%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : KLE150+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 : n014.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 04:35:50 PM UTC 2026
% Result : Theorem 1.29s 1.72s
% Output : CNFRefutation 1.29s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 10
% Syntax : Number of formulae : 39 ( 30 unt; 0 def)
% Number of atoms : 50 ( 36 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 23 ( 12 ~; 7 |; 3 &)
% ( 1 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 62 ( 1 sgn 36 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(goals,conjecture,
! [X4] :
( leq(strong_iteration(multiplication(X4,zero)),addition(one,multiplication(X4,zero)))
& leq(addition(one,multiplication(X4,zero)),strong_iteration(multiplication(X4,zero))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
fof(infty_unfold1,axiom,
! [X1] : strong_iteration(X1) = addition(multiplication(X1,strong_iteration(X1)),one),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax',infty_unfold1) ).
fof(additive_commutativity,axiom,
! [X1,X2] : addition(X1,X2) = addition(X2,X1),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax',additive_commutativity) ).
fof(order,axiom,
! [X1,X2] :
( leq(X1,X2)
<=> addition(X1,X2) = X2 ),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax',order) ).
fof(additive_associativity,axiom,
! [X3,X2,X1] : addition(X1,addition(X2,X3)) = addition(addition(X1,X2),X3),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax',additive_associativity) ).
fof(multiplicative_associativity,axiom,
! [X1,X2,X3] : multiplication(X1,multiplication(X2,X3)) = multiplication(multiplication(X1,X2),X3),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax',multiplicative_associativity) ).
fof(left_annihilation,axiom,
! [X1] : multiplication(zero,X1) = zero,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax',left_annihilation) ).
fof(idempotence,axiom,
! [X1] : addition(X1,X1) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax',idempotence) ).
fof(distributivity1,axiom,
! [X1,X2,X3] : multiplication(X1,addition(X2,X3)) = addition(multiplication(X1,X2),multiplication(X1,X3)),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax',distributivity1) ).
fof(additive_identity,axiom,
! [X1] : addition(X1,zero) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax',additive_identity) ).
fof(c_0_10,negated_conjecture,
~ ! [X4] :
( leq(strong_iteration(multiplication(X4,zero)),addition(one,multiplication(X4,zero)))
& leq(addition(one,multiplication(X4,zero)),strong_iteration(multiplication(X4,zero))) ),
inference(assume_negation,[status(cth)],[goals]) ).
fof(c_0_11,plain,
! [X67] : strong_iteration(X67) = addition(multiplication(X67,strong_iteration(X67)),one),
inference(variable_rename,[status(thm)],[infty_unfold1]) ).
fof(c_0_12,plain,
! [X40,X41] : addition(X40,X41) = addition(X41,X40),
inference(variable_rename,[status(thm)],[additive_commutativity]) ).
fof(c_0_13,negated_conjecture,
( ~ leq(strong_iteration(multiplication(esk1_0,zero)),addition(one,multiplication(esk1_0,zero)))
| ~ leq(addition(one,multiplication(esk1_0,zero)),strong_iteration(multiplication(esk1_0,zero))) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_10])])]) ).
fof(c_0_14,plain,
! [X72,X73] :
( ( ~ leq(X72,X73)
| addition(X72,X73) = X73 )
& ( addition(X72,X73) != X73
| leq(X72,X73) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[order])]) ).
fof(c_0_15,plain,
! [X42,X43,X44] : addition(X44,addition(X43,X42)) = addition(addition(X44,X43),X42),
inference(variable_rename,[status(thm)],[additive_associativity]) ).
cnf(c_0_16,plain,
strong_iteration(X1) = addition(multiplication(X1,strong_iteration(X1)),one),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_17,plain,
addition(X1,X2) = addition(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
fof(c_0_18,plain,
! [X47,X48,X49] : multiplication(X47,multiplication(X48,X49)) = multiplication(multiplication(X47,X48),X49),
inference(variable_rename,[status(thm)],[multiplicative_associativity]) ).
cnf(c_0_19,negated_conjecture,
( ~ leq(strong_iteration(multiplication(esk1_0,zero)),addition(one,multiplication(esk1_0,zero)))
| ~ leq(addition(one,multiplication(esk1_0,zero)),strong_iteration(multiplication(esk1_0,zero))) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_20,plain,
( leq(X1,X2)
| addition(X1,X2) != X2 ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_21,plain,
addition(X1,addition(X2,X3)) = addition(addition(X1,X2),X3),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_22,plain,
addition(one,multiplication(X1,strong_iteration(X1))) = strong_iteration(X1),
inference(rw,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_23,plain,
multiplication(X1,multiplication(X2,X3)) = multiplication(multiplication(X1,X2),X3),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
fof(c_0_24,plain,
! [X58] : multiplication(zero,X58) = zero,
inference(variable_rename,[status(thm)],[left_annihilation]) ).
fof(c_0_25,plain,
! [X46] : addition(X46,X46) = X46,
inference(variable_rename,[status(thm)],[idempotence]) ).
cnf(c_0_26,negated_conjecture,
( addition(one,addition(multiplication(esk1_0,zero),strong_iteration(multiplication(esk1_0,zero)))) != addition(one,multiplication(esk1_0,zero))
| ~ leq(addition(one,multiplication(esk1_0,zero)),strong_iteration(multiplication(esk1_0,zero))) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_20]),c_0_17]),c_0_21]) ).
cnf(c_0_27,plain,
addition(one,multiplication(X1,multiplication(X2,strong_iteration(multiplication(X1,X2))))) = strong_iteration(multiplication(X1,X2)),
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_28,plain,
multiplication(zero,X1) = zero,
inference(split_conjunct,[status(thm)],[c_0_24]) ).
fof(c_0_29,plain,
! [X52,X53,X54] : multiplication(X52,addition(X53,X54)) = addition(multiplication(X52,X53),multiplication(X52,X54)),
inference(variable_rename,[status(thm)],[distributivity1]) ).
fof(c_0_30,plain,
! [X45] : addition(X45,zero) = X45,
inference(variable_rename,[status(thm)],[additive_identity]) ).
cnf(c_0_31,plain,
addition(X1,X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_32,negated_conjecture,
( addition(one,addition(multiplication(esk1_0,zero),strong_iteration(multiplication(esk1_0,zero)))) != addition(one,multiplication(esk1_0,zero))
| addition(one,addition(multiplication(esk1_0,zero),strong_iteration(multiplication(esk1_0,zero)))) != strong_iteration(multiplication(esk1_0,zero)) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_20]),c_0_21]) ).
cnf(c_0_33,plain,
strong_iteration(multiplication(X1,zero)) = addition(one,multiplication(X1,zero)),
inference(spm,[status(thm)],[c_0_27,c_0_28]) ).
cnf(c_0_34,plain,
addition(X1,addition(X2,X3)) = addition(X2,addition(X3,X1)),
inference(spm,[status(thm)],[c_0_21,c_0_17]) ).
cnf(c_0_35,plain,
multiplication(X1,addition(X2,X3)) = addition(multiplication(X1,X2),multiplication(X1,X3)),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_36,plain,
addition(X1,zero) = X1,
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_37,plain,
addition(X1,addition(X1,X2)) = addition(X1,X2),
inference(spm,[status(thm)],[c_0_21,c_0_31]) ).
cnf(c_0_38,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(rw,[status(thm)],[c_0_32,c_0_33]),c_0_34]),c_0_35]),c_0_36]),c_0_37]),c_0_33]),c_0_34]),c_0_35]),c_0_36]),c_0_37]),c_0_33])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : KLE150+2 : TPTP v9.2.1. Released v4.0.0.
% 0.00/0.11 % 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
% 0.13/0.31 % Computer : n014.cluster.edu
% 0.13/0.31 % Model : x86_64 x86_64
% 0.13/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.31 % Memory : 8042.1875MB
% 0.13/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.31 % CPULimit : 300
% 0.13/0.31 % WCLimit : 300
% 0.13/0.31 % DateTime : Mon May 4 20:33:06 EDT 2026
% 0.13/0.31 % CPUTime :
% 0.13/0.32 % start to proof: theBenchmark
% 1.29/1.72 % Version : CSE_E---1.7
% 1.29/1.72 % Problem : theBenchmark.p
% 1.29/1.72 % SZS status Theorem for theBenchmark.p
% 1.29/1.72 % SZS output start CNFRefutation
% See solution above
% 1.29/1.72 % Total time : 1.371s
%------------------------------------------------------------------------------