%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : LCL087-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n003.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 02:00:54 PM UTC 2026
% Result : Unsatisfiable 5.75s 1.21s
% Output : Proof 5.75s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 3
% Syntax : Number of formulae : 26 ( 22 unt; 0 def)
% Number of atoms : 34 ( 13 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 : 6 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-4 aty)
% Number of variables : 63 ( 19 sgn 14 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f0,axiom,
( is_a_theorem(Y)
| ~ is_a_theorem(X)
| ~ is_a_theorem(implies(X,Y)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',condensed_detachment) ).
fof(f0_nnf,plain,
! [X,Y] :
( is_a_theorem(Y)
| ~ is_a_theorem(X)
| ~ is_a_theorem(implies(X,Y)) ),
inference(nnf_transformation,[status(thm)],[f0]) ).
fof(f0_sk,plain,
! [X,Y] :
( is_a_theorem(Y)
| ~ is_a_theorem(X)
| ~ is_a_theorem(implies(X,Y)) ),
inference(skolemisation,[status(esa)],[f0_nnf]) ).
cnf(c0,plain,
( is_a_theorem(X1)
| ~ is_a_theorem(X0)
| ~ is_a_theorem(implies(X0,X1)) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(hi0,axiom,
ifeq(is_a_theorem(implies(X0,X1)),true,ifeq(is_a_theorem(X0),true,is_a_theorem(X1),true),true) = true,
inference(equality_encoding,[status(esa)],[c0]) ).
cnf(f1,axiom,
is_a_theorem(implies(implies(implies(P,Q),implies(R,S)),implies(T,implies(implies(S,P),implies(R,P))))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ic_JLukasiewicz_4) ).
fof(f1_nnf,plain,
! [P,Q,R,S,T] : is_a_theorem(implies(implies(implies(P,Q),implies(R,S)),implies(T,implies(implies(S,P),implies(R,P))))),
inference(nnf_transformation,[status(thm)],[f1]) ).
fof(f1_sk,plain,
! [P,Q,R,S,T] : is_a_theorem(implies(implies(implies(P,Q),implies(R,S)),implies(T,implies(implies(S,P),implies(R,P))))),
inference(skolemisation,[status(esa)],[f1_nnf]) ).
cnf(c1,plain,
is_a_theorem(implies(implies(implies(X0,X1),implies(X2,X3)),implies(X4,implies(implies(X3,X0),implies(X2,X0))))),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(hi1,axiom,
is_a_theorem(implies(implies(implies(X0,X1),implies(X2,X3)),implies(X4,implies(implies(X3,X0),implies(X2,X0))))) = true,
inference(equality_encoding,[status(esa)],[c1]) ).
cnf(h0,plain,
is_a_theorem(implies(V0,implies(implies(implies(implies(V1,V2),implies(V3,V2)),implies(V2,V4)),implies(V5,implies(V2,V4))))) = true,
inference(hyper_resolution,[status(thm)],[hi0,hi1,hi1]) ).
cnf(h1,plain,
is_a_theorem(implies(implies(implies(implies(V0,V1),implies(V2,V1)),implies(V1,V3)),implies(V4,implies(V1,V3)))) = true,
inference(hyper_resolution,[status(thm)],[hi0,h0,h0]) ).
cnf(h3,plain,
is_a_theorem(implies(V0,implies(implies(V1,V2),implies(V2,implies(V1,V2))))) = true,
inference(hyper_resolution,[status(thm)],[hi0,h1,h1]) ).
cnf(h8,plain,
is_a_theorem(implies(implies(V0,V1),implies(V1,implies(V0,V1)))) = true,
inference(hyper_resolution,[status(thm)],[hi0,h3,h3]) ).
cnf(h24,plain,
is_a_theorem(implies(V0,implies(implies(implies(V1,V2),V1),implies(V2,V1)))) = true,
inference(hyper_resolution,[status(thm)],[hi0,hi1,h8]) ).
cnf(h81,plain,
is_a_theorem(implies(implies(implies(V0,V1),V0),implies(V1,V0))) = true,
inference(hyper_resolution,[status(thm)],[hi0,h24,h24]) ).
cnf(h104,plain,
is_a_theorem(implies(V0,implies(V1,implies(V2,V1)))) = true,
inference(hyper_resolution,[status(thm)],[hi0,h1,h81]) ).
cnf(t2,plain,
is_a_theorem(implies(X1,implies(X2,X1))) = true,
inference(hyper_resolution,[status(thm)],[hi0,h104,h104]) ).
cnf(t204,plain,
is_a_theorem(implies(X1,implies(X2,X1))) = true,
inference(orient,[status(thm)],[t2]) ).
cnf(f2,negated_conjecture,
~ is_a_theorem(implies(a,implies(b,a))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_ic_2) ).
fof(f2_nnf,plain,
~ is_a_theorem(implies(a,implies(b,a))),
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
~ is_a_theorem(implies(a,implies(b,a))),
inference(skolemisation,[status(esa)],[f2_nnf]) ).
cnf(c2,plain,
~ is_a_theorem(implies(a,implies(b,a))),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(goal_0,negated_conjecture,
is_a_theorem(implies(a,implies(b,a))) != true,
inference(equality_encoding,[status(esa)],[c2]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t204]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL087-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.10/0.37 % Computer : n003.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Wed Sep 23 21:54:34 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 5.75/1.21 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 5.75/1.21 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------