%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : LCL456+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n008.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 37.53s 5.39s
% Output : Proof 37.53s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 11
% Syntax : Number of formulae : 60 ( 40 unt; 0 def)
% Number of atoms : 112 ( 22 equ)
% Maximal formula atoms : 8 ( 1 avg)
% Number of connectives : 89 ( 37 ~; 31 |; 15 &)
% ( 5 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 8 ( 6 usr; 6 prp; 0-2 aty)
% Number of functors : 15 ( 15 usr; 12 con; 0-4 aty)
% Number of variables : 82 ( 8 sgn 33 !; 11 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f23,axiom,
( r3
<=> ! [P,Q] : is_a_theorem(implies(or(P,Q),or(Q,P))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',r3) ).
fof(f23_nnf,plain,
( ( ? [P,Q] : ~ is_a_theorem(implies(or(P,Q),or(Q,P)))
| r3 )
& ( ! [P,Q] : is_a_theorem(implies(or(P,Q),or(Q,P)))
| ~ r3 ) ),
inference(nnf_transformation,[status(thm)],[f23]) ).
fof(f23_sk,plain,
! [P,Q] :
( ( ~ is_a_theorem(implies(or(sk47,sk48),or(sk48,sk47)))
| r3 )
& ( is_a_theorem(implies(or(P,Q),or(Q,P)))
| ~ r3 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk47,sk48])],[f23_nnf]) ).
cnf(c50,plain,
( ~ is_a_theorem(implies(or(sk47,sk48),or(sk48,sk47)))
| r3 ),
inference(cnf_transformation,[status(esa)],[f23_sk]) ).
cnf(t221,plain,
ifeq(is_a_theorem(implies(or(sk47,sk48),or(sk48,sk47))),true,r3,true) = true,
inference(equality_encoding,[status(esa)],[c50]) ).
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/sandbox/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]) ).
cnf(hi25,axiom,
ifeq(or_3,true,is_a_theorem(implies(implies(X0,X1),implies(implies(X2,X1),implies(or(X0,X2),X1)))),true) = true,
inference(equality_encoding,[status(esa)],[c25]) ).
fof(f44,axiom,
or_3,
file('/export/starexec/sandbox/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(hi73,axiom,
or_3 = true,
inference(equality_encoding,[status(esa)],[c73]) ).
cnf(h12,plain,
is_a_theorem(implies(implies(V0,V1),implies(implies(V2,V1),implies(or(V0,V2),V1)))) = true,
inference(hyper_resolution,[status(thm)],[hi25,hi73]) ).
fof(f10,axiom,
( or_2
<=> ! [X,Y] : is_a_theorem(implies(Y,or(X,Y))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',or_2) ).
fof(f10_nnf,plain,
( ( ? [X,Y] : ~ is_a_theorem(implies(Y,or(X,Y)))
| or_2 )
& ( ! [X,Y] : is_a_theorem(implies(Y,or(X,Y)))
| ~ or_2 ) ),
inference(nnf_transformation,[status(thm)],[f10]) ).
fof(f10_sk,plain,
! [Y,X] :
( ( ~ is_a_theorem(implies(sk22,or(sk21,sk22)))
| or_2 )
& ( is_a_theorem(implies(Y,or(X,Y)))
| ~ or_2 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk21,sk22])],[f10_nnf]) ).
cnf(c23,plain,
( is_a_theorem(implies(X1,or(X0,X1)))
| ~ or_2 ),
inference(cnf_transformation,[status(esa)],[f10_sk]) ).
cnf(hi23,axiom,
ifeq(or_2,true,is_a_theorem(implies(X0,or(X1,X0))),true) = true,
inference(equality_encoding,[status(esa)],[c23]) ).
fof(f43,axiom,
or_2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hilbert_or_2) ).
fof(f43_nnf,plain,
or_2,
inference(nnf_transformation,[status(thm)],[f43]) ).
cnf(c72,plain,
or_2,
inference(cnf_transformation,[status(esa)],[f43_nnf]) ).
cnf(hi72,axiom,
or_2 = true,
inference(equality_encoding,[status(esa)],[c72]) ).
cnf(h11,plain,
is_a_theorem(implies(V0,or(V1,V0))) = true,
inference(hyper_resolution,[status(thm)],[hi23,hi72]) ).
fof(f0,axiom,
( modus_ponens
<=> ! [X,Y] :
( ( is_a_theorem(implies(X,Y))
& is_a_theorem(X) )
=> is_a_theorem(Y) ) ),
file('/export/starexec/sandbox/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]) ).
cnf(hi0,axiom,
ifeq(modus_ponens,true,ifeq(is_a_theorem(X0),true,ifeq(is_a_theorem(implies(X0,X1)),true,is_a_theorem(X1),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c0]) ).
fof(f34,axiom,
modus_ponens,
file('/export/starexec/sandbox/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(hi63,axiom,
modus_ponens = true,
inference(equality_encoding,[status(esa)],[c63]) ).
cnf(h70,plain,
is_a_theorem(implies(implies(V0,or(V1,V2)),implies(or(V2,V0),or(V1,V2)))) = true,
inference(hyper_resolution,[status(thm)],[hi0,hi63,h11,h12]) ).
fof(f9,axiom,
( or_1
<=> ! [X,Y] : is_a_theorem(implies(X,or(X,Y))) ),
file('/export/starexec/sandbox/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(hi21,axiom,
ifeq(or_1,true,is_a_theorem(implies(X0,or(X0,X1))),true) = true,
inference(equality_encoding,[status(esa)],[c21]) ).
fof(f42,axiom,
or_1,
file('/export/starexec/sandbox/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]) ).
cnf(hi71,axiom,
or_1 = true,
inference(equality_encoding,[status(esa)],[c71]) ).
cnf(h10,plain,
is_a_theorem(implies(V0,or(V0,V1))) = true,
inference(hyper_resolution,[status(thm)],[hi21,hi71]) ).
cnf(t100,plain,
is_a_theorem(implies(or(X1,X2),or(X2,X1))) = true,
inference(hyper_resolution,[status(thm)],[hi0,hi63,h10,h70]) ).
cnf(t304,plain,
is_a_theorem(implies(or(X1,X2),or(X2,X1))) = true,
inference(orient,[status(thm)],[t100]) ).
cnf(t487,plain,
ifeq(true,true,r3,true) = true,
inference(step,[status(thm)],[t221,t304]) ).
cnf(t37,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t258,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t37]) ).
cnf(t488,plain,
r3 = true,
inference(step,[status(thm)],[t487,t258]) ).
cnf(t447,plain,
r3 = true,
inference(orient,[status(thm)],[t488]) ).
fof(f52,conjecture,
r3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',principia_r3) ).
fof(f52_neg,negated_conjecture,
~ r3,
inference(negated_conjecture,[status(cth)],[f52]) ).
fof(f52_nnf,plain,
~ r3,
inference(nnf_transformation,[status(thm)],[f52_neg]) ).
fof(f52_sk,plain,
~ r3,
inference(skolemisation,[status(esa)],[f52_nnf]) ).
cnf(c81,plain,
~ r3,
inference(cnf_transformation,[status(esa)],[f52_sk]) ).
cnf(goal_0,negated_conjecture,
true != r3,
inference(equality_encoding,[status(esa)],[c81]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t447]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL456+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.09/0.34 % Computer : n008.cluster.edu
% 0.09/0.34 % Model : x86_64 x86_64
% 0.09/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.34 % Memory : 8046.5625MB
% 0.09/0.34 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Wed Sep 23 23:27:54 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.09/0.35 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 37.53/5.39 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 37.53/5.39 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------