%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : LCL008-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n005.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 02:00:40 PM UTC 2026
% Result : Unsatisfiable 3.16s 0.91s
% Output : Proof 3.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% 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 : 5 ( 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 : 47 ( 0 sgn 10 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f0,axiom,
( is_a_theorem(Y)
| ~ is_a_theorem(X)
| ~ is_a_theorem(equivalent(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(equivalent(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(equivalent(X,Y)) ),
inference(skolemisation,[status(esa)],[f0_nnf]) ).
cnf(c0,plain,
( is_a_theorem(X1)
| ~ is_a_theorem(X0)
| ~ is_a_theorem(equivalent(X0,X1)) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(hi0,axiom,
ifeq(is_a_theorem(equivalent(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(equivalent(equivalent(X,Y),equivalent(equivalent(Z,Y),equivalent(X,Z)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',yql) ).
fof(f1_nnf,plain,
! [X,Y,Z] : is_a_theorem(equivalent(equivalent(X,Y),equivalent(equivalent(Z,Y),equivalent(X,Z)))),
inference(nnf_transformation,[status(thm)],[f1]) ).
fof(f1_sk,plain,
! [X,Y,Z] : is_a_theorem(equivalent(equivalent(X,Y),equivalent(equivalent(Z,Y),equivalent(X,Z)))),
inference(skolemisation,[status(esa)],[f1_nnf]) ).
cnf(c1,plain,
is_a_theorem(equivalent(equivalent(X0,X1),equivalent(equivalent(X2,X1),equivalent(X0,X2)))),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(hi1,axiom,
is_a_theorem(equivalent(equivalent(X0,X1),equivalent(equivalent(X2,X1),equivalent(X0,X2)))) = true,
inference(equality_encoding,[status(esa)],[c1]) ).
cnf(h0,plain,
is_a_theorem(equivalent(equivalent(V0,equivalent(equivalent(V1,V2),equivalent(V3,V1))),equivalent(equivalent(V3,V2),V0))) = true,
inference(hyper_resolution,[status(thm)],[hi0,hi1,hi1]) ).
cnf(h3,plain,
is_a_theorem(equivalent(equivalent(V0,V1),equivalent(V0,V1))) = true,
inference(hyper_resolution,[status(thm)],[hi0,h0,hi1]) ).
cnf(h1,plain,
is_a_theorem(equivalent(equivalent(V0,V1),equivalent(equivalent(V0,V2),equivalent(equivalent(V3,V1),equivalent(V2,V3))))) = true,
inference(hyper_resolution,[status(thm)],[hi0,h0,h0]) ).
cnf(h5,plain,
is_a_theorem(equivalent(equivalent(equivalent(V0,V1),V2),equivalent(equivalent(V2,V0),V1))) = true,
inference(hyper_resolution,[status(thm)],[hi0,h0,h1]) ).
cnf(h33,plain,
is_a_theorem(equivalent(equivalent(equivalent(V0,V1),V0),V1)) = true,
inference(hyper_resolution,[status(thm)],[hi0,h5,h3]) ).
cnf(h51,plain,
is_a_theorem(equivalent(equivalent(V0,equivalent(V1,V0)),V1)) = true,
inference(hyper_resolution,[status(thm)],[hi0,h5,h33]) ).
cnf(h103,plain,
is_a_theorem(equivalent(V0,V0)) = true,
inference(hyper_resolution,[status(thm)],[hi0,h33,h51]) ).
cnf(t3,plain,
is_a_theorem(equivalent(equivalent(X1,X2),equivalent(X2,X1))) = true,
inference(hyper_resolution,[status(thm)],[hi0,hi1,h103]) ).
cnf(t212,plain,
is_a_theorem(equivalent(equivalent(X1,X2),equivalent(X2,X1))) = true,
inference(orient,[status(thm)],[t3]) ).
cnf(f2,negated_conjecture,
~ is_a_theorem(equivalent(equivalent(a,b),equivalent(b,a))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_ec_4) ).
fof(f2_nnf,plain,
~ is_a_theorem(equivalent(equivalent(a,b),equivalent(b,a))),
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
~ is_a_theorem(equivalent(equivalent(a,b),equivalent(b,a))),
inference(skolemisation,[status(esa)],[f2_nnf]) ).
cnf(c2,plain,
~ is_a_theorem(equivalent(equivalent(a,b),equivalent(b,a))),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(goal_0,negated_conjecture,
is_a_theorem(equivalent(equivalent(a,b),equivalent(b,a))) != true,
inference(equality_encoding,[status(esa)],[c2]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t212]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL008-1 : 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 : n005.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 21:37:03 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 3.16/0.91 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.16/0.91 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------