%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : LCL128-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n004.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 02:01:02 PM UTC 2026
% Result : Unsatisfiable 25.64s 3.67s
% Output : Proof 25.64s
% Verified :
% SZS Type : Refutation
% Derivation depth : 80
% Number of leaves : 4
% Syntax : Number of formulae : 133 ( 129 unt; 0 def)
% Number of atoms : 141 ( 120 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 : 7 ( 7 usr; 5 con; 0-4 aty)
% Number of variables : 448 ( 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(equivalent(Y,Z),equivalent(U,Z)),equivalent(Y,U))))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s_3) ).
fof(f1_nnf,plain,
! [X,Y,Z,U] : is_a_theorem(equivalent(X,equivalent(X,equivalent(equivalent(equivalent(Y,Z),equivalent(U,Z)),equivalent(Y,U))))),
inference(nnf_transformation,[status(thm)],[f1]) ).
fof(f1_sk,plain,
! [X,Y,Z,U] : is_a_theorem(equivalent(X,equivalent(X,equivalent(equivalent(equivalent(Y,Z),equivalent(U,Z)),equivalent(Y,U))))),
inference(skolemisation,[status(esa)],[f1_nnf]) ).
cnf(c1,plain,
is_a_theorem(equivalent(X0,equivalent(X0,equivalent(equivalent(equivalent(X1,X2),equivalent(X3,X2)),equivalent(X1,X3))))),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(t2,plain,
is_a_theorem(equivalent(X1,equivalent(X1,equivalent(equivalent(equivalent(X2,X3),equivalent(X4,X3)),equivalent(X2,X4))))) = true,
inference(equality_encoding,[status(esa)],[c1]) ).
cnf(t4,plain,
is_a_theorem(equivalent(X1,equivalent(X1,equivalent(equivalent(equivalent(X2,X3),equivalent(X4,X3)),equivalent(X2,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(equivalent(X2,X3),equivalent(X4,X3)),equivalent(X2,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(t119887,plain,
true = ifeq(is_a_theorem(X1),true,is_a_theorem(equivalent(X1,equivalent(equivalent(equivalent(X2,X3),equivalent(X4,X3)),equivalent(X2,X4)))),true),
inference(step,[status(thm)],[t6,t3]) ).
cnf(t9,plain,
ifeq(is_a_theorem(X1),true,is_a_theorem(equivalent(X1,equivalent(equivalent(equivalent(X2,X3),equivalent(X4,X3)),equivalent(X2,X4)))),true) = true,
inference(orient,[status(thm)],[t119887]) ).
cnf(t10,plain,
true = ifeq(true,true,is_a_theorem(equivalent(equivalent(X1,equivalent(X1,equivalent(equivalent(equivalent(X2,X3),equivalent(X4,X3)),equivalent(X2,X4)))),equivalent(equivalent(equivalent(Y4,Y5),equivalent(Y6,Y5)),equivalent(Y4,Y6)))),true),
inference(cp,[status(thm)],[t9,t4]) ).
cnf(t119889,plain,
true = is_a_theorem(equivalent(equivalent(X1,equivalent(X1,equivalent(equivalent(equivalent(X2,X3),equivalent(X4,X3)),equivalent(X2,X4)))),equivalent(equivalent(equivalent(Y4,Y5),equivalent(Y6,Y5)),equivalent(Y4,Y6)))),
inference(step,[status(thm)],[t10,t3]) ).
cnf(t22,plain,
is_a_theorem(equivalent(equivalent(X1,equivalent(X1,equivalent(equivalent(equivalent(X2,X3),equivalent(X4,X3)),equivalent(X2,X4)))),equivalent(equivalent(equivalent(Y4,Y5),equivalent(Y6,Y5)),equivalent(Y4,Y6)))) = true,
inference(orient,[status(thm)],[t119889]) ).
cnf(t23,plain,
true = ifeq(true,true,ifeq(is_a_theorem(equivalent(X1,equivalent(X1,equivalent(equivalent(equivalent(X2,X3),equivalent(X4,X3)),equivalent(X2,X4))))),true,is_a_theorem(equivalent(equivalent(equivalent(Y4,Y5),equivalent(Y6,Y5)),equivalent(Y4,Y6))),true),true),
inference(cp,[status(thm)],[t5,t22]) ).
cnf(t119890,plain,
true = ifeq(is_a_theorem(equivalent(X1,equivalent(X1,equivalent(equivalent(equivalent(X2,X3),equivalent(X4,X3)),equivalent(X2,X4))))),true,is_a_theorem(equivalent(equivalent(equivalent(Y4,Y5),equivalent(Y6,Y5)),equivalent(Y4,Y6))),true),
inference(step,[status(thm)],[t23,t3]) ).
cnf(t119891,plain,
true = ifeq(true,true,is_a_theorem(equivalent(equivalent(equivalent(Y4,Y5),equivalent(Y6,Y5)),equivalent(Y4,Y6))),true),
inference(step,[status(thm)],[t119890,t4]) ).
cnf(t119892,plain,
true = is_a_theorem(equivalent(equivalent(equivalent(Y4,Y5),equivalent(Y6,Y5)),equivalent(Y4,Y6))),
inference(step,[status(thm)],[t119891,t3]) ).
cnf(t30,plain,
is_a_theorem(equivalent(equivalent(equivalent(X1,X2),equivalent(X3,X2)),equivalent(X1,X3))) = true,
inference(orient,[status(thm)],[t119892]) ).
cnf(t31,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,t30]) ).
cnf(t119893,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)],[t31,t3]) ).
cnf(t37,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)],[t119893]) ).
cnf(t34,plain,
true = ifeq(true,true,is_a_theorem(equivalent(equivalent(equivalent(equivalent(X1,X2),equivalent(X3,X2)),equivalent(X1,X3)),equivalent(equivalent(equivalent(X4,Y4),equivalent(Y5,Y4)),equivalent(X4,Y5)))),true),
inference(cp,[status(thm)],[t9,t30]) ).
cnf(t119899,plain,
true = is_a_theorem(equivalent(equivalent(equivalent(equivalent(X1,X2),equivalent(X3,X2)),equivalent(X1,X3)),equivalent(equivalent(equivalent(X4,Y4),equivalent(Y5,Y4)),equivalent(X4,Y5)))),
inference(step,[status(thm)],[t34,t3]) ).
cnf(t92,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(X1,X2),equivalent(X3,X2)),equivalent(X1,X3)),equivalent(equivalent(equivalent(X4,Y4),equivalent(Y5,Y4)),equivalent(X4,Y5)))) = true,
inference(orient,[status(thm)],[t119899]) ).
cnf(t95,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)],[t37,t92]) ).
cnf(t119900,plain,
true = is_a_theorem(equivalent(equivalent(equivalent(X1,X2),equivalent(X3,X2)),equivalent(equivalent(X1,X4),equivalent(X3,X4)))),
inference(step,[status(thm)],[t95,t3]) ).
cnf(t105,plain,
is_a_theorem(equivalent(equivalent(equivalent(X1,X2),equivalent(X3,X2)),equivalent(equivalent(X1,X4),equivalent(X3,X4)))) = true,
inference(orient,[status(thm)],[t119900]) ).
cnf(t106,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,t105]) ).
cnf(t119911,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)],[t106,t3]) ).
cnf(t280,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)],[t119911]) ).
cnf(t32,plain,
true = ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(X1,X2),equivalent(X3,X2)),equivalent(X1,X3)),X4)),true,ifeq(true,true,is_a_theorem(X4),true),true),
inference(cp,[status(thm)],[t5,t30]) ).
cnf(t119894,plain,
true = ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(X1,X2),equivalent(X3,X2)),equivalent(X1,X3)),X4)),true,is_a_theorem(X4),true),
inference(step,[status(thm)],[t32,t3]) ).
cnf(t41,plain,
ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(X1,X2),equivalent(X3,X2)),equivalent(X1,X3)),X4)),true,is_a_theorem(X4),true) = true,
inference(orient,[status(thm)],[t119894]) ).
cnf(t109,plain,
true = ifeq(true,true,is_a_theorem(equivalent(equivalent(X1,X2),equivalent(X1,X2))),true),
inference(cp,[status(thm)],[t37,t105]) ).
cnf(t119901,plain,
true = is_a_theorem(equivalent(equivalent(X1,X2),equivalent(X1,X2))),
inference(step,[status(thm)],[t109,t3]) ).
cnf(t120,plain,
is_a_theorem(equivalent(equivalent(X1,X2),equivalent(X1,X2))) = true,
inference(orient,[status(thm)],[t119901]) ).
cnf(t124,plain,
true = ifeq(true,true,is_a_theorem(equivalent(X1,X1)),true),
inference(cp,[status(thm)],[t37,t120]) ).
cnf(t119902,plain,
true = is_a_theorem(equivalent(X1,X1)),
inference(step,[status(thm)],[t124,t3]) ).
cnf(t132,plain,
is_a_theorem(equivalent(X1,X1)) = true,
inference(orient,[status(thm)],[t119902]) ).
cnf(t138,plain,
true = ifeq(true,true,is_a_theorem(equivalent(equivalent(X1,X1),equivalent(equivalent(equivalent(X2,X3),equivalent(X4,X3)),equivalent(X2,X4)))),true),
inference(cp,[status(thm)],[t9,t132]) ).
cnf(t119905,plain,
true = is_a_theorem(equivalent(equivalent(X1,X1),equivalent(equivalent(equivalent(X2,X3),equivalent(X4,X3)),equivalent(X2,X4)))),
inference(step,[status(thm)],[t138,t3]) ).
cnf(t176,plain,
is_a_theorem(equivalent(equivalent(X1,X1),equivalent(equivalent(equivalent(X2,X3),equivalent(X4,X3)),equivalent(X2,X4)))) = true,
inference(orient,[status(thm)],[t119905]) ).
cnf(t181,plain,
true = ifeq(true,true,is_a_theorem(equivalent(equivalent(X1,X2),equivalent(equivalent(X1,X3),equivalent(X2,X3)))),true),
inference(cp,[status(thm)],[t37,t176]) ).
cnf(t119906,plain,
true = is_a_theorem(equivalent(equivalent(X1,X2),equivalent(equivalent(X1,X3),equivalent(X2,X3)))),
inference(step,[status(thm)],[t181,t3]) ).
cnf(t190,plain,
is_a_theorem(equivalent(equivalent(X1,X2),equivalent(equivalent(X1,X3),equivalent(X2,X3)))) = true,
inference(orient,[status(thm)],[t119906]) ).
cnf(t198,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)],[t41,t190]) ).
cnf(t119908,plain,
true = is_a_theorem(equivalent(equivalent(equivalent(equivalent(X1,X2),equivalent(X3,X2)),X4),equivalent(equivalent(X1,X3),X4))),
inference(step,[status(thm)],[t198,t3]) ).
cnf(t224,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(X1,X2),equivalent(X3,X2)),X4),equivalent(equivalent(X1,X3),X4))) = true,
inference(orient,[status(thm)],[t119908]) ).
cnf(t225,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,t224]) ).
cnf(t119914,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)],[t225,t3]) ).
cnf(t329,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)],[t119914]) ).
cnf(t331,plain,
true = ifeq(true,true,is_a_theorem(equivalent(equivalent(equivalent(X1,X2),X3),equivalent(equivalent(X1,X4),equivalent(X3,equivalent(X4,X2))))),true),
inference(cp,[status(thm)],[t329,t224]) ).
cnf(t119916,plain,
true = is_a_theorem(equivalent(equivalent(equivalent(X1,X2),X3),equivalent(equivalent(X1,X4),equivalent(X3,equivalent(X4,X2))))),
inference(step,[status(thm)],[t331,t3]) ).
cnf(t367,plain,
is_a_theorem(equivalent(equivalent(equivalent(X1,X2),X3),equivalent(equivalent(X1,X4),equivalent(X3,equivalent(X4,X2))))) = true,
inference(orient,[status(thm)],[t119916]) ).
cnf(t368,plain,
true = ifeq(true,true,ifeq(is_a_theorem(equivalent(equivalent(X1,X2),X3)),true,is_a_theorem(equivalent(equivalent(X1,X4),equivalent(X3,equivalent(X4,X2)))),true),true),
inference(cp,[status(thm)],[t5,t367]) ).
cnf(t119922,plain,
true = ifeq(is_a_theorem(equivalent(equivalent(X1,X2),X3)),true,is_a_theorem(equivalent(equivalent(X1,X4),equivalent(X3,equivalent(X4,X2)))),true),
inference(step,[status(thm)],[t368,t3]) ).
cnf(t481,plain,
ifeq(is_a_theorem(equivalent(equivalent(X1,X2),X3)),true,is_a_theorem(equivalent(equivalent(X1,X4),equivalent(X3,equivalent(X4,X2)))),true) = true,
inference(orient,[status(thm)],[t119922]) ).
cnf(t134,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,t132]) ).
cnf(t119904,plain,
true = ifeq(is_a_theorem(equivalent(equivalent(X1,X1),X2)),true,is_a_theorem(X2),true),
inference(step,[status(thm)],[t134,t3]) ).
cnf(t144,plain,
ifeq(is_a_theorem(equivalent(equivalent(X1,X1),X2)),true,is_a_theorem(X2),true) = true,
inference(orient,[status(thm)],[t119904]) ).
cnf(t7,plain,
true = ifeq(is_a_theorem(equivalent(equivalent(X1,equivalent(X1,equivalent(equivalent(equivalent(X2,X3),equivalent(X4,X3)),equivalent(X2,X4)))),Y4)),true,ifeq(true,true,is_a_theorem(Y4),true),true),
inference(cp,[status(thm)],[t5,t4]) ).
cnf(t119888,plain,
true = ifeq(is_a_theorem(equivalent(equivalent(X1,equivalent(X1,equivalent(equivalent(equivalent(X2,X3),equivalent(X4,X3)),equivalent(X2,X4)))),Y4)),true,is_a_theorem(Y4),true),
inference(step,[status(thm)],[t7,t3]) ).
cnf(t13,plain,
ifeq(is_a_theorem(equivalent(equivalent(X1,equivalent(X1,equivalent(equivalent(equivalent(X2,X3),equivalent(X4,X3)),equivalent(X2,X4)))),Y4)),true,is_a_theorem(Y4),true) = true,
inference(orient,[status(thm)],[t119888]) ).
cnf(t115,plain,
true = ifeq(true,true,is_a_theorem(equivalent(equivalent(X1,X2),equivalent(equivalent(X1,equivalent(equivalent(equivalent(X3,X4),equivalent(Y4,X4)),equivalent(X3,Y4))),X2))),true),
inference(cp,[status(thm)],[t13,t105]) ).
cnf(t119924,plain,
true = is_a_theorem(equivalent(equivalent(X1,X2),equivalent(equivalent(X1,equivalent(equivalent(equivalent(X3,X4),equivalent(Y4,X4)),equivalent(X3,Y4))),X2))),
inference(step,[status(thm)],[t115,t3]) ).
cnf(t518,plain,
is_a_theorem(equivalent(equivalent(X1,X2),equivalent(equivalent(X1,equivalent(equivalent(equivalent(X3,X4),equivalent(Y4,X4)),equivalent(X3,Y4))),X2))) = true,
inference(orient,[status(thm)],[t119924]) ).
cnf(t524,plain,
true = ifeq(true,true,is_a_theorem(equivalent(equivalent(X1,equivalent(equivalent(equivalent(X2,X3),equivalent(X4,X3)),equivalent(X2,X4))),X1)),true),
inference(cp,[status(thm)],[t144,t518]) ).
cnf(t119925,plain,
true = is_a_theorem(equivalent(equivalent(X1,equivalent(equivalent(equivalent(X2,X3),equivalent(X4,X3)),equivalent(X2,X4))),X1)),
inference(step,[status(thm)],[t524,t3]) ).
cnf(t550,plain,
is_a_theorem(equivalent(equivalent(X1,equivalent(equivalent(equivalent(X2,X3),equivalent(X4,X3)),equivalent(X2,X4))),X1)) = true,
inference(orient,[status(thm)],[t119925]) ).
cnf(t569,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)],[t329,t550]) ).
cnf(t119926,plain,
true = is_a_theorem(equivalent(equivalent(X1,equivalent(equivalent(X2,X3),equivalent(X4,X3))),equivalent(X1,equivalent(X2,X4)))),
inference(step,[status(thm)],[t569,t3]) ).
cnf(t579,plain,
is_a_theorem(equivalent(equivalent(X1,equivalent(equivalent(X2,X3),equivalent(X4,X3))),equivalent(X1,equivalent(X2,X4)))) = true,
inference(orient,[status(thm)],[t119926]) ).
cnf(t595,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)],[t329,t579]) ).
cnf(t119927,plain,
true = is_a_theorem(equivalent(equivalent(X1,equivalent(X2,X3)),equivalent(equivalent(X1,equivalent(X4,X3)),equivalent(X2,X4)))),
inference(step,[status(thm)],[t595,t3]) ).
cnf(t614,plain,
is_a_theorem(equivalent(equivalent(X1,equivalent(X2,X3)),equivalent(equivalent(X1,equivalent(X4,X3)),equivalent(X2,X4)))) = true,
inference(orient,[status(thm)],[t119927]) ).
cnf(t623,plain,
true = ifeq(true,true,is_a_theorem(equivalent(X1,equivalent(X1,equivalent(X2,X2)))),true),
inference(cp,[status(thm)],[t37,t614]) ).
cnf(t119928,plain,
true = is_a_theorem(equivalent(X1,equivalent(X1,equivalent(X2,X2)))),
inference(step,[status(thm)],[t623,t3]) ).
cnf(t644,plain,
is_a_theorem(equivalent(X1,equivalent(X1,equivalent(X2,X2)))) = true,
inference(orient,[status(thm)],[t119928]) ).
cnf(t652,plain,
true = ifeq(true,true,is_a_theorem(equivalent(equivalent(X1,X1),equivalent(X2,X2))),true),
inference(cp,[status(thm)],[t144,t644]) ).
cnf(t119929,plain,
true = is_a_theorem(equivalent(equivalent(X1,X1),equivalent(X2,X2))),
inference(step,[status(thm)],[t652,t3]) ).
cnf(t676,plain,
is_a_theorem(equivalent(equivalent(X1,X1),equivalent(X2,X2))) = true,
inference(orient,[status(thm)],[t119929]) ).
cnf(t683,plain,
true = ifeq(true,true,is_a_theorem(equivalent(equivalent(X1,X2),equivalent(equivalent(X3,X3),equivalent(X2,X1)))),true),
inference(cp,[status(thm)],[t481,t676]) ).
cnf(t119935,plain,
true = is_a_theorem(equivalent(equivalent(X1,X2),equivalent(equivalent(X3,X3),equivalent(X2,X1)))),
inference(step,[status(thm)],[t683,t3]) ).
cnf(t835,plain,
is_a_theorem(equivalent(equivalent(X1,X2),equivalent(equivalent(X3,X3),equivalent(X2,X1)))) = true,
inference(orient,[status(thm)],[t119935]) ).
cnf(t836,plain,
true = ifeq(true,true,ifeq(is_a_theorem(equivalent(X1,X2)),true,is_a_theorem(equivalent(equivalent(X3,X3),equivalent(X2,X1))),true),true),
inference(cp,[status(thm)],[t5,t835]) ).
cnf(t119959,plain,
true = ifeq(is_a_theorem(equivalent(X1,X2)),true,is_a_theorem(equivalent(equivalent(X3,X3),equivalent(X2,X1))),true),
inference(step,[status(thm)],[t836,t3]) ).
cnf(t1663,plain,
ifeq(is_a_theorem(equivalent(X1,X2)),true,is_a_theorem(equivalent(equivalent(X3,X3),equivalent(X2,X1))),true) = true,
inference(orient,[status(thm)],[t119959]) ).
cnf(t618,plain,
true = ifeq(true,true,is_a_theorem(equivalent(equivalent(X1,X2),equivalent(equivalent(X1,equivalent(X3,X3)),X2))),true),
inference(cp,[status(thm)],[t280,t614]) ).
cnf(t119931,plain,
true = is_a_theorem(equivalent(equivalent(X1,X2),equivalent(equivalent(X1,equivalent(X3,X3)),X2))),
inference(step,[status(thm)],[t618,t3]) ).
cnf(t719,plain,
is_a_theorem(equivalent(equivalent(X1,X2),equivalent(equivalent(X1,equivalent(X3,X3)),X2))) = true,
inference(orient,[status(thm)],[t119931]) ).
cnf(t726,plain,
true = ifeq(true,true,is_a_theorem(equivalent(equivalent(X1,equivalent(X2,X2)),X1)),true),
inference(cp,[status(thm)],[t144,t719]) ).
cnf(t119932,plain,
true = is_a_theorem(equivalent(equivalent(X1,equivalent(X2,X2)),X1)),
inference(step,[status(thm)],[t726,t3]) ).
cnf(t750,plain,
is_a_theorem(equivalent(equivalent(X1,equivalent(X2,X2)),X1)) = true,
inference(orient,[status(thm)],[t119932]) ).
cnf(t755,plain,
true = ifeq(true,true,is_a_theorem(equivalent(equivalent(equivalent(X1,equivalent(X2,X2)),X3),equivalent(X1,X3))),true),
inference(cp,[status(thm)],[t280,t750]) ).
cnf(t119939,plain,
true = is_a_theorem(equivalent(equivalent(equivalent(X1,equivalent(X2,X2)),X3),equivalent(X1,X3))),
inference(step,[status(thm)],[t755,t3]) ).
cnf(t942,plain,
is_a_theorem(equivalent(equivalent(equivalent(X1,equivalent(X2,X2)),X3),equivalent(X1,X3))) = true,
inference(orient,[status(thm)],[t119939]) ).
cnf(t943,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,t942]) ).
cnf(t119960,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)],[t943,t3]) ).
cnf(t1708,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)],[t119960]) ).
cnf(t1709,plain,
true = ifeq(true,true,is_a_theorem(equivalent(X1,equivalent(equivalent(X1,equivalent(X2,X3)),equivalent(X3,X2)))),true),
inference(cp,[status(thm)],[t1708,t614]) ).
cnf(t119961,plain,
true = is_a_theorem(equivalent(X1,equivalent(equivalent(X1,equivalent(X2,X3)),equivalent(X3,X2)))),
inference(step,[status(thm)],[t1709,t3]) ).
cnf(t1767,plain,
is_a_theorem(equivalent(X1,equivalent(equivalent(X1,equivalent(X2,X3)),equivalent(X3,X2)))) = true,
inference(orient,[status(thm)],[t119961]) ).
cnf(t1771,plain,
true = ifeq(true,true,is_a_theorem(equivalent(equivalent(X1,X1),equivalent(equivalent(equivalent(X2,equivalent(X3,X4)),equivalent(X4,X3)),X2))),true),
inference(cp,[status(thm)],[t1663,t1767]) ).
cnf(t120117,plain,
true = is_a_theorem(equivalent(equivalent(X1,X1),equivalent(equivalent(equivalent(X2,equivalent(X3,X4)),equivalent(X4,X3)),X2))),
inference(step,[status(thm)],[t1771,t3]) ).
cnf(t10301,plain,
is_a_theorem(equivalent(equivalent(X1,X1),equivalent(equivalent(equivalent(X2,equivalent(X3,X4)),equivalent(X4,X3)),X2))) = true,
inference(orient,[status(thm)],[t120117]) ).
cnf(t10302,plain,
true = ifeq(true,true,ifeq(is_a_theorem(equivalent(X1,X1)),true,is_a_theorem(equivalent(equivalent(equivalent(X2,equivalent(X3,X4)),equivalent(X4,X3)),X2)),true),true),
inference(cp,[status(thm)],[t5,t10301]) ).
cnf(t120118,plain,
true = ifeq(is_a_theorem(equivalent(X1,X1)),true,is_a_theorem(equivalent(equivalent(equivalent(X2,equivalent(X3,X4)),equivalent(X4,X3)),X2)),true),
inference(step,[status(thm)],[t10302,t3]) ).
cnf(t120119,plain,
true = ifeq(true,true,is_a_theorem(equivalent(equivalent(equivalent(X2,equivalent(X3,X4)),equivalent(X4,X3)),X2)),true),
inference(step,[status(thm)],[t120118,t132]) ).
cnf(t120120,plain,
true = is_a_theorem(equivalent(equivalent(equivalent(X2,equivalent(X3,X4)),equivalent(X4,X3)),X2)),
inference(step,[status(thm)],[t120119,t3]) ).
cnf(t10351,plain,
is_a_theorem(equivalent(equivalent(equivalent(X1,equivalent(X2,X3)),equivalent(X3,X2)),X1)) = true,
inference(orient,[status(thm)],[t120120]) ).
cnf(t10359,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)],[t280,t10351]) ).
cnf(t120216,plain,
true = is_a_theorem(equivalent(equivalent(equivalent(equivalent(X1,equivalent(X2,X3)),equivalent(X3,X2)),X4),equivalent(X1,X4))),
inference(step,[status(thm)],[t10359,t3]) ).
cnf(t16062,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(X1,equivalent(X2,X3)),equivalent(X3,X2)),X4),equivalent(X1,X4))) = true,
inference(orient,[status(thm)],[t120216]) ).
cnf(t16063,plain,
true = ifeq(true,true,ifeq(is_a_theorem(equivalent(equivalent(equivalent(X1,equivalent(X2,X3)),equivalent(X3,X2)),X4)),true,is_a_theorem(equivalent(X1,X4)),true),true),
inference(cp,[status(thm)],[t5,t16062]) ).
cnf(t120568,plain,
true = ifeq(is_a_theorem(equivalent(equivalent(equivalent(X1,equivalent(X2,X3)),equivalent(X3,X2)),X4)),true,is_a_theorem(equivalent(X1,X4)),true),
inference(step,[status(thm)],[t16063,t3]) ).
cnf(t118320,plain,
ifeq(is_a_theorem(equivalent(equivalent(equivalent(X1,equivalent(X2,X3)),equivalent(X3,X2)),X4)),true,is_a_theorem(equivalent(X1,X4)),true) = true,
inference(orient,[status(thm)],[t120568]) ).
cnf(t118323,plain,
true = ifeq(true,true,is_a_theorem(equivalent(X1,equivalent(X1,equivalent(equivalent(X2,X3),equivalent(equivalent(X2,X4),equivalent(X3,X4)))))),true),
inference(cp,[status(thm)],[t118320,t550]) ).
cnf(t120571,plain,
true = is_a_theorem(equivalent(X1,equivalent(X1,equivalent(equivalent(X2,X3),equivalent(equivalent(X2,X4),equivalent(X3,X4)))))),
inference(step,[status(thm)],[t118323,t3]) ).
cnf(t119542,plain,
is_a_theorem(equivalent(X1,equivalent(X1,equivalent(equivalent(X2,X3),equivalent(equivalent(X2,X4),equivalent(X3,X4)))))) = true,
inference(orient,[status(thm)],[t120571]) ).
cnf(f2,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(f2_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)],[f2]) ).
fof(f2_sk,plain,
~ is_a_theorem(equivalent(a,equivalent(a,equivalent(equivalent(b,c),equivalent(equivalent(b,e),equivalent(c,e)))))),
inference(skolemisation,[status(esa)],[f2_nnf]) ).
cnf(c2,plain,
~ is_a_theorem(equivalent(a,equivalent(a,equivalent(equivalent(b,c),equivalent(equivalent(b,e),equivalent(c,e)))))),
inference(cnf_transformation,[status(esa)],[f2_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)],[c2]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t119542]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL128-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.09/0.36 % Computer : n004.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Wed Sep 23 22:01:51 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 25.64/3.67 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 25.64/3.67 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------