%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : LCL125-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n002.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 02:01:01 PM UTC 2026
% Result : Unsatisfiable 270.87s 34.90s
% Output : Proof 270.87s
% Verified :
% SZS Type : Refutation
% Derivation depth : 29
% Number of leaves : 4
% Syntax : Number of formulae : 67 ( 63 unt; 0 def)
% Number of atoms : 75 ( 50 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 : 7 ( 7 usr; 5 con; 0-4 aty)
% Number of variables : 217 ( 0 sgn 16 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f0,axiom,
( is_a_theorem(Y)
| ~ is_a_theorem(X)
| ~ is_a_theorem(equivalent(X,Y)) ),
file('/export/starexec/sandbox/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(f2,axiom,
is_a_theorem(equivalent(X,equivalent(equivalent(X,equivalent(Y,Z)),equivalent(Z,Y)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',q_3) ).
fof(f2_nnf,plain,
! [X,Y,Z] : is_a_theorem(equivalent(X,equivalent(equivalent(X,equivalent(Y,Z)),equivalent(Z,Y)))),
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
! [X,Y,Z] : is_a_theorem(equivalent(X,equivalent(equivalent(X,equivalent(Y,Z)),equivalent(Z,Y)))),
inference(skolemisation,[status(esa)],[f2_nnf]) ).
cnf(c2,plain,
is_a_theorem(equivalent(X0,equivalent(equivalent(X0,equivalent(X1,X2)),equivalent(X2,X1)))),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(hi2,axiom,
is_a_theorem(equivalent(X0,equivalent(equivalent(X0,equivalent(X1,X2)),equivalent(X2,X1)))) = true,
inference(equality_encoding,[status(esa)],[c2]) ).
cnf(h0,plain,
is_a_theorem(equivalent(equivalent(equivalent(V0,equivalent(equivalent(V0,equivalent(V1,V2)),equivalent(V2,V1))),equivalent(V3,V4)),equivalent(V4,V3))) = true,
inference(hyper_resolution,[status(thm)],[hi0,hi2,hi2]) ).
cnf(f1,axiom,
is_a_theorem(equivalent(equivalent(equivalent(X,Y),equivalent(Z,Y)),equivalent(X,Z))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',q_2) ).
fof(f1_nnf,plain,
! [X,Y,Z] : is_a_theorem(equivalent(equivalent(equivalent(X,Y),equivalent(Z,Y)),equivalent(X,Z))),
inference(nnf_transformation,[status(thm)],[f1]) ).
fof(f1_sk,plain,
! [X,Y,Z] : is_a_theorem(equivalent(equivalent(equivalent(X,Y),equivalent(Z,Y)),equivalent(X,Z))),
inference(skolemisation,[status(esa)],[f1_nnf]) ).
cnf(c1,plain,
is_a_theorem(equivalent(equivalent(equivalent(X0,X1),equivalent(X2,X1)),equivalent(X0,X2))),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(hi1,axiom,
is_a_theorem(equivalent(equivalent(equivalent(X0,X1),equivalent(X2,X1)),equivalent(X0,X2))) = true,
inference(equality_encoding,[status(esa)],[c1]) ).
cnf(h3,plain,
is_a_theorem(equivalent(equivalent(equivalent(V0,equivalent(V1,V2)),equivalent(V2,V1)),V0)) = true,
inference(hyper_resolution,[status(thm)],[hi0,h0,hi1]) ).
cnf(h6,plain,
is_a_theorem(equivalent(V0,V0)) = true,
inference(hyper_resolution,[status(thm)],[hi0,h3,hi1]) ).
cnf(h7,plain,
is_a_theorem(equivalent(equivalent(equivalent(V0,V0),equivalent(V1,V2)),equivalent(V2,V1))) = true,
inference(hyper_resolution,[status(thm)],[hi0,hi2,h6]) ).
cnf(h9,plain,
is_a_theorem(equivalent(equivalent(V0,V1),equivalent(equivalent(V2,V2),equivalent(V1,V0)))) = true,
inference(hyper_resolution,[status(thm)],[hi0,h7,hi2]) ).
cnf(h11,plain,
is_a_theorem(equivalent(equivalent(V0,V0),equivalent(V1,V1))) = true,
inference(hyper_resolution,[status(thm)],[hi0,h7,h9]) ).
cnf(h18,plain,
is_a_theorem(equivalent(equivalent(V0,V0),equivalent(equivalent(V1,V1),equivalent(V2,V2)))) = true,
inference(hyper_resolution,[status(thm)],[hi0,h9,h11]) ).
cnf(h17,plain,
is_a_theorem(equivalent(equivalent(V0,V0),equivalent(equivalent(V1,V2),equivalent(equivalent(V1,V3),equivalent(V2,V3))))) = true,
inference(hyper_resolution,[status(thm)],[hi0,h9,hi1]) ).
cnf(h28,plain,
is_a_theorem(equivalent(equivalent(V0,V1),equivalent(equivalent(V0,V2),equivalent(V1,V2)))) = true,
inference(hyper_resolution,[status(thm)],[hi0,h17,h18]) ).
cnf(h29,plain,
is_a_theorem(equivalent(equivalent(equivalent(V0,V1),V2),equivalent(equivalent(equivalent(V0,V3),equivalent(V1,V3)),V2))) = true,
inference(hyper_resolution,[status(thm)],[hi0,h28,h28]) ).
cnf(h69,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(V0,equivalent(V1,V2)),V3),equivalent(equivalent(V2,V1),V3)),V0)) = true,
inference(hyper_resolution,[status(thm)],[hi0,h29,h3]) ).
cnf(h200,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(V0,equivalent(equivalent(V1,V2),V3)),equivalent(V2,V1)),V3),V0)) = true,
inference(hyper_resolution,[status(thm)],[hi0,hi1,h69]) ).
cnf(h44,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(V0,V1),equivalent(V2,V1)),V3),equivalent(equivalent(V0,V2),V3))) = true,
inference(hyper_resolution,[status(thm)],[hi0,h28,hi1]) ).
cnf(h130,plain,
is_a_theorem(equivalent(equivalent(equivalent(V0,V1),V2),equivalent(equivalent(V0,V3),equivalent(V2,equivalent(V3,V1))))) = true,
inference(hyper_resolution,[status(thm)],[hi0,h44,h44]) ).
cnf(h409,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(V0,equivalent(equivalent(V1,V2),V3)),equivalent(V2,V1)),V4),equivalent(V0,equivalent(V4,V3)))) = true,
inference(hyper_resolution,[status(thm)],[hi0,h130,h200]) ).
cnf(h64,plain,
is_a_theorem(equivalent(equivalent(equivalent(V0,V1),equivalent(V2,V1)),equivalent(equivalent(V0,V3),equivalent(V2,V3)))) = true,
inference(hyper_resolution,[status(thm)],[hi0,h29,h28]) ).
cnf(h195,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(V0,equivalent(equivalent(V1,V2),V3)),equivalent(V2,V1)),V3),V4),equivalent(V0,V4))) = true,
inference(hyper_resolution,[status(thm)],[hi0,h64,h69]) ).
cnf(h956,plain,
is_a_theorem(equivalent(V0,equivalent(V0,equivalent(V1,V1)))) = true,
inference(hyper_resolution,[status(thm)],[hi0,h195,h409]) ).
cnf(h31,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(V0,equivalent(V1,V2)),equivalent(V2,V1)),V3),equivalent(V0,V3))) = true,
inference(hyper_resolution,[status(thm)],[hi0,h0,h28]) ).
cnf(h272,plain,
is_a_theorem(equivalent(V0,equivalent(equivalent(V0,V1),equivalent(equivalent(V2,V3),equivalent(V1,equivalent(V3,V2)))))) = true,
inference(hyper_resolution,[status(thm)],[hi0,h31,h130]) ).
cnf(h474,plain,
is_a_theorem(equivalent(V0,equivalent(equivalent(V0,equivalent(equivalent(V1,V2),equivalent(V3,equivalent(V2,V1)))),V3))) = true,
inference(hyper_resolution,[status(thm)],[hi0,hi1,h272]) ).
cnf(h1,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(V0,V1),equivalent(V2,V1)),equivalent(V0,V2)),equivalent(V3,V4)),equivalent(V4,V3))) = true,
inference(hyper_resolution,[status(thm)],[hi0,hi2,hi1]) ).
cnf(h577,plain,
is_a_theorem(equivalent(equivalent(equivalent(V0,V1),equivalent(V2,equivalent(V1,V3))),equivalent(equivalent(V0,V3),V2))) = true,
inference(hyper_resolution,[status(thm)],[hi0,h1,h130]) ).
cnf(h590,plain,
is_a_theorem(equivalent(equivalent(V0,V1),equivalent(equivalent(V0,V2),equivalent(equivalent(V3,V4),equivalent(equivalent(V2,V1),equivalent(V4,V3)))))) = true,
inference(hyper_resolution,[status(thm)],[hi0,h577,h474]) ).
cnf(h599,plain,
is_a_theorem(equivalent(equivalent(V0,equivalent(equivalent(V1,equivalent(V2,V3)),equivalent(V3,V2))),equivalent(V0,V1))) = true,
inference(hyper_resolution,[status(thm)],[hi0,h577,h590]) ).
cnf(h978,plain,
is_a_theorem(equivalent(equivalent(V0,equivalent(V1,V1)),V0)) = true,
inference(hyper_resolution,[status(thm)],[hi0,h599,h956]) ).
cnf(h269,plain,
is_a_theorem(equivalent(equivalent(V0,V1),equivalent(equivalent(V0,V2),equivalent(equivalent(V1,V3),equivalent(V2,V3))))) = true,
inference(hyper_resolution,[status(thm)],[hi0,h44,h130]) ).
cnf(h594,plain,
is_a_theorem(equivalent(equivalent(V0,equivalent(V1,equivalent(V2,V3))),equivalent(equivalent(V0,equivalent(V3,V2)),V1))) = true,
inference(hyper_resolution,[status(thm)],[hi0,h577,h272]) ).
cnf(h620,plain,
is_a_theorem(equivalent(equivalent(equivalent(V0,V1),equivalent(equivalent(V2,V3),equivalent(V1,V3))),equivalent(V0,V2))) = true,
inference(hyper_resolution,[status(thm)],[hi0,h594,h269]) ).
cnf(h1156,plain,
is_a_theorem(equivalent(equivalent(equivalent(V0,V1),equivalent(equivalent(V2,V2),V1)),V0)) = true,
inference(hyper_resolution,[status(thm)],[hi0,h620,h978]) ).
cnf(h273,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(V0,V1),V2),equivalent(V3,V2)),equivalent(equivalent(V0,V4),equivalent(V3,equivalent(V4,V1))))) = true,
inference(hyper_resolution,[status(thm)],[hi0,h29,h130]) ).
cnf(h1579,plain,
is_a_theorem(equivalent(equivalent(equivalent(V0,equivalent(equivalent(V1,V1),V2)),V3),equivalent(V0,equivalent(V3,V2)))) = true,
inference(hyper_resolution,[status(thm)],[hi0,h273,h1156]) ).
cnf(h3579,plain,
is_a_theorem(equivalent(equivalent(equivalent(V0,equivalent(equivalent(V1,V1),V2)),V3),equivalent(equivalent(V0,equivalent(V4,V2)),equivalent(V3,V4)))) = true,
inference(hyper_resolution,[status(thm)],[hi0,h130,h1579]) ).
cnf(h139,plain,
is_a_theorem(equivalent(equivalent(V0,V1),equivalent(equivalent(equivalent(V0,V2),equivalent(V3,V2)),equivalent(V1,V3)))) = true,
inference(hyper_resolution,[status(thm)],[hi0,h44,h29]) ).
cnf(h371,plain,
is_a_theorem(equivalent(equivalent(equivalent(V0,V1),V2),equivalent(equivalent(equivalent(equivalent(V0,V3),equivalent(V4,V3)),equivalent(V1,V4)),V2))) = true,
inference(hyper_resolution,[status(thm)],[hi0,h28,h139]) ).
cnf(h1182,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(V0,V1),equivalent(V2,V1)),equivalent(equivalent(V3,V3),V2)),V0)) = true,
inference(hyper_resolution,[status(thm)],[hi0,h371,h978]) ).
cnf(h182,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(V0,V1),V2),equivalent(equivalent(V3,V1),V2)),equivalent(equivalent(V0,V4),equivalent(V3,V4)))) = true,
inference(hyper_resolution,[status(thm)],[hi0,h29,h64]) ).
cnf(h2841,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(V0,equivalent(V1,V2)),equivalent(equivalent(V3,V3),V1)),V2),V4),equivalent(V0,V4))) = true,
inference(hyper_resolution,[status(thm)],[hi0,h182,h1182]) ).
cnf(h6923,plain,
is_a_theorem(equivalent(V0,equivalent(equivalent(equivalent(V0,equivalent(V1,V2)),equivalent(V3,V1)),equivalent(V2,V3)))) = true,
inference(hyper_resolution,[status(thm)],[hi0,h2841,h3579]) ).
cnf(h952,plain,
is_a_theorem(equivalent(equivalent(V0,equivalent(equivalent(V1,equivalent(V2,V3)),V4)),equivalent(equivalent(V0,equivalent(equivalent(V3,V2),V4)),V1))) = true,
inference(hyper_resolution,[status(thm)],[hi0,h409,h409]) ).
cnf(h6947,plain,
is_a_theorem(equivalent(equivalent(V0,equivalent(equivalent(V1,V2),equivalent(V3,V2))),equivalent(V0,equivalent(V1,V3)))) = true,
inference(hyper_resolution,[status(thm)],[hi0,h952,h6923]) ).
cnf(h7016,plain,
is_a_theorem(equivalent(equivalent(equivalent(V0,equivalent(V1,V2)),equivalent(equivalent(V2,V3),equivalent(V1,V3))),V0)) = true,
inference(hyper_resolution,[status(thm)],[hi0,h599,h6947]) ).
cnf(h286,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(V0,equivalent(V1,V2)),V3),V4),equivalent(V0,equivalent(V4,equivalent(equivalent(V2,V1),V3))))) = true,
inference(hyper_resolution,[status(thm)],[hi0,h130,h69]) ).
cnf(t42,plain,
is_a_theorem(equivalent(X1,equivalent(X1,equivalent(equivalent(X2,X3),equivalent(equivalent(X2,X4),equivalent(X3,X4)))))) = true,
inference(hyper_resolution,[status(thm)],[hi0,h286,h7016]) ).
cnf(t271,plain,
is_a_theorem(equivalent(X1,equivalent(X1,equivalent(equivalent(X2,X3),equivalent(equivalent(X2,X4),equivalent(X3,X4)))))) = true,
inference(orient,[status(thm)],[t42]) ).
cnf(f3,negated_conjecture,
~ is_a_theorem(equivalent(a,equivalent(a,equivalent(equivalent(b,c),equivalent(equivalent(b,e),equivalent(c,e)))))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_lg_2) ).
fof(f3_nnf,plain,
~ is_a_theorem(equivalent(a,equivalent(a,equivalent(equivalent(b,c),equivalent(equivalent(b,e),equivalent(c,e)))))),
inference(nnf_transformation,[status(thm)],[f3]) ).
fof(f3_sk,plain,
~ is_a_theorem(equivalent(a,equivalent(a,equivalent(equivalent(b,c),equivalent(equivalent(b,e),equivalent(c,e)))))),
inference(skolemisation,[status(esa)],[f3_nnf]) ).
cnf(c3,plain,
~ is_a_theorem(equivalent(a,equivalent(a,equivalent(equivalent(b,c),equivalent(equivalent(b,e),equivalent(c,e)))))),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(goal_0,negated_conjecture,
is_a_theorem(equivalent(a,equivalent(a,equivalent(equivalent(b,c),equivalent(equivalent(b,e),equivalent(c,e)))))) != true,
inference(equality_encoding,[status(esa)],[c3]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t271]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL125-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.10/0.37 % Computer : n002.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 22:04:03 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 270.87/34.90 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 270.87/34.90 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------