%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : LCL452+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n017.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri Sep 25 02:02:05 PM UTC 2026
% Result : Theorem 32.09s 4.58s
% Output : Proof 32.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 8
% Syntax : Number of formulae : 37 ( 20 unt; 0 def)
% Number of atoms : 62 ( 11 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 46 ( 21 ~; 17 |; 4 &)
% ( 2 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 7 ( 5 usr; 5 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 42 ( 2 sgn 24 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f31,axiom,
op_or,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hilbert_op_or) ).
fof(f31_nnf,plain,
op_or,
inference(nnf_transformation,[status(thm)],[f31]) ).
cnf(c60,plain,
op_or,
inference(cnf_transformation,[status(esa)],[f31_nnf]) ).
fof(f26,axiom,
( op_or
=> ! [X,Y] : or(X,Y) = not(and(not(X),not(Y))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',op_or) ).
fof(f26_nnf,plain,
( ! [X,Y] : or(X,Y) = not(and(not(X),not(Y)))
| ~ op_or ),
inference(nnf_transformation,[status(thm)],[f26]) ).
fof(f26_sk,plain,
! [X,Y] :
( or(X,Y) = not(and(not(X),not(Y)))
| ~ op_or ),
inference(skolemisation,[status(esa)],[f26_nnf]) ).
cnf(c55,plain,
( or(X0,X1) = not(and(not(X0),not(X1)))
| ~ op_or ),
inference(cnf_transformation,[status(esa)],[f26_sk]) ).
cnf(p82,plain,
or(X0,X1) = not(and(not(X0),not(X1))),
inference(resolution,[status(thm)],[c60,c55]) ).
fof(f32,axiom,
op_implies_and,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hilbert_op_implies_and) ).
fof(f32_nnf,plain,
op_implies_and,
inference(nnf_transformation,[status(thm)],[f32]) ).
cnf(c61,plain,
op_implies_and,
inference(cnf_transformation,[status(esa)],[f32_nnf]) ).
fof(f28,axiom,
( op_implies_and
=> ! [X,Y] : implies(X,Y) = not(and(X,not(Y))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',op_implies_and) ).
fof(f28_nnf,plain,
( ! [X,Y] : implies(X,Y) = not(and(X,not(Y)))
| ~ op_implies_and ),
inference(nnf_transformation,[status(thm)],[f28]) ).
fof(f28_sk,plain,
! [X,Y] :
( implies(X,Y) = not(and(X,not(Y)))
| ~ op_implies_and ),
inference(skolemisation,[status(esa)],[f28_nnf]) ).
cnf(c57,plain,
( implies(X0,X1) = not(and(X0,not(X1)))
| ~ op_implies_and ),
inference(cnf_transformation,[status(esa)],[f28_sk]) ).
cnf(p83,plain,
implies(X0,X1) = not(and(X0,not(X1))),
inference(resolution,[status(thm)],[c61,c57]) ).
cnf(p103,plain,
implies(not(X0),X1) = or(X0,X1),
inference(superposition,[status(thm)],[p82,p83]) ).
fof(f19,axiom,
( cn2
<=> ! [P,Q] : is_a_theorem(implies(P,implies(not(P),Q))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cn2) ).
fof(f19_nnf,plain,
( ( ? [P,Q] : ~ is_a_theorem(implies(P,implies(not(P),Q)))
| cn2 )
& ( ! [P,Q] : is_a_theorem(implies(P,implies(not(P),Q)))
| ~ cn2 ) ),
inference(nnf_transformation,[status(thm)],[f19]) ).
fof(f19_sk,plain,
! [P,Q] :
( ( ~ is_a_theorem(implies(sk41,implies(not(sk41),sk42)))
| cn2 )
& ( is_a_theorem(implies(P,implies(not(P),Q)))
| ~ cn2 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk41,sk42])],[f19_nnf]) ).
cnf(c42,plain,
( ~ is_a_theorem(implies(sk41,implies(not(sk41),sk42)))
| cn2 ),
inference(cnf_transformation,[status(esa)],[f19_sk]) ).
cnf(p106,plain,
( ~ is_a_theorem(implies(sk41,or(sk41,sk42)))
| cn2 ),
inference(demodulation,[status(thm)],[p103,c42]) ).
fof(f42,axiom,
or_1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hilbert_or_1) ).
fof(f42_nnf,plain,
or_1,
inference(nnf_transformation,[status(thm)],[f42]) ).
cnf(c71,plain,
or_1,
inference(cnf_transformation,[status(esa)],[f42_nnf]) ).
fof(f9,axiom,
( or_1
<=> ! [X,Y] : is_a_theorem(implies(X,or(X,Y))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',or_1) ).
fof(f9_nnf,plain,
( ( ? [X,Y] : ~ is_a_theorem(implies(X,or(X,Y)))
| or_1 )
& ( ! [X,Y] : is_a_theorem(implies(X,or(X,Y)))
| ~ or_1 ) ),
inference(nnf_transformation,[status(thm)],[f9]) ).
fof(f9_sk,plain,
! [X,Y] :
( ( ~ is_a_theorem(implies(sk19,or(sk19,sk20)))
| or_1 )
& ( is_a_theorem(implies(X,or(X,Y)))
| ~ or_1 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk19,sk20])],[f9_nnf]) ).
cnf(c21,plain,
( is_a_theorem(implies(X0,or(X0,X1)))
| ~ or_1 ),
inference(cnf_transformation,[status(esa)],[f9_sk]) ).
cnf(p93,plain,
is_a_theorem(implies(X0,or(X0,X1))),
inference(resolution,[status(thm)],[c71,c21]) ).
cnf(p162,plain,
cn2,
inference(resolution,[status(thm)],[p106,p93]) ).
fof(f52,conjecture,
cn2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',luka_cn2) ).
fof(f52_neg,negated_conjecture,
~ cn2,
inference(negated_conjecture,[status(cth)],[f52]) ).
fof(f52_nnf,plain,
~ cn2,
inference(nnf_transformation,[status(thm)],[f52_neg]) ).
fof(f52_sk,plain,
~ cn2,
inference(skolemisation,[status(esa)],[f52_nnf]) ).
cnf(c81,plain,
~ cn2,
inference(cnf_transformation,[status(esa)],[f52_sk]) ).
cnf(p731,plain,
$false,
inference(resolution,[status(thm)],[p162,c81]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : LCL452+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% 0.00/0.06 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.18/0.43 % Computer : n017.cluster.edu
% 0.18/0.43 % Model : x86_64 x86_64
% 0.18/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.43 % Memory : 8046.5625MB
% 0.18/0.43 % OS : Linux 6.8.0-71-generic
% 0.18/0.43 % CPULimit : 300
% 0.18/0.43 % WCLimit : 300
% 0.18/0.43 % DateTime : Wed Sep 23 23:22:00 UTC 2026
% 0.18/0.43 % CPUTime :
% 0.18/0.43 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 32.09/4.58 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 32.09/4.58 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------