%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : LCL460+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 : n015.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 02:02:07 PM UTC 2026
% Result : Theorem 13.66s 2.23s
% Output : Proof 13.66s
% 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(f16,axiom,
( kn2
<=> ! [P,Q] : is_a_theorem(implies(and(P,Q),P)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',kn2) ).
fof(f16_nnf,plain,
( ( ? [P,Q] : ~ is_a_theorem(implies(and(P,Q),P))
| kn2 )
& ( ! [P,Q] : is_a_theorem(implies(and(P,Q),P))
| ~ kn2 ) ),
inference(nnf_transformation,[status(thm)],[f16]) ).
fof(f16_sk,plain,
! [P,Q] :
( ( ~ is_a_theorem(implies(and(sk33,sk34),sk33))
| kn2 )
& ( is_a_theorem(implies(and(P,Q),P))
| ~ kn2 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk33,sk34])],[f16_nnf]) ).
cnf(c36,plain,
( ~ is_a_theorem(implies(and(sk33,sk34),sk33))
| kn2 ),
inference(cnf_transformation,[status(esa)],[f16_sk]) ).
cnf(t49,plain,
ifeq(is_a_theorem(implies(and(sk33,sk34),sk33)),true,kn2,true) = true,
inference(equality_encoding,[status(esa)],[c36]) ).
fof(f6,axiom,
( and_1
<=> ! [X,Y] : is_a_theorem(implies(and(X,Y),X)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',and_1) ).
fof(f6_nnf,plain,
( ( ? [X,Y] : ~ is_a_theorem(implies(and(X,Y),X))
| and_1 )
& ( ! [X,Y] : is_a_theorem(implies(and(X,Y),X))
| ~ and_1 ) ),
inference(nnf_transformation,[status(thm)],[f6]) ).
fof(f6_sk,plain,
! [X,Y] :
( ( ~ is_a_theorem(implies(and(sk13,sk14),sk13))
| and_1 )
& ( is_a_theorem(implies(and(X,Y),X))
| ~ and_1 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk13,sk14])],[f6_nnf]) ).
cnf(c15,plain,
( is_a_theorem(implies(and(X0,X1),X0))
| ~ and_1 ),
inference(cnf_transformation,[status(esa)],[f6_sk]) ).
cnf(hi15,axiom,
ifeq(and_1,true,is_a_theorem(implies(and(X0,X1),X0)),true) = true,
inference(equality_encoding,[status(esa)],[c15]) ).
fof(f39,axiom,
and_1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hilbert_and_1) ).
fof(f39_nnf,plain,
and_1,
inference(nnf_transformation,[status(thm)],[f39]) ).
cnf(c68,plain,
and_1,
inference(cnf_transformation,[status(esa)],[f39_nnf]) ).
cnf(hi68,axiom,
and_1 = true,
inference(equality_encoding,[status(esa)],[c68]) ).
cnf(t34,plain,
is_a_theorem(implies(and(X1,X2),X1)) = true,
inference(hyper_resolution,[status(thm)],[hi15,hi68]) ).
cnf(t111,plain,
is_a_theorem(implies(and(X1,X2),X1)) = true,
inference(orient,[status(thm)],[t34]) ).
cnf(t133,plain,
ifeq(true,true,kn2,true) = true,
inference(step,[status(thm)],[t49,t111]) ).
cnf(t28,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t99,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t28]) ).
cnf(t134,plain,
kn2 = true,
inference(step,[status(thm)],[t133,t99]) ).
cnf(t128,plain,
kn2 = true,
inference(orient,[status(thm)],[t134]) ).
fof(f52,conjecture,
kn2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rosser_kn2) ).
fof(f52_neg,negated_conjecture,
~ kn2,
inference(negated_conjecture,[status(cth)],[f52]) ).
fof(f52_nnf,plain,
~ kn2,
inference(nnf_transformation,[status(thm)],[f52_neg]) ).
fof(f52_sk,plain,
~ kn2,
inference(skolemisation,[status(esa)],[f52_nnf]) ).
cnf(c81,plain,
~ kn2,
inference(cnf_transformation,[status(esa)],[f52_sk]) ).
cnf(goal_0,negated_conjecture,
true != kn2,
inference(equality_encoding,[status(esa)],[c81]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t128]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL460+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.11/0.38 % Computer : n015.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Wed Sep 23 23:30:55 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 13.66/2.23 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 13.66/2.23 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------