%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : KLE016+2 : 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 : n004.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 284.95s 116.40s
% Output : CNFRefutation 285.75s
% Verified :
% SZS Type : Refutation
% Derivation depth : 32
% Number of leaves : 14
% Syntax : Number of formulae : 197 ( 121 unt; 0 def)
% Number of atoms : 312 ( 213 equ)
% Maximal formula atoms : 10 ( 1 avg)
% Number of connectives : 219 ( 104 ~; 98 |; 11 &)
% ( 3 <=>; 3 =>; 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 : 219 ( 5 sgn 54 !; 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) )
=> c(multiplication(X4,X5)) = addition(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(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(multiplicative_left_identity,axiom,
! [X1] : multiplication(one,X1) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',multiplicative_left_identity) ).
fof(left_annihilation,axiom,
! [X1] : multiplication(zero,X1) = zero,
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',left_annihilation) ).
fof(c_0_14,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_15,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_16,plain,
( complement(X1,X2)
| c(X1) != X2
| ~ test(X1) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
fof(c_0_17,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_18,plain,
( multiplication(X1,X2) = zero
| ~ complement(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_19,plain,
( complement(X1,c(X1))
| ~ test(X1) ),
inference(er,[status(thm)],[c_0_16]) ).
fof(c_0_20,plain,
! [X42] : addition(X42,zero) = X42,
inference(variable_rename,[status(thm)],[additive_identity]) ).
fof(c_0_21,plain,
! [X37,X38] : addition(X37,X38) = addition(X38,X37),
inference(variable_rename,[status(thm)],[additive_commutativity]) ).
cnf(c_0_22,plain,
multiplication(X1,addition(X2,X3)) = addition(multiplication(X1,X2),multiplication(X1,X3)),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_23,plain,
( multiplication(X1,c(X1)) = zero
| ~ test(X1) ),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_24,plain,
addition(X1,zero) = X1,
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_25,plain,
( addition(X1,X2) = one
| ~ complement(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_26,plain,
addition(X1,X2) = addition(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
fof(c_0_27,plain,
! [X47] : multiplication(X47,one) = X47,
inference(variable_rename,[status(thm)],[multiplicative_right_identity]) ).
fof(c_0_28,negated_conjecture,
~ ! [X4,X5] :
( ( test(X5)
& test(X4) )
=> c(multiplication(X4,X5)) = addition(c(X4),c(X5)) ),
inference(assume_negation,[status(cth)],[goals]) ).
fof(c_0_29,plain,
! [X44,X45,X46] : multiplication(X44,multiplication(X45,X46)) = multiplication(multiplication(X44,X45),X46),
inference(variable_rename,[status(thm)],[multiplicative_associativity]) ).
cnf(c_0_30,plain,
( multiplication(X1,addition(X2,c(X1))) = multiplication(X1,X2)
| ~ test(X1) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_23]),c_0_24]) ).
cnf(c_0_31,plain,
( addition(X1,c(X1)) = one
| ~ test(X1) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_19]),c_0_26]) ).
cnf(c_0_32,plain,
multiplication(X1,one) = X1,
inference(split_conjunct,[status(thm)],[c_0_27]) ).
fof(c_0_33,negated_conjecture,
( test(esk3_0)
& test(esk2_0)
& c(multiplication(esk2_0,esk3_0)) != addition(c(esk2_0),c(esk3_0)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_28])])]) ).
cnf(c_0_34,plain,
multiplication(X1,multiplication(X2,X3)) = multiplication(multiplication(X1,X2),X3),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_35,plain,
( multiplication(X1,X1) = X1
| ~ test(X1) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_31]),c_0_32]) ).
cnf(c_0_36,negated_conjecture,
test(esk3_0),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
cnf(c_0_37,plain,
( multiplication(X1,multiplication(X2,c(multiplication(X1,X2)))) = zero
| ~ test(multiplication(X1,X2)) ),
inference(spm,[status(thm)],[c_0_23,c_0_34]) ).
cnf(c_0_38,negated_conjecture,
multiplication(esk3_0,esk3_0) = esk3_0,
inference(spm,[status(thm)],[c_0_35,c_0_36]) ).
fof(c_0_39,plain,
! [X39,X40,X41] : addition(X41,addition(X40,X39)) = addition(addition(X41,X40),X39),
inference(variable_rename,[status(thm)],[additive_associativity]) ).
fof(c_0_40,plain,
! [X43] : addition(X43,X43) = X43,
inference(variable_rename,[status(thm)],[additive_idempotence]) ).
fof(c_0_41,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_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_37,c_0_38]),c_0_36])]) ).
cnf(c_0_43,negated_conjecture,
multiplication(esk3_0,multiplication(esk3_0,X1)) = multiplication(esk3_0,X1),
inference(spm,[status(thm)],[c_0_34,c_0_38]) ).
cnf(c_0_44,plain,
addition(X1,addition(X2,X3)) = addition(addition(X1,X2),X3),
inference(split_conjunct,[status(thm)],[c_0_39]) ).
cnf(c_0_45,plain,
addition(X1,X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_40]) ).
cnf(c_0_46,plain,
( complement(esk1_1(X1),X1)
| ~ test(X1) ),
inference(split_conjunct,[status(thm)],[c_0_41]) ).
fof(c_0_47,plain,
! [X52,X53,X54] : multiplication(addition(X52,X53),X54) = addition(multiplication(X52,X54),multiplication(X53,X54)),
inference(variable_rename,[status(thm)],[left_distributivity]) ).
fof(c_0_48,plain,
! [X48] : multiplication(one,X48) = X48,
inference(variable_rename,[status(thm)],[multiplicative_left_identity]) ).
cnf(c_0_49,negated_conjecture,
multiplication(esk3_0,c(esk3_0)) = zero,
inference(rw,[status(thm)],[c_0_42,c_0_43]) ).
cnf(c_0_50,plain,
addition(zero,X1) = X1,
inference(spm,[status(thm)],[c_0_24,c_0_26]) ).
cnf(c_0_51,plain,
addition(X1,addition(X1,X2)) = addition(X1,X2),
inference(spm,[status(thm)],[c_0_44,c_0_45]) ).
cnf(c_0_52,plain,
( addition(X1,esk1_1(X1)) = one
| ~ test(X1) ),
inference(spm,[status(thm)],[c_0_25,c_0_46]) ).
cnf(c_0_53,plain,
( test(X2)
| ~ complement(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_41]) ).
cnf(c_0_54,plain,
( complement(X2,X1)
| multiplication(X1,X2) != zero
| multiplication(X2,X1) != zero
| addition(X1,X2) != one ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_55,plain,
multiplication(addition(X1,X2),X3) = addition(multiplication(X1,X3),multiplication(X2,X3)),
inference(split_conjunct,[status(thm)],[c_0_47]) ).
cnf(c_0_56,plain,
multiplication(one,X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_48]) ).
cnf(c_0_57,negated_conjecture,
multiplication(esk3_0,addition(c(esk3_0),X1)) = multiplication(esk3_0,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_49]),c_0_50]) ).
cnf(c_0_58,plain,
( addition(X1,one) = one
| ~ test(X1) ),
inference(spm,[status(thm)],[c_0_51,c_0_52]) ).
cnf(c_0_59,plain,
( test(X1)
| addition(X1,X2) != one
| multiplication(X2,X1) != zero
| multiplication(X1,X2) != zero ),
inference(spm,[status(thm)],[c_0_53,c_0_54]) ).
cnf(c_0_60,negated_conjecture,
test(esk2_0),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
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_55,c_0_56]),c_0_26]) ).
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_57,c_0_31]),c_0_32]) ).
cnf(c_0_63,negated_conjecture,
addition(one,esk3_0) = one,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_36]),c_0_26]) ).
cnf(c_0_64,plain,
( c(X1) = X2
| ~ complement(X1,X2)
| ~ test(X1) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_65,plain,
( test(X1)
| addition(X2,X1) != one
| multiplication(X2,X1) != zero
| multiplication(X1,X2) != zero ),
inference(spm,[status(thm)],[c_0_59,c_0_26]) ).
cnf(c_0_66,plain,
( multiplication(X1,X2) = zero
| ~ complement(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_67,negated_conjecture,
multiplication(esk2_0,esk2_0) = esk2_0,
inference(spm,[status(thm)],[c_0_35,c_0_60]) ).
cnf(c_0_68,plain,
( addition(X1,addition(X2,c(addition(X1,X2)))) = one
| ~ test(addition(X1,X2)) ),
inference(spm,[status(thm)],[c_0_44,c_0_31]) ).
cnf(c_0_69,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_26]),c_0_63]),c_0_56]),c_0_26]) ).
cnf(c_0_70,plain,
( test(c(X1))
| ~ test(X1) ),
inference(spm,[status(thm)],[c_0_53,c_0_19]) ).
cnf(c_0_71,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_64,c_0_54]),c_0_65]) ).
cnf(c_0_72,plain,
( multiplication(c(X1),X1) = zero
| ~ test(X1) ),
inference(spm,[status(thm)],[c_0_66,c_0_19]) ).
cnf(c_0_73,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_37,c_0_67]),c_0_60])]) ).
cnf(c_0_74,negated_conjecture,
multiplication(esk2_0,multiplication(esk2_0,X1)) = multiplication(esk2_0,X1),
inference(spm,[status(thm)],[c_0_34,c_0_67]) ).
cnf(c_0_75,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_68,c_0_69]),c_0_70]) ).
cnf(c_0_76,plain,
( c(c(X1)) = X1
| ~ test(X1) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_31]),c_0_23]),c_0_72]) ).
cnf(c_0_77,negated_conjecture,
( multiplication(c(esk3_0),c(c(esk3_0))) = multiplication(c(esk3_0),esk3_0)
| ~ test(c(esk3_0)) ),
inference(spm,[status(thm)],[c_0_30,c_0_69]) ).
cnf(c_0_78,negated_conjecture,
multiplication(esk2_0,c(esk2_0)) = zero,
inference(rw,[status(thm)],[c_0_73,c_0_74]) ).
cnf(c_0_79,negated_conjecture,
( addition(esk3_0,c(esk3_0)) = one
| ~ test(c(esk3_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_75,c_0_76]),c_0_51]),c_0_36])]) ).
cnf(c_0_80,negated_conjecture,
( multiplication(c(esk3_0),esk3_0) = zero
| ~ test(c(esk3_0)) ),
inference(spm,[status(thm)],[c_0_23,c_0_77]) ).
cnf(c_0_81,negated_conjecture,
multiplication(esk2_0,addition(c(esk2_0),X1)) = multiplication(esk2_0,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_78]),c_0_50]) ).
cnf(c_0_82,negated_conjecture,
addition(esk3_0,c(esk3_0)) = one,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_79,c_0_70]),c_0_36])]) ).
cnf(c_0_83,negated_conjecture,
multiplication(c(esk3_0),esk3_0) = zero,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_80,c_0_70]),c_0_36])]) ).
cnf(c_0_84,plain,
( multiplication(X1,esk1_1(X1)) = zero
| ~ test(X1) ),
inference(spm,[status(thm)],[c_0_66,c_0_46]) ).
fof(c_0_85,plain,
! [X56] : multiplication(zero,X56) = zero,
inference(variable_rename,[status(thm)],[left_annihilation]) ).
cnf(c_0_86,negated_conjecture,
( multiplication(esk2_0,c(c(esk2_0))) = esk2_0
| ~ test(c(esk2_0)) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_81,c_0_31]),c_0_32]) ).
cnf(c_0_87,negated_conjecture,
addition(one,esk2_0) = one,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_60]),c_0_26]) ).
cnf(c_0_88,plain,
addition(X1,multiplication(X1,X2)) = multiplication(X1,addition(X2,one)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_32]),c_0_26]) ).
cnf(c_0_89,negated_conjecture,
addition(one,addition(esk3_0,X1)) = addition(one,X1),
inference(spm,[status(thm)],[c_0_44,c_0_63]) ).
cnf(c_0_90,plain,
( multiplication(X1,addition(c(X1),X2)) = multiplication(X1,X2)
| ~ test(X1) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_23]),c_0_50]) ).
cnf(c_0_91,negated_conjecture,
c(c(esk3_0)) = esk3_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_82]),c_0_83]),c_0_49])]) ).
cnf(c_0_92,negated_conjecture,
test(c(esk3_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_82]),c_0_49]),c_0_83])]) ).
cnf(c_0_93,plain,
( multiplication(addition(X1,X2),esk1_1(X1)) = multiplication(X2,esk1_1(X1))
| ~ test(X1) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_84]),c_0_50]) ).
cnf(c_0_94,plain,
multiplication(zero,X1) = zero,
inference(split_conjunct,[status(thm)],[c_0_85]) ).
cnf(c_0_95,negated_conjecture,
( addition(esk2_0,c(c(esk2_0))) = c(c(esk2_0))
| ~ test(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_61,c_0_86]),c_0_26]),c_0_87]),c_0_56]),c_0_26]) ).
cnf(c_0_96,plain,
( multiplication(esk1_1(X1),X1) = zero
| ~ test(X1) ),
inference(spm,[status(thm)],[c_0_18,c_0_46]) ).
cnf(c_0_97,negated_conjecture,
addition(multiplication(esk3_0,X1),multiplication(X2,addition(c(esk3_0),X1))) = multiplication(addition(esk3_0,X2),addition(c(esk3_0),X1)),
inference(spm,[status(thm)],[c_0_55,c_0_57]) ).
cnf(c_0_98,negated_conjecture,
multiplication(esk2_0,addition(X1,one)) = multiplication(esk2_0,addition(esk2_0,X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_67]),c_0_88]) ).
cnf(c_0_99,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_89,c_0_31]),c_0_45]),c_0_36])]) ).
cnf(c_0_100,negated_conjecture,
multiplication(c(esk3_0),addition(esk3_0,X1)) = multiplication(c(esk3_0),X1),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_90,c_0_91]),c_0_92])]) ).
cnf(c_0_101,negated_conjecture,
multiplication(c(esk3_0),esk1_1(esk3_0)) = esk1_1(esk3_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_93,c_0_82]),c_0_56]),c_0_36])]) ).
cnf(c_0_102,plain,
( multiplication(c(X1),multiplication(X1,X2)) = zero
| ~ test(X1) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_72]),c_0_94]) ).
cnf(c_0_103,negated_conjecture,
( addition(esk2_0,addition(c(c(esk2_0)),c(c(c(esk2_0))))) = one
| ~ test(c(esk2_0)) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_95]),c_0_70]) ).
cnf(c_0_104,plain,
( multiplication(esk1_1(X1),addition(X1,X2)) = multiplication(esk1_1(X1),X2)
| ~ test(X1) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_96]),c_0_50]) ).
cnf(c_0_105,negated_conjecture,
addition(esk3_0,multiplication(esk2_0,addition(esk2_0,c(esk3_0)))) = addition(esk2_0,esk3_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_97,c_0_98]),c_0_32]),c_0_26]),c_0_26]),c_0_99]),c_0_32]) ).
cnf(c_0_106,negated_conjecture,
esk1_1(esk3_0) = c(esk3_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_100,c_0_52]),c_0_32]),c_0_101]),c_0_36])]) ).
cnf(c_0_107,negated_conjecture,
multiplication(c(esk3_0),addition(X1,esk3_0)) = multiplication(c(esk3_0),X1),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_91]),c_0_92])]) ).
cnf(c_0_108,plain,
addition(multiplication(X1,X2),addition(multiplication(X1,X3),X4)) = addition(multiplication(X1,addition(X2,X3)),X4),
inference(spm,[status(thm)],[c_0_44,c_0_22]) ).
cnf(c_0_109,negated_conjecture,
multiplication(c(esk2_0),esk2_0) = zero,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_102,c_0_67]),c_0_60])]) ).
cnf(c_0_110,negated_conjecture,
( addition(esk2_0,c(esk2_0)) = one
| ~ test(c(esk2_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_103,c_0_76]),c_0_51]),c_0_60])]) ).
cnf(c_0_111,negated_conjecture,
multiplication(c(esk3_0),multiplication(esk2_0,addition(esk2_0,c(esk3_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(spm,[status(thm)],[c_0_104,c_0_105]),c_0_106]),c_0_107]),c_0_106]),c_0_36])]) ).
cnf(c_0_112,negated_conjecture,
addition(multiplication(esk2_0,addition(esk2_0,X1)),X2) = addition(esk2_0,addition(multiplication(esk2_0,X1),X2)),
inference(spm,[status(thm)],[c_0_108,c_0_67]) ).
cnf(c_0_113,negated_conjecture,
multiplication(addition(c(esk2_0),X1),esk2_0) = multiplication(X1,esk2_0),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_109]),c_0_50]) ).
cnf(c_0_114,negated_conjecture,
addition(esk2_0,c(esk2_0)) = one,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_110,c_0_70]),c_0_60])]) ).
cnf(c_0_115,plain,
( multiplication(addition(X1,X2),c(X1)) = multiplication(X2,c(X1))
| ~ test(X1) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_23]),c_0_50]) ).
cnf(c_0_116,negated_conjecture,
addition(esk2_0,addition(multiplication(esk2_0,c(esk3_0)),multiplication(c(esk3_0),esk2_0))) = multiplication(esk2_0,addition(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_61,c_0_111]),c_0_112]),c_0_26]),c_0_99]),c_0_56]) ).
cnf(c_0_117,negated_conjecture,
( multiplication(esk1_1(c(esk2_0)),esk2_0) = esk2_0
| ~ test(c(esk2_0)) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_113,c_0_52]),c_0_56]) ).
cnf(c_0_118,negated_conjecture,
test(c(esk2_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_114]),c_0_78]),c_0_109])]) ).
cnf(c_0_119,negated_conjecture,
multiplication(c(esk2_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_115,c_0_114]),c_0_56]),c_0_60])]) ).
cnf(c_0_120,negated_conjecture,
multiplication(addition(c(esk3_0),X1),esk3_0) = multiplication(X1,esk3_0),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_83]),c_0_50]) ).
cnf(c_0_121,plain,
( addition(X1,addition(c(X2),multiplication(X2,X1))) = multiplication(addition(X2,one),addition(X1,c(X2)))
| ~ test(X2) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_30]),c_0_44]) ).
cnf(c_0_122,negated_conjecture,
multiplication(esk2_0,addition(esk2_0,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(spm,[status(thm)],[c_0_51,c_0_116]),c_0_88]),c_0_44]),c_0_26]),c_0_99]),c_0_26]),c_0_87]),c_0_32]) ).
cnf(c_0_123,plain,
addition(X1,addition(X2,X3)) = addition(X2,addition(X1,X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_26]),c_0_44]) ).
cnf(c_0_124,negated_conjecture,
multiplication(esk1_1(c(esk2_0)),esk2_0) = esk2_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_117,c_0_118])]) ).
cnf(c_0_125,plain,
( multiplication(addition(X1,X2),c(X2)) = multiplication(X1,c(X2))
| ~ test(X2) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_23]),c_0_24]) ).
cnf(c_0_126,negated_conjecture,
multiplication(c(esk2_0),addition(X1,c(esk2_0))) = multiplication(c(esk2_0),addition(X1,one)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_119]),c_0_26]),c_0_88]) ).
cnf(c_0_127,negated_conjecture,
( multiplication(esk1_1(c(esk3_0)),esk3_0) = esk3_0
| ~ test(c(esk3_0)) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_120,c_0_52]),c_0_56]) ).
cnf(c_0_128,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(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(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_121,c_0_122]),c_0_26]),c_0_114]),c_0_44]),c_0_26]),c_0_99]),c_0_26]),c_0_87]),c_0_26]),c_0_87]),c_0_44]),c_0_26]),c_0_56]),c_0_60])]) ).
cnf(c_0_129,plain,
( addition(X1,addition(X2,esk1_1(X1))) = addition(X2,one)
| ~ test(X1) ),
inference(spm,[status(thm)],[c_0_123,c_0_52]) ).
cnf(c_0_130,negated_conjecture,
addition(esk2_0,esk1_1(c(esk2_0))) = esk1_1(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_88,c_0_124]),c_0_26]),c_0_87]),c_0_32]),c_0_26]) ).
cnf(c_0_131,plain,
( multiplication(X1,addition(X2,esk1_1(X1))) = multiplication(X1,X2)
| ~ test(X1) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_84]),c_0_24]) ).
cnf(c_0_132,plain,
( multiplication(esk1_1(X1),multiplication(X1,X2)) = zero
| ~ test(X1) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_96]),c_0_94]) ).
cnf(c_0_133,plain,
( addition(multiplication(X1,c(X2)),multiplication(addition(X1,X2),X3)) = multiplication(addition(X1,X2),addition(c(X2),X3))
| ~ test(X2) ),
inference(spm,[status(thm)],[c_0_22,c_0_125]) ).
cnf(c_0_134,negated_conjecture,
multiplication(addition(esk3_0,c(esk2_0)),addition(c(esk2_0),c(esk3_0))) = c(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(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_97,c_0_126]),c_0_26]),c_0_99]),c_0_32]),c_0_26]),c_0_61]),c_0_26]),c_0_63]),c_0_56]),c_0_26]) ).
cnf(c_0_135,negated_conjecture,
c(c(esk2_0)) = esk2_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_114]),c_0_109]),c_0_78])]) ).
cnf(c_0_136,plain,
( addition(multiplication(X1,X2),multiplication(X3,addition(c(X1),X2))) = multiplication(addition(X3,X1),addition(c(X1),X2))
| ~ test(X1) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_90]),c_0_26]) ).
cnf(c_0_137,negated_conjecture,
multiplication(esk1_1(c(esk3_0)),esk3_0) = esk3_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_127,c_0_92])]) ).
cnf(c_0_138,plain,
( addition(multiplication(addition(X1,X2),X3),multiplication(X1,c(X2))) = multiplication(addition(X1,X2),addition(X3,c(X2)))
| ~ test(X2) ),
inference(spm,[status(thm)],[c_0_22,c_0_125]) ).
cnf(c_0_139,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_115,c_0_128]),c_0_56]),c_0_60])]) ).
cnf(c_0_140,plain,
( c(X1) = X2
| addition(X1,X2) != one
| multiplication(X1,X2) != zero
| multiplication(X2,X1) != zero ),
inference(spm,[status(thm)],[c_0_71,c_0_26]) ).
cnf(c_0_141,negated_conjecture,
addition(c(esk2_0),esk1_1(c(esk2_0))) = one,
inference(cn,[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_26]),c_0_87]),c_0_118])]) ).
cnf(c_0_142,negated_conjecture,
multiplication(c(esk2_0),esk1_1(c(esk2_0))) = zero,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_131,c_0_130]),c_0_109]),c_0_118])]) ).
cnf(c_0_143,negated_conjecture,
multiplication(esk1_1(c(esk2_0)),c(esk2_0)) = zero,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_132,c_0_119]),c_0_118])]) ).
cnf(c_0_144,negated_conjecture,
multiplication(esk3_0,addition(multiplication(esk3_0,X1),X2)) = multiplication(esk3_0,addition(X1,X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_43]),c_0_22]) ).
cnf(c_0_145,negated_conjecture,
addition(multiplication(esk3_0,esk2_0),c(esk2_0)) = addition(esk3_0,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(spm,[status(thm)],[c_0_133,c_0_134]),c_0_135]),c_0_135]),c_0_128]),c_0_32]),c_0_118])]) ).
cnf(c_0_146,negated_conjecture,
addition(one,addition(esk2_0,X1)) = addition(one,X1),
inference(spm,[status(thm)],[c_0_44,c_0_87]) ).
cnf(c_0_147,plain,
( multiplication(X1,addition(X2,c(addition(c(X1),X2)))) = X1
| ~ test(addition(c(X1),X2))
| ~ test(X1) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_90,c_0_68]),c_0_32]) ).
cnf(c_0_148,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(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_136,c_0_134]),c_0_26]),c_0_44]),c_0_26]),c_0_114]),c_0_26]),c_0_63]),c_0_56]),c_0_60])]) ).
cnf(c_0_149,negated_conjecture,
multiplication(esk2_0,addition(multiplication(esk2_0,X1),X2)) = multiplication(esk2_0,addition(X1,X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_74]),c_0_22]) ).
cnf(c_0_150,negated_conjecture,
multiplication(c(esk3_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_115,c_0_82]),c_0_56]),c_0_36])]) ).
cnf(c_0_151,negated_conjecture,
addition(esk3_0,esk1_1(c(esk3_0))) = esk1_1(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_88,c_0_137]),c_0_26]),c_0_63]),c_0_32]),c_0_26]) ).
cnf(c_0_152,plain,
( addition(multiplication(X1,X2),multiplication(X3,addition(X2,c(X1)))) = multiplication(addition(X3,X1),addition(X2,c(X1)))
| ~ test(X1) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_30]),c_0_26]) ).
cnf(c_0_153,negated_conjecture,
multiplication(addition(c(esk2_0),c(esk3_0)),addition(esk3_0,c(esk2_0))) = 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(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_138,c_0_139]),c_0_91]),c_0_88]),c_0_26]),c_0_63]),c_0_32]),c_0_91]),c_0_26]),c_0_92])]) ).
cnf(c_0_154,plain,
( multiplication(esk1_1(X1),addition(X2,X1)) = multiplication(esk1_1(X1),X2)
| ~ test(X1) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_96]),c_0_24]) ).
cnf(c_0_155,negated_conjecture,
esk1_1(c(esk2_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_140,c_0_141]),c_0_135]),c_0_142]),c_0_143])]) ).
cnf(c_0_156,negated_conjecture,
multiplication(esk2_0,addition(X1,c(esk2_0))) = multiplication(esk2_0,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_78]),c_0_24]) ).
cnf(c_0_157,negated_conjecture,
multiplication(esk3_0,addition(esk3_0,c(esk2_0))) = esk3_0,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_144,c_0_145]),c_0_114]),c_0_32]) ).
cnf(c_0_158,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_146,c_0_31]),c_0_45]),c_0_60])]) ).
cnf(c_0_159,negated_conjecture,
( multiplication(esk2_0,addition(c(esk3_0),c(addition(c(esk2_0),c(esk3_0))))) = esk2_0
| ~ test(addition(c(esk2_0),c(esk3_0))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_147,c_0_148]),c_0_149]),c_0_60])]) ).
cnf(c_0_160,negated_conjecture,
multiplication(addition(X1,c(esk3_0)),c(esk3_0)) = multiplication(addition(X1,one),c(esk3_0)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_150]),c_0_26]),c_0_61]) ).
cnf(c_0_161,negated_conjecture,
addition(c(esk3_0),esk1_1(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_129,c_0_151]),c_0_26]),c_0_63]),c_0_92])]) ).
cnf(c_0_162,negated_conjecture,
multiplication(c(esk3_0),esk1_1(c(esk3_0))) = zero,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_131,c_0_151]),c_0_83]),c_0_92])]) ).
cnf(c_0_163,negated_conjecture,
multiplication(esk1_1(c(esk3_0)),c(esk3_0)) = zero,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_132,c_0_150]),c_0_92])]) ).
cnf(c_0_164,negated_conjecture,
addition(multiplication(esk2_0,esk3_0),c(esk2_0)) = addition(esk3_0,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_152,c_0_153]),c_0_44]),c_0_26]),c_0_123]),c_0_128]),c_0_56]),c_0_60])]) ).
cnf(c_0_165,negated_conjecture,
multiplication(addition(X1,c(esk2_0)),esk2_0) = multiplication(X1,esk2_0),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_109]),c_0_24]) ).
cnf(c_0_166,negated_conjecture,
multiplication(esk2_0,multiplication(esk3_0,esk2_0)) = multiplication(esk2_0,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_154,c_0_145]),c_0_155]),c_0_156]),c_0_155]),c_0_118])]) ).
cnf(c_0_167,negated_conjecture,
addition(esk3_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(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(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_121,c_0_157]),c_0_26]),c_0_82]),c_0_44]),c_0_26]),c_0_158]),c_0_26]),c_0_63]),c_0_26]),c_0_63]),c_0_44]),c_0_56]),c_0_36])]) ).
cnf(c_0_168,negated_conjecture,
( addition(c(esk3_0),c(addition(c(esk2_0),c(esk3_0)))) = addition(esk2_0,c(esk3_0))
| ~ test(addition(c(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(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_152,c_0_159]),c_0_160]),c_0_26]),c_0_158]),c_0_56]),c_0_26]),c_0_128]),c_0_56]) ).
cnf(c_0_169,negated_conjecture,
esk1_1(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_140,c_0_161]),c_0_91]),c_0_162]),c_0_163])]) ).
cnf(c_0_170,negated_conjecture,
multiplication(esk3_0,addition(X1,c(esk3_0))) = multiplication(esk3_0,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_49]),c_0_24]) ).
cnf(c_0_171,negated_conjecture,
multiplication(esk3_0,esk2_0) = multiplication(esk2_0,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_125,c_0_164]),c_0_135]),c_0_165]),c_0_135]),c_0_34]),c_0_166]),c_0_118])]) ).
cnf(c_0_172,plain,
addition(X1,addition(X2,X3)) = addition(X3,addition(X1,X2)),
inference(spm,[status(thm)],[c_0_26,c_0_44]) ).
cnf(c_0_173,negated_conjecture,
addition(multiplication(esk2_0,X1),multiplication(X2,addition(c(esk2_0),X1))) = multiplication(addition(esk2_0,X2),addition(c(esk2_0),X1)),
inference(spm,[status(thm)],[c_0_55,c_0_81]) ).
cnf(c_0_174,negated_conjecture,
multiplication(c(esk3_0),addition(X1,c(esk3_0))) = multiplication(c(esk3_0),addition(X1,one)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_150]),c_0_26]),c_0_88]) ).
cnf(c_0_175,negated_conjecture,
( multiplication(esk3_0,c(addition(c(esk2_0),c(esk3_0)))) = c(addition(c(esk2_0),c(esk3_0)))
| ~ test(addition(c(esk2_0),c(esk3_0))) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_125,c_0_167]),c_0_56]) ).
cnf(c_0_176,negated_conjecture,
( multiplication(esk3_0,c(addition(c(esk2_0),c(esk3_0)))) = multiplication(esk2_0,esk3_0)
| ~ test(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(spm,[status(thm)],[c_0_104,c_0_168]),c_0_169]),c_0_170]),c_0_171]),c_0_169]),c_0_92])]) ).
cnf(c_0_177,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_59,c_0_44]) ).
cnf(c_0_178,plain,
addition(X1,addition(X2,X3)) = addition(X3,addition(X2,X1)),
inference(spm,[status(thm)],[c_0_172,c_0_26]) ).
cnf(c_0_179,plain,
( addition(multiplication(X1,addition(X2,X3)),multiplication(esk1_1(X3),X2)) = multiplication(addition(X1,esk1_1(X3)),addition(X2,X3))
| ~ test(X3) ),
inference(spm,[status(thm)],[c_0_55,c_0_154]) ).
cnf(c_0_180,negated_conjecture,
multiplication(addition(esk2_0,c(esk3_0)),addition(c(esk2_0),c(esk3_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(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_173,c_0_174]),c_0_26]),c_0_158]),c_0_32]),c_0_26]),c_0_61]),c_0_26]),c_0_87]),c_0_56]) ).
cnf(c_0_181,negated_conjecture,
( c(addition(c(esk2_0),c(esk3_0))) = multiplication(esk2_0,esk3_0)
| ~ test(addition(c(esk2_0),c(esk3_0))) ),
inference(spm,[status(thm)],[c_0_175,c_0_176]) ).
cnf(c_0_182,negated_conjecture,
c(multiplication(esk2_0,esk3_0)) != addition(c(esk2_0),c(esk3_0)),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
cnf(c_0_183,plain,
( test(addition(X1,X2))
| addition(X3,addition(X2,X1)) != one
| multiplication(X3,addition(X1,X2)) != zero
| multiplication(addition(X1,X2),X3) != zero ),
inference(spm,[status(thm)],[c_0_177,c_0_178]) ).
cnf(c_0_184,negated_conjecture,
addition(c(esk3_0),multiplication(esk3_0,c(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(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_179,c_0_180]),c_0_169]),c_0_169]),c_0_44]),c_0_26]),c_0_82]),c_0_26]),c_0_87]),c_0_56]),c_0_92])]) ).
cnf(c_0_185,negated_conjecture,
~ test(addition(c(esk2_0),c(esk3_0))),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_181]),c_0_182]) ).
cnf(c_0_186,plain,
( multiplication(addition(X1,X2),esk1_1(X2)) = multiplication(X1,esk1_1(X2))
| ~ test(X2) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_84]),c_0_24]) ).
cnf(c_0_187,negated_conjecture,
( addition(X1,addition(c(esk2_0),c(esk3_0))) != one
| multiplication(X1,addition(c(esk2_0),c(esk3_0))) != zero
| multiplication(addition(c(esk2_0),c(esk3_0)),X1) != zero ),
inference(sr,[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_183,c_0_184]),c_0_26]),c_0_184]),c_0_26]),c_0_184]),c_0_26]),c_0_184]),c_0_185]) ).
cnf(c_0_188,plain,
( addition(multiplication(X1,esk1_1(X2)),multiplication(addition(X1,X2),X3)) = multiplication(addition(X1,X2),addition(esk1_1(X2),X3))
| ~ test(X2) ),
inference(spm,[status(thm)],[c_0_22,c_0_186]) ).
cnf(c_0_189,plain,
( multiplication(X1,multiplication(addition(X2,c(X1)),X3)) = multiplication(X1,multiplication(X2,X3))
| ~ test(X1) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_30]),c_0_34]) ).
cnf(c_0_190,negated_conjecture,
multiplication(c(esk2_0),multiplication(esk2_0,X1)) = zero,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_102,c_0_74]),c_0_60])]) ).
cnf(c_0_191,negated_conjecture,
( addition(c(esk2_0),addition(X1,c(esk3_0))) != one
| multiplication(X1,addition(c(esk2_0),c(esk3_0))) != zero
| multiplication(addition(c(esk2_0),c(esk3_0)),X1) != zero ),
inference(spm,[status(thm)],[c_0_187,c_0_123]) ).
cnf(c_0_192,negated_conjecture,
addition(multiplication(esk2_0,esk3_0),c(esk3_0)) = addition(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_188,c_0_180]),c_0_169]),c_0_169]),c_0_167]),c_0_32]),c_0_92])]) ).
cnf(c_0_193,negated_conjecture,
multiplication(esk2_0,multiplication(esk3_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_189,c_0_134]),c_0_78]),c_0_170]),c_0_60])]) ).
cnf(c_0_194,negated_conjecture,
multiplication(addition(c(esk2_0),X1),multiplication(esk2_0,X2)) = multiplication(X1,multiplication(esk2_0,X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_190]),c_0_50]) ).
cnf(c_0_195,negated_conjecture,
multiplication(c(esk3_0),multiplication(esk2_0,esk3_0)) = zero,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_132,c_0_171]),c_0_106]),c_0_36])]) ).
cnf(c_0_196,negated_conjecture,
$false,
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(spm,[status(thm)],[c_0_191,c_0_192]),c_0_123]),c_0_128]),c_0_34]),c_0_170]),c_0_193]),c_0_194]),c_0_195])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : KLE016+2 : TPTP v9.2.1. Released v4.0.0.
% 0.00/0.13 % 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
% 0.14/0.32 % Computer : n004.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 20:24:47 EDT 2026
% 0.14/0.33 % CPUTime :
% 0.14/0.34 % start to proof: theBenchmark
% 284.95/116.40 % Version : CSE_E---1.7
% 284.95/116.40 % Problem : theBenchmark.p
% 284.95/116.40 % SZS status Theorem for theBenchmark.p
% 284.95/116.40 % SZS output start CNFRefutation
% See solution above
% 285.75/117.20 % Total time : 86.354s
%------------------------------------------------------------------------------