%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : KLE013+1 : TPTP v9.2.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n014.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 04:35:28 PM UTC 2026
% Result : Theorem 18.26s 12.14s
% Output : CNFRefutation 18.34s
% Verified :
% SZS Type : Refutation
% Derivation depth : 31
% Number of leaves : 16
% Syntax : Number of formulae : 154 ( 84 unt; 0 def)
% Number of atoms : 259 ( 166 equ)
% Maximal formula atoms : 10 ( 1 avg)
% Number of connectives : 196 ( 91 ~; 86 |; 11 &)
% ( 3 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 2 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 175 ( 4 sgn 59 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
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(test_2,axiom,
! [X4,X5] :
( complement(X5,X4)
<=> ( multiplication(X4,X5) = zero
& multiplication(X5,X4) = zero
& addition(X4,X5) = one ) ),
file('/export/starexec/sandbox/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/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(additive_commutativity,axiom,
! [X1,X2] : addition(X1,X2) = addition(X2,X1),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',additive_commutativity) ).
fof(multiplicative_right_identity,axiom,
! [X1] : multiplication(X1,one) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',multiplicative_right_identity) ).
fof(goals,conjecture,
! [X4,X5] :
( ( test(X5)
& test(X4) )
=> one = addition(addition(X4,X5),multiplication(c(X4),c(X5))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
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(multiplicative_left_identity,axiom,
! [X1] : multiplication(one,X1) = X1,
file('/export/starexec/sandbox/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/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_1,axiom,
! [X4] :
( test(X4)
<=> ? [X5] : complement(X5,X4) ),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+1.ax',test_1) ).
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(left_annihilation,axiom,
! [X1] : multiplication(zero,X1) = zero,
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',left_annihilation) ).
fof(right_annihilation,axiom,
! [X1] : multiplication(X1,zero) = zero,
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',right_annihilation) ).
fof(test_4,axiom,
! [X4] :
( ~ test(X4)
=> c(X4) = zero ),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+1.ax',test_4) ).
fof(c_0_16,plain,
! [X65,X66] :
( ( c(X65) != X66
| complement(X65,X66)
| ~ test(X65) )
& ( ~ complement(X65,X66)
| c(X65) = X66
| ~ test(X65) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[test_3])])]) ).
fof(c_0_17,plain,
! [X63,X64] :
( ( multiplication(X63,X64) = zero
| ~ complement(X64,X63) )
& ( multiplication(X64,X63) = zero
| ~ complement(X64,X63) )
& ( addition(X63,X64) = one
| ~ complement(X64,X63) )
& ( multiplication(X63,X64) != zero
| multiplication(X64,X63) != zero
| addition(X63,X64) != one
| complement(X64,X63) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[test_2])])]) ).
cnf(c_0_18,plain,
( complement(X1,X2)
| c(X1) != X2
| ~ test(X1) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
fof(c_0_19,plain,
! [X49,X50,X51] : multiplication(X49,addition(X50,X51)) = addition(multiplication(X49,X50),multiplication(X49,X51)),
inference(variable_rename,[status(thm)],[right_distributivity]) ).
cnf(c_0_20,plain,
( multiplication(X1,X2) = zero
| ~ complement(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_21,plain,
( complement(X1,c(X1))
| ~ test(X1) ),
inference(er,[status(thm)],[c_0_18]) ).
fof(c_0_22,plain,
! [X42] : addition(X42,zero) = X42,
inference(variable_rename,[status(thm)],[additive_identity]) ).
fof(c_0_23,plain,
! [X37,X38] : addition(X37,X38) = addition(X38,X37),
inference(variable_rename,[status(thm)],[additive_commutativity]) ).
cnf(c_0_24,plain,
multiplication(X1,addition(X2,X3)) = addition(multiplication(X1,X2),multiplication(X1,X3)),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_25,plain,
( multiplication(X1,c(X1)) = zero
| ~ test(X1) ),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_26,plain,
addition(X1,zero) = X1,
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_27,plain,
( addition(X1,X2) = one
| ~ complement(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_28,plain,
addition(X1,X2) = addition(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
fof(c_0_29,plain,
! [X47] : multiplication(X47,one) = X47,
inference(variable_rename,[status(thm)],[multiplicative_right_identity]) ).
fof(c_0_30,negated_conjecture,
~ ! [X4,X5] :
( ( test(X5)
& test(X4) )
=> one = addition(addition(X4,X5),multiplication(c(X4),c(X5))) ),
inference(assume_negation,[status(cth)],[goals]) ).
fof(c_0_31,plain,
! [X44,X45,X46] : multiplication(X44,multiplication(X45,X46)) = multiplication(multiplication(X44,X45),X46),
inference(variable_rename,[status(thm)],[multiplicative_associativity]) ).
cnf(c_0_32,plain,
( multiplication(X1,addition(X2,c(X1))) = multiplication(X1,X2)
| ~ test(X1) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_26]) ).
cnf(c_0_33,plain,
( addition(X1,c(X1)) = one
| ~ test(X1) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_21]),c_0_28]) ).
cnf(c_0_34,plain,
multiplication(X1,one) = X1,
inference(split_conjunct,[status(thm)],[c_0_29]) ).
fof(c_0_35,negated_conjecture,
( test(esk3_0)
& test(esk2_0)
& one != addition(addition(esk2_0,esk3_0),multiplication(c(esk2_0),c(esk3_0))) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_30])])]) ).
cnf(c_0_36,plain,
multiplication(X1,multiplication(X2,X3)) = multiplication(multiplication(X1,X2),X3),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
cnf(c_0_37,plain,
( multiplication(X1,X1) = X1
| ~ test(X1) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_33]),c_0_34]) ).
cnf(c_0_38,negated_conjecture,
test(esk3_0),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
cnf(c_0_39,plain,
( multiplication(X1,multiplication(X2,c(multiplication(X1,X2)))) = zero
| ~ test(multiplication(X1,X2)) ),
inference(spm,[status(thm)],[c_0_36,c_0_25]) ).
cnf(c_0_40,negated_conjecture,
multiplication(esk3_0,esk3_0) = esk3_0,
inference(spm,[status(thm)],[c_0_37,c_0_38]) ).
cnf(c_0_41,plain,
addition(X1,multiplication(X1,X2)) = multiplication(X1,addition(X2,one)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_34]),c_0_28]) ).
cnf(c_0_42,negated_conjecture,
multiplication(esk3_0,multiplication(esk3_0,c(esk3_0))) = zero,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_40]),c_0_38])]) ).
cnf(c_0_43,negated_conjecture,
multiplication(esk3_0,addition(one,multiplication(esk3_0,c(esk3_0)))) = esk3_0,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_42]),c_0_26]),c_0_28]) ).
fof(c_0_44,plain,
! [X48] : multiplication(one,X48) = X48,
inference(variable_rename,[status(thm)],[multiplicative_left_identity]) ).
fof(c_0_45,plain,
! [X39,X40,X41] : addition(X41,addition(X40,X39)) = addition(addition(X41,X40),X39),
inference(variable_rename,[status(thm)],[additive_associativity]) ).
fof(c_0_46,plain,
! [X43] : addition(X43,X43) = X43,
inference(variable_rename,[status(thm)],[additive_idempotence]) ).
fof(c_0_47,plain,
! [X59,X61,X62] :
( ( ~ test(X59)
| complement(esk1_1(X59),X59) )
& ( ~ complement(X62,X61)
| test(X61) ) ),
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_48,negated_conjecture,
multiplication(esk3_0,multiplication(addition(one,multiplication(esk3_0,c(esk3_0))),c(esk3_0))) = zero,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_43]),c_0_38])]) ).
cnf(c_0_49,plain,
multiplication(one,X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_44]) ).
cnf(c_0_50,plain,
addition(X1,addition(X2,X3)) = addition(addition(X1,X2),X3),
inference(split_conjunct,[status(thm)],[c_0_45]) ).
cnf(c_0_51,plain,
addition(X1,X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_46]) ).
cnf(c_0_52,plain,
( complement(esk1_1(X1),X1)
| ~ test(X1) ),
inference(split_conjunct,[status(thm)],[c_0_47]) ).
fof(c_0_53,plain,
! [X52,X53,X54] : multiplication(addition(X52,X53),X54) = addition(multiplication(X52,X54),multiplication(X53,X54)),
inference(variable_rename,[status(thm)],[left_distributivity]) ).
cnf(c_0_54,negated_conjecture,
multiplication(esk3_0,c(esk3_0)) = zero,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_25]),c_0_26]),c_0_49]),c_0_38])]) ).
cnf(c_0_55,plain,
addition(zero,X1) = X1,
inference(spm,[status(thm)],[c_0_26,c_0_28]) ).
cnf(c_0_56,plain,
addition(X1,addition(X1,X2)) = addition(X1,X2),
inference(spm,[status(thm)],[c_0_50,c_0_51]) ).
cnf(c_0_57,plain,
( addition(X1,esk1_1(X1)) = one
| ~ test(X1) ),
inference(spm,[status(thm)],[c_0_27,c_0_52]) ).
cnf(c_0_58,plain,
multiplication(addition(X1,X2),X3) = addition(multiplication(X1,X3),multiplication(X2,X3)),
inference(split_conjunct,[status(thm)],[c_0_53]) ).
cnf(c_0_59,negated_conjecture,
multiplication(esk3_0,addition(c(esk3_0),X1)) = multiplication(esk3_0,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_54]),c_0_55]) ).
cnf(c_0_60,plain,
( addition(X1,one) = one
| ~ test(X1) ),
inference(spm,[status(thm)],[c_0_56,c_0_57]) ).
cnf(c_0_61,plain,
addition(X1,multiplication(X2,X1)) = multiplication(addition(X2,one),X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_49]),c_0_28]) ).
cnf(c_0_62,negated_conjecture,
( multiplication(esk3_0,c(c(esk3_0))) = esk3_0
| ~ test(c(esk3_0)) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_33]),c_0_34]) ).
cnf(c_0_63,negated_conjecture,
addition(one,esk3_0) = one,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_38]),c_0_28]) ).
cnf(c_0_64,plain,
( test(X2)
| ~ complement(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_47]) ).
cnf(c_0_65,plain,
( multiplication(X1,X2) = zero
| ~ complement(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_66,plain,
( addition(X1,addition(X2,c(addition(X1,X2)))) = one
| ~ test(addition(X1,X2)) ),
inference(spm,[status(thm)],[c_0_50,c_0_33]) ).
cnf(c_0_67,negated_conjecture,
( addition(esk3_0,c(c(esk3_0))) = c(c(esk3_0))
| ~ test(c(esk3_0)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_62]),c_0_28]),c_0_63]),c_0_49]),c_0_28]) ).
cnf(c_0_68,plain,
( test(c(X1))
| ~ test(X1) ),
inference(spm,[status(thm)],[c_0_64,c_0_21]) ).
cnf(c_0_69,plain,
( multiplication(c(X1),X1) = zero
| ~ test(X1) ),
inference(spm,[status(thm)],[c_0_65,c_0_21]) ).
cnf(c_0_70,plain,
( multiplication(addition(X1,X2),c(X1)) = multiplication(X2,c(X1))
| ~ test(X1) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_25]),c_0_55]) ).
cnf(c_0_71,negated_conjecture,
( addition(esk3_0,addition(c(c(esk3_0)),c(c(c(esk3_0))))) = one
| ~ test(c(esk3_0)) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_67]),c_0_68]) ).
cnf(c_0_72,plain,
( multiplication(addition(c(X1),X2),X1) = multiplication(X2,X1)
| ~ test(X1) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_69]),c_0_55]) ).
cnf(c_0_73,negated_conjecture,
( multiplication(addition(c(c(esk3_0)),c(c(c(esk3_0)))),c(esk3_0)) = c(esk3_0)
| ~ test(c(esk3_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_71]),c_0_49]),c_0_38])]) ).
cnf(c_0_74,negated_conjecture,
addition(one,addition(esk3_0,X1)) = addition(one,X1),
inference(spm,[status(thm)],[c_0_50,c_0_63]) ).
cnf(c_0_75,negated_conjecture,
( multiplication(c(c(c(esk3_0))),c(esk3_0)) = c(esk3_0)
| ~ test(c(esk3_0)) ),
inference(spm,[status(thm)],[c_0_72,c_0_73]) ).
cnf(c_0_76,negated_conjecture,
addition(one,c(esk3_0)) = one,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_74,c_0_33]),c_0_51]),c_0_38])]) ).
cnf(c_0_77,plain,
( multiplication(addition(X1,X2),c(X2)) = multiplication(X1,c(X2))
| ~ test(X2) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_25]),c_0_26]) ).
cnf(c_0_78,negated_conjecture,
( addition(c(esk3_0),c(c(c(esk3_0)))) = c(c(c(esk3_0)))
| ~ test(c(esk3_0)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_75]),c_0_28]),c_0_76]),c_0_34]),c_0_28]) ).
cnf(c_0_79,plain,
( complement(X2,X1)
| multiplication(X1,X2) != zero
| multiplication(X2,X1) != zero
| addition(X1,X2) != one ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_80,negated_conjecture,
test(esk2_0),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
cnf(c_0_81,negated_conjecture,
( multiplication(c(c(esk3_0)),c(c(c(esk3_0)))) = multiplication(esk3_0,c(c(c(esk3_0))))
| ~ test(c(esk3_0)) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_67]),c_0_68]) ).
cnf(c_0_82,negated_conjecture,
( multiplication(c(c(esk3_0)),c(c(c(esk3_0)))) = multiplication(c(c(esk3_0)),c(esk3_0))
| ~ test(c(esk3_0)) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_78]),c_0_68]) ).
cnf(c_0_83,plain,
( test(X1)
| addition(X1,X2) != one
| multiplication(X2,X1) != zero
| multiplication(X1,X2) != zero ),
inference(spm,[status(thm)],[c_0_64,c_0_79]) ).
cnf(c_0_84,negated_conjecture,
multiplication(esk2_0,esk2_0) = esk2_0,
inference(spm,[status(thm)],[c_0_37,c_0_80]) ).
fof(c_0_85,plain,
! [X56] : multiplication(zero,X56) = zero,
inference(variable_rename,[status(thm)],[left_annihilation]) ).
cnf(c_0_86,negated_conjecture,
( multiplication(c(c(esk3_0)),c(esk3_0)) = multiplication(esk3_0,c(c(c(esk3_0))))
| ~ test(c(esk3_0)) ),
inference(spm,[status(thm)],[c_0_81,c_0_82]) ).
cnf(c_0_87,plain,
( c(X1) = X2
| ~ complement(X1,X2)
| ~ test(X1) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_88,plain,
( test(X1)
| addition(X2,X1) != one
| multiplication(X2,X1) != zero
| multiplication(X1,X2) != zero ),
inference(spm,[status(thm)],[c_0_83,c_0_28]) ).
cnf(c_0_89,negated_conjecture,
multiplication(esk2_0,multiplication(esk2_0,c(esk2_0))) = zero,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_84]),c_0_80])]) ).
cnf(c_0_90,plain,
multiplication(zero,X1) = zero,
inference(split_conjunct,[status(thm)],[c_0_85]) ).
cnf(c_0_91,plain,
( addition(X1,addition(c(X1),X2)) = addition(one,X2)
| ~ test(X1) ),
inference(spm,[status(thm)],[c_0_50,c_0_33]) ).
cnf(c_0_92,negated_conjecture,
( addition(c(c(esk3_0)),multiplication(esk3_0,c(c(c(esk3_0))))) = c(c(esk3_0))
| ~ test(c(esk3_0)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_86]),c_0_28]),c_0_76]),c_0_34]) ).
cnf(c_0_93,plain,
( c(X1) = X2
| addition(X2,X1) != one
| multiplication(X1,X2) != zero
| multiplication(X2,X1) != zero ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_87,c_0_79]),c_0_88]) ).
cnf(c_0_94,negated_conjecture,
multiplication(esk2_0,addition(one,multiplication(esk2_0,c(esk2_0)))) = esk2_0,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_89]),c_0_26]),c_0_28]) ).
cnf(c_0_95,plain,
( multiplication(c(X1),multiplication(X1,X2)) = zero
| ~ test(X1) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_69]),c_0_90]) ).
cnf(c_0_96,plain,
addition(X1,addition(X2,X3)) = addition(X3,addition(X1,X2)),
inference(spm,[status(thm)],[c_0_28,c_0_50]) ).
cnf(c_0_97,negated_conjecture,
( addition(one,multiplication(esk3_0,c(c(c(esk3_0))))) = addition(c(esk3_0),c(c(esk3_0)))
| ~ test(c(esk3_0)) ),
inference(spm,[status(thm)],[c_0_91,c_0_92]) ).
cnf(c_0_98,negated_conjecture,
addition(one,addition(c(esk3_0),X1)) = addition(one,X1),
inference(spm,[status(thm)],[c_0_50,c_0_76]) ).
cnf(c_0_99,plain,
( multiplication(c(X1),addition(X1,X2)) = multiplication(c(X1),X2)
| ~ test(X1) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_69]),c_0_55]) ).
fof(c_0_100,plain,
! [X55] : multiplication(X55,zero) = zero,
inference(variable_rename,[status(thm)],[right_annihilation]) ).
cnf(c_0_101,negated_conjecture,
( c(c(esk3_0)) = one
| c(esk3_0) != zero ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_93,c_0_76]),c_0_34]),c_0_49])]) ).
cnf(c_0_102,negated_conjecture,
( test(c(esk3_0))
| c(esk3_0) != zero ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_88,c_0_76]),c_0_49]),c_0_34])]) ).
cnf(c_0_103,negated_conjecture,
multiplication(esk2_0,multiplication(addition(one,multiplication(esk2_0,c(esk2_0))),c(esk2_0))) = zero,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_94]),c_0_80])]) ).
cnf(c_0_104,negated_conjecture,
addition(one,esk2_0) = one,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_80]),c_0_28]) ).
cnf(c_0_105,plain,
( test(addition(c(X1),X2))
| multiplication(X1,addition(c(X1),X2)) != zero
| multiplication(addition(c(X1),X2),X1) != zero
| addition(one,X2) != one
| ~ test(X1) ),
inference(spm,[status(thm)],[c_0_88,c_0_91]) ).
cnf(c_0_106,negated_conjecture,
multiplication(esk3_0,addition(X1,c(esk3_0))) = multiplication(esk3_0,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_54]),c_0_26]) ).
cnf(c_0_107,negated_conjecture,
multiplication(c(esk3_0),esk3_0) = zero,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_95,c_0_40]),c_0_38])]) ).
cnf(c_0_108,plain,
addition(X1,addition(X2,addition(X3,X1))) = addition(X2,addition(X3,X1)),
inference(spm,[status(thm)],[c_0_56,c_0_96]) ).
cnf(c_0_109,negated_conjecture,
( addition(c(esk3_0),c(c(esk3_0))) = addition(one,c(c(esk3_0)))
| ~ test(c(esk3_0)) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_97]),c_0_98]) ).
cnf(c_0_110,plain,
( multiplication(X1,addition(c(X1),X2)) = multiplication(X1,X2)
| ~ test(X1) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_55]) ).
cnf(c_0_111,negated_conjecture,
( multiplication(c(esk3_0),addition(c(c(esk3_0)),c(c(c(esk3_0))))) = c(esk3_0)
| ~ test(c(esk3_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_99,c_0_71]),c_0_34]),c_0_38])]) ).
fof(c_0_112,plain,
! [X4] :
( ~ test(X4)
=> c(X4) = zero ),
inference(fof_simplification,[status(thm)],[test_4]) ).
cnf(c_0_113,plain,
( test(addition(X1,X2))
| addition(X1,addition(X2,X3)) != one
| multiplication(X3,addition(X1,X2)) != zero
| multiplication(addition(X1,X2),X3) != zero ),
inference(spm,[status(thm)],[c_0_83,c_0_50]) ).
cnf(c_0_114,plain,
multiplication(X1,zero) = zero,
inference(split_conjunct,[status(thm)],[c_0_100]) ).
cnf(c_0_115,negated_conjecture,
( addition(c(esk3_0),X1) = X1
| c(esk3_0) != zero ),
inference(csr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_101]),c_0_34]),c_0_34]),c_0_102]) ).
cnf(c_0_116,negated_conjecture,
multiplication(esk2_0,c(esk2_0)) = zero,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_103,c_0_25]),c_0_26]),c_0_49]),c_0_80])]) ).
cnf(c_0_117,negated_conjecture,
addition(one,addition(esk2_0,X1)) = addition(one,X1),
inference(spm,[status(thm)],[c_0_50,c_0_104]) ).
cnf(c_0_118,negated_conjecture,
test(c(esk3_0)),
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(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_105,c_0_106]),c_0_51]),c_0_54]),c_0_51]),c_0_107]),c_0_76]),c_0_38])]) ).
cnf(c_0_119,negated_conjecture,
( addition(one,c(c(c(esk3_0)))) = one
| ~ test(c(esk3_0)) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_108,c_0_71]),c_0_28]) ).
cnf(c_0_120,negated_conjecture,
( multiplication(addition(one,c(c(esk3_0))),esk3_0) = multiplication(c(c(esk3_0)),esk3_0)
| ~ test(c(esk3_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_72,c_0_109]),c_0_38])]) ).
cnf(c_0_121,plain,
( addition(one,c(X1)) = one
| ~ test(X1) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_68]),c_0_28]) ).
cnf(c_0_122,negated_conjecture,
( multiplication(c(esk3_0),c(c(c(esk3_0)))) = c(esk3_0)
| ~ test(c(esk3_0)) ),
inference(spm,[status(thm)],[c_0_110,c_0_111]) ).
fof(c_0_123,plain,
! [X67] :
( test(X67)
| c(X67) = zero ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_112])]) ).
cnf(c_0_124,plain,
( test(addition(X1,X2))
| addition(X1,X2) != one ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_113,c_0_26]),c_0_90]),c_0_114])]) ).
cnf(c_0_125,negated_conjecture,
( addition(one,c(c(esk3_0))) = c(c(esk3_0))
| c(esk3_0) != zero ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_115,c_0_109]),c_0_102]) ).
cnf(c_0_126,negated_conjecture,
multiplication(esk2_0,addition(X1,c(esk2_0))) = multiplication(esk2_0,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_116]),c_0_26]) ).
cnf(c_0_127,negated_conjecture,
multiplication(c(esk2_0),esk2_0) = zero,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_95,c_0_84]),c_0_80])]) ).
cnf(c_0_128,negated_conjecture,
addition(one,c(esk2_0)) = one,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_117,c_0_33]),c_0_51]),c_0_80])]) ).
cnf(c_0_129,negated_conjecture,
addition(c(esk3_0),c(c(c(esk3_0)))) = c(c(c(esk3_0))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_78,c_0_118])]) ).
cnf(c_0_130,negated_conjecture,
addition(one,c(c(c(esk3_0)))) = one,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_119,c_0_118])]) ).
cnf(c_0_131,negated_conjecture,
( multiplication(c(c(esk3_0)),esk3_0) = esk3_0
| ~ test(c(esk3_0)) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_120,c_0_121]),c_0_49]) ).
cnf(c_0_132,negated_conjecture,
multiplication(c(esk3_0),c(c(c(esk3_0)))) = c(esk3_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_122,c_0_118])]) ).
cnf(c_0_133,plain,
( test(X1)
| c(X1) = zero ),
inference(split_conjunct,[status(thm)],[c_0_123]) ).
cnf(c_0_134,negated_conjecture,
( test(c(c(esk3_0)))
| c(esk3_0) != zero ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_124,c_0_125]),c_0_101]) ).
cnf(c_0_135,plain,
addition(multiplication(X1,X2),multiplication(X3,multiplication(X4,X2))) = multiplication(addition(X1,multiplication(X3,X4)),X2),
inference(spm,[status(thm)],[c_0_58,c_0_36]) ).
cnf(c_0_136,plain,
addition(X1,multiplication(X2,multiplication(X3,X1))) = multiplication(addition(one,multiplication(X2,X3)),X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_36]),c_0_28]) ).
cnf(c_0_137,negated_conjecture,
test(c(esk2_0)),
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(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_105,c_0_126]),c_0_51]),c_0_116]),c_0_51]),c_0_127]),c_0_128]),c_0_80])]) ).
cnf(c_0_138,negated_conjecture,
addition(esk3_0,c(c(c(esk3_0)))) = one,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_91,c_0_129]),c_0_130]),c_0_38])]) ).
cnf(c_0_139,negated_conjecture,
multiplication(c(c(esk3_0)),esk3_0) = esk3_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_131,c_0_118])]) ).
cnf(c_0_140,negated_conjecture,
test(c(c(esk3_0))),
inference(csr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_132,c_0_133]),c_0_114]),c_0_134]) ).
cnf(c_0_141,negated_conjecture,
multiplication(addition(esk3_0,multiplication(X1,X2)),esk3_0) = multiplication(addition(one,multiplication(X1,X2)),esk3_0),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_135,c_0_40]),c_0_136]) ).
cnf(c_0_142,negated_conjecture,
multiplication(c(esk2_0),c(esk2_0)) = c(esk2_0),
inference(spm,[status(thm)],[c_0_37,c_0_137]) ).
cnf(c_0_143,negated_conjecture,
c(c(esk3_0)) = esk3_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_138]),c_0_34]),c_0_139]),c_0_140])]) ).
cnf(c_0_144,negated_conjecture,
one != addition(addition(esk2_0,esk3_0),multiplication(c(esk2_0),c(esk3_0))),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
cnf(c_0_145,plain,
( addition(multiplication(addition(X1,X2),X3),multiplication(X2,c(X1))) = multiplication(addition(X1,X2),addition(X3,c(X1)))
| ~ test(X1) ),
inference(spm,[status(thm)],[c_0_24,c_0_70]) ).
cnf(c_0_146,negated_conjecture,
multiplication(addition(esk3_0,c(esk2_0)),esk3_0) = esk3_0,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_141,c_0_142]),c_0_128]),c_0_49]) ).
cnf(c_0_147,negated_conjecture,
addition(esk3_0,c(esk3_0)) = one,
inference(rw,[status(thm)],[c_0_138,c_0_143]) ).
cnf(c_0_148,negated_conjecture,
addition(esk2_0,addition(esk3_0,multiplication(c(esk2_0),c(esk3_0)))) != one,
inference(rw,[status(thm)],[c_0_144,c_0_50]) ).
cnf(c_0_149,negated_conjecture,
addition(esk3_0,multiplication(c(esk2_0),c(esk3_0))) = addition(esk3_0,c(esk2_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_145,c_0_146]),c_0_147]),c_0_34]),c_0_38])]) ).
cnf(c_0_150,plain,
addition(X1,addition(X2,X3)) = addition(X2,addition(X1,X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_28]),c_0_50]) ).
cnf(c_0_151,negated_conjecture,
addition(esk2_0,addition(esk3_0,c(esk2_0))) != one,
inference(rw,[status(thm)],[c_0_148,c_0_149]) ).
cnf(c_0_152,plain,
( addition(X1,addition(X2,c(X1))) = addition(X2,one)
| ~ test(X1) ),
inference(spm,[status(thm)],[c_0_150,c_0_33]) ).
cnf(c_0_153,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_151,c_0_152]),c_0_28]),c_0_63]),c_0_80])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : KLE013+1 : TPTP v9.2.1. Released v4.0.0.
% 0.00/0.12 % Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.16/0.33 % Computer : n014.cluster.edu
% 0.16/0.33 % Model : x86_64 x86_64
% 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.33 % Memory : 8042.1875MB
% 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.33 % CPULimit : 300
% 0.16/0.33 % WCLimit : 300
% 0.16/0.33 % DateTime : Mon May 4 20:25:06 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.34 % start to proof: theBenchmark
% 18.26/12.14 % Version : CSE_E---1.7
% 18.26/12.14 % Problem : theBenchmark.p
% 18.26/12.14 % SZS status Theorem for theBenchmark.p
% 18.26/12.14 % SZS output start CNFRefutation
% See solution above
% 18.34/12.21 % Total time : 9.383s
%------------------------------------------------------------------------------