%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : KLE028+2 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n001.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 12:58:40 PM UTC 2026
% Result : Theorem 15.64s 2.60s
% Output : CNFRefutation 16.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 15
% Syntax : Number of formulae : 164 ( 132 unt; 0 def)
% Number of atoms : 222 ( 165 equ)
% Maximal formula atoms : 10 ( 1 avg)
% Number of connectives : 106 ( 48 ~; 37 |; 14 &)
% ( 4 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 2 avg)
% Maximal term depth : 11 ( 2 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 8 con; 0-2 aty)
% Number of variables : 185 ( 5 sgn 66 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
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(goals,conjecture,
! [X4,X5,X6,X7,X8,X9] :
( ( test(X9)
& test(X8) )
=> ( leq(addition(multiplication(X9,addition(multiplication(X8,X4),multiplication(c(X8),X6))),multiplication(c(X9),addition(multiplication(X8,X5),multiplication(c(X8),X7)))),addition(multiplication(X8,addition(multiplication(X9,X4),multiplication(c(X9),X5))),multiplication(c(X8),addition(multiplication(X9,X6),multiplication(c(X9),X7)))))
& leq(addition(multiplication(X8,addition(multiplication(X9,X4),multiplication(c(X9),X5))),multiplication(c(X8),addition(multiplication(X9,X6),multiplication(c(X9),X7)))),addition(multiplication(X9,addition(multiplication(X8,X4),multiplication(c(X8),X6))),multiplication(c(X9),addition(multiplication(X8,X5),multiplication(c(X8),X7))))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
fof(test_2,axiom,
! [X4,X5] :
( complement(X5,X4)
<=> ( addition(X4,X5) = one
& multiplication(X5,X4) = zero
& multiplication(X4,X5) = zero ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+1.ax',test_2) ).
fof(additive_identity,axiom,
! [X1] : addition(X1,zero) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',additive_identity) ).
fof(additive_commutativity,axiom,
! [X1,X2] : addition(X1,X2) = addition(X2,X1),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',additive_commutativity) ).
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(test_1,axiom,
! [X4] :
( test(X4)
<=> ? [X5] : complement(X5,X4) ),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+1.ax',test_1) ).
fof(additive_associativity,axiom,
! [X3,X2,X1] : addition(X1,addition(X2,X3)) = addition(addition(X1,X2),X3),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',additive_associativity) ).
fof(additive_idempotence,axiom,
! [X1] : addition(X1,X1) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',additive_idempotence) ).
fof(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(right_annihilation,axiom,
! [X1] : multiplication(X1,zero) = zero,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',right_annihilation) ).
fof(order,axiom,
! [X1,X2] :
( leq(X1,X2)
<=> addition(X1,X2) = X2 ),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',order) ).
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_15,plain,
! [X38,X39] :
( ( ~ test(X38)
| c(X38) = X39
| ~ complement(X38,X39) )
& ( ~ test(X38)
| complement(X38,X39)
| c(X38) != X39 ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[test_3])])])]) ).
fof(c_0_16,negated_conjecture,
~ ! [X4,X5,X6,X7,X8,X9] :
( ( test(X9)
& test(X8) )
=> ( leq(addition(multiplication(X9,addition(multiplication(X8,X4),multiplication(c(X8),X6))),multiplication(c(X9),addition(multiplication(X8,X5),multiplication(c(X8),X7)))),addition(multiplication(X8,addition(multiplication(X9,X4),multiplication(c(X9),X5))),multiplication(c(X8),addition(multiplication(X9,X6),multiplication(c(X9),X7)))))
& leq(addition(multiplication(X8,addition(multiplication(X9,X4),multiplication(c(X9),X5))),multiplication(c(X8),addition(multiplication(X9,X6),multiplication(c(X9),X7)))),addition(multiplication(X9,addition(multiplication(X8,X4),multiplication(c(X8),X6))),multiplication(c(X9),addition(multiplication(X8,X5),multiplication(c(X8),X7))))) ) ),
inference(assume_negation,[status(cth)],[goals]) ).
cnf(c_0_17,plain,
( ~ test(X1)
| c(X1) != X2
| complement(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
fof(c_0_18,negated_conjecture,
( ( ~ leq(addition(multiplication(esk7_0,addition(multiplication(esk6_0,esk2_0),multiplication(c(esk6_0),esk4_0))),multiplication(c(esk7_0),addition(multiplication(esk6_0,esk3_0),multiplication(c(esk6_0),esk5_0)))),addition(multiplication(esk6_0,addition(multiplication(esk7_0,esk2_0),multiplication(c(esk7_0),esk3_0))),multiplication(c(esk6_0),addition(multiplication(esk7_0,esk4_0),multiplication(c(esk7_0),esk5_0)))))
| ~ leq(addition(multiplication(esk6_0,addition(multiplication(esk7_0,esk2_0),multiplication(c(esk7_0),esk3_0))),multiplication(c(esk6_0),addition(multiplication(esk7_0,esk4_0),multiplication(c(esk7_0),esk5_0)))),addition(multiplication(esk7_0,addition(multiplication(esk6_0,esk2_0),multiplication(c(esk6_0),esk4_0))),multiplication(c(esk7_0),addition(multiplication(esk6_0,esk3_0),multiplication(c(esk6_0),esk5_0))))) )
& test(esk7_0)
& test(esk6_0) ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_16])])])]) ).
fof(c_0_19,plain,
! [X36,X37] :
( ( complement(X37,X36)
| addition(X36,X37) != one
| multiplication(X37,X36) != zero
| multiplication(X36,X37) != zero )
& ( ~ complement(X37,X36)
| addition(X36,X37) = one )
& ( ~ complement(X37,X36)
| multiplication(X37,X36) = zero )
& ( ~ complement(X37,X36)
| multiplication(X36,X37) = zero ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[test_2])])])]) ).
cnf(c_0_20,plain,
( ~ test(X1)
| complement(X1,c(X1)) ),
inference(er,[status(thm)],[c_0_17]) ).
cnf(c_0_21,negated_conjecture,
test(esk7_0),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_22,plain,
( ~ complement(X2,X1)
| multiplication(X1,X2) = zero ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_23,negated_conjecture,
complement(esk7_0,c(esk7_0)),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_24,plain,
( ~ complement(X1,X2)
| multiplication(X1,X2) = zero ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_25,negated_conjecture,
zero = multiplication(c(esk7_0),esk7_0),
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_26,plain,
( ~ complement(X1,X2)
| multiplication(X1,X2) = multiplication(c(esk7_0),esk7_0) ),
inference(rw,[status(thm)],[c_0_24,c_0_25]) ).
fof(c_0_27,plain,
! [X15] : addition(X15,zero) = X15,
inference(variable_rename,[status(thm)],[additive_identity]) ).
fof(c_0_28,plain,
! [X10,X11] : addition(X10,X11) = addition(X11,X10),
inference(variable_rename,[status(thm)],[additive_commutativity]) ).
cnf(c_0_29,negated_conjecture,
multiplication(c(esk7_0),esk7_0) = multiplication(esk7_0,c(esk7_0)),
inference(spm,[status(thm)],[c_0_26,c_0_23]) ).
cnf(c_0_30,negated_conjecture,
test(esk6_0),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_31,plain,
addition(X1,zero) = X1,
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_32,plain,
addition(X1,X2) = addition(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_33,plain,
( ~ complement(X2,X1)
| multiplication(X1,X2) = multiplication(esk7_0,c(esk7_0)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_22,c_0_25]),c_0_29]) ).
cnf(c_0_34,negated_conjecture,
complement(esk6_0,c(esk6_0)),
inference(spm,[status(thm)],[c_0_20,c_0_30]) ).
cnf(c_0_35,plain,
( ~ complement(X2,X1)
| addition(X1,X2) = one ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_36,plain,
addition(zero,X1) = X1,
inference(spm,[status(thm)],[c_0_31,c_0_32]) ).
cnf(c_0_37,negated_conjecture,
multiplication(esk7_0,c(esk7_0)) = multiplication(c(esk6_0),esk6_0),
inference(spm,[status(thm)],[c_0_33,c_0_34]) ).
fof(c_0_38,plain,
! [X20] : multiplication(X20,one) = X20,
inference(variable_rename,[status(thm)],[multiplicative_right_identity]) ).
cnf(c_0_39,negated_conjecture,
one = addition(esk7_0,c(esk7_0)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_23]),c_0_32]) ).
fof(c_0_40,plain,
! [X21] : multiplication(one,X21) = X21,
inference(variable_rename,[status(thm)],[multiplicative_left_identity]) ).
cnf(c_0_41,plain,
addition(multiplication(c(esk7_0),esk7_0),X1) = X1,
inference(rw,[status(thm)],[c_0_36,c_0_25]) ).
cnf(c_0_42,plain,
( ~ complement(X1,X2)
| multiplication(X1,X2) = multiplication(c(esk6_0),esk6_0) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_26,c_0_29]),c_0_37]) ).
fof(c_0_43,plain,
! [X32,X34,X35] :
( ( test(X34)
| ~ complement(X35,X34) )
& ( complement(esk1_1(X32),X32)
| ~ test(X32) ) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[test_1])])])])])]) ).
cnf(c_0_44,plain,
multiplication(X1,one) = X1,
inference(split_conjunct,[status(thm)],[c_0_38]) ).
cnf(c_0_45,plain,
( ~ complement(X2,X1)
| addition(X1,X2) = addition(esk7_0,c(esk7_0)) ),
inference(rw,[status(thm)],[c_0_35,c_0_39]) ).
fof(c_0_46,plain,
! [X12,X13,X14] : addition(X14,addition(X13,X12)) = addition(addition(X14,X13),X12),
inference(variable_rename,[status(thm)],[additive_associativity]) ).
fof(c_0_47,plain,
! [X16] : addition(X16,X16) = X16,
inference(variable_rename,[status(thm)],[additive_idempotence]) ).
cnf(c_0_48,plain,
multiplication(one,X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_40]) ).
fof(c_0_49,plain,
! [X25,X26,X27] : multiplication(addition(X25,X26),X27) = addition(multiplication(X25,X27),multiplication(X26,X27)),
inference(variable_rename,[status(thm)],[left_distributivity]) ).
cnf(c_0_50,plain,
addition(multiplication(c(esk6_0),esk6_0),X1) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_41,c_0_29]),c_0_37]) ).
cnf(c_0_51,negated_conjecture,
multiplication(c(esk6_0),esk6_0) = multiplication(esk6_0,c(esk6_0)),
inference(spm,[status(thm)],[c_0_42,c_0_34]) ).
cnf(c_0_52,plain,
addition(X1,multiplication(c(esk7_0),esk7_0)) = X1,
inference(rw,[status(thm)],[c_0_31,c_0_25]) ).
cnf(c_0_53,plain,
( ~ complement(X1,X2)
| test(X2) ),
inference(split_conjunct,[status(thm)],[c_0_43]) ).
fof(c_0_54,plain,
! [X22,X23,X24] : multiplication(X22,addition(X23,X24)) = addition(multiplication(X22,X23),multiplication(X22,X24)),
inference(variable_rename,[status(thm)],[right_distributivity]) ).
cnf(c_0_55,plain,
multiplication(X1,addition(esk7_0,c(esk7_0))) = X1,
inference(rw,[status(thm)],[c_0_44,c_0_39]) ).
cnf(c_0_56,negated_conjecture,
addition(esk7_0,c(esk7_0)) = addition(esk6_0,c(esk6_0)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_34]),c_0_32]) ).
cnf(c_0_57,plain,
addition(X1,addition(X2,X3)) = addition(addition(X1,X2),X3),
inference(split_conjunct,[status(thm)],[c_0_46]) ).
cnf(c_0_58,plain,
addition(X1,X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_47]) ).
cnf(c_0_59,plain,
multiplication(addition(esk7_0,c(esk7_0)),X1) = X1,
inference(rw,[status(thm)],[c_0_48,c_0_39]) ).
cnf(c_0_60,plain,
multiplication(addition(X1,X2),X3) = addition(multiplication(X1,X3),multiplication(X2,X3)),
inference(split_conjunct,[status(thm)],[c_0_49]) ).
cnf(c_0_61,plain,
addition(multiplication(esk6_0,c(esk6_0)),X1) = X1,
inference(rw,[status(thm)],[c_0_50,c_0_51]) ).
cnf(c_0_62,plain,
addition(X1,multiplication(c(esk6_0),esk6_0)) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_52,c_0_29]),c_0_37]) ).
cnf(c_0_63,negated_conjecture,
test(c(esk7_0)),
inference(spm,[status(thm)],[c_0_53,c_0_23]) ).
fof(c_0_64,plain,
! [X28] : multiplication(X28,zero) = zero,
inference(variable_rename,[status(thm)],[right_annihilation]) ).
cnf(c_0_65,plain,
multiplication(X1,addition(X2,X3)) = addition(multiplication(X1,X2),multiplication(X1,X3)),
inference(split_conjunct,[status(thm)],[c_0_54]) ).
cnf(c_0_66,plain,
multiplication(X1,addition(esk6_0,c(esk6_0))) = X1,
inference(rw,[status(thm)],[c_0_55,c_0_56]) ).
cnf(c_0_67,plain,
addition(X1,addition(X2,X3)) = addition(X3,addition(X1,X2)),
inference(spm,[status(thm)],[c_0_32,c_0_57]) ).
cnf(c_0_68,plain,
addition(X1,addition(X1,X2)) = addition(X1,X2),
inference(spm,[status(thm)],[c_0_57,c_0_58]) ).
cnf(c_0_69,plain,
multiplication(addition(esk6_0,c(esk6_0)),X1) = X1,
inference(rw,[status(thm)],[c_0_59,c_0_56]) ).
cnf(c_0_70,plain,
multiplication(addition(esk6_0,X1),c(esk6_0)) = multiplication(X1,c(esk6_0)),
inference(spm,[status(thm)],[c_0_60,c_0_61]) ).
cnf(c_0_71,plain,
multiplication(addition(X1,c(esk6_0)),esk6_0) = multiplication(X1,esk6_0),
inference(spm,[status(thm)],[c_0_60,c_0_62]) ).
cnf(c_0_72,plain,
( ~ complement(X2,X1)
| addition(X1,X2) = addition(esk6_0,c(esk6_0)) ),
inference(rw,[status(thm)],[c_0_45,c_0_56]) ).
cnf(c_0_73,negated_conjecture,
complement(c(esk7_0),c(c(esk7_0))),
inference(spm,[status(thm)],[c_0_20,c_0_63]) ).
cnf(c_0_74,plain,
multiplication(X1,zero) = zero,
inference(split_conjunct,[status(thm)],[c_0_64]) ).
fof(c_0_75,plain,
! [X30,X31] :
( ( leq(X30,X31)
| addition(X30,X31) != X31 )
& ( addition(X30,X31) = X31
| ~ leq(X30,X31) ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[order])])]) ).
cnf(c_0_76,negated_conjecture,
multiplication(esk7_0,c(esk7_0)) = multiplication(esk6_0,c(esk6_0)),
inference(rw,[status(thm)],[c_0_37,c_0_51]) ).
cnf(c_0_77,plain,
addition(X1,multiplication(X1,X2)) = multiplication(X1,addition(esk6_0,addition(c(esk6_0),X2))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_66]),c_0_57]) ).
cnf(c_0_78,plain,
addition(X1,addition(X2,X1)) = addition(X2,X1),
inference(spm,[status(thm)],[c_0_67,c_0_58]) ).
fof(c_0_79,plain,
! [X17,X18,X19] : multiplication(X17,multiplication(X18,X19)) = multiplication(multiplication(X17,X18),X19),
inference(variable_rename,[status(thm)],[multiplicative_associativity]) ).
cnf(c_0_80,negated_conjecture,
multiplication(c(esk7_0),esk7_0) = multiplication(c(esk6_0),esk6_0),
inference(rw,[status(thm)],[c_0_29,c_0_37]) ).
cnf(c_0_81,plain,
addition(multiplication(addition(X1,X2),X3),X4) = addition(multiplication(X1,X3),addition(multiplication(X2,X3),X4)),
inference(spm,[status(thm)],[c_0_57,c_0_60]) ).
cnf(c_0_82,negated_conjecture,
addition(esk6_0,addition(c(esk6_0),esk7_0)) = addition(esk6_0,c(esk6_0)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_56]),c_0_32]),c_0_57]) ).
cnf(c_0_83,plain,
multiplication(c(esk6_0),c(esk6_0)) = c(esk6_0),
inference(spm,[status(thm)],[c_0_69,c_0_70]) ).
cnf(c_0_84,plain,
multiplication(esk6_0,esk6_0) = esk6_0,
inference(spm,[status(thm)],[c_0_69,c_0_71]) ).
cnf(c_0_85,negated_conjecture,
addition(c(esk7_0),c(c(esk7_0))) = addition(esk6_0,c(esk6_0)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_72,c_0_73]),c_0_32]) ).
cnf(c_0_86,plain,
multiplication(X1,multiplication(c(esk7_0),esk7_0)) = multiplication(c(esk7_0),esk7_0),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_74,c_0_25]),c_0_25]) ).
cnf(c_0_87,negated_conjecture,
( ~ leq(addition(multiplication(esk7_0,addition(multiplication(esk6_0,esk2_0),multiplication(c(esk6_0),esk4_0))),multiplication(c(esk7_0),addition(multiplication(esk6_0,esk3_0),multiplication(c(esk6_0),esk5_0)))),addition(multiplication(esk6_0,addition(multiplication(esk7_0,esk2_0),multiplication(c(esk7_0),esk3_0))),multiplication(c(esk6_0),addition(multiplication(esk7_0,esk4_0),multiplication(c(esk7_0),esk5_0)))))
| ~ leq(addition(multiplication(esk6_0,addition(multiplication(esk7_0,esk2_0),multiplication(c(esk7_0),esk3_0))),multiplication(c(esk6_0),addition(multiplication(esk7_0,esk4_0),multiplication(c(esk7_0),esk5_0)))),addition(multiplication(esk7_0,addition(multiplication(esk6_0,esk2_0),multiplication(c(esk6_0),esk4_0))),multiplication(c(esk7_0),addition(multiplication(esk6_0,esk3_0),multiplication(c(esk6_0),esk5_0))))) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_88,plain,
( addition(X1,X2) != X2
| leq(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_75]) ).
cnf(c_0_89,negated_conjecture,
multiplication(addition(esk7_0,X1),c(esk7_0)) = multiplication(X1,c(esk7_0)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_76]),c_0_61]) ).
cnf(c_0_90,plain,
addition(X1,multiplication(X1,esk6_0)) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_78]),c_0_32]),c_0_66]) ).
cnf(c_0_91,plain,
multiplication(X1,multiplication(X2,X3)) = multiplication(multiplication(X1,X2),X3),
inference(split_conjunct,[status(thm)],[c_0_79]) ).
cnf(c_0_92,negated_conjecture,
multiplication(addition(c(esk7_0),X1),esk7_0) = multiplication(X1,esk7_0),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_80]),c_0_50]) ).
cnf(c_0_93,plain,
addition(multiplication(X1,X2),addition(multiplication(c(esk6_0),X2),multiplication(X1,esk6_0))) = multiplication(addition(X1,c(esk6_0)),addition(X2,esk6_0)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_71]),c_0_81]) ).
cnf(c_0_94,negated_conjecture,
multiplication(addition(c(esk6_0),esk7_0),c(esk6_0)) = c(esk6_0),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_82]),c_0_70]),c_0_83]) ).
cnf(c_0_95,plain,
multiplication(addition(c(esk6_0),X1),esk6_0) = multiplication(X1,esk6_0),
inference(spm,[status(thm)],[c_0_60,c_0_50]) ).
cnf(c_0_96,plain,
addition(esk6_0,multiplication(esk6_0,X1)) = multiplication(esk6_0,addition(esk6_0,X1)),
inference(spm,[status(thm)],[c_0_65,c_0_84]) ).
cnf(c_0_97,negated_conjecture,
addition(X1,multiplication(X1,esk7_0)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_82]),c_0_66]) ).
cnf(c_0_98,negated_conjecture,
addition(esk6_0,addition(c(esk6_0),c(esk7_0))) = addition(esk6_0,c(esk6_0)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_85]),c_0_32]),c_0_57]) ).
cnf(c_0_99,plain,
multiplication(X1,multiplication(esk7_0,c(esk7_0))) = multiplication(esk7_0,c(esk7_0)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_86,c_0_29]),c_0_29]) ).
cnf(c_0_100,negated_conjecture,
( ~ leq(addition(multiplication(esk6_0,addition(multiplication(esk7_0,esk2_0),multiplication(c(esk7_0),esk3_0))),multiplication(c(esk6_0),addition(multiplication(esk7_0,esk4_0),multiplication(c(esk7_0),esk5_0)))),addition(multiplication(esk7_0,addition(multiplication(esk6_0,esk2_0),multiplication(c(esk6_0),esk4_0))),multiplication(c(esk7_0),addition(multiplication(esk6_0,esk3_0),multiplication(c(esk6_0),esk5_0)))))
| addition(multiplication(esk7_0,addition(multiplication(esk6_0,esk2_0),multiplication(c(esk6_0),esk4_0))),addition(multiplication(c(esk7_0),addition(multiplication(esk6_0,esk3_0),multiplication(c(esk6_0),esk5_0))),addition(multiplication(esk6_0,addition(multiplication(esk7_0,esk2_0),multiplication(c(esk7_0),esk3_0))),multiplication(c(esk6_0),addition(multiplication(esk7_0,esk4_0),multiplication(c(esk7_0),esk5_0)))))) != addition(multiplication(esk6_0,addition(multiplication(esk7_0,esk2_0),multiplication(c(esk7_0),esk3_0))),multiplication(c(esk6_0),addition(multiplication(esk7_0,esk4_0),multiplication(c(esk7_0),esk5_0)))) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_87,c_0_88]),c_0_57]) ).
cnf(c_0_101,negated_conjecture,
multiplication(esk7_0,multiplication(esk6_0,c(esk7_0))) = multiplication(esk6_0,c(esk6_0)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_89,c_0_90]),c_0_37]),c_0_51]),c_0_91]) ).
cnf(c_0_102,negated_conjecture,
multiplication(addition(X1,c(esk7_0)),esk7_0) = multiplication(X1,esk7_0),
inference(spm,[status(thm)],[c_0_92,c_0_32]) ).
cnf(c_0_103,plain,
addition(X1,multiplication(esk6_0,c(esk6_0))) = X1,
inference(rw,[status(thm)],[c_0_62,c_0_51]) ).
cnf(c_0_104,plain,
multiplication(esk6_0,addition(c(esk6_0),X1)) = multiplication(esk6_0,X1),
inference(spm,[status(thm)],[c_0_65,c_0_61]) ).
cnf(c_0_105,negated_conjecture,
addition(c(esk6_0),multiplication(esk7_0,esk6_0)) = addition(c(esk6_0),esk7_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_93,c_0_94]),c_0_83]),c_0_95]),c_0_68]),c_0_57]),c_0_78]),c_0_32]),c_0_32]),c_0_66]) ).
cnf(c_0_106,plain,
addition(multiplication(X1,addition(X2,X3)),X4) = addition(multiplication(X1,X2),addition(multiplication(X1,X3),X4)),
inference(spm,[status(thm)],[c_0_57,c_0_65]) ).
cnf(c_0_107,negated_conjecture,
multiplication(esk6_0,addition(esk6_0,esk7_0)) = esk6_0,
inference(spm,[status(thm)],[c_0_96,c_0_97]) ).
cnf(c_0_108,negated_conjecture,
multiplication(addition(c(esk6_0),c(esk7_0)),c(esk6_0)) = c(esk6_0),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_98]),c_0_70]),c_0_83]) ).
cnf(c_0_109,negated_conjecture,
addition(X1,multiplication(X1,c(esk7_0))) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_98]),c_0_66]) ).
cnf(c_0_110,plain,
addition(multiplication(X1,esk6_0),multiplication(addition(X1,c(esk6_0)),X2)) = multiplication(addition(X1,c(esk6_0)),addition(esk6_0,X2)),
inference(spm,[status(thm)],[c_0_65,c_0_71]) ).
cnf(c_0_111,plain,
multiplication(X1,multiplication(c(esk6_0),esk6_0)) = multiplication(c(esk6_0),esk6_0),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_99,c_0_37]),c_0_37]) ).
cnf(c_0_112,negated_conjecture,
( addition(multiplication(esk6_0,addition(multiplication(esk7_0,esk2_0),multiplication(c(esk7_0),esk3_0))),addition(multiplication(c(esk6_0),addition(multiplication(esk7_0,esk4_0),multiplication(c(esk7_0),esk5_0))),addition(multiplication(esk7_0,addition(multiplication(esk6_0,esk2_0),multiplication(c(esk6_0),esk4_0))),multiplication(c(esk7_0),addition(multiplication(esk6_0,esk3_0),multiplication(c(esk6_0),esk5_0)))))) != addition(multiplication(esk7_0,addition(multiplication(esk6_0,esk2_0),multiplication(c(esk6_0),esk4_0))),multiplication(c(esk7_0),addition(multiplication(esk6_0,esk3_0),multiplication(c(esk6_0),esk5_0))))
| addition(multiplication(esk7_0,addition(multiplication(esk6_0,esk2_0),multiplication(c(esk6_0),esk4_0))),addition(multiplication(c(esk7_0),addition(multiplication(esk6_0,esk3_0),multiplication(c(esk6_0),esk5_0))),addition(multiplication(esk6_0,addition(multiplication(esk7_0,esk2_0),multiplication(c(esk7_0),esk3_0))),multiplication(c(esk6_0),addition(multiplication(esk7_0,esk4_0),multiplication(c(esk7_0),esk5_0)))))) != addition(multiplication(esk6_0,addition(multiplication(esk7_0,esk2_0),multiplication(c(esk7_0),esk3_0))),multiplication(c(esk6_0),addition(multiplication(esk7_0,esk4_0),multiplication(c(esk7_0),esk5_0)))) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_100,c_0_88]),c_0_57]) ).
cnf(c_0_113,negated_conjecture,
multiplication(esk7_0,addition(multiplication(esk6_0,c(esk7_0)),X1)) = multiplication(esk7_0,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_101]),c_0_61]) ).
cnf(c_0_114,negated_conjecture,
addition(multiplication(X1,X2),addition(multiplication(c(esk7_0),X2),multiplication(X1,esk7_0))) = multiplication(addition(X1,c(esk7_0)),addition(X2,esk7_0)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_102]),c_0_81]) ).
cnf(c_0_115,negated_conjecture,
multiplication(esk7_0,addition(X1,c(esk7_0))) = multiplication(esk7_0,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_76]),c_0_103]) ).
cnf(c_0_116,negated_conjecture,
multiplication(c(esk7_0),c(esk7_0)) = c(esk7_0),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_89,c_0_56]),c_0_69]) ).
cnf(c_0_117,negated_conjecture,
multiplication(esk7_0,addition(c(esk7_0),X1)) = multiplication(esk7_0,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_76]),c_0_61]) ).
cnf(c_0_118,plain,
addition(X1,multiplication(X2,X1)) = multiplication(addition(esk6_0,addition(c(esk6_0),X2)),X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_69]),c_0_57]) ).
cnf(c_0_119,negated_conjecture,
multiplication(esk6_0,multiplication(esk7_0,esk6_0)) = multiplication(esk6_0,esk7_0),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_104,c_0_105]),c_0_104]) ).
cnf(c_0_120,negated_conjecture,
multiplication(esk6_0,multiplication(esk7_0,c(esk6_0))) = multiplication(esk6_0,c(esk6_0)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_97]),c_0_91]) ).
cnf(c_0_121,negated_conjecture,
addition(esk6_0,addition(multiplication(esk6_0,esk7_0),X1)) = addition(esk6_0,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_106,c_0_107]),c_0_84]) ).
cnf(c_0_122,negated_conjecture,
addition(c(esk6_0),multiplication(c(esk7_0),esk6_0)) = addition(c(esk6_0),c(esk7_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_93,c_0_108]),c_0_83]),c_0_95]),c_0_68]),c_0_57]),c_0_78]),c_0_32]),c_0_32]),c_0_66]) ).
cnf(c_0_123,negated_conjecture,
multiplication(esk6_0,multiplication(c(esk7_0),c(esk6_0))) = multiplication(esk6_0,c(esk6_0)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_109]),c_0_91]) ).
cnf(c_0_124,negated_conjecture,
multiplication(esk6_0,addition(esk6_0,c(esk7_0))) = esk6_0,
inference(spm,[status(thm)],[c_0_96,c_0_109]) ).
cnf(c_0_125,plain,
multiplication(c(esk6_0),addition(esk6_0,X1)) = multiplication(c(esk6_0),X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_110,c_0_61]),c_0_91]),c_0_111]),c_0_51]),c_0_61]) ).
cnf(c_0_126,negated_conjecture,
( addition(multiplication(esk6_0,addition(multiplication(esk7_0,esk2_0),multiplication(c(esk7_0),esk3_0))),addition(multiplication(esk7_0,addition(multiplication(esk6_0,esk2_0),multiplication(c(esk6_0),esk4_0))),addition(multiplication(c(esk7_0),addition(multiplication(esk6_0,esk3_0),multiplication(c(esk6_0),esk5_0))),multiplication(c(esk6_0),addition(multiplication(esk7_0,esk4_0),multiplication(c(esk7_0),esk5_0)))))) != addition(multiplication(esk7_0,addition(multiplication(esk6_0,esk2_0),multiplication(c(esk6_0),esk4_0))),multiplication(c(esk7_0),addition(multiplication(esk6_0,esk3_0),multiplication(c(esk6_0),esk5_0))))
| addition(multiplication(esk7_0,addition(multiplication(esk6_0,esk2_0),multiplication(c(esk6_0),esk4_0))),addition(multiplication(c(esk7_0),addition(multiplication(esk6_0,esk3_0),multiplication(c(esk6_0),esk5_0))),addition(multiplication(esk6_0,addition(multiplication(esk7_0,esk2_0),multiplication(c(esk7_0),esk3_0))),multiplication(c(esk6_0),addition(multiplication(esk7_0,esk4_0),multiplication(c(esk7_0),esk5_0)))))) != addition(multiplication(esk6_0,addition(multiplication(esk7_0,esk2_0),multiplication(c(esk7_0),esk3_0))),multiplication(c(esk6_0),addition(multiplication(esk7_0,esk4_0),multiplication(c(esk7_0),esk5_0)))) ),
inference(rw,[status(thm)],[c_0_112,c_0_67]) ).
cnf(c_0_127,plain,
addition(X1,addition(X2,X3)) = addition(X2,addition(X1,X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_32]),c_0_57]) ).
cnf(c_0_128,negated_conjecture,
multiplication(esk7_0,multiplication(esk6_0,esk7_0)) = multiplication(esk7_0,esk6_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_113,c_0_114]),c_0_32]),c_0_56]),c_0_66]),c_0_115]),c_0_116]),c_0_117]) ).
cnf(c_0_129,negated_conjecture,
addition(multiplication(esk6_0,esk7_0),multiplication(esk7_0,esk6_0)) = multiplication(esk7_0,esk6_0),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_118,c_0_119]),c_0_32]),c_0_68]),c_0_69]),c_0_32]) ).
cnf(c_0_130,negated_conjecture,
addition(X1,multiplication(esk7_0,multiplication(esk6_0,X1))) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_118,c_0_105]),c_0_91]),c_0_82]),c_0_69]) ).
cnf(c_0_131,negated_conjecture,
multiplication(esk6_0,addition(esk6_0,multiplication(esk7_0,c(esk6_0)))) = esk6_0,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_96,c_0_120]),c_0_103]) ).
cnf(c_0_132,negated_conjecture,
addition(esk6_0,multiplication(c(esk6_0),esk7_0)) = addition(esk6_0,esk7_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_121,c_0_93]),c_0_32]),c_0_69]),c_0_68]),c_0_84]),c_0_78]),c_0_32]) ).
cnf(c_0_133,negated_conjecture,
addition(esk7_0,addition(c(esk7_0),X1)) = addition(esk6_0,addition(c(esk6_0),X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_56]),c_0_57]) ).
cnf(c_0_134,plain,
addition(X1,multiplication(esk6_0,X1)) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_118,c_0_78]),c_0_32]),c_0_69]) ).
cnf(c_0_135,negated_conjecture,
addition(X1,multiplication(c(esk7_0),multiplication(esk6_0,X1))) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_118,c_0_122]),c_0_91]),c_0_98]),c_0_69]) ).
cnf(c_0_136,negated_conjecture,
multiplication(esk6_0,addition(esk6_0,multiplication(c(esk7_0),c(esk6_0)))) = esk6_0,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_96,c_0_123]),c_0_103]) ).
cnf(c_0_137,negated_conjecture,
addition(esk6_0,multiplication(c(esk6_0),c(esk7_0))) = addition(esk6_0,c(esk7_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_93,c_0_124]),c_0_125]),c_0_84]),c_0_78]),c_0_57]),c_0_78]),c_0_32]),c_0_69]),c_0_32]) ).
cnf(c_0_138,negated_conjecture,
( addition(multiplication(esk6_0,addition(multiplication(esk7_0,esk2_0),multiplication(c(esk7_0),esk3_0))),addition(multiplication(esk7_0,addition(multiplication(esk6_0,esk2_0),multiplication(c(esk6_0),esk4_0))),addition(multiplication(c(esk7_0),addition(multiplication(esk6_0,esk3_0),multiplication(c(esk6_0),esk5_0))),multiplication(c(esk6_0),addition(multiplication(esk7_0,esk4_0),multiplication(c(esk7_0),esk5_0)))))) != addition(multiplication(esk7_0,addition(multiplication(esk6_0,esk2_0),multiplication(c(esk6_0),esk4_0))),multiplication(c(esk7_0),addition(multiplication(esk6_0,esk3_0),multiplication(c(esk6_0),esk5_0))))
| addition(multiplication(esk6_0,addition(multiplication(esk7_0,esk2_0),multiplication(c(esk7_0),esk3_0))),addition(multiplication(esk7_0,addition(multiplication(esk6_0,esk2_0),multiplication(c(esk6_0),esk4_0))),addition(multiplication(c(esk7_0),addition(multiplication(esk6_0,esk3_0),multiplication(c(esk6_0),esk5_0))),multiplication(c(esk6_0),addition(multiplication(esk7_0,esk4_0),multiplication(c(esk7_0),esk5_0)))))) != addition(multiplication(esk6_0,addition(multiplication(esk7_0,esk2_0),multiplication(c(esk7_0),esk3_0))),multiplication(c(esk6_0),addition(multiplication(esk7_0,esk4_0),multiplication(c(esk7_0),esk5_0)))) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_126,c_0_127]),c_0_127]) ).
cnf(c_0_139,negated_conjecture,
multiplication(esk7_0,esk6_0) = multiplication(esk6_0,esk7_0),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_118,c_0_128]),c_0_129]),c_0_82]),c_0_69]) ).
cnf(c_0_140,negated_conjecture,
addition(esk6_0,multiplication(esk7_0,c(esk6_0))) = addition(esk6_0,esk7_0),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_130,c_0_131]),c_0_57]),c_0_65]),c_0_32]),c_0_66]) ).
cnf(c_0_141,negated_conjecture,
multiplication(c(esk6_0),multiplication(esk7_0,c(esk6_0))) = multiplication(esk7_0,c(esk6_0)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_132]),c_0_70]),c_0_91]) ).
cnf(c_0_142,negated_conjecture,
addition(X1,multiplication(c(esk7_0),X1)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_118,c_0_98]),c_0_69]) ).
cnf(c_0_143,negated_conjecture,
addition(esk6_0,addition(c(esk6_0),multiplication(esk6_0,c(esk7_0)))) = addition(esk6_0,c(esk6_0)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_133,c_0_134]),c_0_56]) ).
cnf(c_0_144,negated_conjecture,
addition(esk6_0,multiplication(c(esk7_0),c(esk6_0))) = addition(esk6_0,c(esk7_0)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_135,c_0_136]),c_0_57]),c_0_65]),c_0_32]),c_0_66]) ).
cnf(c_0_145,negated_conjecture,
multiplication(c(esk6_0),multiplication(c(esk7_0),c(esk6_0))) = multiplication(c(esk7_0),c(esk6_0)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_137]),c_0_70]),c_0_91]) ).
cnf(c_0_146,negated_conjecture,
( addition(multiplication(esk6_0,multiplication(esk7_0,esk2_0)),addition(multiplication(esk7_0,multiplication(esk6_0,esk2_0)),addition(multiplication(esk6_0,multiplication(c(esk7_0),esk3_0)),addition(multiplication(c(esk7_0),multiplication(esk6_0,esk3_0)),addition(multiplication(esk7_0,multiplication(c(esk6_0),esk4_0)),addition(multiplication(c(esk7_0),multiplication(c(esk6_0),esk5_0)),multiplication(c(esk6_0),addition(multiplication(esk7_0,esk4_0),multiplication(c(esk7_0),esk5_0))))))))) != addition(multiplication(esk7_0,multiplication(esk6_0,esk2_0)),addition(multiplication(esk7_0,multiplication(c(esk6_0),esk4_0)),multiplication(c(esk7_0),addition(multiplication(esk6_0,esk3_0),multiplication(c(esk6_0),esk5_0)))))
| addition(multiplication(esk6_0,multiplication(esk7_0,esk2_0)),addition(multiplication(esk7_0,multiplication(esk6_0,esk2_0)),addition(multiplication(esk6_0,multiplication(c(esk7_0),esk3_0)),addition(multiplication(c(esk7_0),multiplication(esk6_0,esk3_0)),addition(multiplication(esk7_0,multiplication(c(esk6_0),esk4_0)),addition(multiplication(c(esk7_0),multiplication(c(esk6_0),esk5_0)),multiplication(c(esk6_0),addition(multiplication(esk7_0,esk4_0),multiplication(c(esk7_0),esk5_0))))))))) != addition(multiplication(esk6_0,multiplication(esk7_0,esk2_0)),addition(multiplication(esk6_0,multiplication(c(esk7_0),esk3_0)),multiplication(c(esk6_0),addition(multiplication(esk7_0,esk4_0),multiplication(c(esk7_0),esk5_0))))) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_138,c_0_106]),c_0_106]),c_0_106]),c_0_127]),c_0_127]),c_0_106]),c_0_106]),c_0_106]),c_0_106]),c_0_127]),c_0_127]),c_0_106]) ).
cnf(c_0_147,negated_conjecture,
multiplication(esk7_0,multiplication(esk6_0,X1)) = multiplication(esk6_0,multiplication(esk7_0,X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_91,c_0_139]),c_0_91]) ).
cnf(c_0_148,negated_conjecture,
multiplication(esk7_0,c(esk6_0)) = multiplication(c(esk6_0),esk7_0),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_125,c_0_140]),c_0_125]),c_0_141]) ).
cnf(c_0_149,negated_conjecture,
addition(X1,multiplication(c(esk7_0),multiplication(c(esk6_0),X1))) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_118,c_0_142]),c_0_91]),c_0_69]) ).
cnf(c_0_150,negated_conjecture,
multiplication(c(esk6_0),addition(c(esk6_0),multiplication(esk6_0,c(esk7_0)))) = c(esk6_0),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_125,c_0_143]),c_0_66]) ).
cnf(c_0_151,negated_conjecture,
multiplication(c(esk7_0),c(esk6_0)) = multiplication(c(esk6_0),c(esk7_0)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_125,c_0_144]),c_0_125]),c_0_145]) ).
cnf(c_0_152,negated_conjecture,
( addition(multiplication(esk6_0,multiplication(esk7_0,esk2_0)),addition(multiplication(esk6_0,multiplication(c(esk7_0),esk3_0)),addition(multiplication(c(esk7_0),multiplication(esk6_0,esk3_0)),addition(multiplication(esk7_0,multiplication(c(esk6_0),esk4_0)),addition(multiplication(c(esk7_0),multiplication(c(esk6_0),esk5_0)),multiplication(c(esk6_0),addition(multiplication(esk7_0,esk4_0),multiplication(c(esk7_0),esk5_0)))))))) != addition(multiplication(esk6_0,multiplication(esk7_0,esk2_0)),addition(multiplication(esk7_0,multiplication(c(esk6_0),esk4_0)),multiplication(c(esk7_0),addition(multiplication(esk6_0,esk3_0),multiplication(c(esk6_0),esk5_0)))))
| addition(multiplication(esk6_0,multiplication(esk7_0,esk2_0)),addition(multiplication(esk6_0,multiplication(c(esk7_0),esk3_0)),addition(multiplication(c(esk7_0),multiplication(esk6_0,esk3_0)),addition(multiplication(esk7_0,multiplication(c(esk6_0),esk4_0)),addition(multiplication(c(esk7_0),multiplication(c(esk6_0),esk5_0)),multiplication(c(esk6_0),addition(multiplication(esk7_0,esk4_0),multiplication(c(esk7_0),esk5_0)))))))) != addition(multiplication(esk6_0,multiplication(esk7_0,esk2_0)),addition(multiplication(esk6_0,multiplication(c(esk7_0),esk3_0)),multiplication(c(esk6_0),addition(multiplication(esk7_0,esk4_0),multiplication(c(esk7_0),esk5_0))))) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_146,c_0_147]),c_0_68]),c_0_147]),c_0_68]),c_0_147]) ).
cnf(c_0_153,plain,
addition(multiplication(X1,X2),addition(multiplication(X1,X3),X4)) = addition(X4,multiplication(X1,addition(X2,X3))),
inference(spm,[status(thm)],[c_0_67,c_0_65]) ).
cnf(c_0_154,negated_conjecture,
multiplication(esk7_0,multiplication(c(esk6_0),X1)) = multiplication(c(esk6_0),multiplication(esk7_0,X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_91,c_0_148]),c_0_91]) ).
cnf(c_0_155,negated_conjecture,
addition(c(esk6_0),multiplication(esk6_0,c(esk7_0))) = addition(c(esk6_0),c(esk7_0)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_149,c_0_150]),c_0_151]),c_0_57]),c_0_60]),c_0_69]) ).
cnf(c_0_156,negated_conjecture,
multiplication(esk6_0,multiplication(c(esk7_0),esk6_0)) = multiplication(esk6_0,c(esk7_0)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_104,c_0_122]),c_0_104]) ).
cnf(c_0_157,negated_conjecture,
( addition(multiplication(esk6_0,multiplication(esk7_0,esk2_0)),addition(multiplication(esk6_0,multiplication(c(esk7_0),esk3_0)),addition(multiplication(c(esk7_0),multiplication(esk6_0,esk3_0)),addition(multiplication(c(esk6_0),multiplication(esk7_0,esk4_0)),addition(multiplication(c(esk6_0),multiplication(c(esk7_0),esk5_0)),multiplication(c(esk7_0),multiplication(c(esk6_0),esk5_0))))))) != addition(multiplication(esk6_0,multiplication(esk7_0,esk2_0)),addition(multiplication(c(esk6_0),multiplication(esk7_0,esk4_0)),multiplication(c(esk7_0),addition(multiplication(esk6_0,esk3_0),multiplication(c(esk6_0),esk5_0)))))
| addition(multiplication(esk6_0,multiplication(esk7_0,esk2_0)),addition(multiplication(esk6_0,multiplication(c(esk7_0),esk3_0)),addition(multiplication(c(esk7_0),multiplication(esk6_0,esk3_0)),addition(multiplication(c(esk6_0),multiplication(esk7_0,esk4_0)),addition(multiplication(c(esk6_0),multiplication(c(esk7_0),esk5_0)),multiplication(c(esk7_0),multiplication(c(esk6_0),esk5_0))))))) != addition(multiplication(esk6_0,multiplication(esk7_0,esk2_0)),addition(multiplication(esk6_0,multiplication(c(esk7_0),esk3_0)),multiplication(c(esk6_0),addition(multiplication(esk7_0,esk4_0),multiplication(c(esk7_0),esk5_0))))) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_152,c_0_153]),c_0_154]),c_0_68]),c_0_154]),c_0_68]),c_0_154]) ).
cnf(c_0_158,plain,
addition(multiplication(X1,X2),addition(X3,multiplication(X1,X4))) = addition(X3,multiplication(X1,addition(X2,X4))),
inference(spm,[status(thm)],[c_0_127,c_0_65]) ).
cnf(c_0_159,negated_conjecture,
multiplication(c(esk7_0),esk6_0) = multiplication(esk6_0,c(esk7_0)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_95,c_0_155]),c_0_95]),c_0_91]),c_0_156]) ).
cnf(c_0_160,negated_conjecture,
( addition(multiplication(esk6_0,multiplication(esk7_0,esk2_0)),addition(multiplication(esk6_0,multiplication(c(esk7_0),esk3_0)),addition(multiplication(c(esk7_0),multiplication(esk6_0,esk3_0)),addition(multiplication(c(esk6_0),multiplication(esk7_0,esk4_0)),addition(multiplication(c(esk6_0),multiplication(c(esk7_0),esk5_0)),multiplication(c(esk7_0),multiplication(c(esk6_0),esk5_0))))))) != addition(multiplication(esk6_0,multiplication(esk7_0,esk2_0)),addition(multiplication(esk6_0,multiplication(c(esk7_0),esk3_0)),multiplication(c(esk6_0),addition(multiplication(esk7_0,esk4_0),multiplication(c(esk7_0),esk5_0)))))
| addition(multiplication(esk6_0,multiplication(esk7_0,esk2_0)),addition(multiplication(esk6_0,multiplication(c(esk7_0),esk3_0)),addition(multiplication(c(esk7_0),multiplication(esk6_0,esk3_0)),addition(multiplication(c(esk6_0),multiplication(esk7_0,esk4_0)),addition(multiplication(c(esk6_0),multiplication(c(esk7_0),esk5_0)),multiplication(c(esk7_0),multiplication(c(esk6_0),esk5_0))))))) != addition(multiplication(esk6_0,multiplication(esk7_0,esk2_0)),addition(multiplication(c(esk7_0),multiplication(esk6_0,esk3_0)),addition(multiplication(c(esk6_0),multiplication(esk7_0,esk4_0)),multiplication(c(esk7_0),multiplication(c(esk6_0),esk5_0))))) ),
inference(rw,[status(thm)],[c_0_157,c_0_158]) ).
cnf(c_0_161,negated_conjecture,
multiplication(c(esk7_0),multiplication(c(esk6_0),X1)) = multiplication(c(esk6_0),multiplication(c(esk7_0),X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_91,c_0_151]),c_0_91]) ).
cnf(c_0_162,negated_conjecture,
multiplication(c(esk7_0),multiplication(esk6_0,X1)) = multiplication(esk6_0,multiplication(c(esk7_0),X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_91,c_0_159]),c_0_91]) ).
cnf(c_0_163,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(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_160,c_0_161]),c_0_162]),c_0_58]),c_0_65]),c_0_68]),c_0_162]),c_0_65]),c_0_162]),c_0_58]),c_0_65]),c_0_68])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : KLE028+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.36 % Computer : n001.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sun Sep 20 22:45:27 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.13/0.43 Running first-order theorem proving
% 0.13/0.44 Running: /export/starexec/sandbox2/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 15.64/2.60 % Version: 3.5.1
% 15.64/2.60 % Preprocessing class: FSMSSMSSSSSNFFN.
% 15.64/2.60 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 15.64/2.60 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 15.64/2.60 % Starting new_bool_3 with 300s (1) cores
% 15.64/2.60 % Starting new_bool_1 with 300s (1) cores
% 15.64/2.60 % Starting sh5l with 300s (1) cores
% 15.64/2.60 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 1568460 completed with status 0
% 15.64/2.60 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 15.64/2.60 % Preprocessing class: FSMSSMSSSSSNFFN.
% 15.64/2.60 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 15.64/2.60 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 15.64/2.60 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 15.64/2.60 % No SInE strategy applied
% 15.64/2.60 % Search class: FGHSM-FFMF21-MFFFFFNN
% 15.64/2.60 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 15.64/2.60 % Starting SubtermCWHack with 136s (1) cores
% 15.64/2.60 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 15.64/2.60 % Starting U----_210g_02_B07_00_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 15.64/2.60 % Starting G-E--_208_B00_00_F1_SE_CS_SP_PS_S00EN with 136s (1) cores
% 15.64/2.60 % Starting new_bool_3 with 136s (1) cores
% 15.64/2.60 % U----_210g_02_B07_00_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with pid 1568466 completed with status 0
% 15.64/2.60 % Result found by U----_210g_02_B07_00_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN
% 15.64/2.60 % Preprocessing class: FSMSSMSSSSSNFFN.
% 15.64/2.60 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 15.64/2.60 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 15.64/2.60 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 15.64/2.60 % No SInE strategy applied
% 15.64/2.60 % Search class: FGHSM-FFMF21-MFFFFFNN
% 15.64/2.60 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 15.64/2.60 % Starting SubtermCWHack with 136s (1) cores
% 15.64/2.60 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 15.64/2.60 % Starting U----_210g_02_B07_00_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 15.64/2.60 % Preprocessing time : 0.002 s
% 15.64/2.60 % Presaturation interreduction done
% 15.64/2.60
% 15.64/2.60 % Proof found!
% 15.64/2.60 % SZS status Theorem
% 15.64/2.60 % SZS output start CNFRefutation
% See solution above
% 16.16/2.60 % Parsed axioms : 17
% 16.16/2.60 % Removed by relevancy pruning/SinE : 0
% 16.16/2.60 % Initial clauses : 25
% 16.16/2.60 % Removed in clause preprocessing : 0
% 16.16/2.60 % Initial clauses in saturation : 25
% 16.16/2.60 % Processed clauses : 8696
% 16.16/2.60 % ...of these trivial : 2972
% 16.16/2.60 % ...subsumed : 4056
% 16.16/2.60 % ...remaining for further processing : 1668
% 16.16/2.60 % Other redundant clauses eliminated : 221
% 16.16/2.60 % Clauses deleted for lack of memory : 0
% 16.16/2.60 % Backward-subsumed : 276
% 16.16/2.60 % Backward-rewritten : 368
% 16.16/2.60 % Generated clauses : 106379
% 16.16/2.60 % ...of the previous two non-redundant : 69350
% 16.16/2.60 % ...aggressively subsumed : 0
% 16.16/2.60 % Contextual simplify-reflections : 9
% 16.16/2.60 % Paramodulations : 106156
% 16.16/2.60 % Factorizations : 0
% 16.16/2.60 % NegExts : 0
% 16.16/2.60 % Equation resolutions : 223
% 16.16/2.60 % Disequality decompositions : 0
% 16.16/2.60 % Total rewrite steps : 311984
% 16.16/2.60 % ...of those cached : 275244
% 16.16/2.60 % Propositional unsat checks : 0
% 16.16/2.60 % Propositional check models : 0
% 16.16/2.60 % Propositional check unsatisfiable : 0
% 16.16/2.60 % Propositional clauses : 0
% 16.16/2.60 % Propositional clauses after purity: 0
% 16.16/2.60 % Propositional unsat core size : 0
% 16.16/2.60 % Propositional preprocessing time : 0.000
% 16.16/2.60 % Propositional encoding time : 0.000
% 16.16/2.60 % Propositional solver time : 0.000
% 16.16/2.60 % Success case prop preproc time : 0.000
% 16.16/2.60 % Success case prop encoding time : 0.000
% 16.16/2.60 % Success case prop solver time : 0.000
% 16.16/2.60 % Current number of processed clauses : 998
% 16.16/2.60 % Positive orientable unit clauses : 602
% 16.16/2.60 % Positive unorientable unit clauses: 29
% 16.16/2.60 % Negative unit clauses : 3
% 16.16/2.60 % Non-unit-clauses : 364
% 16.16/2.60 % Current number of unprocessed clauses: 58805
% 16.16/2.60 % ...number of literals in the above : 77314
% 16.16/2.60 % Current number of archived formulas : 0
% 16.16/2.60 % Current number of archived clauses : 669
% 16.16/2.60 % Clause-clause subsumption calls (NU) : 134877
% 16.16/2.60 % Rec. Clause-clause subsumption calls : 108806
% 16.16/2.60 % Non-unit clause-clause subsumptions : 2755
% 16.16/2.60 % Unit Clause-clause subsumption calls : 10253
% 16.16/2.60 % Rewrite failures with RHS unbound : 0
% 16.16/2.60 % BW rewrite match attempts : 5148
% 16.16/2.60 % BW rewrite match successes : 788
% 16.16/2.60 % Condensation attempts : 0
% 16.16/2.60 % Condensation successes : 0
% 16.16/2.60 % Termbank termtop insertions : 2325046
% 16.16/2.60 % Search garbage collected termcells : 218
% 16.16/2.60
% 16.16/2.60 % -------------------------------------------------
% 16.16/2.60 % User time : 1.938 s
% 16.16/2.60 % System time : 0.078 s
% 16.16/2.60 % Total time : 2.017 s
% 16.16/2.60 % Maximum resident set size: 3656 pages
% 16.16/2.60
% 16.16/2.60 % -------------------------------------------------
% 16.16/2.60 % User time : 9.359 s
% 16.16/2.60 % System time : 0.391 s
% 16.16/2.60 % Total time : 9.750 s
% 16.16/2.60 % Maximum resident set size: 4864 pages
% 16.16/2.60 % E exiting
%------------------------------------------------------------------------------