%------------------------------------------------------------------------------
% 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/sandbox2/benchmark/theBenchmark.p 300
% Computer : n006.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 : Unsatisfiable 5.25s 6.37s
% Output : Proof 5.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 4
% Syntax : Number of formulae : 25 ( 21 unt; 0 def)
% Number of atoms : 33 ( 8 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 22 ( 14 ~; 8 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-4 aty)
% Number of variables : 36 ( 4 sgn 14 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f0,negated_conjecture,
( ~ a_truth(implies(A,B))
| ~ a_truth(A)
| a_truth(B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm147_1) ).
fof(f0_nnf,plain,
! [B,A] :
( ~ a_truth(implies(A,B))
| ~ a_truth(A)
| a_truth(B) ),
inference(nnf_transformation,[status(thm)],[f0]) ).
fof(f0_sk,plain,
! [B,A] :
( ~ a_truth(implies(A,B))
| ~ a_truth(A)
| a_truth(B) ),
inference(skolemisation,[status(esa)],[f0_nnf]) ).
cnf(c0,plain,
( ~ a_truth(implies(X1,X0))
| ~ a_truth(X1)
| a_truth(X0) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(hi0,negated_conjecture,
ifeq(a_truth(X0),true,ifeq(a_truth(implies(X0,X1)),true,a_truth(X1),true),true) = true,
inference(equality_encoding,[status(esa)],[c0]) ).
cnf(f1,negated_conjecture,
a_truth(implies(A,implies(B,A))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm147_2) ).
fof(f1_nnf,plain,
! [A,B] : a_truth(implies(A,implies(B,A))),
inference(nnf_transformation,[status(thm)],[f1]) ).
fof(f1_sk,plain,
! [A,B] : a_truth(implies(A,implies(B,A))),
inference(skolemisation,[status(esa)],[f1_nnf]) ).
cnf(c1,plain,
a_truth(implies(X0,implies(X1,X0))),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(hi1,negated_conjecture,
a_truth(implies(X0,implies(X1,X0))) = true,
inference(equality_encoding,[status(esa)],[c1]) ).
cnf(f2,negated_conjecture,
a_truth(implies(implies(A,implies(B,C)),implies(implies(A,B),implies(A,C)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm147_3) ).
fof(f2_nnf,plain,
! [A,B,C] : a_truth(implies(implies(A,implies(B,C)),implies(implies(A,B),implies(A,C)))),
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
! [A,B,C] : a_truth(implies(implies(A,implies(B,C)),implies(implies(A,B),implies(A,C)))),
inference(skolemisation,[status(esa)],[f2_nnf]) ).
cnf(c2,plain,
a_truth(implies(implies(X0,implies(X1,X2)),implies(implies(X0,X1),implies(X0,X2)))),
inference(cnf_transformation,[status(esa)],[f2_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(h0,plain,
a_truth(implies(implies(sk1,implies(V0,sk1)),implies(sk1,sk1))) = true,
inference(hyper_resolution,[status(thm)],[hi0,hi1,hi2]) ).
cnf(t0,plain,
a_truth(implies(sk1,sk1)) = true,
inference(hyper_resolution,[status(thm)],[hi0,hi1,h0]) ).
cnf(t10,plain,
a_truth(implies(sk1,sk1)) = true,
inference(orient,[status(thm)],[t0]) ).
cnf(f4,negated_conjecture,
~ a_truth(implies(sk1,sk1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm147_5) ).
fof(f4_nnf,plain,
~ a_truth(implies(sk1,sk1)),
inference(nnf_transformation,[status(thm)],[f4]) ).
fof(f4_sk,plain,
~ a_truth(implies(sk1,sk1)),
inference(skolemisation,[status(esa)],[f4_nnf]) ).
cnf(c4,plain,
~ a_truth(implies(sk1,sk1)),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(goal_0,negated_conjecture,
a_truth(implies(sk1,sk1)) != true,
inference(equality_encoding,[status(esa)],[c4]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t10]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : LCL414-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.07 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.18/5.64 % Computer : n006.cluster.edu
% 0.18/5.64 % Model : x86_64 x86_64
% 0.18/5.64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/5.64 % Memory : 8046.5625MB
% 0.18/5.64 % OS : Linux 6.8.0-71-generic
% 0.18/5.64 % CPULimit : 300
% 0.18/5.64 % WCLimit : 300
% 0.18/5.64 % DateTime : Wed Sep 23 23:14:34 UTC 2026
% 0.18/5.64 % CPUTime :
% 0.18/5.64 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 5.25/6.37 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 5.25/6.37 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------