%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : KLE019+1 : TPTP v9.2.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n031.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 04:35:29 PM UTC 2026
% Result : Theorem 34.68s 21.08s
% Output : CNFRefutation 34.86s
% Verified :
% SZS Type : Refutation
% Derivation depth : 29
% Number of leaves : 16
% Syntax : Number of formulae : 192 ( 133 unt; 0 def)
% Number of atoms : 290 ( 193 equ)
% Maximal formula atoms : 10 ( 1 avg)
% Number of connectives : 176 ( 78 ~; 73 |; 16 &)
% ( 4 <=>; 4 =>; 1 <=; 0 <~>)
% Maximal formula depth : 10 ( 2 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 5 con; 0-2 aty)
% Number of variables : 228 ( 14 sgn 62 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(goals,conjecture,
! [X4,X5,X6] :
( ( test(X4)
& test(X5)
& test(X6) )
=> ( leq(multiplication(X4,c(X5)),X6)
<= leq(X4,addition(X5,X6)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
fof(order,axiom,
! [X1,X2] :
( leq(X1,X2)
<=> addition(X1,X2) = X2 ),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',order) ).
fof(test_3,axiom,
! [X4,X5] :
( test(X4)
=> ( c(X4) = X5
<=> complement(X4,X5) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+1.ax',test_3) ).
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(test_2,axiom,
! [X4,X5] :
( complement(X5,X4)
<=> ( multiplication(X4,X5) = zero
& multiplication(X5,X4) = zero
& addition(X4,X5) = one ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+1.ax',test_2) ).
fof(additive_commutativity,axiom,
! [X1,X2] : addition(X1,X2) = addition(X2,X1),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',additive_commutativity) ).
fof(additive_idempotence,axiom,
! [X1] : addition(X1,X1) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',additive_idempotence) ).
fof(test_1,axiom,
! [X4] :
( test(X4)
<=> ? [X5] : complement(X5,X4) ),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+1.ax',test_1) ).
fof(additive_identity,axiom,
! [X1] : addition(X1,zero) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',additive_identity) ).
fof(left_annihilation,axiom,
! [X1] : multiplication(zero,X1) = zero,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',left_annihilation) ).
fof(right_annihilation,axiom,
! [X1] : multiplication(X1,zero) = zero,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',right_annihilation) ).
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(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(multiplicative_right_identity,axiom,
! [X1] : multiplication(X1,one) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',multiplicative_right_identity) ).
fof(multiplicative_left_identity,axiom,
! [X1] : multiplication(one,X1) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',multiplicative_left_identity) ).
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(c_0_16,negated_conjecture,
~ ! [X4,X5,X6] :
( ( test(X4)
& test(X5)
& test(X6) )
=> ( leq(X4,addition(X5,X6))
=> leq(multiplication(X4,c(X5)),X6) ) ),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[goals])]) ).
fof(c_0_17,plain,
! [X59,X60] :
( ( ~ leq(X59,X60)
| addition(X59,X60) = X60 )
& ( addition(X59,X60) != X60
| leq(X59,X60) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[order])]) ).
fof(c_0_18,negated_conjecture,
( test(esk2_0)
& test(esk3_0)
& test(esk4_0)
& leq(esk2_0,addition(esk3_0,esk4_0))
& ~ leq(multiplication(esk2_0,c(esk3_0)),esk4_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_16])])]) ).
fof(c_0_19,plain,
! [X67,X68] :
( ( c(X67) != X68
| complement(X67,X68)
| ~ test(X67) )
& ( ~ complement(X67,X68)
| c(X67) = X68
| ~ test(X67) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[test_3])])]) ).
fof(c_0_20,plain,
! [X41,X42,X43] : addition(X43,addition(X42,X41)) = addition(addition(X43,X42),X41),
inference(variable_rename,[status(thm)],[additive_associativity]) ).
cnf(c_0_21,plain,
( addition(X1,X2) = X2
| ~ leq(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_22,negated_conjecture,
leq(esk2_0,addition(esk3_0,esk4_0)),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
fof(c_0_23,plain,
! [X65,X66] :
( ( multiplication(X65,X66) = zero
| ~ complement(X66,X65) )
& ( multiplication(X66,X65) = zero
| ~ complement(X66,X65) )
& ( addition(X65,X66) = one
| ~ complement(X66,X65) )
& ( multiplication(X65,X66) != zero
| multiplication(X66,X65) != zero
| addition(X65,X66) != one
| complement(X66,X65) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[test_2])])]) ).
cnf(c_0_24,plain,
( complement(X1,X2)
| c(X1) != X2
| ~ test(X1) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
fof(c_0_25,plain,
! [X39,X40] : addition(X39,X40) = addition(X40,X39),
inference(variable_rename,[status(thm)],[additive_commutativity]) ).
fof(c_0_26,plain,
! [X45] : addition(X45,X45) = X45,
inference(variable_rename,[status(thm)],[additive_idempotence]) ).
cnf(c_0_27,plain,
addition(X1,addition(X2,X3)) = addition(addition(X1,X2),X3),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_28,negated_conjecture,
addition(esk2_0,addition(esk3_0,esk4_0)) = addition(esk3_0,esk4_0),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_29,plain,
( addition(X1,X2) = one
| ~ complement(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_30,plain,
( complement(X1,c(X1))
| ~ test(X1) ),
inference(er,[status(thm)],[c_0_24]) ).
cnf(c_0_31,plain,
addition(X1,X2) = addition(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_32,plain,
addition(X1,X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_33,negated_conjecture,
addition(esk2_0,addition(esk3_0,addition(esk4_0,X1))) = addition(esk3_0,addition(esk4_0,X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_28]),c_0_27]),c_0_27]) ).
cnf(c_0_34,plain,
( addition(X1,c(X1)) = one
| ~ test(X1) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_30]),c_0_31]) ).
cnf(c_0_35,negated_conjecture,
test(esk4_0),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_36,plain,
addition(X1,addition(X2,addition(X1,X2))) = addition(X1,X2),
inference(spm,[status(thm)],[c_0_32,c_0_27]) ).
cnf(c_0_37,negated_conjecture,
addition(esk2_0,addition(one,esk3_0)) = addition(one,esk3_0),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_34]),c_0_35])]),c_0_31]),c_0_31]) ).
cnf(c_0_38,plain,
addition(X1,addition(X2,X3)) = addition(X3,addition(X1,X2)),
inference(spm,[status(thm)],[c_0_31,c_0_27]) ).
fof(c_0_39,plain,
! [X61,X63,X64] :
( ( ~ test(X61)
| complement(esk1_1(X61),X61) )
& ( ~ complement(X64,X63)
| test(X63) ) ),
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_40,negated_conjecture,
addition(esk3_0,addition(esk4_0,addition(X1,addition(esk3_0,addition(esk4_0,X1))))) = addition(esk3_0,addition(esk4_0,X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_33]),c_0_27]),c_0_27]),c_0_33]) ).
cnf(c_0_41,negated_conjecture,
addition(one,addition(esk2_0,esk3_0)) = addition(one,esk3_0),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_37,c_0_38]),c_0_31]) ).
cnf(c_0_42,plain,
( complement(esk1_1(X1),X1)
| ~ test(X1) ),
inference(split_conjunct,[status(thm)],[c_0_39]) ).
cnf(c_0_43,negated_conjecture,
addition(esk3_0,addition(esk3_0,esk4_0)) = addition(esk3_0,esk4_0),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_32]),c_0_38]),c_0_32]),c_0_38]),c_0_32]) ).
cnf(c_0_44,negated_conjecture,
addition(one,addition(esk2_0,addition(esk3_0,X1))) = addition(one,addition(esk3_0,X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_41]),c_0_27]),c_0_27]) ).
cnf(c_0_45,negated_conjecture,
test(esk3_0),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_46,plain,
addition(X1,addition(X1,X2)) = addition(X1,X2),
inference(spm,[status(thm)],[c_0_27,c_0_32]) ).
cnf(c_0_47,plain,
( addition(X1,esk1_1(X1)) = one
| ~ test(X1) ),
inference(spm,[status(thm)],[c_0_29,c_0_42]) ).
cnf(c_0_48,negated_conjecture,
addition(esk3_0,addition(esk3_0,addition(esk4_0,X1))) = addition(esk3_0,addition(esk4_0,X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_43]),c_0_27]),c_0_27]) ).
cnf(c_0_49,negated_conjecture,
addition(one,addition(one,esk2_0)) = one,
inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_34]),c_0_32]),c_0_45])]),c_0_31]) ).
cnf(c_0_50,plain,
( addition(X1,addition(X2,c(addition(X1,X2)))) = one
| ~ test(addition(X1,X2)) ),
inference(spm,[status(thm)],[c_0_27,c_0_34]) ).
cnf(c_0_51,negated_conjecture,
addition(esk2_0,addition(esk3_0,addition(X1,esk4_0))) = addition(esk3_0,addition(X1,esk4_0)),
inference(spm,[status(thm)],[c_0_33,c_0_31]) ).
cnf(c_0_52,plain,
( addition(X1,one) = one
| ~ test(X1) ),
inference(spm,[status(thm)],[c_0_46,c_0_47]) ).
cnf(c_0_53,plain,
addition(X1,addition(X2,X3)) = addition(X2,addition(X1,X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_31]),c_0_27]) ).
cnf(c_0_54,negated_conjecture,
addition(esk3_0,addition(X1,addition(esk3_0,esk4_0))) = addition(X1,addition(esk3_0,esk4_0)),
inference(spm,[status(thm)],[c_0_48,c_0_38]) ).
cnf(c_0_55,negated_conjecture,
addition(one,esk2_0) = one,
inference(rw,[status(thm)],[c_0_49,c_0_46]) ).
cnf(c_0_56,plain,
( addition(X1,one) = one
| ~ test(addition(X1,X2)) ),
inference(spm,[status(thm)],[c_0_46,c_0_50]) ).
cnf(c_0_57,negated_conjecture,
addition(esk2_0,addition(X1,addition(esk3_0,esk4_0))) = addition(X1,addition(esk3_0,esk4_0)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_38]),c_0_31]),c_0_31]) ).
cnf(c_0_58,plain,
( addition(X1,addition(c(X1),X2)) = addition(one,X2)
| ~ test(X1) ),
inference(spm,[status(thm)],[c_0_27,c_0_34]) ).
cnf(c_0_59,negated_conjecture,
addition(one,addition(esk3_0,esk4_0)) = addition(one,esk3_0),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_52]),c_0_31]),c_0_46]),c_0_31]),c_0_35])]),c_0_38]),c_0_31]),c_0_53]),c_0_54]) ).
cnf(c_0_60,negated_conjecture,
test(esk2_0),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_61,negated_conjecture,
addition(one,addition(esk2_0,X1)) = addition(one,X1),
inference(spm,[status(thm)],[c_0_27,c_0_55]) ).
cnf(c_0_62,plain,
( test(X2)
| ~ complement(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_39]) ).
cnf(c_0_63,plain,
( complement(X2,X1)
| multiplication(X1,X2) != zero
| multiplication(X2,X1) != zero
| addition(X1,X2) != one ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
fof(c_0_64,plain,
! [X44] : addition(X44,zero) = X44,
inference(variable_rename,[status(thm)],[additive_identity]) ).
fof(c_0_65,plain,
! [X58] : multiplication(zero,X58) = zero,
inference(variable_rename,[status(thm)],[left_annihilation]) ).
fof(c_0_66,plain,
! [X57] : multiplication(X57,zero) = zero,
inference(variable_rename,[status(thm)],[right_annihilation]) ).
cnf(c_0_67,plain,
( addition(X1,one) = one
| ~ test(addition(X2,X1)) ),
inference(spm,[status(thm)],[c_0_56,c_0_31]) ).
cnf(c_0_68,negated_conjecture,
addition(esk3_0,addition(esk4_0,c(esk2_0))) = addition(one,esk3_0),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_58]),c_0_59]),c_0_60])]),c_0_38]),c_0_31]),c_0_53]) ).
cnf(c_0_69,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_61,c_0_34]),c_0_32]),c_0_60])]) ).
cnf(c_0_70,plain,
( test(X1)
| addition(X1,X2) != one
| multiplication(X2,X1) != zero
| multiplication(X1,X2) != zero ),
inference(spm,[status(thm)],[c_0_62,c_0_63]) ).
cnf(c_0_71,plain,
addition(X1,zero) = X1,
inference(split_conjunct,[status(thm)],[c_0_64]) ).
cnf(c_0_72,plain,
multiplication(zero,X1) = zero,
inference(split_conjunct,[status(thm)],[c_0_65]) ).
cnf(c_0_73,plain,
multiplication(X1,zero) = zero,
inference(split_conjunct,[status(thm)],[c_0_66]) ).
cnf(c_0_74,negated_conjecture,
( addition(one,esk3_0) = one
| ~ test(addition(esk3_0,addition(esk4_0,X1))) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_40]),c_0_31]) ).
cnf(c_0_75,negated_conjecture,
( addition(one,esk4_0) = one
| ~ test(addition(one,esk3_0)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_68]),c_0_27]),c_0_31]),c_0_69]),c_0_31]) ).
cnf(c_0_76,plain,
( addition(one,X1) = one
| ~ test(X1) ),
inference(spm,[status(thm)],[c_0_31,c_0_52]) ).
cnf(c_0_77,plain,
test(one),
inference(er,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_71]),c_0_72]),c_0_73])])]) ).
fof(c_0_78,plain,
! [X54,X55,X56] : multiplication(addition(X54,X55),X56) = addition(multiplication(X54,X56),multiplication(X55,X56)),
inference(variable_rename,[status(thm)],[left_distributivity]) ).
cnf(c_0_79,plain,
( multiplication(X1,X2) = zero
| ~ complement(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_80,negated_conjecture,
addition(one,addition(esk3_0,addition(esk4_0,c(esk4_0)))) = addition(one,esk3_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)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_34]),c_0_31]),c_0_31]),c_0_35])]),c_0_38]),c_0_31]),c_0_53]),c_0_53]),c_0_53]),c_0_53]),c_0_46]) ).
cnf(c_0_81,negated_conjecture,
( addition(one,esk3_0) = one
| ~ test(addition(esk3_0,addition(X1,esk4_0))) ),
inference(spm,[status(thm)],[c_0_74,c_0_31]) ).
cnf(c_0_82,negated_conjecture,
addition(one,esk4_0) = one,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_75,c_0_76]),c_0_77]),c_0_45])]) ).
fof(c_0_83,plain,
! [X51,X52,X53] : multiplication(X51,addition(X52,X53)) = addition(multiplication(X51,X52),multiplication(X51,X53)),
inference(variable_rename,[status(thm)],[right_distributivity]) ).
fof(c_0_84,plain,
! [X49] : multiplication(X49,one) = X49,
inference(variable_rename,[status(thm)],[multiplicative_right_identity]) ).
cnf(c_0_85,plain,
multiplication(addition(X1,X2),X3) = addition(multiplication(X1,X3),multiplication(X2,X3)),
inference(split_conjunct,[status(thm)],[c_0_78]) ).
cnf(c_0_86,plain,
( multiplication(X1,c(X1)) = zero
| ~ test(X1) ),
inference(spm,[status(thm)],[c_0_79,c_0_30]) ).
cnf(c_0_87,plain,
addition(zero,X1) = X1,
inference(spm,[status(thm)],[c_0_71,c_0_31]) ).
cnf(c_0_88,negated_conjecture,
addition(esk3_0,addition(esk4_0,c(esk4_0))) = addition(one,esk3_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_58]),c_0_53]),c_0_46]),c_0_80]),c_0_35])]) ).
cnf(c_0_89,negated_conjecture,
addition(one,esk3_0) = one,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_81,c_0_58]),c_0_82]),c_0_77]),c_0_45])]) ).
fof(c_0_90,plain,
! [X50] : multiplication(one,X50) = X50,
inference(variable_rename,[status(thm)],[multiplicative_left_identity]) ).
cnf(c_0_91,negated_conjecture,
addition(esk3_0,addition(esk4_0,c(esk3_0))) = addition(one,esk3_0),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_58]),c_0_59]),c_0_45])]),c_0_38]),c_0_31]),c_0_53]) ).
cnf(c_0_92,plain,
( multiplication(X1,X2) = zero
| ~ complement(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_93,plain,
multiplication(X1,addition(X2,X3)) = addition(multiplication(X1,X2),multiplication(X1,X3)),
inference(split_conjunct,[status(thm)],[c_0_83]) ).
cnf(c_0_94,plain,
multiplication(X1,one) = X1,
inference(split_conjunct,[status(thm)],[c_0_84]) ).
cnf(c_0_95,plain,
( multiplication(addition(X1,X2),c(X1)) = multiplication(X2,c(X1))
| ~ test(X1) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_85,c_0_86]),c_0_87]) ).
cnf(c_0_96,negated_conjecture,
addition(esk3_0,addition(esk4_0,c(esk4_0))) = one,
inference(rw,[status(thm)],[c_0_88,c_0_89]) ).
cnf(c_0_97,plain,
multiplication(one,X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_90]) ).
cnf(c_0_98,plain,
( addition(X1,one) = one
| ~ test(addition(X2,addition(X3,X1))) ),
inference(spm,[status(thm)],[c_0_56,c_0_38]) ).
cnf(c_0_99,negated_conjecture,
addition(esk3_0,addition(esk4_0,c(esk3_0))) = one,
inference(rw,[status(thm)],[c_0_91,c_0_89]) ).
cnf(c_0_100,plain,
( multiplication(c(X1),X1) = zero
| ~ test(X1) ),
inference(spm,[status(thm)],[c_0_92,c_0_30]) ).
fof(c_0_101,plain,
! [X46,X47,X48] : multiplication(X46,multiplication(X47,X48)) = multiplication(multiplication(X46,X47),X48),
inference(variable_rename,[status(thm)],[multiplicative_associativity]) ).
cnf(c_0_102,plain,
addition(X1,multiplication(X1,X2)) = multiplication(X1,addition(X2,one)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_93,c_0_94]),c_0_31]) ).
cnf(c_0_103,negated_conjecture,
multiplication(addition(esk4_0,c(esk4_0)),c(esk3_0)) = c(esk3_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_95,c_0_96]),c_0_97]),c_0_45])]) ).
cnf(c_0_104,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_98,c_0_99]),c_0_31]),c_0_77])]) ).
cnf(c_0_105,plain,
( multiplication(addition(X1,c(X2)),X2) = multiplication(X1,X2)
| ~ test(X2) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_85,c_0_100]),c_0_71]) ).
cnf(c_0_106,plain,
multiplication(X1,multiplication(X2,X3)) = multiplication(multiplication(X1,X2),X3),
inference(split_conjunct,[status(thm)],[c_0_101]) ).
cnf(c_0_107,plain,
( multiplication(c(X1),addition(X1,X2)) = multiplication(c(X1),X2)
| ~ test(X1) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_93,c_0_100]),c_0_87]) ).
cnf(c_0_108,negated_conjecture,
addition(esk4_0,addition(c(esk3_0),c(esk4_0))) = addition(esk4_0,c(esk4_0)),
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_102,c_0_103]),c_0_27]),c_0_31]),c_0_104]),c_0_94]),c_0_31]) ).
cnf(c_0_109,negated_conjecture,
addition(esk3_0,addition(esk4_0,c(esk2_0))) = one,
inference(rw,[status(thm)],[c_0_68,c_0_89]) ).
cnf(c_0_110,plain,
( multiplication(X1,X1) = X1
| ~ test(X1) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_105,c_0_34]),c_0_97]) ).
cnf(c_0_111,plain,
( multiplication(X1,multiplication(c(X1),X2)) = zero
| ~ test(X1) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_106,c_0_86]),c_0_72]) ).
cnf(c_0_112,negated_conjecture,
multiplication(c(esk4_0),addition(c(esk3_0),c(esk4_0))) = multiplication(c(esk4_0),addition(esk4_0,c(esk4_0))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_107,c_0_108]),c_0_35])]) ).
cnf(c_0_113,negated_conjecture,
multiplication(addition(esk4_0,c(esk2_0)),c(esk3_0)) = c(esk3_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_95,c_0_109]),c_0_97]),c_0_45])]) ).
cnf(c_0_114,plain,
addition(X1,multiplication(X1,X2)) = multiplication(X1,addition(one,X2)),
inference(spm,[status(thm)],[c_0_93,c_0_94]) ).
cnf(c_0_115,plain,
( c(X1) = X2
| ~ complement(X1,X2)
| ~ test(X1) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_116,plain,
( addition(X1,addition(X2,c(X1))) = addition(X2,one)
| ~ test(X1) ),
inference(spm,[status(thm)],[c_0_53,c_0_34]) ).
cnf(c_0_117,plain,
( multiplication(c(X1),multiplication(X1,X2)) = zero
| ~ test(X1) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_106,c_0_100]),c_0_72]) ).
cnf(c_0_118,negated_conjecture,
multiplication(esk4_0,esk4_0) = esk4_0,
inference(spm,[status(thm)],[c_0_110,c_0_35]) ).
cnf(c_0_119,negated_conjecture,
multiplication(esk4_0,multiplication(c(esk4_0),addition(esk4_0,c(esk4_0)))) = zero,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_111,c_0_112]),c_0_35])]) ).
cnf(c_0_120,negated_conjecture,
addition(esk4_0,addition(c(esk2_0),c(esk3_0))) = addition(esk4_0,c(esk2_0)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_102,c_0_113]),c_0_27]),c_0_31]),c_0_104]),c_0_94]) ).
cnf(c_0_121,plain,
( multiplication(X1,multiplication(X2,c(multiplication(X1,X2)))) = zero
| ~ test(multiplication(X1,X2)) ),
inference(spm,[status(thm)],[c_0_106,c_0_86]) ).
cnf(c_0_122,negated_conjecture,
multiplication(esk2_0,esk2_0) = esk2_0,
inference(spm,[status(thm)],[c_0_110,c_0_60]) ).
cnf(c_0_123,negated_conjecture,
addition(X1,multiplication(X1,c(esk2_0))) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_114,c_0_69]),c_0_94]) ).
cnf(c_0_124,plain,
( c(X1) = X2
| addition(X2,X1) != one
| multiplication(X1,X2) != zero
| multiplication(X2,X1) != zero
| ~ test(X1) ),
inference(spm,[status(thm)],[c_0_115,c_0_63]) ).
cnf(c_0_125,negated_conjecture,
addition(esk4_0,c(esk4_0)) = one,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_108,c_0_116]),c_0_31]),c_0_104]),c_0_35])]) ).
cnf(c_0_126,negated_conjecture,
multiplication(c(esk4_0),esk4_0) = zero,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_117,c_0_118]),c_0_35])]) ).
cnf(c_0_127,negated_conjecture,
multiplication(esk4_0,c(esk4_0)) = zero,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_119,c_0_34]),c_0_94]),c_0_35])]) ).
cnf(c_0_128,plain,
( test(X1)
| addition(X2,X1) != one
| multiplication(X2,X1) != zero
| multiplication(X1,X2) != zero ),
inference(spm,[status(thm)],[c_0_70,c_0_31]) ).
cnf(c_0_129,plain,
addition(X1,multiplication(X2,X1)) = multiplication(addition(X2,one),X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_85,c_0_97]),c_0_31]) ).
cnf(c_0_130,negated_conjecture,
multiplication(c(esk4_0),addition(c(esk2_0),c(esk3_0))) = multiplication(c(esk4_0),addition(esk4_0,c(esk2_0))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_107,c_0_120]),c_0_35])]) ).
cnf(c_0_131,negated_conjecture,
addition(one,c(esk4_0)) = one,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_98,c_0_96]),c_0_31]),c_0_77])]) ).
cnf(c_0_132,plain,
( addition(X1,addition(multiplication(X1,X2),c(multiplication(X1,addition(X2,one))))) = one
| ~ test(multiplication(X1,addition(X2,one))) ),
inference(spm,[status(thm)],[c_0_50,c_0_102]) ).
cnf(c_0_133,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_121,c_0_122]),c_0_60])]) ).
cnf(c_0_134,negated_conjecture,
multiplication(esk2_0,multiplication(esk2_0,X1)) = multiplication(esk2_0,X1),
inference(spm,[status(thm)],[c_0_106,c_0_122]) ).
cnf(c_0_135,negated_conjecture,
addition(X1,addition(X2,multiplication(addition(X1,X2),c(esk2_0)))) = addition(X1,X2),
inference(spm,[status(thm)],[c_0_27,c_0_123]) ).
cnf(c_0_136,negated_conjecture,
( c(c(esk4_0)) = esk4_0
| ~ test(c(esk4_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_124,c_0_125]),c_0_126]),c_0_127])]) ).
cnf(c_0_137,negated_conjecture,
test(c(esk4_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_128,c_0_125]),c_0_127]),c_0_126])]) ).
cnf(c_0_138,negated_conjecture,
multiplication(addition(c(esk2_0),c(esk3_0)),c(esk4_0)) = multiplication(addition(esk4_0,c(esk2_0)),c(esk4_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_95,c_0_120]),c_0_35])]) ).
cnf(c_0_139,plain,
( addition(X1,addition(c(X1),X2)) = addition(one,addition(c(X1),X2))
| ~ test(X1) ),
inference(spm,[status(thm)],[c_0_58,c_0_46]) ).
cnf(c_0_140,negated_conjecture,
addition(c(esk2_0),addition(c(esk3_0),multiplication(c(esk4_0),addition(esk4_0,c(esk2_0))))) = addition(c(esk2_0),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_129,c_0_130]),c_0_27]),c_0_31]),c_0_131]),c_0_97]) ).
cnf(c_0_141,negated_conjecture,
addition(one,addition(c(esk2_0),X1)) = addition(one,X1),
inference(spm,[status(thm)],[c_0_27,c_0_69]) ).
cnf(c_0_142,negated_conjecture,
addition(esk2_0,c(esk2_0)) = one,
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(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_132,c_0_122]),c_0_31]),c_0_55]),c_0_94]),c_0_46]),c_0_31]),c_0_55]),c_0_94]),c_0_60])]) ).
cnf(c_0_143,negated_conjecture,
multiplication(c(esk2_0),esk2_0) = zero,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_117,c_0_122]),c_0_60])]) ).
cnf(c_0_144,negated_conjecture,
multiplication(esk2_0,c(esk2_0)) = zero,
inference(rw,[status(thm)],[c_0_133,c_0_134]) ).
cnf(c_0_145,plain,
( multiplication(c(X1),addition(X2,addition(X3,X1))) = multiplication(c(X1),addition(X2,X3))
| ~ test(X1) ),
inference(spm,[status(thm)],[c_0_107,c_0_38]) ).
cnf(c_0_146,negated_conjecture,
addition(esk4_0,addition(c(esk2_0),c(esk4_0))) = one,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_135,c_0_125]),c_0_97]),c_0_31]) ).
cnf(c_0_147,negated_conjecture,
c(c(esk4_0)) = esk4_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_136,c_0_137])]) ).
cnf(c_0_148,negated_conjecture,
addition(c(esk2_0),addition(c(esk3_0),multiplication(addition(esk4_0,c(esk2_0)),c(esk4_0)))) = addition(c(esk2_0),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_102,c_0_138]),c_0_27]),c_0_31]),c_0_131]),c_0_94]) ).
cnf(c_0_149,negated_conjecture,
addition(esk2_0,addition(c(esk2_0),c(esk3_0))) = one,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_139,c_0_140]),c_0_141]),c_0_104]),c_0_60])]) ).
cnf(c_0_150,negated_conjecture,
( c(c(esk2_0)) = esk2_0
| ~ test(c(esk2_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_124,c_0_142]),c_0_143]),c_0_144])]) ).
cnf(c_0_151,negated_conjecture,
test(c(esk2_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_128,c_0_142]),c_0_144]),c_0_143])]) ).
cnf(c_0_152,plain,
addition(multiplication(X1,X2),addition(multiplication(X3,X2),X4)) = addition(multiplication(addition(X1,X3),X2),X4),
inference(spm,[status(thm)],[c_0_27,c_0_85]) ).
cnf(c_0_153,plain,
( multiplication(addition(c(X1),X2),X1) = multiplication(X2,X1)
| ~ test(X1) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_85,c_0_100]),c_0_87]) ).
cnf(c_0_154,negated_conjecture,
addition(c(esk2_0),addition(c(esk3_0),multiplication(c(esk4_0),c(esk2_0)))) = addition(c(esk2_0),c(esk3_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_140,c_0_107]),c_0_35])]) ).
cnf(c_0_155,plain,
addition(multiplication(X1,X2),multiplication(X3,multiplication(X4,X2))) = multiplication(addition(X1,multiplication(X3,X4)),X2),
inference(spm,[status(thm)],[c_0_85,c_0_106]) ).
cnf(c_0_156,plain,
( addition(multiplication(X1,addition(X2,X3)),multiplication(c(X2),X3)) = multiplication(addition(X1,c(X2)),addition(X2,X3))
| ~ test(X2) ),
inference(spm,[status(thm)],[c_0_85,c_0_107]) ).
cnf(c_0_157,negated_conjecture,
multiplication(esk4_0,addition(esk4_0,c(esk2_0))) = esk4_0,
inference(cn,[status(thm)],[inference(rw,[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_94]),c_0_147]),c_0_147]),c_0_137])]) ).
cnf(c_0_158,plain,
addition(multiplication(X1,X2),addition(multiplication(X1,X3),X4)) = addition(multiplication(X1,addition(X2,X3)),X4),
inference(spm,[status(thm)],[c_0_27,c_0_93]) ).
cnf(c_0_159,plain,
( multiplication(X1,addition(c(X1),X2)) = multiplication(X1,X2)
| ~ test(X1) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_93,c_0_86]),c_0_87]) ).
cnf(c_0_160,negated_conjecture,
addition(c(esk2_0),addition(c(esk3_0),multiplication(c(esk2_0),c(esk4_0)))) = addition(c(esk2_0),c(esk3_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_148,c_0_95]),c_0_35])]) ).
cnf(c_0_161,plain,
( addition(multiplication(c(X1),X2),multiplication(X3,addition(X1,X2))) = multiplication(addition(c(X1),X3),addition(X1,X2))
| ~ test(X1) ),
inference(spm,[status(thm)],[c_0_85,c_0_107]) ).
cnf(c_0_162,negated_conjecture,
multiplication(c(esk2_0),addition(c(esk2_0),c(esk3_0))) = c(esk2_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_107,c_0_149]),c_0_94]),c_0_60])]) ).
cnf(c_0_163,negated_conjecture,
c(c(esk2_0)) = esk2_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_150,c_0_151])]) ).
cnf(c_0_164,plain,
addition(multiplication(X1,X2),multiplication(X3,multiplication(X2,addition(X4,one)))) = addition(multiplication(addition(X1,X3),X2),multiplication(X3,multiplication(X2,X4))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_152,c_0_102]),c_0_106]),c_0_106]) ).
cnf(c_0_165,negated_conjecture,
multiplication(addition(c(esk3_0),multiplication(c(esk4_0),c(esk2_0))),esk2_0) = multiplication(addition(c(esk2_0),c(esk3_0)),esk2_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_153,c_0_154]),c_0_60])]) ).
cnf(c_0_166,negated_conjecture,
multiplication(c(esk2_0),multiplication(esk2_0,X1)) = zero,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_106,c_0_143]),c_0_72]) ).
cnf(c_0_167,plain,
( multiplication(addition(X1,multiplication(X2,X3)),c(X3)) = multiplication(X1,c(X3))
| ~ test(X3) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_155,c_0_86]),c_0_73]),c_0_71]) ).
cnf(c_0_168,negated_conjecture,
addition(esk4_0,multiplication(c(esk4_0),c(esk2_0))) = addition(esk4_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_156,c_0_157]),c_0_125]),c_0_97]),c_0_35])]) ).
cnf(c_0_169,plain,
( addition(multiplication(X1,X2),multiplication(addition(c(X2),X1),X3)) = multiplication(addition(c(X2),X1),addition(X2,X3))
| ~ test(X2) ),
inference(spm,[status(thm)],[c_0_93,c_0_153]) ).
cnf(c_0_170,negated_conjecture,
multiplication(addition(c(esk2_0),c(esk3_0)),c(esk2_0)) = c(esk2_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_95,c_0_149]),c_0_97]),c_0_60])]) ).
cnf(c_0_171,plain,
addition(multiplication(X1,X2),multiplication(addition(X3,one),multiplication(X1,X4))) = addition(multiplication(X1,addition(X2,X4)),multiplication(X3,multiplication(X1,X4))),
inference(spm,[status(thm)],[c_0_158,c_0_129]) ).
cnf(c_0_172,negated_conjecture,
multiplication(esk2_0,addition(c(esk3_0),multiplication(c(esk2_0),c(esk4_0)))) = multiplication(esk2_0,addition(c(esk2_0),c(esk3_0))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_159,c_0_160]),c_0_60])]) ).
cnf(c_0_173,negated_conjecture,
multiplication(esk2_0,multiplication(c(esk2_0),X1)) = zero,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_106,c_0_144]),c_0_72]) ).
cnf(c_0_174,negated_conjecture,
addition(c(esk2_0),multiplication(esk2_0,c(esk3_0))) = addition(c(esk2_0),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_161,c_0_162]),c_0_163]),c_0_31]),c_0_163]),c_0_142]),c_0_97]),c_0_151])]) ).
cnf(c_0_175,negated_conjecture,
multiplication(addition(c(esk2_0),c(esk3_0)),esk2_0) = multiplication(c(esk3_0),esk2_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)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_164,c_0_165]),c_0_106]),c_0_166]),c_0_73]),c_0_71]),c_0_106]),c_0_166]),c_0_73]),c_0_71]) ).
cnf(c_0_176,negated_conjecture,
addition(X1,multiplication(X1,esk2_0)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_114,c_0_55]),c_0_94]) ).
cnf(c_0_177,plain,
( multiplication(addition(X1,addition(c(X2),X3)),X2) = multiplication(addition(X1,X3),X2)
| ~ test(X2) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_85,c_0_153]),c_0_85]) ).
cnf(c_0_178,negated_conjecture,
multiplication(addition(esk4_0,c(esk2_0)),esk2_0) = multiplication(esk4_0,esk2_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_167,c_0_168]),c_0_163]),c_0_163]),c_0_151])]) ).
cnf(c_0_179,negated_conjecture,
addition(c(esk2_0),multiplication(c(esk3_0),esk2_0)) = addition(c(esk2_0),c(esk3_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_169,c_0_170]),c_0_31]),c_0_142]),c_0_94]),c_0_60])]) ).
cnf(c_0_180,negated_conjecture,
multiplication(esk2_0,addition(c(esk2_0),c(esk3_0))) = multiplication(esk2_0,c(esk3_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)],[inference(spm,[status(thm)],[c_0_171,c_0_172]),c_0_173]),c_0_73]),c_0_71]),c_0_173]),c_0_73]),c_0_71]) ).
cnf(c_0_181,negated_conjecture,
multiplication(esk2_0,multiplication(c(esk3_0),esk2_0)) = multiplication(c(esk3_0),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(spm,[status(thm)],[c_0_95,c_0_174]),c_0_163]),c_0_175]),c_0_163]),c_0_106]),c_0_151])]) ).
cnf(c_0_182,negated_conjecture,
~ leq(multiplication(esk2_0,c(esk3_0)),esk4_0),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_183,plain,
( leq(X1,X2)
| addition(X1,X2) != X2 ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_184,negated_conjecture,
addition(multiplication(addition(X1,X2),X3),multiplication(X2,multiplication(X3,esk2_0))) = multiplication(addition(X1,X2),X3),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_152,c_0_176]),c_0_85]),c_0_106]) ).
cnf(c_0_185,negated_conjecture,
multiplication(addition(esk4_0,c(esk3_0)),esk2_0) = multiplication(esk4_0,esk2_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_177,c_0_120]),c_0_178]),c_0_60])]) ).
cnf(c_0_186,negated_conjecture,
multiplication(c(esk3_0),esk2_0) = multiplication(esk2_0,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(spm,[status(thm)],[c_0_107,c_0_179]),c_0_163]),c_0_180]),c_0_163]),c_0_181]),c_0_151])]) ).
cnf(c_0_187,negated_conjecture,
addition(multiplication(esk2_0,c(esk3_0)),esk4_0) != esk4_0,
inference(spm,[status(thm)],[c_0_182,c_0_183]) ).
cnf(c_0_188,plain,
addition(X1,addition(multiplication(X1,X2),X3)) = addition(multiplication(X1,addition(X2,one)),X3),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_158,c_0_94]),c_0_53]) ).
cnf(c_0_189,negated_conjecture,
addition(multiplication(esk4_0,esk2_0),multiplication(esk2_0,c(esk3_0))) = multiplication(esk4_0,esk2_0),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_184,c_0_185]),c_0_122]),c_0_186]) ).
cnf(c_0_190,negated_conjecture,
addition(esk4_0,multiplication(esk2_0,c(esk3_0))) != esk4_0,
inference(rw,[status(thm)],[c_0_187,c_0_31]) ).
cnf(c_0_191,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_188,c_0_189]),c_0_176]),c_0_31]),c_0_55]),c_0_94]),c_0_190]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : KLE019+1 : TPTP v9.2.1. Released v4.0.0.
% 0.00/0.12 % Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.14/0.32 % Computer : n031.cluster.edu
% 0.14/0.32 % Model : x86_64 x86_64
% 0.14/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.32 % Memory : 8042.1875MB
% 0.14/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.32 % CPULimit : 300
% 0.14/0.32 % WCLimit : 300
% 0.14/0.32 % DateTime : Mon May 4 20:27:38 EDT 2026
% 0.14/0.32 % CPUTime :
% 0.14/0.33 % start to proof: theBenchmark
% 34.68/21.08 % Version : CSE_E---1.7
% 34.68/21.08 % Problem : theBenchmark.p
% 34.68/21.08 % SZS status Theorem for theBenchmark.p
% 34.68/21.08 % SZS output start CNFRefutation
% See solution above
% 34.86/21.23 % Total time : 15.394s
%------------------------------------------------------------------------------