%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : LCL414+1 : TPTP v9.3.1. Released v2.5.0.
% 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 02:01:56 PM UTC 2026
% Result : Theorem 3.49s 0.82s
% Output : Proof 3.49s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 1
% Syntax : Number of formulae : 18 ( 13 unt; 0 def)
% Number of atoms : 44 ( 9 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 46 ( 20 ~; 10 |; 16 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-4 aty)
% Number of variables : 54 ( 5 sgn 30 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f0,conjecture,
~ ( ? [A] : ~ a_truth(implies(A,A))
& ! [P,Q] : a_truth(implies(implies(not(P),not(Q)),implies(Q,P)))
& ! [P,Q,R] : a_truth(implies(implies(P,implies(Q,R)),implies(implies(P,Q),implies(P,R))))
& ! [P,Q] : a_truth(implies(P,implies(Q,P)))
& ! [P,Q] :
( a_truth(Q)
| ~ a_truth(P)
| ~ a_truth(implies(P,Q)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm147) ).
fof(f0_neg,negated_conjecture,
~ ~ ( ? [A] : ~ a_truth(implies(A,A))
& ! [P,Q] : a_truth(implies(implies(not(P),not(Q)),implies(Q,P)))
& ! [P,Q,R] : a_truth(implies(implies(P,implies(Q,R)),implies(implies(P,Q),implies(P,R))))
& ! [P,Q] : a_truth(implies(P,implies(Q,P)))
& ! [P,Q] :
( a_truth(Q)
| ~ a_truth(P)
| ~ a_truth(implies(P,Q)) ) ),
inference(negated_conjecture,[status(cth)],[f0]) ).
fof(f0_nnf,plain,
( ? [A] : ~ a_truth(implies(A,A))
& ! [P,Q] : a_truth(implies(implies(not(P),not(Q)),implies(Q,P)))
& ! [P,Q,R] : a_truth(implies(implies(P,implies(Q,R)),implies(implies(P,Q),implies(P,R))))
& ! [P,Q] : a_truth(implies(P,implies(Q,P)))
& ! [P,Q] :
( a_truth(Q)
| ~ a_truth(P)
| ~ a_truth(implies(P,Q)) ) ),
inference(nnf_transformation,[status(thm)],[f0_neg]) ).
fof(f0_sk,plain,
! [P,Q,R] :
( ~ a_truth(implies(sk0,sk0))
& a_truth(implies(implies(not(P),not(Q)),implies(Q,P)))
& a_truth(implies(implies(P,implies(Q,R)),implies(implies(P,Q),implies(P,R))))
& a_truth(implies(P,implies(Q,P)))
& ( a_truth(Q)
| ~ a_truth(P)
| ~ a_truth(implies(P,Q)) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0])],[f0_nnf]) ).
cnf(c0,plain,
( a_truth(X1)
| ~ a_truth(X0)
| ~ a_truth(implies(X0,X1)) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(hi0,negated_conjecture,
ifeq(a_truth(implies(X0,X1)),true,ifeq(a_truth(X0),true,a_truth(X1),true),true) = true,
inference(equality_encoding,[status(esa)],[c0]) ).
cnf(c1,plain,
a_truth(implies(X0,implies(X1,X0))),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(hi1,negated_conjecture,
a_truth(implies(X0,implies(X1,X0))) = true,
inference(equality_encoding,[status(esa)],[c1]) ).
cnf(h0,plain,
a_truth(implies(V0,implies(V1,implies(V2,V1)))) = true,
inference(hyper_resolution,[status(thm)],[hi0,hi1,hi1]) ).
cnf(c2,plain,
a_truth(implies(implies(X0,implies(X1,X2)),implies(implies(X0,X1),implies(X0,X2)))),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(hi2,negated_conjecture,
a_truth(implies(implies(X0,implies(X1,X2)),implies(implies(X0,X1),implies(X0,X2)))) = true,
inference(equality_encoding,[status(esa)],[c2]) ).
cnf(h3,plain,
a_truth(implies(implies(V0,V1),implies(V0,V0))) = true,
inference(hyper_resolution,[status(thm)],[hi0,hi2,hi1]) ).
cnf(t0,plain,
a_truth(implies(X1,X1)) = true,
inference(hyper_resolution,[status(thm)],[hi0,h3,h0]) ).
cnf(t18,plain,
a_truth(implies(X1,X1)) = true,
inference(orient,[status(thm)],[t0]) ).
cnf(c4,plain,
~ a_truth(implies(sk0,sk0)),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(goal_0,negated_conjecture,
a_truth(implies(sk0,sk0)) != true,
inference(equality_encoding,[status(esa)],[c4]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t18]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL414+1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.10/0.35 % Computer : n008.cluster.edu
% 0.10/0.35 % Model : x86_64 x86_64
% 0.10/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.35 % Memory : 8046.5625MB
% 0.10/0.35 % OS : Linux 6.8.0-71-generic
% 0.10/0.35 % CPULimit : 300
% 0.10/0.35 % WCLimit : 300
% 0.10/0.35 % DateTime : Wed Sep 23 23:15:10 UTC 2026
% 0.14/0.36 % CPUTime :
% 0.14/0.36 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 3.49/0.82 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.49/0.82 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------