%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : KLE025+2 : 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 : n001.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 04:35:31 PM UTC 2026
% Result : Theorem 3.93s 3.21s
% Output : CNFRefutation 3.93s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 10
% Syntax : Number of formulae : 49 ( 29 unt; 0 def)
% Number of atoms : 95 ( 55 equ)
% Maximal formula atoms : 10 ( 1 avg)
% Number of connectives : 76 ( 30 ~; 26 |; 12 &)
% ( 2 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 69 ( 0 sgn 40 !; 0 ?)
% 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(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(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(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(goals,conjecture,
! [X4,X5,X6] :
( ( test(X5)
& test(X6) )
=> ( multiplication(multiplication(X5,X4),c(X6)) = zero
=> multiplication(X5,X4) = multiplication(multiplication(X5,X4),X6) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
fof(additive_idempotence,axiom,
! [X1] : addition(X1,X1) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',additive_idempotence) ).
fof(test_deMorgan2,axiom,
! [X4,X5] :
( ( test(X4)
& test(X5) )
=> c(multiplication(X4,X5)) = addition(c(X4),c(X5)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+2.ax',test_deMorgan2) ).
fof(multiplicative_right_identity,axiom,
! [X1] : multiplication(X1,one) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',multiplicative_right_identity) ).
fof(multiplicative_associativity,axiom,
! [X1,X2,X3] : multiplication(X1,multiplication(X2,X3)) = multiplication(multiplication(X1,X2),X3),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',multiplicative_associativity) ).
fof(c_0_10,plain,
! [X71,X72] :
( ( c(X71) != X72
| complement(X71,X72)
| ~ test(X71) )
& ( ~ complement(X71,X72)
| c(X71) = X72
| ~ test(X71) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[test_3])])]) ).
fof(c_0_11,plain,
! [X69,X70] :
( ( multiplication(X69,X70) = zero
| ~ complement(X70,X69) )
& ( multiplication(X70,X69) = zero
| ~ complement(X70,X69) )
& ( addition(X69,X70) = one
| ~ complement(X70,X69) )
& ( multiplication(X69,X70) != zero
| multiplication(X70,X69) != zero
| addition(X69,X70) != one
| complement(X70,X69) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[test_2])])]) ).
cnf(c_0_12,plain,
( complement(X1,X2)
| c(X1) != X2
| ~ test(X1) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
fof(c_0_13,plain,
! [X55,X56,X57] : multiplication(X55,addition(X56,X57)) = addition(multiplication(X55,X56),multiplication(X55,X57)),
inference(variable_rename,[status(thm)],[right_distributivity]) ).
cnf(c_0_14,plain,
( multiplication(X1,X2) = zero
| ~ complement(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_15,plain,
( complement(X1,c(X1))
| ~ test(X1) ),
inference(er,[status(thm)],[c_0_12]) ).
fof(c_0_16,plain,
! [X48] : addition(X48,zero) = X48,
inference(variable_rename,[status(thm)],[additive_identity]) ).
fof(c_0_17,plain,
! [X43,X44] : addition(X43,X44) = addition(X44,X43),
inference(variable_rename,[status(thm)],[additive_commutativity]) ).
fof(c_0_18,negated_conjecture,
~ ! [X4,X5,X6] :
( ( test(X5)
& test(X6) )
=> ( multiplication(multiplication(X5,X4),c(X6)) = zero
=> multiplication(X5,X4) = multiplication(multiplication(X5,X4),X6) ) ),
inference(assume_negation,[status(cth)],[goals]) ).
fof(c_0_19,plain,
! [X49] : addition(X49,X49) = X49,
inference(variable_rename,[status(thm)],[additive_idempotence]) ).
fof(c_0_20,plain,
! [X76,X77] :
( ~ test(X76)
| ~ test(X77)
| c(multiplication(X76,X77)) = addition(c(X76),c(X77)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[test_deMorgan2])]) ).
cnf(c_0_21,plain,
multiplication(X1,addition(X2,X3)) = addition(multiplication(X1,X2),multiplication(X1,X3)),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_22,plain,
( multiplication(X1,c(X1)) = zero
| ~ test(X1) ),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_23,plain,
addition(X1,zero) = X1,
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_24,plain,
( addition(X1,X2) = one
| ~ complement(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_25,plain,
addition(X1,X2) = addition(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
fof(c_0_26,plain,
! [X53] : multiplication(X53,one) = X53,
inference(variable_rename,[status(thm)],[multiplicative_right_identity]) ).
fof(c_0_27,negated_conjecture,
( test(esk3_0)
& test(esk4_0)
& multiplication(multiplication(esk3_0,esk2_0),c(esk4_0)) = zero
& multiplication(esk3_0,esk2_0) != multiplication(multiplication(esk3_0,esk2_0),esk4_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_18])])]) ).
fof(c_0_28,plain,
! [X50,X51,X52] : multiplication(X50,multiplication(X51,X52)) = multiplication(multiplication(X50,X51),X52),
inference(variable_rename,[status(thm)],[multiplicative_associativity]) ).
cnf(c_0_29,plain,
addition(X1,X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_30,plain,
( c(multiplication(X1,X2)) = addition(c(X1),c(X2))
| ~ test(X1)
| ~ test(X2) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_31,plain,
( multiplication(X1,addition(X2,c(X1))) = multiplication(X1,X2)
| ~ test(X1) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_22]),c_0_23]) ).
cnf(c_0_32,plain,
( addition(X1,c(X1)) = one
| ~ test(X1) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_15]),c_0_25]) ).
cnf(c_0_33,plain,
multiplication(X1,one) = X1,
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_34,negated_conjecture,
multiplication(multiplication(esk3_0,esk2_0),c(esk4_0)) = zero,
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_35,plain,
multiplication(X1,multiplication(X2,X3)) = multiplication(multiplication(X1,X2),X3),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_36,plain,
( c(multiplication(X1,X1)) = c(X1)
| ~ test(X1) ),
inference(spm,[status(thm)],[c_0_29,c_0_30]) ).
cnf(c_0_37,plain,
( multiplication(X1,X1) = X1
| ~ test(X1) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_32]),c_0_33]) ).
cnf(c_0_38,negated_conjecture,
test(esk4_0),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_39,negated_conjecture,
multiplication(esk3_0,multiplication(esk2_0,c(esk4_0))) = zero,
inference(rw,[status(thm)],[c_0_34,c_0_35]) ).
cnf(c_0_40,plain,
( complement(multiplication(X1,X1),c(X1))
| ~ test(multiplication(X1,X1))
| ~ test(X1) ),
inference(spm,[status(thm)],[c_0_15,c_0_36]) ).
cnf(c_0_41,negated_conjecture,
multiplication(esk4_0,esk4_0) = esk4_0,
inference(spm,[status(thm)],[c_0_37,c_0_38]) ).
cnf(c_0_42,negated_conjecture,
multiplication(esk3_0,addition(X1,multiplication(esk2_0,c(esk4_0)))) = multiplication(esk3_0,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_39]),c_0_23]) ).
cnf(c_0_43,negated_conjecture,
complement(esk4_0,c(esk4_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_41]),c_0_38])]) ).
cnf(c_0_44,negated_conjecture,
multiplication(esk3_0,esk2_0) != multiplication(multiplication(esk3_0,esk2_0),esk4_0),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_45,negated_conjecture,
multiplication(esk3_0,multiplication(esk2_0,addition(X1,c(esk4_0)))) = multiplication(esk3_0,multiplication(esk2_0,X1)),
inference(spm,[status(thm)],[c_0_42,c_0_21]) ).
cnf(c_0_46,negated_conjecture,
addition(esk4_0,c(esk4_0)) = one,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_43]),c_0_25]) ).
cnf(c_0_47,negated_conjecture,
multiplication(esk3_0,multiplication(esk2_0,esk4_0)) != multiplication(esk3_0,esk2_0),
inference(rw,[status(thm)],[c_0_44,c_0_35]) ).
cnf(c_0_48,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_46]),c_0_33]),c_0_47]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : KLE025+2 : TPTP v9.2.1. Released v4.0.0.
% 0.00/0.12 % Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.16/0.33 % Computer : n001.cluster.edu
% 0.16/0.33 % Model : x86_64 x86_64
% 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.33 % Memory : 8042.1875MB
% 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.33 % CPULimit : 300
% 0.16/0.33 % WCLimit : 300
% 0.16/0.33 % DateTime : Mon May 4 20:27:18 EDT 2026
% 0.16/0.34 % CPUTime :
% 0.16/0.35 % start to proof: theBenchmark
% 3.93/3.21 % Version : CSE_E---1.7
% 3.93/3.21 % Problem : theBenchmark.p
% 3.93/3.21 % SZS status Theorem for theBenchmark.p
% 3.93/3.21 % SZS output start CNFRefutation
% See solution above
% 3.93/3.23 % Total time : 2.374s
%------------------------------------------------------------------------------