%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : LCL098-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : 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 02:00:56 PM UTC 2026
% Result : Unsatisfiable 9.87s 7.07s
% Output : Proof 9.87s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 3
% Syntax : Number of formulae : 22 ( 18 unt; 0 def)
% Number of atoms : 30 ( 9 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 : 8 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 6 con; 0-4 aty)
% Number of variables : 62 ( 0 sgn 14 !; 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(equivalent(equivalent(equivalent(equivalent(X,Y),equivalent(X,Z)),U),equivalent(equivalent(Y,Z),U)),V),V)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lg_3) ).
fof(f1_nnf,plain,
! [X,Y,Z,U,V] : is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X,Y),equivalent(X,Z)),U),equivalent(equivalent(Y,Z),U)),V),V)),
inference(nnf_transformation,[status(thm)],[f1]) ).
fof(f1_sk,plain,
! [X,Y,Z,U,V] : is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X,Y),equivalent(X,Z)),U),equivalent(equivalent(Y,Z),U)),V),V)),
inference(skolemisation,[status(esa)],[f1_nnf]) ).
cnf(c1,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X0,X1),equivalent(X0,X2)),X3),equivalent(equivalent(X1,X2),X3)),X4),X4)),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(hi1,axiom,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X0,X1),equivalent(X0,X2)),X3),equivalent(equivalent(X1,X2),X3)),X4),X4)) = true,
inference(equality_encoding,[status(esa)],[c1]) ).
cnf(h0,plain,
is_a_theorem(equivalent(equivalent(equivalent(V0,V1),V2),equivalent(equivalent(V3,V1),equivalent(equivalent(V0,V3),V2)))) = true,
inference(hyper_resolution,[status(thm)],[hi0,hi1,hi1]) ).
cnf(h2,plain,
is_a_theorem(equivalent(equivalent(V0,V1),equivalent(equivalent(equivalent(equivalent(V2,V3),equivalent(V2,V4)),V0),equivalent(equivalent(V3,V4),V1)))) = true,
inference(hyper_resolution,[status(thm)],[hi0,hi1,h0]) ).
cnf(h15,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(V0,V1),equivalent(V0,V2)),equivalent(equivalent(equivalent(equivalent(equivalent(V3,V4),equivalent(V3,V5)),V6),equivalent(equivalent(V4,V5),V6)),V7)),equivalent(equivalent(V1,V2),V7))) = true,
inference(hyper_resolution,[status(thm)],[hi0,h2,hi1]) ).
cnf(t9,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(X1,X2),X3),X4),equivalent(equivalent(equivalent(X1,X5),X3),equivalent(equivalent(X2,X5),X4)))) = true,
inference(hyper_resolution,[status(thm)],[hi0,h15,h2]) ).
cnf(t457,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(X1,X2),X3),X4),equivalent(equivalent(equivalent(X1,X5),X3),equivalent(equivalent(X2,X5),X4)))) = true,
inference(orient,[status(thm)],[t9]) ).
cnf(f2,negated_conjecture,
~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(a,b),c),e),equivalent(equivalent(equivalent(a,falsehood),c),equivalent(equivalent(b,falsehood),e)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_lg_4) ).
fof(f2_nnf,plain,
~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(a,b),c),e),equivalent(equivalent(equivalent(a,falsehood),c),equivalent(equivalent(b,falsehood),e)))),
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(a,b),c),e),equivalent(equivalent(equivalent(a,falsehood),c),equivalent(equivalent(b,falsehood),e)))),
inference(skolemisation,[status(esa)],[f2_nnf]) ).
cnf(c2,plain,
~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(a,b),c),e),equivalent(equivalent(equivalent(a,falsehood),c),equivalent(equivalent(b,falsehood),e)))),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(goal_0,negated_conjecture,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(a,b),c),e),equivalent(equivalent(equivalent(a,falsehood),c),equivalent(equivalent(b,falsehood),e)))) != true,
inference(equality_encoding,[status(esa)],[c2]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t457]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : LCL098-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.06 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.18/5.43 % Computer : n008.cluster.edu
% 0.18/5.43 % Model : x86_64 x86_64
% 0.18/5.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/5.43 % Memory : 8046.5625MB
% 0.18/5.43 % OS : Linux 6.8.0-71-generic
% 0.18/5.43 % CPULimit : 300
% 0.18/5.43 % WCLimit : 300
% 0.18/5.43 % DateTime : Wed Sep 23 21:55:47 UTC 2026
% 0.18/5.44 % CPUTime :
% 0.18/5.44 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 9.87/7.07 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 9.87/7.07 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------