%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : LCL121-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n009.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 24.52s 3.63s
% Output : Proof 24.52s
% Verified :
% SZS Type : Refutation
% Derivation depth : 87
% Number of leaves : 4
% Syntax : Number of formulae : 140 ( 136 unt; 0 def)
% Number of atoms : 148 ( 127 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 22 ( 14 ~; 8 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 1 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-4 aty)
% Number of variables : 464 ( 2 sgn 12 !; 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(t1,plain,
ifeq(is_a_theorem(equivalent(X1,X2)),true,ifeq(is_a_theorem(X1),true,is_a_theorem(X2),true),true) = true,
inference(equality_encoding,[status(esa)],[c0]) ).
cnf(t5,plain,
ifeq(is_a_theorem(equivalent(X1,X2)),true,ifeq(is_a_theorem(X1),true,is_a_theorem(X2),true),true) = true,
inference(orient,[status(thm)],[t1]) ).
cnf(f1,axiom,
is_a_theorem(equivalent(X,equivalent(X,equivalent(equivalent(Y,Z),equivalent(equivalent(Y,U),equivalent(Z,U)))))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lg_2) ).
fof(f1_nnf,plain,
! [X,Y,Z,U] : is_a_theorem(equivalent(X,equivalent(X,equivalent(equivalent(Y,Z),equivalent(equivalent(Y,U),equivalent(Z,U)))))),
inference(nnf_transformation,[status(thm)],[f1]) ).
fof(f1_sk,plain,
! [X,Y,Z,U] : is_a_theorem(equivalent(X,equivalent(X,equivalent(equivalent(Y,Z),equivalent(equivalent(Y,U),equivalent(Z,U)))))),
inference(skolemisation,[status(esa)],[f1_nnf]) ).
cnf(c1,plain,
is_a_theorem(equivalent(X0,equivalent(X0,equivalent(equivalent(X1,X2),equivalent(equivalent(X1,X3),equivalent(X2,X3)))))),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(t2,plain,
is_a_theorem(equivalent(X1,equivalent(X1,equivalent(equivalent(X2,X3),equivalent(equivalent(X2,X4),equivalent(X3,X4)))))) = true,
inference(equality_encoding,[status(esa)],[c1]) ).
cnf(t4,plain,
is_a_theorem(equivalent(X1,equivalent(X1,equivalent(equivalent(X2,X3),equivalent(equivalent(X2,X4),equivalent(X3,X4)))))) = true,
inference(orient,[status(thm)],[t2]) ).
cnf(t6,plain,
true = ifeq(true,true,ifeq(is_a_theorem(X1),true,is_a_theorem(equivalent(X1,equivalent(equivalent(X2,X3),equivalent(equivalent(X2,X4),equivalent(X3,X4))))),true),true),
inference(cp,[status(thm)],[t5,t4]) ).
cnf(t0,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t3,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t0]) ).
cnf(t43612,plain,
true = ifeq(is_a_theorem(X1),true,is_a_theorem(equivalent(X1,equivalent(equivalent(X2,X3),equivalent(equivalent(X2,X4),equivalent(X3,X4))))),true),
inference(step,[status(thm)],[t6,t3]) ).
cnf(t9,plain,
ifeq(is_a_theorem(X1),true,is_a_theorem(equivalent(X1,equivalent(equivalent(X2,X3),equivalent(equivalent(X2,X4),equivalent(X3,X4))))),true) = true,
inference(orient,[status(thm)],[t43612]) ).
cnf(t10,plain,
true = ifeq(true,true,is_a_theorem(equivalent(equivalent(X1,equivalent(X1,equivalent(equivalent(X2,X3),equivalent(equivalent(X2,X4),equivalent(X3,X4))))),equivalent(equivalent(Y4,Y5),equivalent(equivalent(Y4,Y6),equivalent(Y5,Y6))))),true),
inference(cp,[status(thm)],[t9,t4]) ).
cnf(t43614,plain,
true = is_a_theorem(equivalent(equivalent(X1,equivalent(X1,equivalent(equivalent(X2,X3),equivalent(equivalent(X2,X4),equivalent(X3,X4))))),equivalent(equivalent(Y4,Y5),equivalent(equivalent(Y4,Y6),equivalent(Y5,Y6))))),
inference(step,[status(thm)],[t10,t3]) ).
cnf(t19,plain,
is_a_theorem(equivalent(equivalent(X1,equivalent(X1,equivalent(equivalent(X2,X3),equivalent(equivalent(X2,X4),equivalent(X3,X4))))),equivalent(equivalent(Y4,Y5),equivalent(equivalent(Y4,Y6),equivalent(Y5,Y6))))) = true,
inference(orient,[status(thm)],[t43614]) ).
cnf(t20,plain,
true = ifeq(true,true,ifeq(is_a_theorem(equivalent(X1,equivalent(X1,equivalent(equivalent(X2,X3),equivalent(equivalent(X2,X4),equivalent(X3,X4)))))),true,is_a_theorem(equivalent(equivalent(Y4,Y5),equivalent(equivalent(Y4,Y6),equivalent(Y5,Y6)))),true),true),
inference(cp,[status(thm)],[t5,t19]) ).
cnf(t43615,plain,
true = ifeq(is_a_theorem(equivalent(X1,equivalent(X1,equivalent(equivalent(X2,X3),equivalent(equivalent(X2,X4),equivalent(X3,X4)))))),true,is_a_theorem(equivalent(equivalent(Y4,Y5),equivalent(equivalent(Y4,Y6),equivalent(Y5,Y6)))),true),
inference(step,[status(thm)],[t20,t3]) ).
cnf(t43616,plain,
true = ifeq(true,true,is_a_theorem(equivalent(equivalent(Y4,Y5),equivalent(equivalent(Y4,Y6),equivalent(Y5,Y6)))),true),
inference(step,[status(thm)],[t43615,t4]) ).
cnf(t43617,plain,
true = is_a_theorem(equivalent(equivalent(Y4,Y5),equivalent(equivalent(Y4,Y6),equivalent(Y5,Y6)))),
inference(step,[status(thm)],[t43616,t3]) ).
cnf(t27,plain,
is_a_theorem(equivalent(equivalent(X1,X2),equivalent(equivalent(X1,X3),equivalent(X2,X3)))) = true,
inference(orient,[status(thm)],[t43617]) ).
cnf(t29,plain,
true = ifeq(is_a_theorem(equivalent(equivalent(equivalent(X1,X2),equivalent(equivalent(X1,X3),equivalent(X2,X3))),X4)),true,ifeq(true,true,is_a_theorem(X4),true),true),
inference(cp,[status(thm)],[t5,t27]) ).
cnf(t43620,plain,
true = ifeq(is_a_theorem(equivalent(equivalent(equivalent(X1,X2),equivalent(equivalent(X1,X3),equivalent(X2,X3))),X4)),true,is_a_theorem(X4),true),
inference(step,[status(thm)],[t29,t3]) ).
cnf(t50,plain,
ifeq(is_a_theorem(equivalent(equivalent(equivalent(X1,X2),equivalent(equivalent(X1,X3),equivalent(X2,X3))),X4)),true,is_a_theorem(X4),true) = true,
inference(orient,[status(thm)],[t43620]) ).
cnf(t28,plain,
true = ifeq(true,true,ifeq(is_a_theorem(equivalent(X1,X2)),true,is_a_theorem(equivalent(equivalent(X1,X3),equivalent(X2,X3))),true),true),
inference(cp,[status(thm)],[t5,t27]) ).
cnf(t43618,plain,
true = ifeq(is_a_theorem(equivalent(X1,X2)),true,is_a_theorem(equivalent(equivalent(X1,X3),equivalent(X2,X3))),true),
inference(step,[status(thm)],[t28,t3]) ).
cnf(t34,plain,
ifeq(is_a_theorem(equivalent(X1,X2)),true,is_a_theorem(equivalent(equivalent(X1,X3),equivalent(X2,X3))),true) = true,
inference(orient,[status(thm)],[t43618]) ).
cnf(t37,plain,
true = ifeq(true,true,is_a_theorem(equivalent(equivalent(equivalent(X1,X2),X3),equivalent(equivalent(equivalent(X1,X4),equivalent(X2,X4)),X3))),true),
inference(cp,[status(thm)],[t34,t27]) ).
cnf(t43619,plain,
true = is_a_theorem(equivalent(equivalent(equivalent(X1,X2),X3),equivalent(equivalent(equivalent(X1,X4),equivalent(X2,X4)),X3))),
inference(step,[status(thm)],[t37,t3]) ).
cnf(t39,plain,
is_a_theorem(equivalent(equivalent(equivalent(X1,X2),X3),equivalent(equivalent(equivalent(X1,X4),equivalent(X2,X4)),X3))) = true,
inference(orient,[status(thm)],[t43619]) ).
cnf(t51,plain,
true = ifeq(true,true,is_a_theorem(equivalent(equivalent(equivalent(X1,X2),equivalent(X3,X2)),equivalent(equivalent(X1,X4),equivalent(X3,X4)))),true),
inference(cp,[status(thm)],[t50,t39]) ).
cnf(t43621,plain,
true = is_a_theorem(equivalent(equivalent(equivalent(X1,X2),equivalent(X3,X2)),equivalent(equivalent(X1,X4),equivalent(X3,X4)))),
inference(step,[status(thm)],[t51,t3]) ).
cnf(t58,plain,
is_a_theorem(equivalent(equivalent(equivalent(X1,X2),equivalent(X3,X2)),equivalent(equivalent(X1,X4),equivalent(X3,X4)))) = true,
inference(orient,[status(thm)],[t43621]) ).
cnf(t59,plain,
true = ifeq(true,true,ifeq(is_a_theorem(equivalent(equivalent(X1,X2),equivalent(X3,X2))),true,is_a_theorem(equivalent(equivalent(X1,X4),equivalent(X3,X4))),true),true),
inference(cp,[status(thm)],[t5,t58]) ).
cnf(t43623,plain,
true = ifeq(is_a_theorem(equivalent(equivalent(X1,X2),equivalent(X3,X2))),true,is_a_theorem(equivalent(equivalent(X1,X4),equivalent(X3,X4))),true),
inference(step,[status(thm)],[t59,t3]) ).
cnf(t80,plain,
ifeq(is_a_theorem(equivalent(equivalent(X1,X2),equivalent(X3,X2))),true,is_a_theorem(equivalent(equivalent(X1,X4),equivalent(X3,X4))),true) = true,
inference(orient,[status(thm)],[t43623]) ).
cnf(t82,plain,
true = ifeq(true,true,is_a_theorem(equivalent(equivalent(equivalent(X1,X2),X3),equivalent(equivalent(X1,X2),X3))),true),
inference(cp,[status(thm)],[t80,t58]) ).
cnf(t43624,plain,
true = is_a_theorem(equivalent(equivalent(equivalent(X1,X2),X3),equivalent(equivalent(X1,X2),X3))),
inference(step,[status(thm)],[t82,t3]) ).
cnf(t86,plain,
is_a_theorem(equivalent(equivalent(equivalent(X1,X2),X3),equivalent(equivalent(X1,X2),X3))) = true,
inference(orient,[status(thm)],[t43624]) ).
cnf(t88,plain,
true = ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(X1,X2),X3),equivalent(equivalent(X1,X2),X3)),X4)),true,ifeq(true,true,is_a_theorem(X4),true),true),
inference(cp,[status(thm)],[t5,t86]) ).
cnf(t43627,plain,
true = ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(X1,X2),X3),equivalent(equivalent(X1,X2),X3)),X4)),true,is_a_theorem(X4),true),
inference(step,[status(thm)],[t88,t3]) ).
cnf(t107,plain,
ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(X1,X2),X3),equivalent(equivalent(X1,X2),X3)),X4)),true,is_a_theorem(X4),true) = true,
inference(orient,[status(thm)],[t43627]) ).
cnf(t40,plain,
true = ifeq(true,true,ifeq(is_a_theorem(equivalent(equivalent(X1,X2),X3)),true,is_a_theorem(equivalent(equivalent(equivalent(X1,X4),equivalent(X2,X4)),X3)),true),true),
inference(cp,[status(thm)],[t5,t39]) ).
cnf(t43622,plain,
true = ifeq(is_a_theorem(equivalent(equivalent(X1,X2),X3)),true,is_a_theorem(equivalent(equivalent(equivalent(X1,X4),equivalent(X2,X4)),X3)),true),
inference(step,[status(thm)],[t40,t3]) ).
cnf(t72,plain,
ifeq(is_a_theorem(equivalent(equivalent(X1,X2),X3)),true,is_a_theorem(equivalent(equivalent(equivalent(X1,X4),equivalent(X2,X4)),X3)),true) = true,
inference(orient,[status(thm)],[t43622]) ).
cnf(t90,plain,
true = ifeq(true,true,is_a_theorem(equivalent(equivalent(equivalent(equivalent(X1,X2),X3),equivalent(X4,X3)),equivalent(equivalent(X1,X2),X4))),true),
inference(cp,[status(thm)],[t72,t86]) ).
cnf(t43626,plain,
true = is_a_theorem(equivalent(equivalent(equivalent(equivalent(X1,X2),X3),equivalent(X4,X3)),equivalent(equivalent(X1,X2),X4))),
inference(step,[status(thm)],[t90,t3]) ).
cnf(t96,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(X1,X2),X3),equivalent(X4,X3)),equivalent(equivalent(X1,X2),X4))) = true,
inference(orient,[status(thm)],[t43626]) ).
cnf(t108,plain,
true = ifeq(true,true,is_a_theorem(equivalent(equivalent(X1,X2),equivalent(X1,X2))),true),
inference(cp,[status(thm)],[t107,t96]) ).
cnf(t43628,plain,
true = is_a_theorem(equivalent(equivalent(X1,X2),equivalent(X1,X2))),
inference(step,[status(thm)],[t108,t3]) ).
cnf(t118,plain,
is_a_theorem(equivalent(equivalent(X1,X2),equivalent(X1,X2))) = true,
inference(orient,[status(thm)],[t43628]) ).
cnf(t120,plain,
true = ifeq(is_a_theorem(equivalent(equivalent(equivalent(X1,X2),equivalent(X1,X2)),X3)),true,ifeq(true,true,is_a_theorem(X3),true),true),
inference(cp,[status(thm)],[t5,t118]) ).
cnf(t43631,plain,
true = ifeq(is_a_theorem(equivalent(equivalent(equivalent(X1,X2),equivalent(X1,X2)),X3)),true,is_a_theorem(X3),true),
inference(step,[status(thm)],[t120,t3]) ).
cnf(t144,plain,
ifeq(is_a_theorem(equivalent(equivalent(equivalent(X1,X2),equivalent(X1,X2)),X3)),true,is_a_theorem(X3),true) = true,
inference(orient,[status(thm)],[t43631]) ).
cnf(t123,plain,
true = ifeq(true,true,is_a_theorem(equivalent(equivalent(equivalent(X1,X2),equivalent(X3,X2)),equivalent(X1,X3))),true),
inference(cp,[status(thm)],[t72,t118]) ).
cnf(t43630,plain,
true = is_a_theorem(equivalent(equivalent(equivalent(X1,X2),equivalent(X3,X2)),equivalent(X1,X3))),
inference(step,[status(thm)],[t123,t3]) ).
cnf(t132,plain,
is_a_theorem(equivalent(equivalent(equivalent(X1,X2),equivalent(X3,X2)),equivalent(X1,X3))) = true,
inference(orient,[status(thm)],[t43630]) ).
cnf(t145,plain,
true = ifeq(true,true,is_a_theorem(equivalent(X1,X1)),true),
inference(cp,[status(thm)],[t144,t132]) ).
cnf(t43632,plain,
true = is_a_theorem(equivalent(X1,X1)),
inference(step,[status(thm)],[t145,t3]) ).
cnf(t155,plain,
is_a_theorem(equivalent(X1,X1)) = true,
inference(orient,[status(thm)],[t43632]) ).
cnf(t157,plain,
true = ifeq(is_a_theorem(equivalent(equivalent(X1,X1),X2)),true,ifeq(true,true,is_a_theorem(X2),true),true),
inference(cp,[status(thm)],[t5,t155]) ).
cnf(t43634,plain,
true = ifeq(is_a_theorem(equivalent(equivalent(X1,X1),X2)),true,is_a_theorem(X2),true),
inference(step,[status(thm)],[t157,t3]) ).
cnf(t165,plain,
ifeq(is_a_theorem(equivalent(equivalent(X1,X1),X2)),true,is_a_theorem(X2),true) = true,
inference(orient,[status(thm)],[t43634]) ).
cnf(t136,plain,
true = ifeq(true,true,is_a_theorem(equivalent(equivalent(equivalent(equivalent(X1,X2),equivalent(X3,X2)),X4),equivalent(equivalent(X1,X3),X4))),true),
inference(cp,[status(thm)],[t34,t132]) ).
cnf(t43636,plain,
true = is_a_theorem(equivalent(equivalent(equivalent(equivalent(X1,X2),equivalent(X3,X2)),X4),equivalent(equivalent(X1,X3),X4))),
inference(step,[status(thm)],[t136,t3]) ).
cnf(t196,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(X1,X2),equivalent(X3,X2)),X4),equivalent(equivalent(X1,X3),X4))) = true,
inference(orient,[status(thm)],[t43636]) ).
cnf(t197,plain,
true = ifeq(true,true,ifeq(is_a_theorem(equivalent(equivalent(equivalent(X1,X2),equivalent(X3,X2)),X4)),true,is_a_theorem(equivalent(equivalent(X1,X3),X4)),true),true),
inference(cp,[status(thm)],[t5,t196]) ).
cnf(t43642,plain,
true = ifeq(is_a_theorem(equivalent(equivalent(equivalent(X1,X2),equivalent(X3,X2)),X4)),true,is_a_theorem(equivalent(equivalent(X1,X3),X4)),true),
inference(step,[status(thm)],[t197,t3]) ).
cnf(t293,plain,
ifeq(is_a_theorem(equivalent(equivalent(equivalent(X1,X2),equivalent(X3,X2)),X4)),true,is_a_theorem(equivalent(equivalent(X1,X3),X4)),true) = true,
inference(orient,[status(thm)],[t43642]) ).
cnf(t133,plain,
true = ifeq(true,true,ifeq(is_a_theorem(equivalent(equivalent(X1,X2),equivalent(X3,X2))),true,is_a_theorem(equivalent(X1,X3)),true),true),
inference(cp,[status(thm)],[t5,t132]) ).
cnf(t43635,plain,
true = ifeq(is_a_theorem(equivalent(equivalent(X1,X2),equivalent(X3,X2))),true,is_a_theorem(equivalent(X1,X3)),true),
inference(step,[status(thm)],[t133,t3]) ).
cnf(t179,plain,
ifeq(is_a_theorem(equivalent(equivalent(X1,X2),equivalent(X3,X2))),true,is_a_theorem(equivalent(X1,X3)),true) = true,
inference(orient,[status(thm)],[t43635]) ).
cnf(t180,plain,
true = ifeq(true,true,is_a_theorem(equivalent(equivalent(X1,equivalent(equivalent(X2,X3),equivalent(X4,X3))),equivalent(X1,equivalent(X2,X4)))),true),
inference(cp,[status(thm)],[t179,t19]) ).
cnf(t43639,plain,
true = is_a_theorem(equivalent(equivalent(X1,equivalent(equivalent(X2,X3),equivalent(X4,X3))),equivalent(X1,equivalent(X2,X4)))),
inference(step,[status(thm)],[t180,t3]) ).
cnf(t239,plain,
is_a_theorem(equivalent(equivalent(X1,equivalent(equivalent(X2,X3),equivalent(X4,X3))),equivalent(X1,equivalent(X2,X4)))) = true,
inference(orient,[status(thm)],[t43639]) ).
cnf(t296,plain,
true = ifeq(true,true,is_a_theorem(equivalent(equivalent(X1,equivalent(X2,X3)),equivalent(equivalent(X1,equivalent(X4,X3)),equivalent(X2,X4)))),true),
inference(cp,[status(thm)],[t293,t239]) ).
cnf(t43645,plain,
true = is_a_theorem(equivalent(equivalent(X1,equivalent(X2,X3)),equivalent(equivalent(X1,equivalent(X4,X3)),equivalent(X2,X4)))),
inference(step,[status(thm)],[t296,t3]) ).
cnf(t346,plain,
is_a_theorem(equivalent(equivalent(X1,equivalent(X2,X3)),equivalent(equivalent(X1,equivalent(X4,X3)),equivalent(X2,X4)))) = true,
inference(orient,[status(thm)],[t43645]) ).
cnf(t354,plain,
true = ifeq(true,true,is_a_theorem(equivalent(equivalent(X1,X2),equivalent(equivalent(X1,equivalent(X3,X3)),X2))),true),
inference(cp,[status(thm)],[t80,t346]) ).
cnf(t43649,plain,
true = is_a_theorem(equivalent(equivalent(X1,X2),equivalent(equivalent(X1,equivalent(X3,X3)),X2))),
inference(step,[status(thm)],[t354,t3]) ).
cnf(t420,plain,
is_a_theorem(equivalent(equivalent(X1,X2),equivalent(equivalent(X1,equivalent(X3,X3)),X2))) = true,
inference(orient,[status(thm)],[t43649]) ).
cnf(t427,plain,
true = ifeq(true,true,is_a_theorem(equivalent(equivalent(X1,equivalent(X2,X2)),X1)),true),
inference(cp,[status(thm)],[t165,t420]) ).
cnf(t43650,plain,
true = is_a_theorem(equivalent(equivalent(X1,equivalent(X2,X2)),X1)),
inference(step,[status(thm)],[t427,t3]) ).
cnf(t444,plain,
is_a_theorem(equivalent(equivalent(X1,equivalent(X2,X2)),X1)) = true,
inference(orient,[status(thm)],[t43650]) ).
cnf(t452,plain,
true = ifeq(true,true,is_a_theorem(equivalent(equivalent(equivalent(X1,equivalent(X2,X2)),X3),equivalent(X1,X3))),true),
inference(cp,[status(thm)],[t80,t444]) ).
cnf(t43656,plain,
true = is_a_theorem(equivalent(equivalent(equivalent(X1,equivalent(X2,X2)),X3),equivalent(X1,X3))),
inference(step,[status(thm)],[t452,t3]) ).
cnf(t556,plain,
is_a_theorem(equivalent(equivalent(equivalent(X1,equivalent(X2,X2)),X3),equivalent(X1,X3))) = true,
inference(orient,[status(thm)],[t43656]) ).
cnf(t557,plain,
true = ifeq(true,true,ifeq(is_a_theorem(equivalent(equivalent(X1,equivalent(X2,X2)),X3)),true,is_a_theorem(equivalent(X1,X3)),true),true),
inference(cp,[status(thm)],[t5,t556]) ).
cnf(t43677,plain,
true = ifeq(is_a_theorem(equivalent(equivalent(X1,equivalent(X2,X2)),X3)),true,is_a_theorem(equivalent(X1,X3)),true),
inference(step,[status(thm)],[t557,t3]) ).
cnf(t1106,plain,
ifeq(is_a_theorem(equivalent(equivalent(X1,equivalent(X2,X2)),X3)),true,is_a_theorem(equivalent(X1,X3)),true) = true,
inference(orient,[status(thm)],[t43677]) ).
cnf(t1107,plain,
true = ifeq(true,true,is_a_theorem(equivalent(X1,equivalent(equivalent(X1,equivalent(X2,X3)),equivalent(X3,X2)))),true),
inference(cp,[status(thm)],[t1106,t346]) ).
cnf(t43678,plain,
true = is_a_theorem(equivalent(X1,equivalent(equivalent(X1,equivalent(X2,X3)),equivalent(X3,X2)))),
inference(step,[status(thm)],[t1107,t3]) ).
cnf(t1156,plain,
is_a_theorem(equivalent(X1,equivalent(equivalent(X1,equivalent(X2,X3)),equivalent(X3,X2)))) = true,
inference(orient,[status(thm)],[t43678]) ).
cnf(t1158,plain,
true = ifeq(is_a_theorem(equivalent(equivalent(X1,equivalent(equivalent(X1,equivalent(X2,X3)),equivalent(X3,X2))),X4)),true,ifeq(true,true,is_a_theorem(X4),true),true),
inference(cp,[status(thm)],[t5,t1156]) ).
cnf(t44056,plain,
true = ifeq(is_a_theorem(equivalent(equivalent(X1,equivalent(equivalent(X1,equivalent(X2,X3)),equivalent(X3,X2))),X4)),true,is_a_theorem(X4),true),
inference(step,[status(thm)],[t1158,t3]) ).
cnf(t32466,plain,
ifeq(is_a_theorem(equivalent(equivalent(X1,equivalent(equivalent(X1,equivalent(X2,X3)),equivalent(X3,X2))),X4)),true,is_a_theorem(X4),true) = true,
inference(orient,[status(thm)],[t44056]) ).
cnf(t347,plain,
true = ifeq(true,true,ifeq(is_a_theorem(equivalent(X1,equivalent(X2,X3))),true,is_a_theorem(equivalent(equivalent(X1,equivalent(X4,X3)),equivalent(X2,X4))),true),true),
inference(cp,[status(thm)],[t5,t346]) ).
cnf(t44030,plain,
true = ifeq(is_a_theorem(equivalent(X1,equivalent(X2,X3))),true,is_a_theorem(equivalent(equivalent(X1,equivalent(X4,X3)),equivalent(X2,X4))),true),
inference(step,[status(thm)],[t347,t3]) ).
cnf(t20289,plain,
ifeq(is_a_theorem(equivalent(X1,equivalent(X2,X3))),true,is_a_theorem(equivalent(equivalent(X1,equivalent(X4,X3)),equivalent(X2,X4))),true) = true,
inference(orient,[status(thm)],[t44030]) ).
cnf(t456,plain,
true = ifeq(true,true,is_a_theorem(equivalent(equivalent(equivalent(X1,X2),equivalent(equivalent(X3,X3),X2)),X1)),true),
inference(cp,[status(thm)],[t72,t444]) ).
cnf(t43657,plain,
true = is_a_theorem(equivalent(equivalent(equivalent(X1,X2),equivalent(equivalent(X3,X3),X2)),X1)),
inference(step,[status(thm)],[t456,t3]) ).
cnf(t579,plain,
is_a_theorem(equivalent(equivalent(equivalent(X1,X2),equivalent(equivalent(X3,X3),X2)),X1)) = true,
inference(orient,[status(thm)],[t43657]) ).
cnf(t589,plain,
true = ifeq(true,true,is_a_theorem(equivalent(equivalent(equivalent(equivalent(X1,equivalent(equivalent(X2,X2),X3)),X3),X4),equivalent(X1,X4))),true),
inference(cp,[status(thm)],[t80,t579]) ).
cnf(t43724,plain,
true = is_a_theorem(equivalent(equivalent(equivalent(equivalent(X1,equivalent(equivalent(X2,X2),X3)),X3),X4),equivalent(X1,X4))),
inference(step,[status(thm)],[t589,t3]) ).
cnf(t3081,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(X1,equivalent(equivalent(X2,X2),X3)),X3),X4),equivalent(X1,X4))) = true,
inference(orient,[status(thm)],[t43724]) ).
cnf(t3082,plain,
true = ifeq(true,true,ifeq(is_a_theorem(equivalent(equivalent(equivalent(X1,equivalent(equivalent(X2,X2),X3)),X3),X4)),true,is_a_theorem(equivalent(X1,X4)),true),true),
inference(cp,[status(thm)],[t5,t3081]) ).
cnf(t44077,plain,
true = ifeq(is_a_theorem(equivalent(equivalent(equivalent(X1,equivalent(equivalent(X2,X2),X3)),X3),X4)),true,is_a_theorem(equivalent(X1,X4)),true),
inference(step,[status(thm)],[t3082,t3]) ).
cnf(t40586,plain,
ifeq(is_a_theorem(equivalent(equivalent(equivalent(X1,equivalent(equivalent(X2,X2),X3)),X3),X4)),true,is_a_theorem(equivalent(X1,X4)),true) = true,
inference(orient,[status(thm)],[t44077]) ).
cnf(t1167,plain,
true = ifeq(true,true,is_a_theorem(equivalent(equivalent(X1,X2),equivalent(equivalent(equivalent(X1,equivalent(X3,X4)),equivalent(X4,X3)),X2))),true),
inference(cp,[status(thm)],[t80,t1156]) ).
cnf(t43799,plain,
true = is_a_theorem(equivalent(equivalent(X1,X2),equivalent(equivalent(equivalent(X1,equivalent(X3,X4)),equivalent(X4,X3)),X2))),
inference(step,[status(thm)],[t1167,t3]) ).
cnf(t6536,plain,
is_a_theorem(equivalent(equivalent(X1,X2),equivalent(equivalent(equivalent(X1,equivalent(X3,X4)),equivalent(X4,X3)),X2))) = true,
inference(orient,[status(thm)],[t43799]) ).
cnf(t6548,plain,
true = ifeq(true,true,is_a_theorem(equivalent(equivalent(equivalent(X1,equivalent(X2,X3)),equivalent(X3,X2)),X1)),true),
inference(cp,[status(thm)],[t165,t6536]) ).
cnf(t43800,plain,
true = is_a_theorem(equivalent(equivalent(equivalent(X1,equivalent(X2,X3)),equivalent(X3,X2)),X1)),
inference(step,[status(thm)],[t6548,t3]) ).
cnf(t6591,plain,
is_a_theorem(equivalent(equivalent(equivalent(X1,equivalent(X2,X3)),equivalent(X3,X2)),X1)) = true,
inference(orient,[status(thm)],[t43800]) ).
cnf(t6602,plain,
true = ifeq(true,true,is_a_theorem(equivalent(equivalent(equivalent(equivalent(X1,equivalent(X2,X3)),equivalent(X3,X2)),X4),equivalent(X1,X4))),true),
inference(cp,[status(thm)],[t80,t6591]) ).
cnf(t43907,plain,
true = is_a_theorem(equivalent(equivalent(equivalent(equivalent(X1,equivalent(X2,X3)),equivalent(X3,X2)),X4),equivalent(X1,X4))),
inference(step,[status(thm)],[t6602,t3]) ).
cnf(t11894,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(X1,equivalent(X2,X3)),equivalent(X3,X2)),X4),equivalent(X1,X4))) = true,
inference(orient,[status(thm)],[t43907]) ).
cnf(t11923,plain,
true = ifeq(true,true,is_a_theorem(equivalent(equivalent(equivalent(X1,equivalent(X2,X3)),X4),equivalent(X1,equivalent(X4,equivalent(X3,X2))))),true),
inference(cp,[status(thm)],[t293,t11894]) ).
cnf(t43960,plain,
true = is_a_theorem(equivalent(equivalent(equivalent(X1,equivalent(X2,X3)),X4),equivalent(X1,equivalent(X4,equivalent(X3,X2))))),
inference(step,[status(thm)],[t11923,t3]) ).
cnf(t14510,plain,
is_a_theorem(equivalent(equivalent(equivalent(X1,equivalent(X2,X3)),X4),equivalent(X1,equivalent(X4,equivalent(X3,X2))))) = true,
inference(orient,[status(thm)],[t43960]) ).
cnf(t40587,plain,
true = ifeq(true,true,is_a_theorem(equivalent(X1,equivalent(X1,equivalent(X2,equivalent(X2,equivalent(X3,X3)))))),true),
inference(cp,[status(thm)],[t40586,t14510]) ).
cnf(t44078,plain,
true = is_a_theorem(equivalent(X1,equivalent(X1,equivalent(X2,equivalent(X2,equivalent(X3,X3)))))),
inference(step,[status(thm)],[t40587,t3]) ).
cnf(t41095,plain,
is_a_theorem(equivalent(X1,equivalent(X1,equivalent(X2,equivalent(X2,equivalent(X3,X3)))))) = true,
inference(orient,[status(thm)],[t44078]) ).
cnf(t41127,plain,
true = ifeq(true,true,is_a_theorem(equivalent(equivalent(X1,equivalent(X2,equivalent(X3,equivalent(X3,equivalent(X4,X4))))),equivalent(X1,X2))),true),
inference(cp,[status(thm)],[t20289,t41095]) ).
cnf(t44091,plain,
true = is_a_theorem(equivalent(equivalent(X1,equivalent(X2,equivalent(X3,equivalent(X3,equivalent(X4,X4))))),equivalent(X1,X2))),
inference(step,[status(thm)],[t41127,t3]) ).
cnf(t43346,plain,
is_a_theorem(equivalent(equivalent(X1,equivalent(X2,equivalent(X3,equivalent(X3,equivalent(X4,X4))))),equivalent(X1,X2))) = true,
inference(orient,[status(thm)],[t44091]) ).
cnf(t43436,plain,
true = ifeq(true,true,is_a_theorem(equivalent(X1,equivalent(X1,equivalent(equivalent(X2,equivalent(X3,X3)),X2)))),true),
inference(cp,[status(thm)],[t32466,t43346]) ).
cnf(t44092,plain,
true = is_a_theorem(equivalent(X1,equivalent(X1,equivalent(equivalent(X2,equivalent(X3,X3)),X2)))),
inference(step,[status(thm)],[t43436,t3]) ).
cnf(t43468,plain,
is_a_theorem(equivalent(X1,equivalent(X1,equivalent(equivalent(X2,equivalent(X3,X3)),X2)))) = true,
inference(orient,[status(thm)],[t44092]) ).
cnf(f2,negated_conjecture,
~ is_a_theorem(equivalent(a,equivalent(a,equivalent(equivalent(b,equivalent(c,c)),b)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_lg_1) ).
fof(f2_nnf,plain,
~ is_a_theorem(equivalent(a,equivalent(a,equivalent(equivalent(b,equivalent(c,c)),b)))),
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
~ is_a_theorem(equivalent(a,equivalent(a,equivalent(equivalent(b,equivalent(c,c)),b)))),
inference(skolemisation,[status(esa)],[f2_nnf]) ).
cnf(c2,plain,
~ is_a_theorem(equivalent(a,equivalent(a,equivalent(equivalent(b,equivalent(c,c)),b)))),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(goal_0,negated_conjecture,
is_a_theorem(equivalent(a,equivalent(a,equivalent(equivalent(b,equivalent(c,c)),b)))) != true,
inference(equality_encoding,[status(esa)],[c2]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t43468]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL121-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.09/0.37 % Computer : n009.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.38 % CPULimit : 300
% 0.09/0.38 % WCLimit : 300
% 0.09/0.38 % DateTime : Wed Sep 23 22:00:28 UTC 2026
% 0.09/0.38 % CPUTime :
% 0.09/0.38 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 24.52/3.63 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 24.52/3.63 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------