%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : LCL451+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 : n002.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 17.33s 2.63s
% Output : Proof 17.33s
% 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 : 7 ( 2 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 5 ( 3 usr; 3 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 7 con; 0-4 aty)
% Number of variables : 42 ( 2 sgn 18 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f18,axiom,
( cn1
<=> ! [P,Q,R] : is_a_theorem(implies(implies(P,Q),implies(implies(Q,R),implies(P,R)))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cn1) ).
fof(f18_nnf,plain,
( ( ? [P,Q,R] : ~ is_a_theorem(implies(implies(P,Q),implies(implies(Q,R),implies(P,R))))
| cn1 )
& ( ! [P,Q,R] : is_a_theorem(implies(implies(P,Q),implies(implies(Q,R),implies(P,R))))
| ~ cn1 ) ),
inference(nnf_transformation,[status(thm)],[f18]) ).
fof(f18_sk,plain,
! [P,Q,R] :
( ( ~ is_a_theorem(implies(implies(sk38,sk39),implies(implies(sk39,sk40),implies(sk38,sk40))))
| cn1 )
& ( is_a_theorem(implies(implies(P,Q),implies(implies(Q,R),implies(P,R))))
| ~ cn1 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk38,sk39,sk40])],[f18_nnf]) ).
cnf(c40,plain,
( ~ is_a_theorem(implies(implies(sk38,sk39),implies(implies(sk39,sk40),implies(sk38,sk40))))
| cn1 ),
inference(cnf_transformation,[status(esa)],[f18_sk]) ).
cnf(t98,plain,
ifeq(is_a_theorem(implies(implies(sk38,sk39),implies(implies(sk39,sk40),implies(sk38,sk40)))),true,cn1,true) = true,
inference(equality_encoding,[status(esa)],[c40]) ).
fof(f5,axiom,
( implies_3
<=> ! [X,Y,Z] : is_a_theorem(implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z)))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',implies_3) ).
fof(f5_nnf,plain,
( ( ? [X,Y,Z] : ~ is_a_theorem(implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z))))
| implies_3 )
& ( ! [X,Y,Z] : is_a_theorem(implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z))))
| ~ implies_3 ) ),
inference(nnf_transformation,[status(thm)],[f5]) ).
fof(f5_sk,plain,
! [X,Y,Z] :
( ( ~ is_a_theorem(implies(implies(sk10,sk11),implies(implies(sk11,sk12),implies(sk10,sk12))))
| implies_3 )
& ( is_a_theorem(implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z))))
| ~ implies_3 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk10,sk11,sk12])],[f5_nnf]) ).
cnf(c13,plain,
( is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X2),implies(X0,X2))))
| ~ implies_3 ),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
cnf(hi13,axiom,
ifeq(implies_3,true,is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X2),implies(X0,X2)))),true) = true,
inference(equality_encoding,[status(esa)],[c13]) ).
fof(f38,axiom,
implies_3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hilbert_implies_3) ).
fof(f38_nnf,plain,
implies_3,
inference(nnf_transformation,[status(thm)],[f38]) ).
cnf(c67,plain,
implies_3,
inference(cnf_transformation,[status(esa)],[f38_nnf]) ).
cnf(hi67,axiom,
implies_3 = true,
inference(equality_encoding,[status(esa)],[c67]) ).
cnf(t85,plain,
is_a_theorem(implies(implies(X1,X2),implies(implies(X2,X3),implies(X1,X3)))) = true,
inference(hyper_resolution,[status(thm)],[hi13,hi67]) ).
cnf(t130,plain,
is_a_theorem(implies(implies(X1,X2),implies(implies(X2,X3),implies(X1,X3)))) = true,
inference(orient,[status(thm)],[t85]) ).
cnf(t155,plain,
ifeq(true,true,cn1,true) = true,
inference(step,[status(thm)],[t98,t130]) ).
cnf(t29,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t111,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t29]) ).
cnf(t156,plain,
cn1 = true,
inference(step,[status(thm)],[t155,t111]) ).
cnf(t146,plain,
cn1 = true,
inference(orient,[status(thm)],[t156]) ).
fof(f52,conjecture,
cn1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',luka_cn1) ).
fof(f52_neg,negated_conjecture,
~ cn1,
inference(negated_conjecture,[status(cth)],[f52]) ).
fof(f52_nnf,plain,
~ cn1,
inference(nnf_transformation,[status(thm)],[f52_neg]) ).
fof(f52_sk,plain,
~ cn1,
inference(skolemisation,[status(esa)],[f52_nnf]) ).
cnf(c81,plain,
~ cn1,
inference(cnf_transformation,[status(esa)],[f52_sk]) ).
cnf(goal_0,negated_conjecture,
true != cn1,
inference(equality_encoding,[status(esa)],[c81]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t146]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : LCL451+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% 0.00/0.05 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.15/0.40 % Computer : n002.cluster.edu
% 0.15/0.40 % Model : x86_64 x86_64
% 0.15/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.40 % Memory : 8046.5625MB
% 0.15/0.40 % OS : Linux 6.8.0-71-generic
% 0.15/0.40 % CPULimit : 300
% 0.15/0.40 % WCLimit : 300
% 0.15/0.40 % DateTime : Wed Sep 23 23:29:18 UTC 2026
% 0.15/0.40 % CPUTime :
% 0.15/0.40 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 17.33/2.63 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 17.33/2.63 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------