%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : LCL095-1 : 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 02:00:55 PM UTC 2026
% Result : Unsatisfiable 11.41s 1.98s
% Output : Proof 11.41s
% Verified :
% SZS Type : Refutation
% Derivation depth : 130
% Number of leaves : 4
% Syntax : Number of formulae : 189 ( 185 unt; 0 def)
% Number of atoms : 197 ( 176 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 : 5 ( 5 usr; 3 con; 0-4 aty)
% Number of variables : 792 ( 484 sgn 14 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f0,axiom,
( is_a_theorem(Y)
| ~ is_a_theorem(X)
| ~ is_a_theorem(implies(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(implies(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(implies(X,Y)) ),
inference(skolemisation,[status(esa)],[f0_nnf]) ).
cnf(c0,plain,
( is_a_theorem(X1)
| ~ is_a_theorem(X0)
| ~ is_a_theorem(implies(X0,X1)) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(t1,plain,
ifeq(is_a_theorem(implies(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(implies(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(implies(implies(implies(P,Q),implies(R,S)),implies(implies(S,P),implies(T,implies(R,P))))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ic_JLukasiewicz_5) ).
fof(f1_nnf,plain,
! [P,Q,R,S,T] : is_a_theorem(implies(implies(implies(P,Q),implies(R,S)),implies(implies(S,P),implies(T,implies(R,P))))),
inference(nnf_transformation,[status(thm)],[f1]) ).
fof(f1_sk,plain,
! [P,Q,R,S,T] : is_a_theorem(implies(implies(implies(P,Q),implies(R,S)),implies(implies(S,P),implies(T,implies(R,P))))),
inference(skolemisation,[status(esa)],[f1_nnf]) ).
cnf(c1,plain,
is_a_theorem(implies(implies(implies(X0,X1),implies(X2,X3)),implies(implies(X3,X0),implies(X4,implies(X2,X0))))),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(t2,plain,
is_a_theorem(implies(implies(implies(X1,X2),implies(X3,X4)),implies(implies(X4,X1),implies(X5,implies(X3,X1))))) = true,
inference(equality_encoding,[status(esa)],[c1]) ).
cnf(t4,plain,
is_a_theorem(implies(implies(implies(X1,X2),implies(X3,X4)),implies(implies(X4,X1),implies(X5,implies(X3,X1))))) = true,
inference(orient,[status(thm)],[t2]) ).
cnf(t6,plain,
true = ifeq(true,true,ifeq(is_a_theorem(implies(implies(X1,X2),implies(X3,X4))),true,is_a_theorem(implies(implies(X4,X1),implies(X5,implies(X3,X1)))),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(t2500,plain,
true = ifeq(is_a_theorem(implies(implies(X1,X2),implies(X3,X4))),true,is_a_theorem(implies(implies(X4,X1),implies(X5,implies(X3,X1)))),true),
inference(step,[status(thm)],[t6,t3]) ).
cnf(t9,plain,
ifeq(is_a_theorem(implies(implies(X1,X2),implies(X3,X4))),true,is_a_theorem(implies(implies(X4,X1),implies(X5,implies(X3,X1)))),true) = true,
inference(orient,[status(thm)],[t2500]) ).
cnf(t10,plain,
true = ifeq(true,true,is_a_theorem(implies(implies(implies(X1,implies(X2,X3)),implies(X3,X4)),implies(X5,implies(implies(Y5,X3),implies(X3,X4))))),true),
inference(cp,[status(thm)],[t9,t4]) ).
cnf(t2501,plain,
true = is_a_theorem(implies(implies(implies(X1,implies(X2,X3)),implies(X3,X4)),implies(X5,implies(implies(Y5,X3),implies(X3,X4))))),
inference(step,[status(thm)],[t10,t3]) ).
cnf(t13,plain,
is_a_theorem(implies(implies(implies(X1,implies(X2,X3)),implies(X3,X4)),implies(X5,implies(implies(Y5,X3),implies(X3,X4))))) = true,
inference(orient,[status(thm)],[t2501]) ).
cnf(t14,plain,
true = ifeq(true,true,ifeq(is_a_theorem(implies(implies(X1,implies(X2,X3)),implies(X3,X4))),true,is_a_theorem(implies(X5,implies(implies(Y5,X3),implies(X3,X4)))),true),true),
inference(cp,[status(thm)],[t5,t13]) ).
cnf(t2502,plain,
true = ifeq(is_a_theorem(implies(implies(X1,implies(X2,X3)),implies(X3,X4))),true,is_a_theorem(implies(X5,implies(implies(Y5,X3),implies(X3,X4)))),true),
inference(step,[status(thm)],[t14,t3]) ).
cnf(t20,plain,
ifeq(is_a_theorem(implies(implies(X1,implies(X2,X3)),implies(X3,X4))),true,is_a_theorem(implies(X5,implies(implies(Y5,X3),implies(X3,X4)))),true) = true,
inference(orient,[status(thm)],[t2502]) ).
cnf(t21,plain,
true = ifeq(true,true,is_a_theorem(implies(X1,implies(implies(X2,X3),implies(X3,implies(implies(X4,X5),implies(X5,X3)))))),true),
inference(cp,[status(thm)],[t20,t13]) ).
cnf(t2503,plain,
true = is_a_theorem(implies(X1,implies(implies(X2,X3),implies(X3,implies(implies(X4,X5),implies(X5,X3)))))),
inference(step,[status(thm)],[t21,t3]) ).
cnf(t24,plain,
is_a_theorem(implies(X1,implies(implies(X2,X3),implies(X3,implies(implies(X4,X5),implies(X5,X3)))))) = true,
inference(orient,[status(thm)],[t2503]) ).
cnf(t25,plain,
true = ifeq(true,true,ifeq(is_a_theorem(X1),true,is_a_theorem(implies(implies(X2,X3),implies(X3,implies(implies(X4,X5),implies(X5,X3))))),true),true),
inference(cp,[status(thm)],[t5,t24]) ).
cnf(t2504,plain,
true = ifeq(is_a_theorem(X1),true,is_a_theorem(implies(implies(X2,X3),implies(X3,implies(implies(X4,X5),implies(X5,X3))))),true),
inference(step,[status(thm)],[t25,t3]) ).
cnf(t34,plain,
ifeq(is_a_theorem(X1),true,is_a_theorem(implies(implies(X2,X3),implies(X3,implies(implies(X4,X5),implies(X5,X3))))),true) = true,
inference(orient,[status(thm)],[t2504]) ).
cnf(t35,plain,
true = ifeq(true,true,is_a_theorem(implies(implies(X1,X2),implies(X2,implies(implies(X3,X4),implies(X4,X2))))),true),
inference(cp,[status(thm)],[t34,t24]) ).
cnf(t2505,plain,
true = is_a_theorem(implies(implies(X1,X2),implies(X2,implies(implies(X3,X4),implies(X4,X2))))),
inference(step,[status(thm)],[t35,t3]) ).
cnf(t40,plain,
is_a_theorem(implies(implies(X1,X2),implies(X2,implies(implies(X3,X4),implies(X4,X2))))) = true,
inference(orient,[status(thm)],[t2505]) ).
cnf(t43,plain,
true = ifeq(true,true,is_a_theorem(implies(implies(implies(implies(X1,X2),implies(X2,X3)),X4),implies(X5,implies(X3,X4)))),true),
inference(cp,[status(thm)],[t9,t40]) ).
cnf(t2506,plain,
true = is_a_theorem(implies(implies(implies(implies(X1,X2),implies(X2,X3)),X4),implies(X5,implies(X3,X4)))),
inference(step,[status(thm)],[t43,t3]) ).
cnf(t44,plain,
is_a_theorem(implies(implies(implies(implies(X1,X2),implies(X2,X3)),X4),implies(X5,implies(X3,X4)))) = true,
inference(orient,[status(thm)],[t2506]) ).
cnf(t47,plain,
true = ifeq(true,true,is_a_theorem(implies(X1,implies(implies(X2,X3),implies(X3,implies(X4,implies(X5,X3)))))),true),
inference(cp,[status(thm)],[t20,t44]) ).
cnf(t2507,plain,
true = is_a_theorem(implies(X1,implies(implies(X2,X3),implies(X3,implies(X4,implies(X5,X3)))))),
inference(step,[status(thm)],[t47,t3]) ).
cnf(t49,plain,
is_a_theorem(implies(X1,implies(implies(X2,X3),implies(X3,implies(X4,implies(X5,X3)))))) = true,
inference(orient,[status(thm)],[t2507]) ).
cnf(t50,plain,
true = ifeq(true,true,ifeq(is_a_theorem(X1),true,is_a_theorem(implies(implies(X2,X3),implies(X3,implies(X4,implies(X5,X3))))),true),true),
inference(cp,[status(thm)],[t5,t49]) ).
cnf(t2509,plain,
true = ifeq(is_a_theorem(X1),true,is_a_theorem(implies(implies(X2,X3),implies(X3,implies(X4,implies(X5,X3))))),true),
inference(step,[status(thm)],[t50,t3]) ).
cnf(t60,plain,
ifeq(is_a_theorem(X1),true,is_a_theorem(implies(implies(X2,X3),implies(X3,implies(X4,implies(X5,X3))))),true) = true,
inference(orient,[status(thm)],[t2509]) ).
cnf(t61,plain,
true = ifeq(true,true,is_a_theorem(implies(implies(X1,X2),implies(X2,implies(X3,implies(X4,X2))))),true),
inference(cp,[status(thm)],[t60,t49]) ).
cnf(t2510,plain,
true = is_a_theorem(implies(implies(X1,X2),implies(X2,implies(X3,implies(X4,X2))))),
inference(step,[status(thm)],[t61,t3]) ).
cnf(t66,plain,
is_a_theorem(implies(implies(X1,X2),implies(X2,implies(X3,implies(X4,X2))))) = true,
inference(orient,[status(thm)],[t2510]) ).
cnf(t70,plain,
true = ifeq(true,true,is_a_theorem(implies(implies(implies(X1,implies(X2,X3)),X4),implies(X5,implies(X3,X4)))),true),
inference(cp,[status(thm)],[t9,t66]) ).
cnf(t2511,plain,
true = is_a_theorem(implies(implies(implies(X1,implies(X2,X3)),X4),implies(X5,implies(X3,X4)))),
inference(step,[status(thm)],[t70,t3]) ).
cnf(t71,plain,
is_a_theorem(implies(implies(implies(X1,implies(X2,X3)),X4),implies(X5,implies(X3,X4)))) = true,
inference(orient,[status(thm)],[t2511]) ).
cnf(t72,plain,
true = ifeq(true,true,ifeq(is_a_theorem(implies(implies(X1,implies(X2,X3)),X4)),true,is_a_theorem(implies(X5,implies(X3,X4))),true),true),
inference(cp,[status(thm)],[t5,t71]) ).
cnf(t2516,plain,
true = ifeq(is_a_theorem(implies(implies(X1,implies(X2,X3)),X4)),true,is_a_theorem(implies(X5,implies(X3,X4))),true),
inference(step,[status(thm)],[t72,t3]) ).
cnf(t96,plain,
ifeq(is_a_theorem(implies(implies(X1,implies(X2,X3)),X4)),true,is_a_theorem(implies(X5,implies(X3,X4))),true) = true,
inference(orient,[status(thm)],[t2516]) ).
cnf(t100,plain,
true = ifeq(true,true,is_a_theorem(implies(X1,implies(X2,implies(implies(X2,X3),implies(X4,implies(X5,X3)))))),true),
inference(cp,[status(thm)],[t96,t4]) ).
cnf(t2519,plain,
true = is_a_theorem(implies(X1,implies(X2,implies(implies(X2,X3),implies(X4,implies(X5,X3)))))),
inference(step,[status(thm)],[t100,t3]) ).
cnf(t116,plain,
is_a_theorem(implies(X1,implies(X2,implies(implies(X2,X3),implies(X4,implies(X5,X3)))))) = true,
inference(orient,[status(thm)],[t2519]) ).
cnf(t117,plain,
true = ifeq(true,true,ifeq(is_a_theorem(X1),true,is_a_theorem(implies(X2,implies(implies(X2,X3),implies(X4,implies(X5,X3))))),true),true),
inference(cp,[status(thm)],[t5,t116]) ).
cnf(t2534,plain,
true = ifeq(is_a_theorem(X1),true,is_a_theorem(implies(X2,implies(implies(X2,X3),implies(X4,implies(X5,X3))))),true),
inference(step,[status(thm)],[t117,t3]) ).
cnf(t247,plain,
ifeq(is_a_theorem(X1),true,is_a_theorem(implies(X2,implies(implies(X2,X3),implies(X4,implies(X5,X3))))),true) = true,
inference(orient,[status(thm)],[t2534]) ).
cnf(t67,plain,
true = ifeq(true,true,ifeq(is_a_theorem(implies(X1,X2)),true,is_a_theorem(implies(X2,implies(X3,implies(X4,X2)))),true),true),
inference(cp,[status(thm)],[t5,t66]) ).
cnf(t2512,plain,
true = ifeq(is_a_theorem(implies(X1,X2)),true,is_a_theorem(implies(X2,implies(X3,implies(X4,X2)))),true),
inference(step,[status(thm)],[t67,t3]) ).
cnf(t76,plain,
ifeq(is_a_theorem(implies(X1,X2)),true,is_a_theorem(implies(X2,implies(X3,implies(X4,X2)))),true) = true,
inference(orient,[status(thm)],[t2512]) ).
cnf(t81,plain,
true = ifeq(true,true,is_a_theorem(implies(implies(X1,implies(X2,X3)),implies(X4,implies(X5,implies(X1,implies(X2,X3)))))),true),
inference(cp,[status(thm)],[t76,t71]) ).
cnf(t2513,plain,
true = is_a_theorem(implies(implies(X1,implies(X2,X3)),implies(X4,implies(X5,implies(X1,implies(X2,X3)))))),
inference(step,[status(thm)],[t81,t3]) ).
cnf(t82,plain,
is_a_theorem(implies(implies(X1,implies(X2,X3)),implies(X4,implies(X5,implies(X1,implies(X2,X3)))))) = true,
inference(orient,[status(thm)],[t2513]) ).
cnf(t97,plain,
true = ifeq(true,true,is_a_theorem(implies(X1,implies(X2,implies(X3,implies(X4,implies(X5,implies(Y5,X2))))))),true),
inference(cp,[status(thm)],[t96,t82]) ).
cnf(t2518,plain,
true = is_a_theorem(implies(X1,implies(X2,implies(X3,implies(X4,implies(X5,implies(Y5,X2))))))),
inference(step,[status(thm)],[t97,t3]) ).
cnf(t110,plain,
is_a_theorem(implies(X1,implies(X2,implies(X3,implies(X4,implies(X5,implies(Y5,X2))))))) = true,
inference(orient,[status(thm)],[t2518]) ).
cnf(t111,plain,
true = ifeq(true,true,ifeq(is_a_theorem(X1),true,is_a_theorem(implies(X2,implies(X3,implies(X4,implies(X5,implies(Y5,X2)))))),true),true),
inference(cp,[status(thm)],[t5,t110]) ).
cnf(t2531,plain,
true = ifeq(is_a_theorem(X1),true,is_a_theorem(implies(X2,implies(X3,implies(X4,implies(X5,implies(Y5,X2)))))),true),
inference(step,[status(thm)],[t111,t3]) ).
cnf(t199,plain,
ifeq(is_a_theorem(X1),true,is_a_theorem(implies(X2,implies(X3,implies(X4,implies(X5,implies(Y5,X2)))))),true) = true,
inference(orient,[status(thm)],[t2531]) ).
cnf(t86,plain,
true = ifeq(true,true,is_a_theorem(implies(implies(implies(X1,implies(X2,implies(X3,X4))),X2),implies(X5,implies(Y5,X2)))),true),
inference(cp,[status(thm)],[t9,t82]) ).
cnf(t2515,plain,
true = is_a_theorem(implies(implies(implies(X1,implies(X2,implies(X3,X4))),X2),implies(X5,implies(Y5,X2)))),
inference(step,[status(thm)],[t86,t3]) ).
cnf(t92,plain,
is_a_theorem(implies(implies(implies(X1,implies(X2,implies(X3,X4))),X2),implies(X5,implies(Y5,X2)))) = true,
inference(orient,[status(thm)],[t2515]) ).
cnf(t99,plain,
true = ifeq(true,true,is_a_theorem(implies(X1,implies(X2,implies(X3,implies(X4,implies(X5,X2)))))),true),
inference(cp,[status(thm)],[t96,t92]) ).
cnf(t2517,plain,
true = is_a_theorem(implies(X1,implies(X2,implies(X3,implies(X4,implies(X5,X2)))))),
inference(step,[status(thm)],[t99,t3]) ).
cnf(t105,plain,
is_a_theorem(implies(X1,implies(X2,implies(X3,implies(X4,implies(X5,X2)))))) = true,
inference(orient,[status(thm)],[t2517]) ).
cnf(t106,plain,
true = ifeq(true,true,ifeq(is_a_theorem(X1),true,is_a_theorem(implies(X2,implies(X3,implies(X4,implies(X5,X2))))),true),true),
inference(cp,[status(thm)],[t5,t105]) ).
cnf(t2521,plain,
true = ifeq(is_a_theorem(X1),true,is_a_theorem(implies(X2,implies(X3,implies(X4,implies(X5,X2))))),true),
inference(step,[status(thm)],[t106,t3]) ).
cnf(t127,plain,
ifeq(is_a_theorem(X1),true,is_a_theorem(implies(X2,implies(X3,implies(X4,implies(X5,X2))))),true) = true,
inference(orient,[status(thm)],[t2521]) ).
cnf(t128,plain,
true = ifeq(true,true,is_a_theorem(implies(X1,implies(X2,implies(X3,implies(X4,X1))))),true),
inference(cp,[status(thm)],[t127,t116]) ).
cnf(t2522,plain,
true = is_a_theorem(implies(X1,implies(X2,implies(X3,implies(X4,X1))))),
inference(step,[status(thm)],[t128,t3]) ).
cnf(t139,plain,
is_a_theorem(implies(X1,implies(X2,implies(X3,implies(X4,X1))))) = true,
inference(orient,[status(thm)],[t2522]) ).
cnf(t144,plain,
true = ifeq(true,true,is_a_theorem(implies(implies(implies(X1,implies(X2,implies(X3,X4))),X3),implies(X5,implies(Y5,X3)))),true),
inference(cp,[status(thm)],[t9,t139]) ).
cnf(t2530,plain,
true = is_a_theorem(implies(implies(implies(X1,implies(X2,implies(X3,X4))),X3),implies(X5,implies(Y5,X3)))),
inference(step,[status(thm)],[t144,t3]) ).
cnf(t194,plain,
is_a_theorem(implies(implies(implies(X1,implies(X2,implies(X3,X4))),X3),implies(X5,implies(Y5,X3)))) = true,
inference(orient,[status(thm)],[t2530]) ).
cnf(t200,plain,
true = ifeq(true,true,is_a_theorem(implies(X1,implies(X2,implies(X3,implies(X4,implies(X5,X1)))))),true),
inference(cp,[status(thm)],[t199,t194]) ).
cnf(t2532,plain,
true = is_a_theorem(implies(X1,implies(X2,implies(X3,implies(X4,implies(X5,X1)))))),
inference(step,[status(thm)],[t200,t3]) ).
cnf(t219,plain,
is_a_theorem(implies(X1,implies(X2,implies(X3,implies(X4,implies(X5,X1)))))) = true,
inference(orient,[status(thm)],[t2532]) ).
cnf(t248,plain,
true = ifeq(true,true,is_a_theorem(implies(X1,implies(implies(X1,X2),implies(X3,implies(X4,X2))))),true),
inference(cp,[status(thm)],[t247,t219]) ).
cnf(t2535,plain,
true = is_a_theorem(implies(X1,implies(implies(X1,X2),implies(X3,implies(X4,X2))))),
inference(step,[status(thm)],[t248,t3]) ).
cnf(t268,plain,
is_a_theorem(implies(X1,implies(implies(X1,X2),implies(X3,implies(X4,X2))))) = true,
inference(orient,[status(thm)],[t2535]) ).
cnf(t270,plain,
true = ifeq(is_a_theorem(implies(implies(X1,implies(implies(X1,X2),implies(X3,implies(X4,X2)))),X5)),true,ifeq(true,true,is_a_theorem(X5),true),true),
inference(cp,[status(thm)],[t5,t268]) ).
cnf(t2569,plain,
true = ifeq(is_a_theorem(implies(implies(X1,implies(implies(X1,X2),implies(X3,implies(X4,X2)))),X5)),true,is_a_theorem(X5),true),
inference(step,[status(thm)],[t270,t3]) ).
cnf(t684,plain,
ifeq(is_a_theorem(implies(implies(X1,implies(implies(X1,X2),implies(X3,implies(X4,X2)))),X5)),true,is_a_theorem(X5),true) = true,
inference(orient,[status(thm)],[t2569]) ).
cnf(t141,plain,
true = ifeq(is_a_theorem(implies(implies(X1,implies(X2,implies(X3,implies(X4,X1)))),X5)),true,ifeq(true,true,is_a_theorem(X5),true),true),
inference(cp,[status(thm)],[t5,t139]) ).
cnf(t2537,plain,
true = ifeq(is_a_theorem(implies(implies(X1,implies(X2,implies(X3,implies(X4,X1)))),X5)),true,is_a_theorem(X5),true),
inference(step,[status(thm)],[t141,t3]) ).
cnf(t297,plain,
ifeq(is_a_theorem(implies(implies(X1,implies(X2,implies(X3,implies(X4,X1)))),X5)),true,is_a_theorem(X5),true) = true,
inference(orient,[status(thm)],[t2537]) ).
cnf(t7,plain,
true = ifeq(is_a_theorem(implies(implies(implies(implies(X1,X2),implies(X3,X4)),implies(implies(X4,X1),implies(X5,implies(X3,X1)))),Y5)),true,ifeq(true,true,is_a_theorem(Y5),true),true),
inference(cp,[status(thm)],[t5,t4]) ).
cnf(t2543,plain,
true = ifeq(is_a_theorem(implies(implies(implies(implies(X1,X2),implies(X3,X4)),implies(implies(X4,X1),implies(X5,implies(X3,X1)))),Y5)),true,is_a_theorem(Y5),true),
inference(step,[status(thm)],[t7,t3]) ).
cnf(t362,plain,
ifeq(is_a_theorem(implies(implies(implies(implies(X1,X2),implies(X3,X4)),implies(implies(X4,X1),implies(X5,implies(X3,X1)))),Y5)),true,is_a_theorem(Y5),true) = true,
inference(orient,[status(thm)],[t2543]) ).
cnf(t75,plain,
true = ifeq(true,true,is_a_theorem(implies(implies(implies(X1,X2),implies(X3,implies(X4,X1))),implies(X5,implies(Y5,implies(X3,implies(X4,X1)))))),true),
inference(cp,[status(thm)],[t9,t71]) ).
cnf(t2572,plain,
true = is_a_theorem(implies(implies(implies(X1,X2),implies(X3,implies(X4,X1))),implies(X5,implies(Y5,implies(X3,implies(X4,X1)))))),
inference(step,[status(thm)],[t75,t3]) ).
cnf(t783,plain,
is_a_theorem(implies(implies(implies(X1,X2),implies(X3,implies(X4,X1))),implies(X5,implies(Y5,implies(X3,implies(X4,X1)))))) = true,
inference(orient,[status(thm)],[t2572]) ).
cnf(t795,plain,
true = ifeq(true,true,is_a_theorem(implies(X1,implies(X2,implies(implies(X3,X4),implies(X5,implies(X4,X4)))))),true),
inference(cp,[status(thm)],[t362,t783]) ).
cnf(t2577,plain,
true = is_a_theorem(implies(X1,implies(X2,implies(implies(X3,X4),implies(X5,implies(X4,X4)))))),
inference(step,[status(thm)],[t795,t3]) ).
cnf(t883,plain,
is_a_theorem(implies(X1,implies(X2,implies(implies(X3,X4),implies(X5,implies(X4,X4)))))) = true,
inference(orient,[status(thm)],[t2577]) ).
cnf(t898,plain,
true = ifeq(true,true,is_a_theorem(implies(X1,implies(implies(X2,X3),implies(X4,implies(X3,X3))))),true),
inference(cp,[status(thm)],[t684,t883]) ).
cnf(t2578,plain,
true = is_a_theorem(implies(X1,implies(implies(X2,X3),implies(X4,implies(X3,X3))))),
inference(step,[status(thm)],[t898,t3]) ).
cnf(t906,plain,
is_a_theorem(implies(X1,implies(implies(X2,X3),implies(X4,implies(X3,X3))))) = true,
inference(orient,[status(thm)],[t2578]) ).
cnf(t916,plain,
true = ifeq(true,true,is_a_theorem(implies(implies(X1,X2),implies(X3,implies(X2,X2)))),true),
inference(cp,[status(thm)],[t684,t906]) ).
cnf(t2579,plain,
true = is_a_theorem(implies(implies(X1,X2),implies(X3,implies(X2,X2)))),
inference(step,[status(thm)],[t916,t3]) ).
cnf(t924,plain,
is_a_theorem(implies(implies(X1,X2),implies(X3,implies(X2,X2)))) = true,
inference(orient,[status(thm)],[t2579]) ).
cnf(t930,plain,
true = ifeq(true,true,is_a_theorem(implies(implies(implies(X1,X1),X2),implies(X3,implies(X4,X2)))),true),
inference(cp,[status(thm)],[t9,t924]) ).
cnf(t2580,plain,
true = is_a_theorem(implies(implies(implies(X1,X1),X2),implies(X3,implies(X4,X2)))),
inference(step,[status(thm)],[t930,t3]) ).
cnf(t939,plain,
is_a_theorem(implies(implies(implies(X1,X1),X2),implies(X3,implies(X4,X2)))) = true,
inference(orient,[status(thm)],[t2580]) ).
cnf(t951,plain,
true = ifeq(true,true,is_a_theorem(implies(X1,implies(X2,implies(X3,implies(X4,implies(X5,implies(Y5,Y5))))))),true),
inference(cp,[status(thm)],[t297,t939]) ).
cnf(t2584,plain,
true = is_a_theorem(implies(X1,implies(X2,implies(X3,implies(X4,implies(X5,implies(Y5,Y5))))))),
inference(step,[status(thm)],[t951,t3]) ).
cnf(t1019,plain,
is_a_theorem(implies(X1,implies(X2,implies(X3,implies(X4,implies(X5,implies(Y5,Y5))))))) = true,
inference(orient,[status(thm)],[t2584]) ).
cnf(t1035,plain,
true = ifeq(true,true,is_a_theorem(implies(X1,implies(X2,implies(X3,implies(X4,implies(X5,X5)))))),true),
inference(cp,[status(thm)],[t684,t1019]) ).
cnf(t2585,plain,
true = is_a_theorem(implies(X1,implies(X2,implies(X3,implies(X4,implies(X5,X5)))))),
inference(step,[status(thm)],[t1035,t3]) ).
cnf(t1043,plain,
is_a_theorem(implies(X1,implies(X2,implies(X3,implies(X4,implies(X5,X5)))))) = true,
inference(orient,[status(thm)],[t2585]) ).
cnf(t1053,plain,
true = ifeq(true,true,is_a_theorem(implies(X1,implies(X2,implies(X3,implies(X4,X4))))),true),
inference(cp,[status(thm)],[t684,t1043]) ).
cnf(t2586,plain,
true = is_a_theorem(implies(X1,implies(X2,implies(X3,implies(X4,X4))))),
inference(step,[status(thm)],[t1053,t3]) ).
cnf(t1061,plain,
is_a_theorem(implies(X1,implies(X2,implies(X3,implies(X4,X4))))) = true,
inference(orient,[status(thm)],[t2586]) ).
cnf(t1070,plain,
true = ifeq(true,true,is_a_theorem(implies(X1,implies(X2,implies(X3,X3)))),true),
inference(cp,[status(thm)],[t684,t1061]) ).
cnf(t2587,plain,
true = is_a_theorem(implies(X1,implies(X2,implies(X3,X3)))),
inference(step,[status(thm)],[t1070,t3]) ).
cnf(t1078,plain,
is_a_theorem(implies(X1,implies(X2,implies(X3,X3)))) = true,
inference(orient,[status(thm)],[t2587]) ).
cnf(t1085,plain,
true = ifeq(true,true,is_a_theorem(implies(X1,implies(X2,X2))),true),
inference(cp,[status(thm)],[t684,t1078]) ).
cnf(t2588,plain,
true = is_a_theorem(implies(X1,implies(X2,X2))),
inference(step,[status(thm)],[t1085,t3]) ).
cnf(t1093,plain,
is_a_theorem(implies(X1,implies(X2,X2))) = true,
inference(orient,[status(thm)],[t2588]) ).
cnf(t1100,plain,
true = ifeq(true,true,is_a_theorem(implies(X1,X1)),true),
inference(cp,[status(thm)],[t684,t1093]) ).
cnf(t2589,plain,
true = is_a_theorem(implies(X1,X1)),
inference(step,[status(thm)],[t1100,t3]) ).
cnf(t1108,plain,
is_a_theorem(implies(X1,X1)) = true,
inference(orient,[status(thm)],[t2589]) ).
cnf(t1110,plain,
true = ifeq(is_a_theorem(implies(implies(X1,X1),X2)),true,ifeq(true,true,is_a_theorem(X2),true),true),
inference(cp,[status(thm)],[t5,t1108]) ).
cnf(t2592,plain,
true = ifeq(is_a_theorem(implies(implies(X1,X1),X2)),true,is_a_theorem(X2),true),
inference(step,[status(thm)],[t1110,t3]) ).
cnf(t1129,plain,
ifeq(is_a_theorem(implies(implies(X1,X1),X2)),true,is_a_theorem(X2),true) = true,
inference(orient,[status(thm)],[t2592]) ).
cnf(t1130,plain,
true = ifeq(true,true,is_a_theorem(implies(X1,implies(X2,implies(X3,implies(X4,X3))))),true),
inference(cp,[status(thm)],[t1129,t783]) ).
cnf(t2593,plain,
true = is_a_theorem(implies(X1,implies(X2,implies(X3,implies(X4,X3))))),
inference(step,[status(thm)],[t1130,t3]) ).
cnf(t1136,plain,
is_a_theorem(implies(X1,implies(X2,implies(X3,implies(X4,X3))))) = true,
inference(orient,[status(thm)],[t2593]) ).
cnf(t1139,plain,
true = ifeq(true,true,is_a_theorem(implies(X1,implies(X2,implies(X3,X2)))),true),
inference(cp,[status(thm)],[t1129,t1136]) ).
cnf(t2595,plain,
true = is_a_theorem(implies(X1,implies(X2,implies(X3,X2)))),
inference(step,[status(thm)],[t1139,t3]) ).
cnf(t1176,plain,
is_a_theorem(implies(X1,implies(X2,implies(X3,X2)))) = true,
inference(orient,[status(thm)],[t2595]) ).
cnf(t1179,plain,
true = ifeq(true,true,is_a_theorem(implies(X1,implies(X2,X1))),true),
inference(cp,[status(thm)],[t1129,t1176]) ).
cnf(t2596,plain,
true = is_a_theorem(implies(X1,implies(X2,X1))),
inference(step,[status(thm)],[t1179,t3]) ).
cnf(t1196,plain,
is_a_theorem(implies(X1,implies(X2,X1))) = true,
inference(orient,[status(thm)],[t2596]) ).
cnf(t1202,plain,
true = ifeq(true,true,is_a_theorem(implies(implies(implies(X1,X2),X1),implies(X3,implies(X4,X1)))),true),
inference(cp,[status(thm)],[t9,t1196]) ).
cnf(t2600,plain,
true = is_a_theorem(implies(implies(implies(X1,X2),X1),implies(X3,implies(X4,X1)))),
inference(step,[status(thm)],[t1202,t3]) ).
cnf(t1266,plain,
is_a_theorem(implies(implies(implies(X1,X2),X1),implies(X3,implies(X4,X1)))) = true,
inference(orient,[status(thm)],[t2600]) ).
cnf(t1267,plain,
true = ifeq(true,true,ifeq(is_a_theorem(implies(implies(X1,X2),X1)),true,is_a_theorem(implies(X3,implies(X4,X1))),true),true),
inference(cp,[status(thm)],[t5,t1266]) ).
cnf(t2614,plain,
true = ifeq(is_a_theorem(implies(implies(X1,X2),X1)),true,is_a_theorem(implies(X3,implies(X4,X1))),true),
inference(step,[status(thm)],[t1267,t3]) ).
cnf(t1459,plain,
ifeq(is_a_theorem(implies(implies(X1,X2),X1)),true,is_a_theorem(implies(X3,implies(X4,X1))),true) = true,
inference(orient,[status(thm)],[t2614]) ).
cnf(t273,plain,
true = ifeq(true,true,is_a_theorem(implies(implies(implies(X1,implies(X2,X3)),X4),implies(X5,implies(implies(implies(X4,Y5),X3),X4)))),true),
inference(cp,[status(thm)],[t9,t268]) ).
cnf(t2558,plain,
true = is_a_theorem(implies(implies(implies(X1,implies(X2,X3)),X4),implies(X5,implies(implies(implies(X4,Y5),X3),X4)))),
inference(step,[status(thm)],[t273,t3]) ).
cnf(t542,plain,
is_a_theorem(implies(implies(implies(X1,implies(X2,X3)),X4),implies(X5,implies(implies(implies(X4,Y5),X3),X4)))) = true,
inference(orient,[status(thm)],[t2558]) ).
cnf(t1461,plain,
true = ifeq(true,true,is_a_theorem(implies(X1,implies(X2,implies(X3,implies(implies(implies(X4,X5),X4),X4))))),true),
inference(cp,[status(thm)],[t1459,t542]) ).
cnf(t2620,plain,
true = is_a_theorem(implies(X1,implies(X2,implies(X3,implies(implies(implies(X4,X5),X4),X4))))),
inference(step,[status(thm)],[t1461,t3]) ).
cnf(t1605,plain,
is_a_theorem(implies(X1,implies(X2,implies(X3,implies(implies(implies(X4,X5),X4),X4))))) = true,
inference(orient,[status(thm)],[t2620]) ).
cnf(t1613,plain,
true = ifeq(true,true,is_a_theorem(implies(X1,implies(X2,implies(implies(implies(X3,X4),X3),X3)))),true),
inference(cp,[status(thm)],[t1129,t1605]) ).
cnf(t2621,plain,
true = is_a_theorem(implies(X1,implies(X2,implies(implies(implies(X3,X4),X3),X3)))),
inference(step,[status(thm)],[t1613,t3]) ).
cnf(t1640,plain,
is_a_theorem(implies(X1,implies(X2,implies(implies(implies(X3,X4),X3),X3)))) = true,
inference(orient,[status(thm)],[t2621]) ).
cnf(t1643,plain,
true = ifeq(true,true,is_a_theorem(implies(X1,implies(implies(implies(X2,X3),X2),X2))),true),
inference(cp,[status(thm)],[t1129,t1640]) ).
cnf(t2622,plain,
true = is_a_theorem(implies(X1,implies(implies(implies(X2,X3),X2),X2))),
inference(step,[status(thm)],[t1643,t3]) ).
cnf(t1665,plain,
is_a_theorem(implies(X1,implies(implies(implies(X2,X3),X2),X2))) = true,
inference(orient,[status(thm)],[t2622]) ).
cnf(t1668,plain,
true = ifeq(true,true,is_a_theorem(implies(implies(implies(X1,X2),X1),X1)),true),
inference(cp,[status(thm)],[t1129,t1665]) ).
cnf(t2623,plain,
true = is_a_theorem(implies(implies(implies(X1,X2),X1),X1)),
inference(step,[status(thm)],[t1668,t3]) ).
cnf(t1689,plain,
is_a_theorem(implies(implies(implies(X1,X2),X1),X1)) = true,
inference(orient,[status(thm)],[t2623]) ).
cnf(t1690,plain,
true = ifeq(true,true,ifeq(is_a_theorem(implies(implies(X1,X2),X1)),true,is_a_theorem(X1),true),true),
inference(cp,[status(thm)],[t5,t1689]) ).
cnf(t2625,plain,
true = ifeq(is_a_theorem(implies(implies(X1,X2),X1)),true,is_a_theorem(X1),true),
inference(step,[status(thm)],[t1690,t3]) ).
cnf(t1713,plain,
ifeq(is_a_theorem(implies(implies(X1,X2),X1)),true,is_a_theorem(X1),true) = true,
inference(orient,[status(thm)],[t2625]) ).
cnf(t121,plain,
true = ifeq(true,true,is_a_theorem(implies(implies(implies(implies(X1,X2),implies(X3,implies(X4,X2))),X5),implies(Y5,implies(X1,X5)))),true),
inference(cp,[status(thm)],[t9,t116]) ).
cnf(t2542,plain,
true = is_a_theorem(implies(implies(implies(implies(X1,X2),implies(X3,implies(X4,X2))),X5),implies(Y5,implies(X1,X5)))),
inference(step,[status(thm)],[t121,t3]) ).
cnf(t353,plain,
is_a_theorem(implies(implies(implies(implies(X1,X2),implies(X3,implies(X4,X2))),X5),implies(Y5,implies(X1,X5)))) = true,
inference(orient,[status(thm)],[t2542]) ).
cnf(t1460,plain,
true = ifeq(true,true,is_a_theorem(implies(X1,implies(X2,implies(implies(X3,X4),implies(X3,implies(X5,X4)))))),true),
inference(cp,[status(thm)],[t1459,t353]) ).
cnf(t2615,plain,
true = is_a_theorem(implies(X1,implies(X2,implies(implies(X3,X4),implies(X3,implies(X5,X4)))))),
inference(step,[status(thm)],[t1460,t3]) ).
cnf(t1477,plain,
is_a_theorem(implies(X1,implies(X2,implies(implies(X3,X4),implies(X3,implies(X5,X4)))))) = true,
inference(orient,[status(thm)],[t2615]) ).
cnf(t1484,plain,
true = ifeq(true,true,is_a_theorem(implies(X1,implies(implies(X2,X3),implies(X2,implies(X4,X3))))),true),
inference(cp,[status(thm)],[t1129,t1477]) ).
cnf(t2616,plain,
true = is_a_theorem(implies(X1,implies(implies(X2,X3),implies(X2,implies(X4,X3))))),
inference(step,[status(thm)],[t1484,t3]) ).
cnf(t1511,plain,
is_a_theorem(implies(X1,implies(implies(X2,X3),implies(X2,implies(X4,X3))))) = true,
inference(orient,[status(thm)],[t2616]) ).
cnf(t1521,plain,
true = ifeq(true,true,is_a_theorem(implies(implies(implies(X1,implies(X2,X3)),X4),implies(X5,implies(implies(X1,X3),X4)))),true),
inference(cp,[status(thm)],[t9,t1511]) ).
cnf(t2662,plain,
true = is_a_theorem(implies(implies(implies(X1,implies(X2,X3)),X4),implies(X5,implies(implies(X1,X3),X4)))),
inference(step,[status(thm)],[t1521,t3]) ).
cnf(t2443,plain,
is_a_theorem(implies(implies(implies(X1,implies(X2,X3)),X4),implies(X5,implies(implies(X1,X3),X4)))) = true,
inference(orient,[status(thm)],[t2662]) ).
cnf(t2448,plain,
true = ifeq(true,true,is_a_theorem(implies(X1,implies(implies(X1,X2),X2))),true),
inference(cp,[status(thm)],[t1713,t2443]) ).
cnf(t2663,plain,
true = is_a_theorem(implies(X1,implies(implies(X1,X2),X2))),
inference(step,[status(thm)],[t2448,t3]) ).
cnf(t2467,plain,
is_a_theorem(implies(X1,implies(implies(X1,X2),X2))) = true,
inference(orient,[status(thm)],[t2663]) ).
cnf(f2,negated_conjecture,
~ is_a_theorem(implies(a,implies(implies(a,b),b))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_ic_5) ).
fof(f2_nnf,plain,
~ is_a_theorem(implies(a,implies(implies(a,b),b))),
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
~ is_a_theorem(implies(a,implies(implies(a,b),b))),
inference(skolemisation,[status(esa)],[f2_nnf]) ).
cnf(c2,plain,
~ is_a_theorem(implies(a,implies(implies(a,b),b))),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(goal_0,negated_conjecture,
is_a_theorem(implies(a,implies(implies(a,b),b))) != true,
inference(equality_encoding,[status(esa)],[c2]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t2467]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL095-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.10/0.36 % Computer : n008.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Wed Sep 23 21:54:42 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 11.41/1.98 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 11.41/1.98 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------