%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : LCL455+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 : n019.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 14.30s 2.42s
% Output : Proof 14.30s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 5
% Syntax : Number of formulae : 29 ( 21 unt; 0 def)
% Number of atoms : 45 ( 12 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 32 ( 16 ~; 10 |; 4 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 5 ( 3 usr; 3 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 5 con; 0-4 aty)
% Number of variables : 30 ( 6 sgn 12 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f22,axiom,
( r2
<=> ! [P,Q] : is_a_theorem(implies(Q,or(P,Q))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',r2) ).
fof(f22_nnf,plain,
( ( ? [P,Q] : ~ is_a_theorem(implies(Q,or(P,Q)))
| r2 )
& ( ! [P,Q] : is_a_theorem(implies(Q,or(P,Q)))
| ~ r2 ) ),
inference(nnf_transformation,[status(thm)],[f22]) ).
fof(f22_sk,plain,
! [Q,P] :
( ( ~ is_a_theorem(implies(sk46,or(sk45,sk46)))
| r2 )
& ( is_a_theorem(implies(Q,or(P,Q)))
| ~ r2 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk45,sk46])],[f22_nnf]) ).
cnf(c48,plain,
( ~ is_a_theorem(implies(sk46,or(sk45,sk46)))
| r2 ),
inference(cnf_transformation,[status(esa)],[f22_sk]) ).
cnf(t64,plain,
ifeq(is_a_theorem(implies(sk46,or(sk45,sk46))),true,r2,true) = true,
inference(equality_encoding,[status(esa)],[c48]) ).
fof(f10,axiom,
( or_2
<=> ! [X,Y] : is_a_theorem(implies(Y,or(X,Y))) ),
file('/export/starexec/sandbox2/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/sandbox2/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(t34,plain,
is_a_theorem(implies(X1,or(X2,X1))) = true,
inference(hyper_resolution,[status(thm)],[hi23,hi72]) ).
cnf(t124,plain,
is_a_theorem(implies(X1,or(X2,X1))) = true,
inference(orient,[status(thm)],[t34]) ).
cnf(t175,plain,
ifeq(true,true,r2,true) = true,
inference(step,[status(thm)],[t64,t124]) ).
cnf(t29,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t109,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t29]) ).
cnf(t176,plain,
r2 = true,
inference(step,[status(thm)],[t175,t109]) ).
cnf(t158,plain,
r2 = true,
inference(orient,[status(thm)],[t176]) ).
fof(f52,conjecture,
r2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',principia_r2) ).
fof(f52_neg,negated_conjecture,
~ r2,
inference(negated_conjecture,[status(cth)],[f52]) ).
fof(f52_nnf,plain,
~ r2,
inference(nnf_transformation,[status(thm)],[f52_neg]) ).
fof(f52_sk,plain,
~ r2,
inference(skolemisation,[status(esa)],[f52_nnf]) ).
cnf(c81,plain,
~ r2,
inference(cnf_transformation,[status(esa)],[f52_sk]) ).
cnf(goal_0,negated_conjecture,
true != r2,
inference(equality_encoding,[status(esa)],[c81]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t158]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL455+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% 0.00/0.03 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.09/0.36 % Computer : n019.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Wed Sep 23 23:27:04 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 14.30/2.42 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 14.30/2.42 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------