%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : LCL453+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 : n005.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 02:02:06 PM UTC 2026
% Result : Theorem 24.47s 4.09s
% Output : Proof 24.47s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 14
% Syntax : Number of formulae : 66 ( 34 unt; 0 def)
% Number of atoms : 131 ( 11 equ)
% Maximal formula atoms : 8 ( 1 avg)
% Number of connectives : 111 ( 46 ~; 42 |; 15 &)
% ( 5 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 10 ( 8 usr; 8 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 10 con; 0-2 aty)
% Number of variables : 89 ( 3 sgn 42 !; 10 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f11,axiom,
( or_3
<=> ! [X,Y,Z] : is_a_theorem(implies(implies(X,Z),implies(implies(Y,Z),implies(or(X,Y),Z)))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',or_3) ).
fof(f11_nnf,plain,
( ( ? [X,Y,Z] : ~ is_a_theorem(implies(implies(X,Z),implies(implies(Y,Z),implies(or(X,Y),Z))))
| or_3 )
& ( ! [X,Y,Z] : is_a_theorem(implies(implies(X,Z),implies(implies(Y,Z),implies(or(X,Y),Z))))
| ~ or_3 ) ),
inference(nnf_transformation,[status(thm)],[f11]) ).
fof(f11_sk,plain,
! [X,Z,Y] :
( ( ~ is_a_theorem(implies(implies(sk23,sk25),implies(implies(sk24,sk25),implies(or(sk23,sk24),sk25))))
| or_3 )
& ( is_a_theorem(implies(implies(X,Z),implies(implies(Y,Z),implies(or(X,Y),Z))))
| ~ or_3 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk23,sk24,sk25])],[f11_nnf]) ).
cnf(c25,plain,
( is_a_theorem(implies(implies(X0,X2),implies(implies(X1,X2),implies(or(X0,X1),X2))))
| ~ or_3 ),
inference(cnf_transformation,[status(esa)],[f11_sk]) ).
fof(f44,axiom,
or_3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hilbert_or_3) ).
fof(f44_nnf,plain,
or_3,
inference(nnf_transformation,[status(thm)],[f44]) ).
cnf(c73,plain,
or_3,
inference(cnf_transformation,[status(esa)],[f44_nnf]) ).
cnf(p96,plain,
is_a_theorem(implies(implies(X0,X1),implies(implies(X2,X1),implies(or(X0,X2),X1)))),
inference(resolution,[status(thm)],[c25,c73]) ).
fof(f0,axiom,
( modus_ponens
<=> ! [X,Y] :
( ( is_a_theorem(implies(X,Y))
& is_a_theorem(X) )
=> is_a_theorem(Y) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',modus_ponens) ).
fof(f0_nnf,plain,
( ( ? [X,Y] :
( ~ is_a_theorem(Y)
& is_a_theorem(implies(X,Y))
& is_a_theorem(X) )
| modus_ponens )
& ( ! [X,Y] :
( is_a_theorem(Y)
| ~ is_a_theorem(implies(X,Y))
| ~ is_a_theorem(X) )
| ~ modus_ponens ) ),
inference(nnf_transformation,[status(thm)],[f0]) ).
fof(f0_sk,plain,
! [X,Y] :
( ( ( ~ is_a_theorem(sk1)
& is_a_theorem(implies(sk0,sk1))
& is_a_theorem(sk0) )
| modus_ponens )
& ( is_a_theorem(Y)
| ~ is_a_theorem(implies(X,Y))
| ~ is_a_theorem(X)
| ~ modus_ponens ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0,sk1])],[f0_nnf]) ).
cnf(c0,plain,
( is_a_theorem(X1)
| ~ is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(X0)
| ~ modus_ponens ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
fof(f34,axiom,
modus_ponens,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hilbert_modus_ponens) ).
fof(f34_nnf,plain,
modus_ponens,
inference(nnf_transformation,[status(thm)],[f34]) ).
cnf(c63,plain,
modus_ponens,
inference(cnf_transformation,[status(esa)],[f34_nnf]) ).
cnf(p82,plain,
( is_a_theorem(X1)
| ~ is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(X0) ),
inference(resolution,[status(thm)],[c0,c63]) ).
fof(f3,axiom,
( implies_1
<=> ! [X,Y] : is_a_theorem(implies(X,implies(Y,X))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',implies_1) ).
fof(f3_nnf,plain,
( ( ? [X,Y] : ~ is_a_theorem(implies(X,implies(Y,X)))
| implies_1 )
& ( ! [X,Y] : is_a_theorem(implies(X,implies(Y,X)))
| ~ implies_1 ) ),
inference(nnf_transformation,[status(thm)],[f3]) ).
fof(f3_sk,plain,
! [X,Y] :
( ( ~ is_a_theorem(implies(sk6,implies(sk7,sk6)))
| implies_1 )
& ( is_a_theorem(implies(X,implies(Y,X)))
| ~ implies_1 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk6,sk7])],[f3_nnf]) ).
cnf(c9,plain,
( is_a_theorem(implies(X0,implies(X1,X0)))
| ~ implies_1 ),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
fof(f36,axiom,
implies_1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hilbert_implies_1) ).
fof(f36_nnf,plain,
implies_1,
inference(nnf_transformation,[status(thm)],[f36]) ).
cnf(c65,plain,
implies_1,
inference(cnf_transformation,[status(esa)],[f36_nnf]) ).
cnf(p85,plain,
is_a_theorem(implies(X0,implies(X1,X0))),
inference(resolution,[status(thm)],[c9,c65]) ).
cnf(p98,plain,
( is_a_theorem(X2)
| ~ is_a_theorem(implies(implies(X0,implies(X1,X0)),X2)) ),
inference(resolution,[status(thm)],[p82,p85]) ).
fof(f4,axiom,
( implies_2
<=> ! [X,Y] : is_a_theorem(implies(implies(X,implies(X,Y)),implies(X,Y))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',implies_2) ).
fof(f4_nnf,plain,
( ( ? [X,Y] : ~ is_a_theorem(implies(implies(X,implies(X,Y)),implies(X,Y)))
| implies_2 )
& ( ! [X,Y] : is_a_theorem(implies(implies(X,implies(X,Y)),implies(X,Y)))
| ~ implies_2 ) ),
inference(nnf_transformation,[status(thm)],[f4]) ).
fof(f4_sk,plain,
! [X,Y] :
( ( ~ is_a_theorem(implies(implies(sk8,implies(sk8,sk9)),implies(sk8,sk9)))
| implies_2 )
& ( is_a_theorem(implies(implies(X,implies(X,Y)),implies(X,Y)))
| ~ implies_2 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk8,sk9])],[f4_nnf]) ).
cnf(c11,plain,
( is_a_theorem(implies(implies(X0,implies(X0,X1)),implies(X0,X1)))
| ~ implies_2 ),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
fof(f37,axiom,
implies_2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hilbert_implies_2) ).
fof(f37_nnf,plain,
implies_2,
inference(nnf_transformation,[status(thm)],[f37]) ).
cnf(c66,plain,
implies_2,
inference(cnf_transformation,[status(esa)],[f37_nnf]) ).
cnf(p88,plain,
is_a_theorem(implies(implies(X0,implies(X0,X1)),implies(X0,X1))),
inference(resolution,[status(thm)],[c11,c66]) ).
cnf(p116,plain,
is_a_theorem(implies(X0,X0)),
inference(resolution,[status(thm)],[p98,p88]) ).
cnf(p117,plain,
( is_a_theorem(X1)
| ~ is_a_theorem(implies(implies(X0,X0),X1)) ),
inference(resolution,[status(thm)],[p116,p82]) ).
cnf(p296,plain,
is_a_theorem(implies(implies(X0,X1),implies(or(X1,X0),X1))),
inference(resolution,[status(thm)],[p96,p117]) ).
cnf(p1129,plain,
is_a_theorem(implies(or(X0,X0),X0)),
inference(resolution,[status(thm)],[p296,p117]) ).
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]) ).
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]) ).
cnf(p186,plain,
or(X0,X1) = not(and(not(X0),not(X1))),
inference(resolution,[status(thm)],[c55,c60]) ).
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]) ).
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]) ).
cnf(p109,plain,
implies(X0,X1) = not(and(X0,not(X1))),
inference(resolution,[status(thm)],[c57,c61]) ).
cnf(p191,plain,
implies(not(X0),X1) = or(X0,X1),
inference(superposition,[status(thm)],[p186,p109]) ).
fof(f20,axiom,
( cn3
<=> ! [P] : is_a_theorem(implies(implies(not(P),P),P)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cn3) ).
fof(f20_nnf,plain,
( ( ? [P] : ~ is_a_theorem(implies(implies(not(P),P),P))
| cn3 )
& ( ! [P] : is_a_theorem(implies(implies(not(P),P),P))
| ~ cn3 ) ),
inference(nnf_transformation,[status(thm)],[f20]) ).
fof(f20_sk,plain,
! [P] :
( ( ~ is_a_theorem(implies(implies(not(sk43),sk43),sk43))
| cn3 )
& ( is_a_theorem(implies(implies(not(P),P),P))
| ~ cn3 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk43])],[f20_nnf]) ).
cnf(c44,plain,
( ~ is_a_theorem(implies(implies(not(sk43),sk43),sk43))
| cn3 ),
inference(cnf_transformation,[status(esa)],[f20_sk]) ).
cnf(p195,plain,
( ~ is_a_theorem(implies(or(sk43,sk43),sk43))
| cn3 ),
inference(demodulation,[status(thm)],[p191,c44]) ).
cnf(p1144,plain,
cn3,
inference(resolution,[status(thm)],[p1129,p195]) ).
fof(f52,conjecture,
cn3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',luka_cn3) ).
fof(f52_neg,negated_conjecture,
~ cn3,
inference(negated_conjecture,[status(cth)],[f52]) ).
fof(f52_nnf,plain,
~ cn3,
inference(nnf_transformation,[status(thm)],[f52_neg]) ).
fof(f52_sk,plain,
~ cn3,
inference(skolemisation,[status(esa)],[f52_nnf]) ).
cnf(c81,plain,
~ cn3,
inference(cnf_transformation,[status(esa)],[f52_sk]) ).
cnf(p1146,plain,
$false,
inference(resolution,[status(thm)],[p1144,c81]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL453+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.10/0.36 % Computer : n005.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Wed Sep 23 23:26:17 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 24.47/4.09 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 24.47/4.09 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------