%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : KLE026+1 : 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 : n012.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 1.21s 1.65s
% Output : CNFRefutation 1.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 12
% Syntax : Number of formulae : 50 ( 35 unt; 0 def)
% Number of atoms : 85 ( 52 equ)
% Maximal formula atoms : 10 ( 1 avg)
% Number of connectives : 55 ( 20 ~; 16 |; 12 &)
% ( 3 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 85 ( 0 sgn 52 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
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_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(test_1,axiom,
! [X4] :
( test(X4)
<=> ? [X5] : complement(X5,X4) ),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+1.ax',test_1) ).
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(multiplicative_right_identity,axiom,
! [X1] : multiplication(X1,one) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',multiplicative_right_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(goals,conjecture,
! [X4,X5,X6] :
( ( test(X5)
& test(X6) )
=> ( multiplication(X5,X4) = multiplication(multiplication(X5,X4),X6)
=> leq(multiplication(X5,X4),multiplication(X4,X6)) ) ),
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(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(order,axiom,
! [X1,X2] :
( leq(X1,X2)
<=> addition(X1,X2) = X2 ),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',order) ).
fof(c_0_12,plain,
! [X41,X42,X43] : addition(X43,addition(X42,X41)) = addition(addition(X43,X42),X41),
inference(variable_rename,[status(thm)],[additive_associativity]) ).
fof(c_0_13,plain,
! [X45] : addition(X45,X45) = X45,
inference(variable_rename,[status(thm)],[additive_idempotence]) ).
fof(c_0_14,plain,
! [X65,X66] :
( ( multiplication(X65,X66) = zero
| ~ complement(X66,X65) )
& ( multiplication(X66,X65) = zero
| ~ complement(X66,X65) )
& ( addition(X65,X66) = one
| ~ complement(X66,X65) )
& ( multiplication(X65,X66) != zero
| multiplication(X66,X65) != zero
| addition(X65,X66) != one
| complement(X66,X65) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[test_2])])]) ).
fof(c_0_15,plain,
! [X61,X63,X64] :
( ( ~ test(X61)
| complement(esk1_1(X61),X61) )
& ( ~ complement(X64,X63)
| test(X63) ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[test_1])])])])]) ).
fof(c_0_16,plain,
! [X51,X52,X53] : multiplication(X51,addition(X52,X53)) = addition(multiplication(X51,X52),multiplication(X51,X53)),
inference(variable_rename,[status(thm)],[right_distributivity]) ).
fof(c_0_17,plain,
! [X49] : multiplication(X49,one) = X49,
inference(variable_rename,[status(thm)],[multiplicative_right_identity]) ).
fof(c_0_18,plain,
! [X39,X40] : addition(X39,X40) = addition(X40,X39),
inference(variable_rename,[status(thm)],[additive_commutativity]) ).
cnf(c_0_19,plain,
addition(X1,addition(X2,X3)) = addition(addition(X1,X2),X3),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_20,plain,
addition(X1,X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_21,plain,
( addition(X1,X2) = one
| ~ complement(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_22,plain,
( complement(esk1_1(X1),X1)
| ~ test(X1) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
fof(c_0_23,negated_conjecture,
~ ! [X4,X5,X6] :
( ( test(X5)
& test(X6) )
=> ( multiplication(X5,X4) = multiplication(multiplication(X5,X4),X6)
=> leq(multiplication(X5,X4),multiplication(X4,X6)) ) ),
inference(assume_negation,[status(cth)],[goals]) ).
cnf(c_0_24,plain,
multiplication(X1,addition(X2,X3)) = addition(multiplication(X1,X2),multiplication(X1,X3)),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_25,plain,
multiplication(X1,one) = X1,
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_26,plain,
addition(X1,X2) = addition(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_27,plain,
addition(X1,addition(X1,X2)) = addition(X1,X2),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_28,plain,
( addition(X1,esk1_1(X1)) = one
| ~ test(X1) ),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
fof(c_0_29,negated_conjecture,
( test(esk3_0)
& test(esk4_0)
& multiplication(esk3_0,esk2_0) = multiplication(multiplication(esk3_0,esk2_0),esk4_0)
& ~ leq(multiplication(esk3_0,esk2_0),multiplication(esk2_0,esk4_0)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_23])])]) ).
fof(c_0_30,plain,
! [X46,X47,X48] : multiplication(X46,multiplication(X47,X48)) = multiplication(multiplication(X46,X47),X48),
inference(variable_rename,[status(thm)],[multiplicative_associativity]) ).
cnf(c_0_31,plain,
addition(X1,multiplication(X1,X2)) = multiplication(X1,addition(X2,one)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_26]) ).
cnf(c_0_32,plain,
( addition(X1,one) = one
| ~ test(X1) ),
inference(spm,[status(thm)],[c_0_27,c_0_28]) ).
fof(c_0_33,plain,
! [X54,X55,X56] : multiplication(addition(X54,X55),X56) = addition(multiplication(X54,X56),multiplication(X55,X56)),
inference(variable_rename,[status(thm)],[left_distributivity]) ).
cnf(c_0_34,negated_conjecture,
multiplication(esk3_0,esk2_0) = multiplication(multiplication(esk3_0,esk2_0),esk4_0),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_35,plain,
multiplication(X1,multiplication(X2,X3)) = multiplication(multiplication(X1,X2),X3),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_36,plain,
( addition(X1,multiplication(X1,X2)) = X1
| ~ test(X2) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_32]),c_0_25]) ).
cnf(c_0_37,negated_conjecture,
test(esk3_0),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
fof(c_0_38,plain,
! [X50] : multiplication(one,X50) = X50,
inference(variable_rename,[status(thm)],[multiplicative_left_identity]) ).
fof(c_0_39,plain,
! [X59,X60] :
( ( ~ leq(X59,X60)
| addition(X59,X60) = X60 )
& ( addition(X59,X60) != X60
| leq(X59,X60) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[order])]) ).
cnf(c_0_40,plain,
multiplication(addition(X1,X2),X3) = addition(multiplication(X1,X3),multiplication(X2,X3)),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
cnf(c_0_41,negated_conjecture,
multiplication(esk3_0,multiplication(esk2_0,esk4_0)) = multiplication(esk3_0,esk2_0),
inference(rw,[status(thm)],[c_0_34,c_0_35]) ).
cnf(c_0_42,negated_conjecture,
addition(X1,multiplication(X1,esk3_0)) = X1,
inference(spm,[status(thm)],[c_0_36,c_0_37]) ).
cnf(c_0_43,plain,
multiplication(one,X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_38]) ).
cnf(c_0_44,negated_conjecture,
~ leq(multiplication(esk3_0,esk2_0),multiplication(esk2_0,esk4_0)),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_45,plain,
( leq(X1,X2)
| addition(X1,X2) != X2 ),
inference(split_conjunct,[status(thm)],[c_0_39]) ).
cnf(c_0_46,negated_conjecture,
addition(multiplication(esk3_0,esk2_0),multiplication(X1,multiplication(esk2_0,esk4_0))) = multiplication(addition(X1,esk3_0),multiplication(esk2_0,esk4_0)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_41]),c_0_26]) ).
cnf(c_0_47,negated_conjecture,
addition(one,esk3_0) = one,
inference(spm,[status(thm)],[c_0_42,c_0_43]) ).
cnf(c_0_48,negated_conjecture,
addition(multiplication(esk3_0,esk2_0),multiplication(esk2_0,esk4_0)) != multiplication(esk2_0,esk4_0),
inference(spm,[status(thm)],[c_0_44,c_0_45]) ).
cnf(c_0_49,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_43]),c_0_47]),c_0_43]),c_0_48]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.06 % Problem : KLE026+1 : TPTP v9.2.1. Released v4.0.0.
% 0.00/0.06 % 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
% 0.06/0.24 % Computer : n012.cluster.edu
% 0.06/0.24 % Model : x86_64 x86_64
% 0.06/0.24 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.24 % Memory : 8042.1875MB
% 0.06/0.24 % OS : Linux 3.10.0-693.el7.x86_64
% 0.06/0.24 % CPULimit : 300
% 0.06/0.24 % WCLimit : 300
% 0.06/0.24 % DateTime : Mon May 4 20:26:31 EDT 2026
% 0.06/0.24 % CPUTime :
% 0.06/0.25 % start to proof: theBenchmark
% 1.21/1.65 % Version : CSE_E---1.7
% 1.21/1.65 % Problem : theBenchmark.p
% 1.21/1.65 % SZS status Theorem for theBenchmark.p
% 1.21/1.65 % SZS output start CNFRefutation
% See solution above
% 1.21/1.65 % Total time : 1.361s
%------------------------------------------------------------------------------