%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : KLE093+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 : n020.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 04:35:42 PM UTC 2026
% Result : Theorem 1.34s 1.75s
% Output : CNFRefutation 1.34s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 9
% Syntax : Number of formulae : 34 ( 31 unt; 0 def)
% Number of atoms : 39 ( 31 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 11 ( 6 ~; 3 |; 1 &)
% ( 1 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 2 con; 0-2 aty)
% Number of variables : 45 ( 4 sgn 28 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(domain3,axiom,
! [X4] : addition(domain(X4),one) = one,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+5.ax',domain3) ).
fof(additive_commutativity,axiom,
! [X1,X2] : addition(X1,X2) = addition(X2,X1),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE002+0.ax',additive_commutativity) ).
fof(domain1,axiom,
! [X4] : addition(X4,multiplication(domain(X4),X4)) = multiplication(domain(X4),X4),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+5.ax',domain1) ).
fof(multiplicative_right_identity,axiom,
! [X1] : multiplication(X1,one) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE002+0.ax',multiplicative_right_identity) ).
fof(domain5,axiom,
! [X4,X5] : domain(addition(X4,X5)) = addition(domain(X4),domain(X5)),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+5.ax',domain5) ).
fof(order,axiom,
! [X1,X2] :
( leq(X1,X2)
<=> addition(X1,X2) = X2 ),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE002+0.ax',order) ).
fof(star_unfold_right,axiom,
! [X1] : leq(addition(one,multiplication(X1,star(X1))),star(X1)),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE002+0.ax',star_unfold_right) ).
fof(additive_associativity,axiom,
! [X3,X2,X1] : addition(X1,addition(X2,X3)) = addition(addition(X1,X2),X3),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE002+0.ax',additive_associativity) ).
fof(goals,conjecture,
! [X4] : domain(star(X4)) = one,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
fof(c_0_9,plain,
! [X76] : addition(domain(X76),one) = one,
inference(variable_rename,[status(thm)],[domain3]) ).
fof(c_0_10,plain,
! [X43,X44] : addition(X43,X44) = addition(X44,X43),
inference(variable_rename,[status(thm)],[additive_commutativity]) ).
fof(c_0_11,plain,
! [X73] : addition(X73,multiplication(domain(X73),X73)) = multiplication(domain(X73),X73),
inference(variable_rename,[status(thm)],[domain1]) ).
fof(c_0_12,plain,
! [X53] : multiplication(X53,one) = X53,
inference(variable_rename,[status(thm)],[multiplicative_right_identity]) ).
cnf(c_0_13,plain,
addition(domain(X1),one) = one,
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_14,plain,
addition(X1,X2) = addition(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
fof(c_0_15,plain,
! [X77,X78] : domain(addition(X77,X78)) = addition(domain(X77),domain(X78)),
inference(variable_rename,[status(thm)],[domain5]) ).
cnf(c_0_16,plain,
addition(X1,multiplication(domain(X1),X1)) = multiplication(domain(X1),X1),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_17,plain,
multiplication(X1,one) = X1,
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_18,plain,
addition(one,domain(X1)) = one,
inference(rw,[status(thm)],[c_0_13,c_0_14]) ).
fof(c_0_19,plain,
! [X63,X64] :
( ( ~ leq(X63,X64)
| addition(X63,X64) = X64 )
& ( addition(X63,X64) != X64
| leq(X63,X64) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[order])]) ).
fof(c_0_20,plain,
! [X65] : leq(addition(one,multiplication(X65,star(X65))),star(X65)),
inference(variable_rename,[status(thm)],[star_unfold_right]) ).
fof(c_0_21,plain,
! [X45,X46,X47] : addition(X47,addition(X46,X45)) = addition(addition(X47,X46),X45),
inference(variable_rename,[status(thm)],[additive_associativity]) ).
fof(c_0_22,negated_conjecture,
~ ! [X4] : domain(star(X4)) = one,
inference(assume_negation,[status(cth)],[goals]) ).
cnf(c_0_23,plain,
domain(addition(X1,X2)) = addition(domain(X1),domain(X2)),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_24,plain,
domain(one) = one,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_17]),c_0_18]) ).
cnf(c_0_25,plain,
( addition(X1,X2) = X2
| ~ leq(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_26,plain,
leq(addition(one,multiplication(X1,star(X1))),star(X1)),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_27,plain,
addition(X1,addition(X2,X3)) = addition(addition(X1,X2),X3),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
fof(c_0_28,negated_conjecture,
domain(star(esk1_0)) != one,
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_22])])]) ).
cnf(c_0_29,plain,
domain(addition(one,X1)) = one,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_24]),c_0_18]) ).
cnf(c_0_30,plain,
addition(one,addition(star(X1),multiplication(X1,star(X1)))) = star(X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_26]),c_0_27]),c_0_14]) ).
cnf(c_0_31,negated_conjecture,
domain(star(esk1_0)) != one,
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_32,plain,
domain(star(X1)) = one,
inference(spm,[status(thm)],[c_0_29,c_0_30]) ).
cnf(c_0_33,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_31,c_0_32])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : KLE093+1 : 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
% 0.15/0.33 % Computer : n020.cluster.edu
% 0.15/0.33 % Model : x86_64 x86_64
% 0.15/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.33 % Memory : 8042.1875MB
% 0.15/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.33 % CPULimit : 300
% 0.15/0.33 % WCLimit : 300
% 0.15/0.33 % DateTime : Mon May 4 20:29:50 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 1.34/1.75 % Version : CSE_E---1.7
% 1.34/1.75 % Problem : theBenchmark.p
% 1.34/1.75 % SZS status Theorem for theBenchmark.p
% 1.34/1.75 % SZS output start CNFRefutation
% See solution above
% 1.34/1.75 % Total time : 1.367s
%------------------------------------------------------------------------------