%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : KLE011+1 : TPTP v9.2.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n002.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 5 04:35:28 PM UTC 2026
% Result : Theorem 1.40s 1.78s
% Output : CNFRefutation 1.40s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 11
% Syntax : Number of formulae : 60 ( 47 unt; 0 def)
% Number of atoms : 94 ( 57 equ)
% Maximal formula atoms : 10 ( 1 avg)
% Number of connectives : 59 ( 25 ~; 17 |; 11 &)
% ( 3 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 2 avg)
% Maximal term depth : 7 ( 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 : 75 ( 0 sgn 44 !; 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] :
( ( test(X5)
& test(X4) )
=> one = addition(addition(multiplication(addition(X5,c(X5)),X4),multiplication(addition(X4,c(X4)),X5)),multiplication(c(X4),c(X5))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
fof(additive_commutativity,axiom,
! [X1,X2] : addition(X1,X2) = addition(X2,X1),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',additive_commutativity) ).
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(additive_associativity,axiom,
! [X3,X2,X1] : addition(X1,addition(X2,X3)) = addition(addition(X1,X2),X3),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',additive_associativity) ).
fof(test_2,axiom,
! [X4,X5] :
( complement(X5,X4)
<=> ( multiplication(X4,X5) = zero
& multiplication(X5,X4) = zero
& addition(X4,X5) = one ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+1.ax',test_2) ).
fof(test_1,axiom,
! [X4] :
( test(X4)
<=> ? [X5] : complement(X5,X4) ),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+1.ax',test_1) ).
fof(multiplicative_left_identity,axiom,
! [X1] : multiplication(one,X1) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',multiplicative_left_identity) ).
fof(additive_idempotence,axiom,
! [X1] : addition(X1,X1) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',additive_idempotence) ).
fof(right_distributivity,axiom,
! [X1,X2,X3] : multiplication(X1,addition(X2,X3)) = addition(multiplication(X1,X2),multiplication(X1,X3)),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',right_distributivity) ).
fof(multiplicative_right_identity,axiom,
! [X1] : multiplication(X1,one) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',multiplicative_right_identity) ).
fof(c_0_11,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_12,negated_conjecture,
~ ! [X4,X5] :
( ( test(X5)
& test(X4) )
=> one = addition(addition(multiplication(addition(X5,c(X5)),X4),multiplication(addition(X4,c(X4)),X5)),multiplication(c(X4),c(X5))) ),
inference(assume_negation,[status(cth)],[goals]) ).
cnf(c_0_13,plain,
( complement(X1,X2)
| c(X1) != X2
| ~ test(X1) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
fof(c_0_14,negated_conjecture,
( test(esk3_0)
& test(esk2_0)
& one != addition(addition(multiplication(addition(esk3_0,c(esk3_0)),esk2_0),multiplication(addition(esk2_0,c(esk2_0)),esk3_0)),multiplication(c(esk2_0),c(esk3_0))) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_12])])]) ).
fof(c_0_15,plain,
! [X37,X38] : addition(X37,X38) = addition(X38,X37),
inference(variable_rename,[status(thm)],[additive_commutativity]) ).
fof(c_0_16,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_17,plain,
! [X39,X40,X41] : addition(X41,addition(X40,X39)) = addition(addition(X41,X40),X39),
inference(variable_rename,[status(thm)],[additive_associativity]) ).
fof(c_0_18,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_19,plain,
( complement(X1,c(X1))
| ~ test(X1) ),
inference(er,[status(thm)],[c_0_13]) ).
cnf(c_0_20,negated_conjecture,
test(esk3_0),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
fof(c_0_21,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_22,negated_conjecture,
one != addition(addition(multiplication(addition(esk3_0,c(esk3_0)),esk2_0),multiplication(addition(esk2_0,c(esk2_0)),esk3_0)),multiplication(c(esk2_0),c(esk3_0))),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_23,plain,
addition(X1,X2) = addition(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_24,plain,
multiplication(addition(X1,X2),X3) = addition(multiplication(X1,X3),multiplication(X2,X3)),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_25,plain,
addition(X1,addition(X2,X3)) = addition(addition(X1,X2),X3),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_26,plain,
( addition(X1,X2) = one
| ~ complement(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_27,negated_conjecture,
complement(esk3_0,c(esk3_0)),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
fof(c_0_28,plain,
! [X48] : multiplication(one,X48) = X48,
inference(variable_rename,[status(thm)],[multiplicative_left_identity]) ).
fof(c_0_29,plain,
! [X43] : addition(X43,X43) = X43,
inference(variable_rename,[status(thm)],[additive_idempotence]) ).
cnf(c_0_30,plain,
( complement(esk1_1(X1),X1)
| ~ test(X1) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_31,negated_conjecture,
test(esk2_0),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_32,negated_conjecture,
addition(multiplication(c(esk2_0),c(esk3_0)),addition(multiplication(esk2_0,esk3_0),addition(multiplication(c(esk2_0),esk3_0),addition(multiplication(esk3_0,esk2_0),multiplication(c(esk3_0),esk2_0))))) != one,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_22,c_0_23]),c_0_23]),c_0_24]),c_0_24]),c_0_25]) ).
cnf(c_0_33,plain,
addition(X1,addition(X2,X3)) = addition(X2,addition(X1,X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_23]),c_0_25]) ).
cnf(c_0_34,negated_conjecture,
addition(esk3_0,c(esk3_0)) = one,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_27]),c_0_23]) ).
cnf(c_0_35,plain,
multiplication(one,X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_28]) ).
fof(c_0_36,plain,
! [X49,X50,X51] : multiplication(X49,addition(X50,X51)) = addition(multiplication(X49,X50),multiplication(X49,X51)),
inference(variable_rename,[status(thm)],[right_distributivity]) ).
fof(c_0_37,plain,
! [X47] : multiplication(X47,one) = X47,
inference(variable_rename,[status(thm)],[multiplicative_right_identity]) ).
cnf(c_0_38,plain,
addition(X1,X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_39,negated_conjecture,
complement(esk1_1(esk2_0),esk2_0),
inference(spm,[status(thm)],[c_0_30,c_0_31]) ).
cnf(c_0_40,negated_conjecture,
complement(esk1_1(esk3_0),esk3_0),
inference(spm,[status(thm)],[c_0_30,c_0_20]) ).
cnf(c_0_41,negated_conjecture,
addition(multiplication(esk2_0,esk3_0),addition(multiplication(c(esk2_0),esk3_0),addition(multiplication(c(esk2_0),c(esk3_0)),addition(multiplication(esk3_0,esk2_0),multiplication(c(esk3_0),esk2_0))))) != one,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_32,c_0_33]),c_0_33]) ).
cnf(c_0_42,negated_conjecture,
addition(multiplication(esk3_0,X1),multiplication(c(esk3_0),X1)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_34]),c_0_35]) ).
cnf(c_0_43,plain,
multiplication(X1,addition(X2,X3)) = addition(multiplication(X1,X2),multiplication(X1,X3)),
inference(split_conjunct,[status(thm)],[c_0_36]) ).
cnf(c_0_44,plain,
multiplication(X1,one) = X1,
inference(split_conjunct,[status(thm)],[c_0_37]) ).
cnf(c_0_45,negated_conjecture,
complement(esk2_0,c(esk2_0)),
inference(spm,[status(thm)],[c_0_19,c_0_31]) ).
cnf(c_0_46,plain,
addition(X1,addition(X1,X2)) = addition(X1,X2),
inference(spm,[status(thm)],[c_0_25,c_0_38]) ).
cnf(c_0_47,negated_conjecture,
addition(esk2_0,esk1_1(esk2_0)) = one,
inference(spm,[status(thm)],[c_0_26,c_0_39]) ).
cnf(c_0_48,negated_conjecture,
addition(esk3_0,esk1_1(esk3_0)) = one,
inference(spm,[status(thm)],[c_0_26,c_0_40]) ).
cnf(c_0_49,negated_conjecture,
addition(esk2_0,addition(multiplication(esk2_0,esk3_0),addition(multiplication(c(esk2_0),esk3_0),multiplication(c(esk2_0),c(esk3_0))))) != one,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_41,c_0_42]),c_0_23]),c_0_33]),c_0_33]) ).
cnf(c_0_50,negated_conjecture,
addition(multiplication(X1,esk3_0),multiplication(X1,c(esk3_0))) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_34]),c_0_44]) ).
cnf(c_0_51,negated_conjecture,
addition(esk2_0,c(esk2_0)) = one,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_45]),c_0_23]) ).
cnf(c_0_52,negated_conjecture,
addition(one,esk2_0) = one,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_47]),c_0_23]) ).
cnf(c_0_53,negated_conjecture,
addition(one,esk3_0) = one,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_48]),c_0_23]) ).
cnf(c_0_54,negated_conjecture,
addition(esk2_0,addition(c(esk2_0),multiplication(esk2_0,esk3_0))) != one,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_49,c_0_50]),c_0_23]) ).
cnf(c_0_55,negated_conjecture,
addition(esk2_0,addition(c(esk2_0),X1)) = addition(one,X1),
inference(spm,[status(thm)],[c_0_25,c_0_51]) ).
cnf(c_0_56,negated_conjecture,
addition(one,addition(esk2_0,X1)) = addition(one,X1),
inference(spm,[status(thm)],[c_0_25,c_0_52]) ).
cnf(c_0_57,negated_conjecture,
addition(X1,multiplication(X1,esk3_0)) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_53]),c_0_44]),c_0_44]) ).
cnf(c_0_58,negated_conjecture,
addition(one,multiplication(esk2_0,esk3_0)) != one,
inference(rw,[status(thm)],[c_0_54,c_0_55]) ).
cnf(c_0_59,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_57]),c_0_52]),c_0_58]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.13 % Problem : KLE011+1 : TPTP v9.2.1. Released v4.0.0.
% 0.11/0.13 % Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.16/0.34 % Computer : n002.cluster.edu
% 0.16/0.34 % Model : x86_64 x86_64
% 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.34 % Memory : 8042.1875MB
% 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.34 % CPULimit : 300
% 0.16/0.34 % WCLimit : 300
% 0.16/0.34 % DateTime : Mon May 4 20:25:16 EDT 2026
% 0.16/0.35 % CPUTime :
% 0.19/0.36 % start to proof: theBenchmark
% 1.40/1.78 % Version : CSE_E---1.7
% 1.40/1.78 % Problem : theBenchmark.p
% 1.40/1.78 % SZS status Theorem for theBenchmark.p
% 1.40/1.78 % SZS output start CNFRefutation
% See solution above
% 1.40/1.78 % Total time : 1.369s
%------------------------------------------------------------------------------