%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : KLE032+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n012.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 12:58:41 PM UTC 2026
% Result : Theorem 1.45s 0.63s
% Output : CNFRefutation 1.45s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 14
% Syntax : Number of formulae : 82 ( 46 unt; 0 def)
% Number of atoms : 179 ( 87 equ)
% Maximal formula atoms : 20 ( 2 avg)
% Number of connectives : 174 ( 77 ~; 71 |; 19 &)
% ( 4 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 3 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 5 con; 0-3 aty)
% Number of variables : 114 ( 2 sgn 65 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(goals,conjecture,
! [X4,X5,X6] :
( ( test(X5)
& test(X6) )
=> ismeet(multiplication(multiplication(X5,X6),X4),multiplication(X5,X4),multiplication(X6,X4)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
fof(multiplicative_associativity,axiom,
! [X1,X2,X3] : multiplication(X1,multiplication(X2,X3)) = multiplication(multiplication(X1,X2),X3),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',multiplicative_associativity) ).
fof(ismeet,axiom,
! [X4,X5,X6] :
( ismeet(X6,X4,X5)
<=> ( ! [X7] :
( ( leq(X7,X5)
& leq(X7,X4) )
=> leq(X7,X6) )
& leq(X6,X5)
& leq(X6,X4) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+3.ax',ismeet) ).
fof(order,axiom,
! [X1,X2] :
( leq(X1,X2)
<=> addition(X1,X2) = X2 ),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',order) ).
fof(additive_commutativity,axiom,
! [X1,X2] : addition(X1,X2) = addition(X2,X1),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',additive_commutativity) ).
fof(test_1,axiom,
! [X4] :
( test(X4)
<=> ? [X5] : complement(X5,X4) ),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+1.ax',test_1) ).
fof(test_2,axiom,
! [X4,X5] :
( complement(X5,X4)
<=> ( addition(X4,X5) = one
& multiplication(X5,X4) = zero
& multiplication(X4,X5) = zero ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+1.ax',test_2) ).
fof(right_distributivity,axiom,
! [X1,X2,X3] : multiplication(X1,addition(X2,X3)) = addition(multiplication(X1,X2),multiplication(X1,X3)),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',right_distributivity) ).
fof(left_annihilation,axiom,
! [X1] : multiplication(zero,X1) = zero,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',left_annihilation) ).
fof(additive_identity,axiom,
! [X1] : addition(X1,zero) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',additive_identity) ).
fof(left_distributivity,axiom,
! [X1,X2,X3] : multiplication(addition(X1,X2),X3) = addition(multiplication(X1,X3),multiplication(X2,X3)),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',left_distributivity) ).
fof(multiplicative_left_identity,axiom,
! [X1] : multiplication(one,X1) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',multiplicative_left_identity) ).
fof(additive_associativity,axiom,
! [X3,X2,X1] : addition(X1,addition(X2,X3)) = addition(addition(X1,X2),X3),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',additive_associativity) ).
fof(additive_idempotence,axiom,
! [X1] : addition(X1,X1) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',additive_idempotence) ).
fof(c_0_14,negated_conjecture,
~ ! [X4,X5,X6] :
( ( test(X5)
& test(X6) )
=> ismeet(multiplication(multiplication(X5,X6),X4),multiplication(X5,X4),multiplication(X6,X4)) ),
inference(assume_negation,[status(cth)],[goals]) ).
fof(c_0_15,negated_conjecture,
( ~ ismeet(multiplication(multiplication(esk5_0,esk6_0),esk4_0),multiplication(esk5_0,esk4_0),multiplication(esk6_0,esk4_0))
& test(esk5_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_14])])])]) ).
fof(c_0_16,plain,
! [X15,X16,X17] : multiplication(X15,multiplication(X16,X17)) = multiplication(multiplication(X15,X16),X17),
inference(variable_rename,[status(thm)],[multiplicative_associativity]) ).
cnf(c_0_17,negated_conjecture,
~ ismeet(multiplication(multiplication(esk5_0,esk6_0),esk4_0),multiplication(esk5_0,esk4_0),multiplication(esk6_0,esk4_0)),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_18,plain,
multiplication(X1,multiplication(X2,X3)) = multiplication(multiplication(X1,X2),X3),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
fof(c_0_19,plain,
! [X39,X40,X41,X42,X43,X44,X45] :
( ( ismeet(X45,X43,X44)
| ~ leq(X45,X44)
| ~ leq(X45,X43)
| ~ leq(esk2_3(X43,X44,X45),X45) )
& ( ismeet(X45,X43,X44)
| ~ leq(X45,X44)
| ~ leq(X45,X43)
| leq(esk2_3(X43,X44,X45),X44) )
& ( ismeet(X45,X43,X44)
| ~ leq(X45,X44)
| ~ leq(X45,X43)
| leq(esk2_3(X43,X44,X45),X43) )
& ( ~ ismeet(X41,X39,X40)
| leq(X42,X41)
| ~ leq(X42,X40)
| ~ leq(X42,X39) )
& ( ~ ismeet(X41,X39,X40)
| leq(X41,X40) )
& ( ~ ismeet(X41,X39,X40)
| leq(X41,X39) ) ),
inference(distribute,[status(thm)],[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)],[ismeet])])])])])])]) ).
fof(c_0_20,plain,
! [X28,X29] :
( ( leq(X28,X29)
| addition(X28,X29) != X29 )
& ( addition(X28,X29) = X29
| ~ leq(X28,X29) ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[order])])]) ).
cnf(c_0_21,negated_conjecture,
~ ismeet(multiplication(esk5_0,multiplication(esk6_0,esk4_0)),multiplication(esk5_0,esk4_0),multiplication(esk6_0,esk4_0)),
inference(rw,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_22,plain,
( ~ leq(X3,X2)
| ~ leq(X3,X1)
| ismeet(X3,X1,X2)
| leq(esk2_3(X1,X2,X3),X1) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
fof(c_0_23,plain,
! [X8,X9] : addition(X8,X9) = addition(X9,X8),
inference(variable_rename,[status(thm)],[additive_commutativity]) ).
cnf(c_0_24,plain,
( ~ leq(X1,X2)
| addition(X1,X2) = X2 ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_25,negated_conjecture,
( ~ leq(multiplication(esk5_0,multiplication(esk6_0,esk4_0)),multiplication(esk5_0,esk4_0))
| ~ leq(multiplication(esk5_0,multiplication(esk6_0,esk4_0)),multiplication(esk6_0,esk4_0))
| leq(esk2_3(multiplication(esk5_0,esk4_0),multiplication(esk6_0,esk4_0),multiplication(esk5_0,multiplication(esk6_0,esk4_0))),multiplication(esk5_0,esk4_0)) ),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_26,plain,
addition(X1,X2) = addition(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
fof(c_0_27,plain,
! [X30,X32,X33] :
( ( test(X32)
| ~ complement(X33,X32) )
& ( complement(esk1_1(X30),X30)
| ~ test(X30) ) ),
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_28,plain,
( ~ leq(X3,X2)
| ~ leq(X3,X1)
| ismeet(X3,X1,X2)
| leq(esk2_3(X1,X2,X3),X2) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_29,negated_conjecture,
( ~ leq(multiplication(esk5_0,multiplication(esk6_0,esk4_0)),multiplication(esk5_0,esk4_0))
| ~ leq(multiplication(esk5_0,multiplication(esk6_0,esk4_0)),multiplication(esk6_0,esk4_0))
| addition(multiplication(esk5_0,esk4_0),esk2_3(multiplication(esk5_0,esk4_0),multiplication(esk6_0,esk4_0),multiplication(esk5_0,multiplication(esk6_0,esk4_0)))) = multiplication(esk5_0,esk4_0) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_26]) ).
cnf(c_0_30,plain,
( addition(X1,X2) != X2
| leq(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
fof(c_0_31,plain,
! [X34,X35] :
( ( complement(X35,X34)
| addition(X34,X35) != one
| multiplication(X35,X34) != zero
| multiplication(X34,X35) != zero )
& ( ~ complement(X35,X34)
| addition(X34,X35) = one )
& ( ~ complement(X35,X34)
| multiplication(X35,X34) = zero )
& ( ~ complement(X35,X34)
| multiplication(X34,X35) = 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_32,plain,
( ~ test(X1)
| complement(esk1_1(X1),X1) ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_33,negated_conjecture,
test(esk5_0),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_34,negated_conjecture,
( ~ leq(multiplication(esk5_0,multiplication(esk6_0,esk4_0)),multiplication(esk5_0,esk4_0))
| ~ leq(multiplication(esk5_0,multiplication(esk6_0,esk4_0)),multiplication(esk6_0,esk4_0))
| leq(esk2_3(multiplication(esk5_0,esk4_0),multiplication(esk6_0,esk4_0),multiplication(esk5_0,multiplication(esk6_0,esk4_0))),multiplication(esk6_0,esk4_0)) ),
inference(spm,[status(thm)],[c_0_21,c_0_28]) ).
fof(c_0_35,plain,
! [X20,X21,X22] : multiplication(X20,addition(X21,X22)) = addition(multiplication(X20,X21),multiplication(X20,X22)),
inference(variable_rename,[status(thm)],[right_distributivity]) ).
cnf(c_0_36,negated_conjecture,
( ~ leq(multiplication(esk5_0,multiplication(esk6_0,esk4_0)),multiplication(esk5_0,esk4_0))
| addition(multiplication(esk6_0,esk4_0),multiplication(esk5_0,multiplication(esk6_0,esk4_0))) != multiplication(esk6_0,esk4_0)
| addition(multiplication(esk5_0,esk4_0),esk2_3(multiplication(esk5_0,esk4_0),multiplication(esk6_0,esk4_0),multiplication(esk5_0,multiplication(esk6_0,esk4_0)))) = multiplication(esk5_0,esk4_0) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_30]),c_0_26]) ).
cnf(c_0_37,plain,
( ~ complement(X1,X2)
| multiplication(X1,X2) = zero ),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
cnf(c_0_38,negated_conjecture,
complement(esk1_1(esk5_0),esk5_0),
inference(spm,[status(thm)],[c_0_32,c_0_33]) ).
fof(c_0_39,plain,
! [X27] : multiplication(zero,X27) = zero,
inference(variable_rename,[status(thm)],[left_annihilation]) ).
fof(c_0_40,plain,
! [X13] : addition(X13,zero) = X13,
inference(variable_rename,[status(thm)],[additive_identity]) ).
cnf(c_0_41,plain,
( ~ leq(X3,X2)
| ~ leq(X3,X1)
| ~ leq(esk2_3(X1,X2,X3),X3)
| ismeet(X3,X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_42,negated_conjecture,
( ~ leq(multiplication(esk5_0,multiplication(esk6_0,esk4_0)),multiplication(esk5_0,esk4_0))
| ~ leq(multiplication(esk5_0,multiplication(esk6_0,esk4_0)),multiplication(esk6_0,esk4_0))
| addition(multiplication(esk6_0,esk4_0),esk2_3(multiplication(esk5_0,esk4_0),multiplication(esk6_0,esk4_0),multiplication(esk5_0,multiplication(esk6_0,esk4_0)))) = multiplication(esk6_0,esk4_0) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_34]),c_0_26]) ).
fof(c_0_43,plain,
! [X23,X24,X25] : multiplication(addition(X23,X24),X25) = addition(multiplication(X23,X25),multiplication(X24,X25)),
inference(variable_rename,[status(thm)],[left_distributivity]) ).
cnf(c_0_44,plain,
( ~ complement(X2,X1)
| addition(X1,X2) = one ),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
fof(c_0_45,plain,
! [X19] : multiplication(one,X19) = X19,
inference(variable_rename,[status(thm)],[multiplicative_left_identity]) ).
cnf(c_0_46,plain,
multiplication(X1,addition(X2,X3)) = addition(multiplication(X1,X2),multiplication(X1,X3)),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
cnf(c_0_47,negated_conjecture,
( addition(multiplication(esk5_0,esk4_0),multiplication(esk5_0,multiplication(esk6_0,esk4_0))) != multiplication(esk5_0,esk4_0)
| addition(multiplication(esk6_0,esk4_0),multiplication(esk5_0,multiplication(esk6_0,esk4_0))) != multiplication(esk6_0,esk4_0)
| addition(multiplication(esk5_0,esk4_0),esk2_3(multiplication(esk5_0,esk4_0),multiplication(esk6_0,esk4_0),multiplication(esk5_0,multiplication(esk6_0,esk4_0)))) = multiplication(esk5_0,esk4_0) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_30]),c_0_26]) ).
cnf(c_0_48,negated_conjecture,
multiplication(esk1_1(esk5_0),esk5_0) = zero,
inference(spm,[status(thm)],[c_0_37,c_0_38]) ).
cnf(c_0_49,plain,
multiplication(zero,X1) = zero,
inference(split_conjunct,[status(thm)],[c_0_39]) ).
cnf(c_0_50,plain,
addition(X1,zero) = X1,
inference(split_conjunct,[status(thm)],[c_0_40]) ).
cnf(c_0_51,negated_conjecture,
( ~ leq(multiplication(esk5_0,multiplication(esk6_0,esk4_0)),multiplication(esk5_0,esk4_0))
| ~ leq(multiplication(esk5_0,multiplication(esk6_0,esk4_0)),multiplication(esk6_0,esk4_0))
| ~ leq(esk2_3(multiplication(esk5_0,esk4_0),multiplication(esk6_0,esk4_0),multiplication(esk5_0,multiplication(esk6_0,esk4_0))),multiplication(esk5_0,multiplication(esk6_0,esk4_0))) ),
inference(spm,[status(thm)],[c_0_21,c_0_41]) ).
cnf(c_0_52,negated_conjecture,
test(esk6_0),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_53,negated_conjecture,
( ~ leq(multiplication(esk5_0,multiplication(esk6_0,esk4_0)),multiplication(esk5_0,esk4_0))
| addition(multiplication(esk6_0,esk4_0),multiplication(esk5_0,multiplication(esk6_0,esk4_0))) != multiplication(esk6_0,esk4_0)
| addition(multiplication(esk6_0,esk4_0),esk2_3(multiplication(esk5_0,esk4_0),multiplication(esk6_0,esk4_0),multiplication(esk5_0,multiplication(esk6_0,esk4_0)))) = multiplication(esk6_0,esk4_0) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_30]),c_0_26]) ).
cnf(c_0_54,plain,
multiplication(addition(X1,X2),X3) = addition(multiplication(X1,X3),multiplication(X2,X3)),
inference(split_conjunct,[status(thm)],[c_0_43]) ).
cnf(c_0_55,negated_conjecture,
addition(esk5_0,esk1_1(esk5_0)) = one,
inference(spm,[status(thm)],[c_0_44,c_0_38]) ).
cnf(c_0_56,plain,
multiplication(one,X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_45]) ).
cnf(c_0_57,negated_conjecture,
( addition(multiplication(esk5_0,esk4_0),multiplication(esk5_0,multiplication(esk6_0,esk4_0))) != multiplication(esk5_0,esk4_0)
| addition(multiplication(esk6_0,esk4_0),multiplication(esk5_0,multiplication(esk6_0,esk4_0))) != multiplication(esk6_0,esk4_0)
| addition(multiplication(X1,multiplication(esk5_0,esk4_0)),multiplication(X1,esk2_3(multiplication(esk5_0,esk4_0),multiplication(esk6_0,esk4_0),multiplication(esk5_0,multiplication(esk6_0,esk4_0))))) = multiplication(X1,multiplication(esk5_0,esk4_0)) ),
inference(spm,[status(thm)],[c_0_46,c_0_47]) ).
cnf(c_0_58,negated_conjecture,
multiplication(esk1_1(esk5_0),multiplication(esk5_0,X1)) = zero,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_48]),c_0_49]) ).
cnf(c_0_59,plain,
addition(zero,X1) = X1,
inference(spm,[status(thm)],[c_0_50,c_0_26]) ).
cnf(c_0_60,negated_conjecture,
( ~ leq(multiplication(esk5_0,multiplication(esk6_0,esk4_0)),multiplication(esk5_0,esk4_0))
| ~ leq(multiplication(esk5_0,multiplication(esk6_0,esk4_0)),multiplication(esk6_0,esk4_0))
| addition(multiplication(esk5_0,multiplication(esk6_0,esk4_0)),esk2_3(multiplication(esk5_0,esk4_0),multiplication(esk6_0,esk4_0),multiplication(esk5_0,multiplication(esk6_0,esk4_0)))) != multiplication(esk5_0,multiplication(esk6_0,esk4_0)) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_30]),c_0_26]) ).
fof(c_0_61,plain,
! [X10,X11,X12] : addition(X12,addition(X11,X10)) = addition(addition(X12,X11),X10),
inference(variable_rename,[status(thm)],[additive_associativity]) ).
fof(c_0_62,plain,
! [X14] : addition(X14,X14) = X14,
inference(variable_rename,[status(thm)],[additive_idempotence]) ).
cnf(c_0_63,negated_conjecture,
complement(esk1_1(esk6_0),esk6_0),
inference(spm,[status(thm)],[c_0_32,c_0_52]) ).
cnf(c_0_64,negated_conjecture,
( addition(multiplication(esk5_0,esk4_0),multiplication(esk5_0,multiplication(esk6_0,esk4_0))) != multiplication(esk5_0,esk4_0)
| addition(multiplication(esk6_0,esk4_0),multiplication(esk5_0,multiplication(esk6_0,esk4_0))) != multiplication(esk6_0,esk4_0)
| addition(multiplication(esk6_0,esk4_0),esk2_3(multiplication(esk5_0,esk4_0),multiplication(esk6_0,esk4_0),multiplication(esk5_0,multiplication(esk6_0,esk4_0)))) = multiplication(esk6_0,esk4_0) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_30]),c_0_26]) ).
cnf(c_0_65,negated_conjecture,
addition(multiplication(esk5_0,X1),multiplication(esk1_1(esk5_0),X1)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_55]),c_0_56]) ).
cnf(c_0_66,negated_conjecture,
( addition(multiplication(esk5_0,esk4_0),multiplication(esk5_0,multiplication(esk6_0,esk4_0))) != multiplication(esk5_0,esk4_0)
| addition(multiplication(esk6_0,esk4_0),multiplication(esk5_0,multiplication(esk6_0,esk4_0))) != multiplication(esk6_0,esk4_0)
| multiplication(esk1_1(esk5_0),esk2_3(multiplication(esk5_0,esk4_0),multiplication(esk6_0,esk4_0),multiplication(esk5_0,multiplication(esk6_0,esk4_0)))) = zero ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_58]),c_0_59]) ).
cnf(c_0_67,negated_conjecture,
( ~ leq(multiplication(esk5_0,multiplication(esk6_0,esk4_0)),multiplication(esk5_0,esk4_0))
| addition(multiplication(esk6_0,esk4_0),multiplication(esk5_0,multiplication(esk6_0,esk4_0))) != multiplication(esk6_0,esk4_0)
| addition(multiplication(esk5_0,multiplication(esk6_0,esk4_0)),esk2_3(multiplication(esk5_0,esk4_0),multiplication(esk6_0,esk4_0),multiplication(esk5_0,multiplication(esk6_0,esk4_0)))) != multiplication(esk5_0,multiplication(esk6_0,esk4_0)) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_30]),c_0_26]) ).
cnf(c_0_68,plain,
addition(X1,addition(X2,X3)) = addition(addition(X1,X2),X3),
inference(split_conjunct,[status(thm)],[c_0_61]) ).
cnf(c_0_69,plain,
addition(X1,X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_62]) ).
cnf(c_0_70,negated_conjecture,
addition(esk6_0,esk1_1(esk6_0)) = one,
inference(spm,[status(thm)],[c_0_44,c_0_63]) ).
cnf(c_0_71,negated_conjecture,
( addition(multiplication(esk5_0,esk4_0),multiplication(esk5_0,multiplication(esk6_0,esk4_0))) != multiplication(esk5_0,esk4_0)
| addition(multiplication(esk6_0,esk4_0),multiplication(esk5_0,multiplication(esk6_0,esk4_0))) != multiplication(esk6_0,esk4_0)
| addition(multiplication(X1,multiplication(esk6_0,esk4_0)),multiplication(X1,esk2_3(multiplication(esk5_0,esk4_0),multiplication(esk6_0,esk4_0),multiplication(esk5_0,multiplication(esk6_0,esk4_0))))) = multiplication(X1,multiplication(esk6_0,esk4_0)) ),
inference(spm,[status(thm)],[c_0_46,c_0_64]) ).
cnf(c_0_72,negated_conjecture,
( addition(multiplication(esk5_0,esk4_0),multiplication(esk5_0,multiplication(esk6_0,esk4_0))) != multiplication(esk5_0,esk4_0)
| addition(multiplication(esk6_0,esk4_0),multiplication(esk5_0,multiplication(esk6_0,esk4_0))) != multiplication(esk6_0,esk4_0)
| multiplication(esk5_0,esk2_3(multiplication(esk5_0,esk4_0),multiplication(esk6_0,esk4_0),multiplication(esk5_0,multiplication(esk6_0,esk4_0)))) = esk2_3(multiplication(esk5_0,esk4_0),multiplication(esk6_0,esk4_0),multiplication(esk5_0,multiplication(esk6_0,esk4_0))) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_66]),c_0_50]) ).
cnf(c_0_73,negated_conjecture,
( addition(multiplication(esk5_0,esk4_0),multiplication(esk5_0,multiplication(esk6_0,esk4_0))) != multiplication(esk5_0,esk4_0)
| addition(multiplication(esk6_0,esk4_0),multiplication(esk5_0,multiplication(esk6_0,esk4_0))) != multiplication(esk6_0,esk4_0)
| addition(multiplication(esk5_0,multiplication(esk6_0,esk4_0)),esk2_3(multiplication(esk5_0,esk4_0),multiplication(esk6_0,esk4_0),multiplication(esk5_0,multiplication(esk6_0,esk4_0)))) != multiplication(esk5_0,multiplication(esk6_0,esk4_0)) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_30]),c_0_26]) ).
cnf(c_0_74,plain,
addition(X1,addition(X1,X2)) = addition(X1,X2),
inference(spm,[status(thm)],[c_0_68,c_0_69]) ).
cnf(c_0_75,negated_conjecture,
addition(multiplication(esk6_0,X1),multiplication(esk1_1(esk6_0),X1)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_70]),c_0_56]) ).
cnf(c_0_76,negated_conjecture,
( addition(multiplication(esk5_0,esk4_0),multiplication(esk5_0,multiplication(esk6_0,esk4_0))) != multiplication(esk5_0,esk4_0)
| addition(multiplication(esk6_0,esk4_0),multiplication(esk5_0,multiplication(esk6_0,esk4_0))) != multiplication(esk6_0,esk4_0) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_72]),c_0_73]) ).
cnf(c_0_77,negated_conjecture,
addition(X1,multiplication(esk5_0,X1)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_74,c_0_65]),c_0_26]) ).
cnf(c_0_78,negated_conjecture,
addition(X1,multiplication(esk6_0,X1)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_74,c_0_75]),c_0_26]) ).
cnf(c_0_79,negated_conjecture,
addition(multiplication(esk5_0,esk4_0),multiplication(esk5_0,multiplication(esk6_0,esk4_0))) != multiplication(esk5_0,esk4_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_76,c_0_77])]) ).
cnf(c_0_80,negated_conjecture,
addition(multiplication(X1,X2),multiplication(X1,multiplication(esk6_0,X2))) = multiplication(X1,X2),
inference(spm,[status(thm)],[c_0_46,c_0_78]) ).
cnf(c_0_81,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_79,c_0_80])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : KLE032+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.02 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.04/0.30 % Computer : n012.cluster.edu
% 0.04/0.30 % Model : x86_64 x86_64
% 0.04/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.04/0.30 % Memory : 8046.5625MB
% 0.04/0.30 % OS : Linux 6.8.0-71-generic
% 0.04/0.30 % CPULimit : 300
% 0.04/0.30 % WCLimit : 300
% 0.04/0.30 % DateTime : Sun Sep 20 22:39:37 UTC 2026
% 0.04/0.30 % CPUTime :
% 0.04/0.30 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.04/0.34 Running first-order theorem proving
% 0.04/0.34 Running: /export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p
% 1.45/0.63 % Version: 3.5.1
% 1.45/0.63 % Preprocessing class: FSMSSMSSSSSNFFN.
% 1.45/0.63 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.45/0.63 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 1.45/0.63 % Starting new_bool_3 with 300s (1) cores
% 1.45/0.63 % Starting new_bool_1 with 300s (1) cores
% 1.45/0.63 % Starting sh5l with 300s (1) cores
% 1.45/0.63 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 1013978 completed with status 0
% 1.45/0.63 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 1.45/0.63 % Preprocessing class: FSMSSMSSSSSNFFN.
% 1.45/0.63 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.45/0.63 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 1.45/0.63 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 1.45/0.63 % No SInE strategy applied
% 1.45/0.63 % Search class: FGUSM-FFMF32-SFFFFFNN
% 1.45/0.63 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 1.45/0.63 % Starting SubtermCWHack with 136s (1) cores
% 1.45/0.63 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 1.45/0.63 % Starting G-E--_107_B42_F1_PI_SE_Q4_CS_SP_PS_S0YI with 226s (1) cores
% 1.45/0.63 % Starting new_bool_3 with 226s (1) cores
% 1.45/0.63 % Starting G-E--_215_C46_F1_AE_CS_SP_PS_S2S with 226s (1) cores
% 1.45/0.63 % G-E--_107_B42_F1_PI_SE_Q4_CS_SP_PS_S0YI with pid 1013984 completed with status 0
% 1.45/0.63 % Result found by G-E--_107_B42_F1_PI_SE_Q4_CS_SP_PS_S0YI
% 1.45/0.63 % Preprocessing class: FSMSSMSSSSSNFFN.
% 1.45/0.63 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.45/0.63 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 1.45/0.63 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 1.45/0.63 % No SInE strategy applied
% 1.45/0.63 % Search class: FGUSM-FFMF32-SFFFFFNN
% 1.45/0.63 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 1.45/0.63 % Starting SubtermCWHack with 136s (1) cores
% 1.45/0.63 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 1.45/0.63 % Starting G-E--_107_B42_F1_PI_SE_Q4_CS_SP_PS_S0YI with 226s (1) cores
% 1.45/0.63 % Preprocessing time : 0.001 s
% 1.45/0.63 % Presaturation interreduction done
% 1.45/0.63
% 1.45/0.63 % Proof found!
% 1.45/0.63 % SZS status Theorem
% 1.45/0.63 % SZS output start CNFRefutation
% See solution above
% 1.45/0.63 % Parsed axioms : 19
% 1.45/0.63 % Removed by relevancy pruning/SinE : 0
% 1.45/0.63 % Initial clauses : 37
% 1.45/0.63 % Removed in clause preprocessing : 0
% 1.45/0.63 % Initial clauses in saturation : 37
% 1.45/0.63 % Processed clauses : 1989
% 1.45/0.63 % ...of these trivial : 442
% 1.45/0.63 % ...subsumed : 904
% 1.45/0.63 % ...remaining for further processing : 643
% 1.45/0.63 % Other redundant clauses eliminated : 13
% 1.45/0.63 % Clauses deleted for lack of memory : 0
% 1.45/0.63 % Backward-subsumed : 82
% 1.45/0.63 % Backward-rewritten : 101
% 1.45/0.63 % Generated clauses : 16432
% 1.45/0.63 % ...of the previous two non-redundant : 8887
% 1.45/0.63 % ...aggressively subsumed : 0
% 1.45/0.63 % Contextual simplify-reflections : 2
% 1.45/0.63 % Paramodulations : 16410
% 1.45/0.63 % Factorizations : 9
% 1.45/0.63 % NegExts : 0
% 1.45/0.63 % Equation resolutions : 13
% 1.45/0.63 % Disequality decompositions : 0
% 1.45/0.63 % Total rewrite steps : 29200
% 1.45/0.63 % ...of those cached : 25344
% 1.45/0.63 % Propositional unsat checks : 0
% 1.45/0.63 % Propositional check models : 0
% 1.45/0.63 % Propositional check unsatisfiable : 0
% 1.45/0.63 % Propositional clauses : 0
% 1.45/0.63 % Propositional clauses after purity: 0
% 1.45/0.63 % Propositional unsat core size : 0
% 1.45/0.63 % Propositional preprocessing time : 0.000
% 1.45/0.63 % Propositional encoding time : 0.000
% 1.45/0.63 % Propositional solver time : 0.000
% 1.45/0.63 % Success case prop preproc time : 0.000
% 1.45/0.63 % Success case prop encoding time : 0.000
% 1.45/0.63 % Success case prop solver time : 0.000
% 1.45/0.63 % Current number of processed clauses : 422
% 1.45/0.63 % Positive orientable unit clauses : 259
% 1.45/0.63 % Positive unorientable unit clauses: 4
% 1.45/0.63 % Negative unit clauses : 5
% 1.45/0.63 % Non-unit-clauses : 154
% 1.45/0.63 % Current number of unprocessed clauses: 6514
% 1.45/0.63 % ...number of literals in the above : 10144
% 1.45/0.63 % Current number of archived formulas : 0
% 1.45/0.63 % Current number of archived clauses : 220
% 1.45/0.63 % Clause-clause subsumption calls (NU) : 10983
% 1.45/0.63 % Rec. Clause-clause subsumption calls : 6459
% 1.45/0.63 % Non-unit clause-clause subsumptions : 649
% 1.45/0.63 % Unit Clause-clause subsumption calls : 3055
% 1.45/0.63 % Rewrite failures with RHS unbound : 0
% 1.45/0.63 % BW rewrite match attempts : 1760
% 1.45/0.63 % BW rewrite match successes : 137
% 1.45/0.63 % Condensation attempts : 0
% 1.45/0.63 % Condensation successes : 0
% 1.45/0.63 % Termbank termtop insertions : 225366
% 1.45/0.63 % Search garbage collected termcells : 471
% 1.45/0.63
% 1.45/0.63 % -------------------------------------------------
% 1.45/0.63 % User time : 0.184 s
% 1.45/0.63 % System time : 0.018 s
% 1.45/0.63 % Total time : 0.202 s
% 1.45/0.63 % Maximum resident set size: 3652 pages
% 1.45/0.63
% 1.45/0.63 % -------------------------------------------------
% 1.45/0.63 % User time : 0.828 s
% 1.45/0.63 % System time : 0.062 s
% 1.45/0.63 % Total time : 0.890 s
% 1.45/0.63 % Maximum resident set size: 4864 pages
% 1.45/0.63 % E exiting
%------------------------------------------------------------------------------