%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : LCL089-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n010.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 02:00:54 PM UTC 2026
% Result : Unsatisfiable 2.52s 1.90s
% Output : Proof 2.52s
% Verified :
% SZS Type : Refutation
% Derivation depth : 94
% Number of leaves : 4
% Syntax : Number of formulae : 135 ( 131 unt; 0 def)
% Number of atoms : 143 ( 122 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 : 7 ( 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 : 411 ( 169 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(T,implies(implies(S,P),implies(R,P))))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ic_JLukasiewicz_4) ).
fof(f1_nnf,plain,
! [P,Q,R,S,T] : is_a_theorem(implies(implies(implies(P,Q),implies(R,S)),implies(T,implies(implies(S,P),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(T,implies(implies(S,P),implies(R,P))))),
inference(skolemisation,[status(esa)],[f1_nnf]) ).
cnf(c1,plain,
is_a_theorem(implies(implies(implies(X0,X1),implies(X2,X3)),implies(X4,implies(implies(X3,X0),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(X5,implies(implies(X4,X1),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(X5,implies(implies(X4,X1),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(X5,implies(implies(X4,X1),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(t956,plain,
true = ifeq(is_a_theorem(implies(implies(X1,X2),implies(X3,X4))),true,is_a_theorem(implies(X5,implies(implies(X4,X1),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(X5,implies(implies(X4,X1),implies(X3,X1)))),true) = true,
inference(orient,[status(thm)],[t956]) ).
cnf(t10,plain,
true = ifeq(true,true,is_a_theorem(implies(X1,implies(implies(implies(implies(X2,X3),implies(X4,X3)),implies(X3,X5)),implies(Y5,implies(X3,X5))))),true),
inference(cp,[status(thm)],[t9,t4]) ).
cnf(t957,plain,
true = is_a_theorem(implies(X1,implies(implies(implies(implies(X2,X3),implies(X4,X3)),implies(X3,X5)),implies(Y5,implies(X3,X5))))),
inference(step,[status(thm)],[t10,t3]) ).
cnf(t13,plain,
is_a_theorem(implies(X1,implies(implies(implies(implies(X2,X3),implies(X4,X3)),implies(X3,X5)),implies(Y5,implies(X3,X5))))) = true,
inference(orient,[status(thm)],[t957]) ).
cnf(t14,plain,
true = ifeq(true,true,ifeq(is_a_theorem(X1),true,is_a_theorem(implies(implies(implies(implies(X2,X3),implies(X4,X3)),implies(X3,X5)),implies(Y5,implies(X3,X5)))),true),true),
inference(cp,[status(thm)],[t5,t13]) ).
cnf(t958,plain,
true = ifeq(is_a_theorem(X1),true,is_a_theorem(implies(implies(implies(implies(X2,X3),implies(X4,X3)),implies(X3,X5)),implies(Y5,implies(X3,X5)))),true),
inference(step,[status(thm)],[t14,t3]) ).
cnf(t20,plain,
ifeq(is_a_theorem(X1),true,is_a_theorem(implies(implies(implies(implies(X2,X3),implies(X4,X3)),implies(X3,X5)),implies(Y5,implies(X3,X5)))),true) = true,
inference(orient,[status(thm)],[t958]) ).
cnf(t21,plain,
true = ifeq(true,true,is_a_theorem(implies(implies(implies(implies(X1,X2),implies(X3,X2)),implies(X2,X4)),implies(X5,implies(X2,X4)))),true),
inference(cp,[status(thm)],[t20,t4]) ).
cnf(t959,plain,
true = is_a_theorem(implies(implies(implies(implies(X1,X2),implies(X3,X2)),implies(X2,X4)),implies(X5,implies(X2,X4)))),
inference(step,[status(thm)],[t21,t3]) ).
cnf(t25,plain,
is_a_theorem(implies(implies(implies(implies(X1,X2),implies(X3,X2)),implies(X2,X4)),implies(X5,implies(X2,X4)))) = true,
inference(orient,[status(thm)],[t959]) ).
cnf(t26,plain,
true = ifeq(true,true,ifeq(is_a_theorem(implies(implies(implies(X1,X2),implies(X3,X2)),implies(X2,X4))),true,is_a_theorem(implies(X5,implies(X2,X4))),true),true),
inference(cp,[status(thm)],[t5,t25]) ).
cnf(t960,plain,
true = ifeq(is_a_theorem(implies(implies(implies(X1,X2),implies(X3,X2)),implies(X2,X4))),true,is_a_theorem(implies(X5,implies(X2,X4))),true),
inference(step,[status(thm)],[t26,t3]) ).
cnf(t29,plain,
ifeq(is_a_theorem(implies(implies(implies(X1,X2),implies(X3,X2)),implies(X2,X4))),true,is_a_theorem(implies(X5,implies(X2,X4))),true) = true,
inference(orient,[status(thm)],[t960]) ).
cnf(t31,plain,
true = ifeq(true,true,is_a_theorem(implies(X1,implies(implies(X2,X3),implies(X3,implies(X2,X3))))),true),
inference(cp,[status(thm)],[t29,t25]) ).
cnf(t962,plain,
true = is_a_theorem(implies(X1,implies(implies(X2,X3),implies(X3,implies(X2,X3))))),
inference(step,[status(thm)],[t31,t3]) ).
cnf(t37,plain,
is_a_theorem(implies(X1,implies(implies(X2,X3),implies(X3,implies(X2,X3))))) = true,
inference(orient,[status(thm)],[t962]) ).
cnf(t38,plain,
true = ifeq(true,true,ifeq(is_a_theorem(X1),true,is_a_theorem(implies(implies(X2,X3),implies(X3,implies(X2,X3)))),true),true),
inference(cp,[status(thm)],[t5,t37]) ).
cnf(t966,plain,
true = ifeq(is_a_theorem(X1),true,is_a_theorem(implies(implies(X2,X3),implies(X3,implies(X2,X3)))),true),
inference(step,[status(thm)],[t38,t3]) ).
cnf(t58,plain,
ifeq(is_a_theorem(X1),true,is_a_theorem(implies(implies(X2,X3),implies(X3,implies(X2,X3)))),true) = true,
inference(orient,[status(thm)],[t966]) ).
cnf(t30,plain,
true = ifeq(true,true,is_a_theorem(implies(X1,implies(X2,implies(implies(X2,X3),implies(X4,X3))))),true),
inference(cp,[status(thm)],[t29,t4]) ).
cnf(t961,plain,
true = is_a_theorem(implies(X1,implies(X2,implies(implies(X2,X3),implies(X4,X3))))),
inference(step,[status(thm)],[t30,t3]) ).
cnf(t33,plain,
is_a_theorem(implies(X1,implies(X2,implies(implies(X2,X3),implies(X4,X3))))) = true,
inference(orient,[status(thm)],[t961]) ).
cnf(t34,plain,
true = ifeq(true,true,ifeq(is_a_theorem(X1),true,is_a_theorem(implies(X2,implies(implies(X2,X3),implies(X4,X3)))),true),true),
inference(cp,[status(thm)],[t5,t33]) ).
cnf(t963,plain,
true = ifeq(is_a_theorem(X1),true,is_a_theorem(implies(X2,implies(implies(X2,X3),implies(X4,X3)))),true),
inference(step,[status(thm)],[t34,t3]) ).
cnf(t41,plain,
ifeq(is_a_theorem(X1),true,is_a_theorem(implies(X2,implies(implies(X2,X3),implies(X4,X3)))),true) = true,
inference(orient,[status(thm)],[t963]) ).
cnf(t42,plain,
true = ifeq(true,true,is_a_theorem(implies(X1,implies(implies(X1,X2),implies(X3,X2)))),true),
inference(cp,[status(thm)],[t41,t4]) ).
cnf(t964,plain,
true = is_a_theorem(implies(X1,implies(implies(X1,X2),implies(X3,X2)))),
inference(step,[status(thm)],[t42,t3]) ).
cnf(t47,plain,
is_a_theorem(implies(X1,implies(implies(X1,X2),implies(X3,X2)))) = true,
inference(orient,[status(thm)],[t964]) ).
cnf(t59,plain,
true = ifeq(true,true,is_a_theorem(implies(implies(X1,X2),implies(X2,implies(X1,X2)))),true),
inference(cp,[status(thm)],[t58,t47]) ).
cnf(t967,plain,
true = is_a_theorem(implies(implies(X1,X2),implies(X2,implies(X1,X2)))),
inference(step,[status(thm)],[t59,t3]) ).
cnf(t65,plain,
is_a_theorem(implies(implies(X1,X2),implies(X2,implies(X1,X2)))) = true,
inference(orient,[status(thm)],[t967]) ).
cnf(t69,plain,
true = ifeq(true,true,is_a_theorem(implies(X1,implies(implies(implies(X2,X3),X2),implies(X3,X2)))),true),
inference(cp,[status(thm)],[t9,t65]) ).
cnf(t968,plain,
true = is_a_theorem(implies(X1,implies(implies(implies(X2,X3),X2),implies(X3,X2)))),
inference(step,[status(thm)],[t69,t3]) ).
cnf(t70,plain,
is_a_theorem(implies(X1,implies(implies(implies(X2,X3),X2),implies(X3,X2)))) = true,
inference(orient,[status(thm)],[t968]) ).
cnf(t71,plain,
true = ifeq(true,true,ifeq(is_a_theorem(X1),true,is_a_theorem(implies(implies(implies(X2,X3),X2),implies(X3,X2))),true),true),
inference(cp,[status(thm)],[t5,t70]) ).
cnf(t970,plain,
true = ifeq(is_a_theorem(X1),true,is_a_theorem(implies(implies(implies(X2,X3),X2),implies(X3,X2))),true),
inference(step,[status(thm)],[t71,t3]) ).
cnf(t81,plain,
ifeq(is_a_theorem(X1),true,is_a_theorem(implies(implies(implies(X2,X3),X2),implies(X3,X2))),true) = true,
inference(orient,[status(thm)],[t970]) ).
cnf(t82,plain,
true = ifeq(true,true,is_a_theorem(implies(implies(implies(X1,X2),X1),implies(X2,X1))),true),
inference(cp,[status(thm)],[t81,t65]) ).
cnf(t971,plain,
true = is_a_theorem(implies(implies(implies(X1,X2),X1),implies(X2,X1))),
inference(step,[status(thm)],[t82,t3]) ).
cnf(t90,plain,
is_a_theorem(implies(implies(implies(X1,X2),X1),implies(X2,X1))) = true,
inference(orient,[status(thm)],[t971]) ).
cnf(t94,plain,
true = ifeq(true,true,is_a_theorem(implies(X1,implies(X2,implies(X3,X2)))),true),
inference(cp,[status(thm)],[t29,t90]) ).
cnf(t972,plain,
true = is_a_theorem(implies(X1,implies(X2,implies(X3,X2)))),
inference(step,[status(thm)],[t94,t3]) ).
cnf(t96,plain,
is_a_theorem(implies(X1,implies(X2,implies(X3,X2)))) = true,
inference(orient,[status(thm)],[t972]) ).
cnf(t97,plain,
true = ifeq(true,true,ifeq(is_a_theorem(X1),true,is_a_theorem(implies(X2,implies(X3,X2))),true),true),
inference(cp,[status(thm)],[t5,t96]) ).
cnf(t973,plain,
true = ifeq(is_a_theorem(X1),true,is_a_theorem(implies(X2,implies(X3,X2))),true),
inference(step,[status(thm)],[t97,t3]) ).
cnf(t102,plain,
ifeq(is_a_theorem(X1),true,is_a_theorem(implies(X2,implies(X3,X2))),true) = true,
inference(orient,[status(thm)],[t973]) ).
cnf(t103,plain,
true = ifeq(true,true,is_a_theorem(implies(X1,implies(X2,X1))),true),
inference(cp,[status(thm)],[t102,t47]) ).
cnf(t974,plain,
true = is_a_theorem(implies(X1,implies(X2,X1))),
inference(step,[status(thm)],[t103,t3]) ).
cnf(t111,plain,
is_a_theorem(implies(X1,implies(X2,X1))) = true,
inference(orient,[status(thm)],[t974]) ).
cnf(t113,plain,
true = ifeq(is_a_theorem(implies(implies(X1,implies(X2,X1)),X3)),true,ifeq(true,true,is_a_theorem(X3),true),true),
inference(cp,[status(thm)],[t5,t111]) ).
cnf(t983,plain,
true = ifeq(is_a_theorem(implies(implies(X1,implies(X2,X1)),X3)),true,is_a_theorem(X3),true),
inference(step,[status(thm)],[t113,t3]) ).
cnf(t158,plain,
ifeq(is_a_theorem(implies(implies(X1,implies(X2,X1)),X3)),true,is_a_theorem(X3),true) = true,
inference(orient,[status(thm)],[t983]) ).
cnf(t116,plain,
true = ifeq(true,true,is_a_theorem(implies(X1,implies(implies(implies(X2,X3),X2),implies(X4,X2)))),true),
inference(cp,[status(thm)],[t9,t111]) ).
cnf(t980,plain,
true = is_a_theorem(implies(X1,implies(implies(implies(X2,X3),X2),implies(X4,X2)))),
inference(step,[status(thm)],[t116,t3]) ).
cnf(t146,plain,
is_a_theorem(implies(X1,implies(implies(implies(X2,X3),X2),implies(X4,X2)))) = true,
inference(orient,[status(thm)],[t980]) ).
cnf(t160,plain,
true = ifeq(true,true,is_a_theorem(implies(implies(implies(X1,X2),X1),implies(X3,X1))),true),
inference(cp,[status(thm)],[t158,t146]) ).
cnf(t986,plain,
true = is_a_theorem(implies(implies(implies(X1,X2),X1),implies(X3,X1))),
inference(step,[status(thm)],[t160,t3]) ).
cnf(t174,plain,
is_a_theorem(implies(implies(implies(X1,X2),X1),implies(X3,X1))) = true,
inference(orient,[status(thm)],[t986]) ).
cnf(t175,plain,
true = ifeq(true,true,ifeq(is_a_theorem(implies(implies(X1,X2),X1)),true,is_a_theorem(implies(X3,X1)),true),true),
inference(cp,[status(thm)],[t5,t174]) ).
cnf(t995,plain,
true = ifeq(is_a_theorem(implies(implies(X1,X2),X1)),true,is_a_theorem(implies(X3,X1)),true),
inference(step,[status(thm)],[t175,t3]) ).
cnf(t243,plain,
ifeq(is_a_theorem(implies(implies(X1,X2),X1)),true,is_a_theorem(implies(X3,X1)),true) = true,
inference(orient,[status(thm)],[t995]) ).
cnf(t101,plain,
true = ifeq(true,true,is_a_theorem(implies(X1,implies(implies(implies(X2,X3),X4),implies(X3,X4)))),true),
inference(cp,[status(thm)],[t9,t96]) ).
cnf(t977,plain,
true = is_a_theorem(implies(X1,implies(implies(implies(X2,X3),X4),implies(X3,X4)))),
inference(step,[status(thm)],[t101,t3]) ).
cnf(t128,plain,
is_a_theorem(implies(X1,implies(implies(implies(X2,X3),X4),implies(X3,X4)))) = true,
inference(orient,[status(thm)],[t977]) ).
cnf(t159,plain,
true = ifeq(true,true,is_a_theorem(implies(implies(implies(X1,X2),X3),implies(X2,X3))),true),
inference(cp,[status(thm)],[t158,t128]) ).
cnf(t984,plain,
true = is_a_theorem(implies(implies(implies(X1,X2),X3),implies(X2,X3))),
inference(step,[status(thm)],[t159,t3]) ).
cnf(t162,plain,
is_a_theorem(implies(implies(implies(X1,X2),X3),implies(X2,X3))) = true,
inference(orient,[status(thm)],[t984]) ).
cnf(t244,plain,
true = ifeq(true,true,is_a_theorem(implies(X1,implies(X2,X2))),true),
inference(cp,[status(thm)],[t243,t162]) ).
cnf(t996,plain,
true = is_a_theorem(implies(X1,implies(X2,X2))),
inference(step,[status(thm)],[t244,t3]) ).
cnf(t247,plain,
is_a_theorem(implies(X1,implies(X2,X2))) = true,
inference(orient,[status(thm)],[t996]) ).
cnf(t253,plain,
true = ifeq(true,true,is_a_theorem(implies(X1,X1)),true),
inference(cp,[status(thm)],[t158,t247]) ).
cnf(t997,plain,
true = is_a_theorem(implies(X1,X1)),
inference(step,[status(thm)],[t253,t3]) ).
cnf(t254,plain,
is_a_theorem(implies(X1,X1)) = true,
inference(orient,[status(thm)],[t997]) ).
cnf(t256,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,t254]) ).
cnf(t1003,plain,
true = ifeq(is_a_theorem(implies(implies(X1,X1),X2)),true,is_a_theorem(X2),true),
inference(step,[status(thm)],[t256,t3]) ).
cnf(t288,plain,
ifeq(is_a_theorem(implies(implies(X1,X1),X2)),true,is_a_theorem(X2),true) = true,
inference(orient,[status(thm)],[t1003]) ).
cnf(t178,plain,
true = ifeq(true,true,is_a_theorem(implies(X1,implies(implies(X2,implies(X2,X3)),implies(X4,implies(X2,X3))))),true),
inference(cp,[status(thm)],[t9,t174]) ).
cnf(t1019,plain,
true = is_a_theorem(implies(X1,implies(implies(X2,implies(X2,X3)),implies(X4,implies(X2,X3))))),
inference(step,[status(thm)],[t178,t3]) ).
cnf(t415,plain,
is_a_theorem(implies(X1,implies(implies(X2,implies(X2,X3)),implies(X4,implies(X2,X3))))) = true,
inference(orient,[status(thm)],[t1019]) ).
cnf(t419,plain,
true = ifeq(true,true,is_a_theorem(implies(implies(X1,implies(X1,X2)),implies(X3,implies(X1,X2)))),true),
inference(cp,[status(thm)],[t288,t415]) ).
cnf(t1020,plain,
true = is_a_theorem(implies(implies(X1,implies(X1,X2)),implies(X3,implies(X1,X2)))),
inference(step,[status(thm)],[t419,t3]) ).
cnf(t427,plain,
is_a_theorem(implies(implies(X1,implies(X1,X2)),implies(X3,implies(X1,X2)))) = true,
inference(orient,[status(thm)],[t1020]) ).
cnf(t428,plain,
true = ifeq(true,true,ifeq(is_a_theorem(implies(X1,implies(X1,X2))),true,is_a_theorem(implies(X3,implies(X1,X2))),true),true),
inference(cp,[status(thm)],[t5,t427]) ).
cnf(t1045,plain,
true = ifeq(is_a_theorem(implies(X1,implies(X1,X2))),true,is_a_theorem(implies(X3,implies(X1,X2))),true),
inference(step,[status(thm)],[t428,t3]) ).
cnf(t727,plain,
ifeq(is_a_theorem(implies(X1,implies(X1,X2))),true,is_a_theorem(implies(X3,implies(X1,X2))),true) = true,
inference(orient,[status(thm)],[t1045]) ).
cnf(t735,plain,
true = ifeq(true,true,is_a_theorem(implies(X1,implies(implies(implies(X2,X3),X2),X2))),true),
inference(cp,[status(thm)],[t727,t174]) ).
cnf(t1048,plain,
true = is_a_theorem(implies(X1,implies(implies(implies(X2,X3),X2),X2))),
inference(step,[status(thm)],[t735,t3]) ).
cnf(t764,plain,
is_a_theorem(implies(X1,implies(implies(implies(X2,X3),X2),X2))) = true,
inference(orient,[status(thm)],[t1048]) ).
cnf(t768,plain,
true = ifeq(true,true,is_a_theorem(implies(implies(implies(X1,X2),X1),X1)),true),
inference(cp,[status(thm)],[t288,t764]) ).
cnf(t1049,plain,
true = is_a_theorem(implies(implies(implies(X1,X2),X1),X1)),
inference(step,[status(thm)],[t768,t3]) ).
cnf(t781,plain,
is_a_theorem(implies(implies(implies(X1,X2),X1),X1)) = true,
inference(orient,[status(thm)],[t1049]) ).
cnf(t782,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,t781]) ).
cnf(t1050,plain,
true = ifeq(is_a_theorem(implies(implies(X1,X2),X1)),true,is_a_theorem(X1),true),
inference(step,[status(thm)],[t782,t3]) ).
cnf(t790,plain,
ifeq(is_a_theorem(implies(implies(X1,X2),X1)),true,is_a_theorem(X1),true) = true,
inference(orient,[status(thm)],[t1050]) ).
cnf(t729,plain,
true = ifeq(true,true,is_a_theorem(implies(X1,implies(implies(X2,implies(X2,X3)),implies(X2,X3)))),true),
inference(cp,[status(thm)],[t727,t427]) ).
cnf(t1051,plain,
true = is_a_theorem(implies(X1,implies(implies(X2,implies(X2,X3)),implies(X2,X3)))),
inference(step,[status(thm)],[t729,t3]) ).
cnf(t791,plain,
is_a_theorem(implies(X1,implies(implies(X2,implies(X2,X3)),implies(X2,X3)))) = true,
inference(orient,[status(thm)],[t1051]) ).
cnf(t795,plain,
true = ifeq(true,true,is_a_theorem(implies(implies(X1,implies(X1,X2)),implies(X1,X2))),true),
inference(cp,[status(thm)],[t790,t791]) ).
cnf(t1053,plain,
true = is_a_theorem(implies(implies(X1,implies(X1,X2)),implies(X1,X2))),
inference(step,[status(thm)],[t795,t3]) ).
cnf(t823,plain,
is_a_theorem(implies(implies(X1,implies(X1,X2)),implies(X1,X2))) = true,
inference(orient,[status(thm)],[t1053]) ).
cnf(t824,plain,
true = ifeq(true,true,ifeq(is_a_theorem(implies(X1,implies(X1,X2))),true,is_a_theorem(implies(X1,X2)),true),true),
inference(cp,[status(thm)],[t5,t823]) ).
cnf(t1062,plain,
true = ifeq(is_a_theorem(implies(X1,implies(X1,X2))),true,is_a_theorem(implies(X1,X2)),true),
inference(step,[status(thm)],[t824,t3]) ).
cnf(t930,plain,
ifeq(is_a_theorem(implies(X1,implies(X1,X2))),true,is_a_theorem(implies(X1,X2)),true) = true,
inference(orient,[status(thm)],[t1062]) ).
cnf(t163,plain,
true = ifeq(true,true,ifeq(is_a_theorem(implies(implies(X1,X2),X3)),true,is_a_theorem(implies(X2,X3)),true),true),
inference(cp,[status(thm)],[t5,t162]) ).
cnf(t990,plain,
true = ifeq(is_a_theorem(implies(implies(X1,X2),X3)),true,is_a_theorem(implies(X2,X3)),true),
inference(step,[status(thm)],[t163,t3]) ).
cnf(t205,plain,
ifeq(is_a_theorem(implies(implies(X1,X2),X3)),true,is_a_theorem(implies(X2,X3)),true) = true,
inference(orient,[status(thm)],[t990]) ).
cnf(t206,plain,
true = ifeq(true,true,is_a_theorem(implies(implies(X1,X2),implies(X3,implies(implies(X2,X4),implies(X1,X4))))),true),
inference(cp,[status(thm)],[t205,t4]) ).
cnf(t1025,plain,
true = is_a_theorem(implies(implies(X1,X2),implies(X3,implies(implies(X2,X4),implies(X1,X4))))),
inference(step,[status(thm)],[t206,t3]) ).
cnf(t473,plain,
is_a_theorem(implies(implies(X1,X2),implies(X3,implies(implies(X2,X4),implies(X1,X4))))) = true,
inference(orient,[status(thm)],[t1025]) ).
cnf(t932,plain,
true = ifeq(true,true,is_a_theorem(implies(implies(X1,X2),implies(implies(X2,X3),implies(X1,X3)))),true),
inference(cp,[status(thm)],[t930,t473]) ).
cnf(t1064,plain,
true = is_a_theorem(implies(implies(X1,X2),implies(implies(X2,X3),implies(X1,X3)))),
inference(step,[status(thm)],[t932,t3]) ).
cnf(t945,plain,
is_a_theorem(implies(implies(X1,X2),implies(implies(X2,X3),implies(X1,X3)))) = true,
inference(orient,[status(thm)],[t1064]) ).
cnf(f2,negated_conjecture,
~ is_a_theorem(implies(implies(a,b),implies(implies(b,c),implies(a,c)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_ic_4) ).
fof(f2_nnf,plain,
~ is_a_theorem(implies(implies(a,b),implies(implies(b,c),implies(a,c)))),
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
~ is_a_theorem(implies(implies(a,b),implies(implies(b,c),implies(a,c)))),
inference(skolemisation,[status(esa)],[f2_nnf]) ).
cnf(c2,plain,
~ is_a_theorem(implies(implies(a,b),implies(implies(b,c),implies(a,c)))),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(goal_0,negated_conjecture,
is_a_theorem(implies(implies(a,b),implies(implies(b,c),implies(a,c)))) != true,
inference(equality_encoding,[status(esa)],[c2]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t945]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL089-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.08/0.35 % Computer : n010.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Wed Sep 23 21:53:27 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.35 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 2.52/1.90 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 2.52/1.90 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------