]),c_0_81]) ).
cnf(c_0_88,negated_conjecture,
multiplication(c(esk7_0),multiplication(esk6_0,c(esk7_0))) = multiplication(esk6_0,c(esk7_0)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_75]),c_0_75]),c_0_57]),c_0_64]),c_0_57]) ).
cnf(c_0_89,negated_conjecture,
addition(multiplication(esk7_0,multiplication(esk6_0,esk2_0)),addition(multiplication(esk7_0,multiplication(c(esk6_0),esk4_0)),addition(multiplication(c(esk7_0),multiplication(esk6_0,esk3_0)),multiplication(c(esk7_0),multiplication(c(esk6_0),esk5_0))))) != addition(multiplication(esk6_0,multiplication(esk7_0,esk2_0)),addition(multiplication(c(esk6_0),multiplication(esk7_0,esk4_0)),addition(multiplication(esk6_0,multiplication(c(esk7_0),esk3_0)),multiplication(c(esk6_0),multiplication(c(esk7_0),esk5_0))))),
inference(rw,[status(thm)],[c_0_82,c_0_83]) ).
cnf(c_0_90,negated_conjecture,
multiplication(esk7_0,multiplication(esk6_0,X1)) = multiplication(esk6_0,multiplication(esk7_0,X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_80,c_0_84]),c_0_80]) ).
cnf(c_0_91,negated_conjecture,
multiplication(c(esk7_0),c(esk6_0)) = multiplication(c(esk6_0),c(esk7_0)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_85]),c_0_86]),c_0_87]),c_0_64]) ).
cnf(c_0_92,negated_conjecture,
multiplication(c(esk7_0),esk6_0) = multiplication(esk6_0,c(esk7_0)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_88]),c_0_69]),c_0_64]) ).
cnf(c_0_93,negated_conjecture,
addition(multiplication(esk6_0,multiplication(esk7_0,esk2_0)),addition(multiplication(esk7_0,multiplication(c(esk6_0),esk4_0)),addition(multiplication(c(esk7_0),multiplication(esk6_0,esk3_0)),multiplication(c(esk7_0),multiplication(c(esk6_0),esk5_0))))) != addition(multiplication(esk6_0,multiplication(esk7_0,esk2_0)),addition(multiplication(c(esk6_0),multiplication(esk7_0,esk4_0)),addition(multiplication(esk6_0,multiplication(c(esk7_0),esk3_0)),multiplication(c(esk6_0),multiplication(c(esk7_0),esk5_0))))),
inference(rw,[status(thm)],[c_0_89,c_0_90]) ).
cnf(c_0_94,negated_conjecture,
multiplication(c(esk7_0),multiplication(c(esk6_0),X1)) = multiplication(c(esk6_0),multiplication(c(esk7_0),X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_80,c_0_91]),c_0_80]) ).
cnf(c_0_95,negated_conjecture,
multiplication(c(esk7_0),multiplication(esk6_0,X1)) = multiplication(esk6_0,multiplication(c(esk7_0),X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_80,c_0_92]),c_0_80]) ).
cnf(c_0_96,negated_conjecture,
multiplication(c(esk6_0),multiplication(esk7_0,X1)) = multiplication(esk7_0,multiplication(c(esk6_0),X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_80,c_0_86]),c_0_80]) ).
cnf(c_0_97,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_93,c_0_94]),c_0_95]),c_0_96])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KLE028+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.36 % Computer : n026.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sun Sep 20 22:42:21 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.14/0.44 Running first-order theorem proving
% 0.14/0.44 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
% 148.66/22.48 % Version: 3.5.1
% 148.66/22.48 % Preprocessing class: FSMSSMSSSSSNFFN.
% 148.66/22.48 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 148.66/22.48 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 148.66/22.48 % Starting new_bool_3 with 300s (1) cores
% 148.66/22.48 % Starting new_bool_1 with 300s (1) cores
% 148.66/22.48 % Starting sh5l with 300s (1) cores
% 148.66/22.48 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 750509 completed with status 0
% 148.66/22.48 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 148.66/22.48 % Preprocessing class: FSMSSMSSSSSNFFN.
% 148.66/22.48 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 148.66/22.48 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 148.66/22.48 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 148.66/22.48 % No SInE strategy applied
% 148.66/22.48 % Search class: FGUSM-FFMF21-MFFFFFNN
% 148.66/22.48 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 148.66/22.48 % Starting SubtermCWHack with 136s (1) cores
% 148.66/22.48 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 148.66/22.48 % Starting G-E--_200_B02_F1_AE_CS_SP_PI_S0S with 136s (1) cores
% 148.66/22.48 % Starting new_bool_3 with 136s (1) cores
% 148.66/22.48 % Starting new_bool_1 with 136s (1) cores
% 148.66/22.48 % G-E--_200_B02_F1_AE_CS_SP_PI_S0S with pid 750516 completed with status 0
% 148.66/22.48 % Result found by G-E--_200_B02_F1_AE_CS_SP_PI_S0S
% 148.66/22.48 % Preprocessing class: FSMSSMSSSSSNFFN.
% 148.66/22.48 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 148.66/22.48 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 148.66/22.48 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 148.66/22.48 % No SInE strategy applied
% 148.66/22.48 % Search class: FGUSM-FFMF21-MFFFFFNN
% 148.66/22.48 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 148.66/22.48 % Starting SubtermCWHack with 136s (1) cores
% 148.66/22.48 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 148.66/22.48 % Starting G-E--_200_B02_F1_AE_CS_SP_PI_S0S with 136s (1) cores
% 148.66/22.48 % Preprocessing time : 0.002 s
% 148.66/22.48
% 148.66/22.48 % Proof found!
% 148.66/22.48 % SZS status Theorem
% 148.66/22.48 % SZS output start CNFRefutation
% See solution above
% 148.66/22.48 % Parsed axioms : 17
% 148.66/22.48 % Removed by relevancy pruning/SinE : 0
% 148.66/22.48 % Initial clauses : 25
% 148.66/22.48 % Removed in clause preprocessing : 0
% 148.66/22.48 % Initial clauses in saturation : 25
% 148.66/22.48 % Processed clauses : 35086
% 148.66/22.48 % ...of these trivial : 2186
% 148.66/22.48 % ...subsumed : 29279
% 148.66/22.48 % ...remaining for further processing : 3621
% 148.66/22.48 % Other redundant clauses eliminated : 0
% 148.66/22.48 % Clauses deleted for lack of memory : 0
% 148.66/22.48 % Backward-subsumed : 13
% 148.66/22.48 % Backward-rewritten : 752
% 148.66/22.48 % Generated clauses : 559793
% 148.66/22.48 % ...of the previous two non-redundant : 478436
% 148.66/22.48 % ...aggressively subsumed : 0
% 148.66/22.48 % Contextual simplify-reflections : 0
% 148.66/22.48 % Paramodulations : 559783
% 148.66/22.48 % Factorizations : 0
% 148.66/22.48 % NegExts : 0
% 148.66/22.48 % Equation resolutions : 10
% 148.66/22.48 % Disequality decompositions : 0
% 148.66/22.48 % Total rewrite steps : 2481930
% 148.66/22.48 % ...of those cached : 2403034
% 148.66/22.48 % Propositional unsat checks : 0
% 148.66/22.48 % Propositional check models : 0
% 148.66/22.48 % Propositional check unsatisfiable : 0
% 148.66/22.48 % Propositional clauses : 0
% 148.66/22.48 % Propositional clauses after purity: 0
% 148.66/22.48 % Propositional unsat core size : 0
% 148.66/22.48 % Propositional preprocessing time : 0.000
% 148.66/22.48 % Propositional encoding time : 0.000
% 148.66/22.48 % Propositional solver time : 0.000
% 148.66/22.48 % Success case prop preproc time : 0.000
% 148.66/22.48 % Success case prop encoding time : 0.000
% 148.66/22.48 % Success case prop solver time : 0.000
% 148.66/22.48 % Current number of processed clauses : 2856
% 148.66/22.48 % Positive orientable unit clauses : 926
% 148.66/22.48 % Positive unorientable unit clauses: 8
% 148.66/22.48 % Negative unit clauses : 2
% 148.66/22.48 % Non-unit-clauses : 1920
% 148.66/22.48 % Current number of unprocessed clauses: 439444
% 148.66/22.48 % ...number of literals in the above : 987315
% 148.66/22.48 % Current number of archived formulas : 0
% 148.66/22.48 % Current number of archived clauses : 765
% 148.66/22.48 % Clause-clause subsumption calls (NU) : 1200434
% 148.66/22.48 % Rec. Clause-clause subsumption calls : 1098588
% 148.66/22.48 % Non-unit clause-clause subsumptions : 27748
% 148.66/22.48 % Unit Clause-clause subsumption calls : 47603
% 148.66/22.48 % Rewrite failures with RHS unbound : 0
% 148.66/22.48 % BW rewrite match attempts : 17046
% 148.66/22.48 % BW rewrite match successes : 3325
% 148.66/22.48 % Condensation attempts : 0
% 148.66/22.48 % Condensation successes : 0
% 148.66/22.48 % Termbank termtop insertions : 21448707
% 148.66/22.48 % Search garbage collected termcells : 206
% 148.66/22.48
% 148.66/22.48 % -------------------------------------------------
% 148.66/22.48 % User time : 20.535 s
% 148.66/22.48 % System time : 0.715 s
% 148.66/22.48 % Total time : 21.250 s
% 148.66/22.48 % Maximum resident set size: 3652 pages
% 148.66/22.48
% 148.66/22.48 % -------------------------------------------------
% 148.66/22.48 % User time : 100.985 s
% 148.66/22.48 % System time : 3.829 s
% 148.66/22.48 % Total time : 104.814 s
% 148.66/22.48 % Maximum resident set size: 4864 pages
% 148.66/22.48 % E exiting
%------------------------------------------------------------------------------