%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : LCL016-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n005.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 02:00:41 PM UTC 2026
% Result : Unsatisfiable 71.46s 10.94s
% Output : Proof 71.46s
% Verified :
% SZS Type : Refutation
% Derivation depth : 125
% Number of leaves : 4
% Syntax : Number of formulae : 259 ( 255 unt; 0 def)
% Number of atoms : 267 ( 246 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 : 11 ( 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 : 810 ( 2 sgn 10 !; 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(t2,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(t9,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)],[t2]) ).
cnf(hi0,axiom,
ifeq(is_a_theorem(equivalent(X0,X1)),true,ifeq(is_a_theorem(X0),true,is_a_theorem(X1),true),true) = true,
inference(equality_encoding,[status(esa)],[c0]) ).
cnf(f1,axiom,
is_a_theorem(equivalent(equivalent(X,Y),equivalent(Z,equivalent(equivalent(Z,Y),X)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',yro) ).
fof(f1_nnf,plain,
! [X,Y,Z] : is_a_theorem(equivalent(equivalent(X,Y),equivalent(Z,equivalent(equivalent(Z,Y),X)))),
inference(nnf_transformation,[status(thm)],[f1]) ).
fof(f1_sk,plain,
! [X,Y,Z] : is_a_theorem(equivalent(equivalent(X,Y),equivalent(Z,equivalent(equivalent(Z,Y),X)))),
inference(skolemisation,[status(esa)],[f1_nnf]) ).
cnf(c1,plain,
is_a_theorem(equivalent(equivalent(X0,X1),equivalent(X2,equivalent(equivalent(X2,X1),X0)))),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(hi1,axiom,
is_a_theorem(equivalent(equivalent(X0,X1),equivalent(X2,equivalent(equivalent(X2,X1),X0)))) = true,
inference(equality_encoding,[status(esa)],[c1]) ).
cnf(t3,plain,
is_a_theorem(equivalent(X1,equivalent(equivalent(X1,equivalent(X2,equivalent(equivalent(X2,X3),X4))),equivalent(X4,X3)))) = true,
inference(hyper_resolution,[status(thm)],[hi0,hi1,hi1]) ).
cnf(t6,plain,
is_a_theorem(equivalent(X1,equivalent(equivalent(X1,equivalent(X2,equivalent(equivalent(X2,X3),X4))),equivalent(X4,X3)))) = true,
inference(orient,[status(thm)],[t3]) ).
cnf(t14,plain,
true = ifeq(is_a_theorem(equivalent(equivalent(X1,equivalent(equivalent(X1,equivalent(X2,equivalent(equivalent(X2,X3),X4))),equivalent(X4,X3))),X5)),true,ifeq(true,true,is_a_theorem(X5),true),true),
inference(cp,[status(thm)],[t9,t6]) ).
cnf(t0,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t5,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t0]) ).
cnf(t231097,plain,
true = ifeq(is_a_theorem(equivalent(equivalent(X1,equivalent(equivalent(X1,equivalent(X2,equivalent(equivalent(X2,X3),X4))),equivalent(X4,X3))),X5)),true,is_a_theorem(X5),true),
inference(step,[status(thm)],[t14,t5]) ).
cnf(t39,plain,
ifeq(is_a_theorem(equivalent(equivalent(X1,equivalent(equivalent(X1,equivalent(X2,equivalent(equivalent(X2,X3),X4))),equivalent(X4,X3))),X5)),true,is_a_theorem(X5),true) = true,
inference(orient,[status(thm)],[t231097]) ).
cnf(t1,plain,
is_a_theorem(equivalent(equivalent(X1,X2),equivalent(X3,equivalent(equivalent(X3,X2),X1)))) = true,
inference(equality_encoding,[status(esa)],[c1]) ).
cnf(t8,plain,
is_a_theorem(equivalent(equivalent(X1,X2),equivalent(X3,equivalent(equivalent(X3,X2),X1)))) = true,
inference(orient,[status(thm)],[t1]) ).
cnf(t13,plain,
true = ifeq(is_a_theorem(equivalent(equivalent(equivalent(X1,X2),equivalent(X3,equivalent(equivalent(X3,X2),X1))),X4)),true,ifeq(true,true,is_a_theorem(X4),true),true),
inference(cp,[status(thm)],[t9,t8]) ).
cnf(t231095,plain,
true = ifeq(is_a_theorem(equivalent(equivalent(equivalent(X1,X2),equivalent(X3,equivalent(equivalent(X3,X2),X1))),X4)),true,is_a_theorem(X4),true),
inference(step,[status(thm)],[t13,t5]) ).
cnf(t27,plain,
ifeq(is_a_theorem(equivalent(equivalent(equivalent(X1,X2),equivalent(X3,equivalent(equivalent(X3,X2),X1))),X4)),true,is_a_theorem(X4),true) = true,
inference(orient,[status(thm)],[t231095]) ).
cnf(t10,plain,
true = ifeq(true,true,ifeq(is_a_theorem(X1),true,is_a_theorem(equivalent(equivalent(X1,equivalent(X2,equivalent(equivalent(X2,X3),X4))),equivalent(X4,X3))),true),true),
inference(cp,[status(thm)],[t9,t6]) ).
cnf(t231094,plain,
true = ifeq(is_a_theorem(X1),true,is_a_theorem(equivalent(equivalent(X1,equivalent(X2,equivalent(equivalent(X2,X3),X4))),equivalent(X4,X3))),true),
inference(step,[status(thm)],[t10,t5]) ).
cnf(t23,plain,
ifeq(is_a_theorem(X1),true,is_a_theorem(equivalent(equivalent(X1,equivalent(X2,equivalent(equivalent(X2,X3),X4))),equivalent(X4,X3))),true) = true,
inference(orient,[status(thm)],[t231094]) ).
cnf(t24,plain,
true = ifeq(true,true,is_a_theorem(equivalent(equivalent(equivalent(equivalent(X1,X2),equivalent(X3,equivalent(equivalent(X3,X2),X1))),equivalent(X4,equivalent(equivalent(X4,X5),Y5))),equivalent(Y5,X5))),true),
inference(cp,[status(thm)],[t23,t8]) ).
cnf(t231099,plain,
true = is_a_theorem(equivalent(equivalent(equivalent(equivalent(X1,X2),equivalent(X3,equivalent(equivalent(X3,X2),X1))),equivalent(X4,equivalent(equivalent(X4,X5),Y5))),equivalent(Y5,X5))),
inference(step,[status(thm)],[t24,t5]) ).
cnf(t64,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(X1,X2),equivalent(X3,equivalent(equivalent(X3,X2),X1))),equivalent(X4,equivalent(equivalent(X4,X5),Y5))),equivalent(Y5,X5))) = true,
inference(orient,[status(thm)],[t231099]) ).
cnf(t65,plain,
true = ifeq(true,true,ifeq(is_a_theorem(equivalent(equivalent(equivalent(X1,X2),equivalent(X3,equivalent(equivalent(X3,X2),X1))),equivalent(X4,equivalent(equivalent(X4,X5),Y5)))),true,is_a_theorem(equivalent(Y5,X5)),true),true),
inference(cp,[status(thm)],[t9,t64]) ).
cnf(t231102,plain,
true = ifeq(is_a_theorem(equivalent(equivalent(equivalent(X1,X2),equivalent(X3,equivalent(equivalent(X3,X2),X1))),equivalent(X4,equivalent(equivalent(X4,X5),Y5)))),true,is_a_theorem(equivalent(Y5,X5)),true),
inference(step,[status(thm)],[t65,t5]) ).
cnf(t103,plain,
ifeq(is_a_theorem(equivalent(equivalent(equivalent(X1,X2),equivalent(X3,equivalent(equivalent(X3,X2),X1))),equivalent(X4,equivalent(equivalent(X4,X5),Y5)))),true,is_a_theorem(equivalent(Y5,X5)),true) = true,
inference(orient,[status(thm)],[t231102]) ).
cnf(t104,plain,
true = ifeq(true,true,is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X1,X2),X3),X2),X1),X3)),true),
inference(cp,[status(thm)],[t103,t64]) ).
cnf(t231103,plain,
true = is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X1,X2),X3),X2),X1),X3)),
inference(step,[status(thm)],[t104,t5]) ).
cnf(t110,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X1,X2),X3),X2),X1),X3)) = true,
inference(orient,[status(thm)],[t231103]) ).
cnf(t111,plain,
true = ifeq(true,true,ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(X1,X2),X3),X2),X1)),true,is_a_theorem(X3),true),true),
inference(cp,[status(thm)],[t9,t110]) ).
cnf(t231104,plain,
true = ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(X1,X2),X3),X2),X1)),true,is_a_theorem(X3),true),
inference(step,[status(thm)],[t111,t5]) ).
cnf(t129,plain,
ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(X1,X2),X3),X2),X1)),true,is_a_theorem(X3),true) = true,
inference(orient,[status(thm)],[t231104]) ).
cnf(t112,plain,
true = ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X1,X2),X3),X2),X1),X3),X4)),true,ifeq(true,true,is_a_theorem(X4),true),true),
inference(cp,[status(thm)],[t9,t110]) ).
cnf(t231106,plain,
true = ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X1,X2),X3),X2),X1),X3),X4)),true,is_a_theorem(X4),true),
inference(step,[status(thm)],[t112,t5]) ).
cnf(t154,plain,
ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X1,X2),X3),X2),X1),X3),X4)),true,is_a_theorem(X4),true) = true,
inference(orient,[status(thm)],[t231106]) ).
cnf(t12,plain,
true = ifeq(true,true,ifeq(is_a_theorem(equivalent(X1,X2)),true,is_a_theorem(equivalent(X3,equivalent(equivalent(X3,X2),X1))),true),true),
inference(cp,[status(thm)],[t9,t8]) ).
cnf(t231093,plain,
true = ifeq(is_a_theorem(equivalent(X1,X2)),true,is_a_theorem(equivalent(X3,equivalent(equivalent(X3,X2),X1))),true),
inference(step,[status(thm)],[t12,t5]) ).
cnf(t19,plain,
ifeq(is_a_theorem(equivalent(X1,X2)),true,is_a_theorem(equivalent(X3,equivalent(equivalent(X3,X2),X1))),true) = true,
inference(orient,[status(thm)],[t231093]) ).
cnf(t114,plain,
true = ifeq(true,true,is_a_theorem(equivalent(X1,equivalent(equivalent(X1,X2),equivalent(equivalent(equivalent(equivalent(X3,X4),X2),X4),X3)))),true),
inference(cp,[status(thm)],[t19,t110]) ).
cnf(t231105,plain,
true = is_a_theorem(equivalent(X1,equivalent(equivalent(X1,X2),equivalent(equivalent(equivalent(equivalent(X3,X4),X2),X4),X3)))),
inference(step,[status(thm)],[t114,t5]) ).
cnf(t136,plain,
is_a_theorem(equivalent(X1,equivalent(equivalent(X1,X2),equivalent(equivalent(equivalent(equivalent(X3,X4),X2),X4),X3)))) = true,
inference(orient,[status(thm)],[t231105]) ).
cnf(t144,plain,
true = ifeq(true,true,is_a_theorem(equivalent(equivalent(equivalent(equivalent(X1,X2),equivalent(X3,equivalent(equivalent(X3,X2),X1))),X4),equivalent(equivalent(equivalent(equivalent(X5,Y5),X4),Y5),X5))),true),
inference(cp,[status(thm)],[t27,t136]) ).
cnf(t231113,plain,
true = is_a_theorem(equivalent(equivalent(equivalent(equivalent(X1,X2),equivalent(X3,equivalent(equivalent(X3,X2),X1))),X4),equivalent(equivalent(equivalent(equivalent(X5,Y5),X4),Y5),X5))),
inference(step,[status(thm)],[t144,t5]) ).
cnf(t285,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(X1,X2),equivalent(X3,equivalent(equivalent(X3,X2),X1))),X4),equivalent(equivalent(equivalent(equivalent(X5,Y5),X4),Y5),X5))) = true,
inference(orient,[status(thm)],[t231113]) ).
cnf(t294,plain,
true = ifeq(true,true,is_a_theorem(equivalent(equivalent(equivalent(equivalent(X1,X2),equivalent(X3,equivalent(equivalent(X3,equivalent(X4,equivalent(equivalent(X4,X5),Y5))),equivalent(Y5,X5)))),X2),X1)),true),
inference(cp,[status(thm)],[t27,t285]) ).
cnf(t231117,plain,
true = is_a_theorem(equivalent(equivalent(equivalent(equivalent(X1,X2),equivalent(X3,equivalent(equivalent(X3,equivalent(X4,equivalent(equivalent(X4,X5),Y5))),equivalent(Y5,X5)))),X2),X1)),
inference(step,[status(thm)],[t294,t5]) ).
cnf(t367,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(X1,X2),equivalent(X3,equivalent(equivalent(X3,equivalent(X4,equivalent(equivalent(X4,X5),Y5))),equivalent(Y5,X5)))),X2),X1)) = true,
inference(orient,[status(thm)],[t231117]) ).
cnf(t383,plain,
true = ifeq(true,true,is_a_theorem(equivalent(equivalent(equivalent(X1,equivalent(equivalent(X1,equivalent(X2,equivalent(equivalent(X2,X3),X4))),equivalent(X4,X3))),X5),X5)),true),
inference(cp,[status(thm)],[t154,t367]) ).
cnf(t231118,plain,
true = is_a_theorem(equivalent(equivalent(equivalent(X1,equivalent(equivalent(X1,equivalent(X2,equivalent(equivalent(X2,X3),X4))),equivalent(X4,X3))),X5),X5)),
inference(step,[status(thm)],[t383,t5]) ).
cnf(t396,plain,
is_a_theorem(equivalent(equivalent(equivalent(X1,equivalent(equivalent(X1,equivalent(X2,equivalent(equivalent(X2,X3),X4))),equivalent(X4,X3))),X5),X5)) = true,
inference(orient,[status(thm)],[t231118]) ).
cnf(t400,plain,
true = ifeq(true,true,is_a_theorem(equivalent(equivalent(equivalent(X1,X1),equivalent(X2,equivalent(equivalent(X2,X3),X4))),equivalent(X4,X3))),true),
inference(cp,[status(thm)],[t129,t396]) ).
cnf(t231119,plain,
true = is_a_theorem(equivalent(equivalent(equivalent(X1,X1),equivalent(X2,equivalent(equivalent(X2,X3),X4))),equivalent(X4,X3))),
inference(step,[status(thm)],[t400,t5]) ).
cnf(t422,plain,
is_a_theorem(equivalent(equivalent(equivalent(X1,X1),equivalent(X2,equivalent(equivalent(X2,X3),X4))),equivalent(X4,X3))) = true,
inference(orient,[status(thm)],[t231119]) ).
cnf(t432,plain,
true = ifeq(true,true,is_a_theorem(equivalent(X1,X1)),true),
inference(cp,[status(thm)],[t27,t422]) ).
cnf(t231120,plain,
true = is_a_theorem(equivalent(X1,X1)),
inference(step,[status(thm)],[t432,t5]) ).
cnf(t449,plain,
is_a_theorem(equivalent(X1,X1)) = true,
inference(orient,[status(thm)],[t231120]) ).
cnf(t451,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)],[t9,t449]) ).
cnf(t231123,plain,
true = ifeq(is_a_theorem(equivalent(equivalent(X1,X1),X2)),true,is_a_theorem(X2),true),
inference(step,[status(thm)],[t451,t5]) ).
cnf(t495,plain,
ifeq(is_a_theorem(equivalent(equivalent(X1,X1),X2)),true,is_a_theorem(X2),true) = true,
inference(orient,[status(thm)],[t231123]) ).
cnf(t453,plain,
true = ifeq(true,true,is_a_theorem(equivalent(X1,equivalent(equivalent(X1,X2),X2))),true),
inference(cp,[status(thm)],[t19,t449]) ).
cnf(t231122,plain,
true = is_a_theorem(equivalent(X1,equivalent(equivalent(X1,X2),X2))),
inference(step,[status(thm)],[t453,t5]) ).
cnf(t470,plain,
is_a_theorem(equivalent(X1,equivalent(equivalent(X1,X2),X2))) = true,
inference(orient,[status(thm)],[t231122]) ).
cnf(t474,plain,
true = ifeq(true,true,is_a_theorem(equivalent(X1,equivalent(equivalent(X1,equivalent(equivalent(X2,X3),X3)),X2))),true),
inference(cp,[status(thm)],[t19,t470]) ).
cnf(t231126,plain,
true = is_a_theorem(equivalent(X1,equivalent(equivalent(X1,equivalent(equivalent(X2,X3),X3)),X2))),
inference(step,[status(thm)],[t474,t5]) ).
cnf(t606,plain,
is_a_theorem(equivalent(X1,equivalent(equivalent(X1,equivalent(equivalent(X2,X3),X3)),X2))) = true,
inference(orient,[status(thm)],[t231126]) ).
cnf(t611,plain,
true = ifeq(true,true,is_a_theorem(equivalent(equivalent(equivalent(X1,X1),equivalent(equivalent(X2,X3),X3)),X2)),true),
inference(cp,[status(thm)],[t495,t606]) ).
cnf(t231130,plain,
true = is_a_theorem(equivalent(equivalent(equivalent(X1,X1),equivalent(equivalent(X2,X3),X3)),X2)),
inference(step,[status(thm)],[t611,t5]) ).
cnf(t732,plain,
is_a_theorem(equivalent(equivalent(equivalent(X1,X1),equivalent(equivalent(X2,X3),X3)),X2)) = true,
inference(orient,[status(thm)],[t231130]) ).
cnf(t733,plain,
true = ifeq(true,true,ifeq(is_a_theorem(equivalent(equivalent(X1,X1),equivalent(equivalent(X2,X3),X3))),true,is_a_theorem(X2),true),true),
inference(cp,[status(thm)],[t9,t732]) ).
cnf(t231143,plain,
true = ifeq(is_a_theorem(equivalent(equivalent(X1,X1),equivalent(equivalent(X2,X3),X3))),true,is_a_theorem(X2),true),
inference(step,[status(thm)],[t733,t5]) ).
cnf(t1190,plain,
ifeq(is_a_theorem(equivalent(equivalent(X1,X1),equivalent(equivalent(X2,X3),X3))),true,is_a_theorem(X2),true) = true,
inference(orient,[status(thm)],[t231143]) ).
cnf(t1192,plain,
true = ifeq(true,true,is_a_theorem(equivalent(equivalent(equivalent(X1,X2),X1),X2)),true),
inference(cp,[status(thm)],[t1190,t64]) ).
cnf(t231144,plain,
true = is_a_theorem(equivalent(equivalent(equivalent(X1,X2),X1),X2)),
inference(step,[status(thm)],[t1192,t5]) ).
cnf(t1224,plain,
is_a_theorem(equivalent(equivalent(equivalent(X1,X2),X1),X2)) = true,
inference(orient,[status(thm)],[t231144]) ).
cnf(t1234,plain,
true = ifeq(true,true,is_a_theorem(equivalent(X1,equivalent(equivalent(X1,X2),equivalent(equivalent(X3,X2),X3)))),true),
inference(cp,[status(thm)],[t19,t1224]) ).
cnf(t231148,plain,
true = is_a_theorem(equivalent(X1,equivalent(equivalent(X1,X2),equivalent(equivalent(X3,X2),X3)))),
inference(step,[status(thm)],[t1234,t5]) ).
cnf(t1342,plain,
is_a_theorem(equivalent(X1,equivalent(equivalent(X1,X2),equivalent(equivalent(X3,X2),X3)))) = true,
inference(orient,[status(thm)],[t231148]) ).
cnf(t1349,plain,
true = ifeq(true,true,is_a_theorem(equivalent(equivalent(equivalent(X1,X1),X2),equivalent(equivalent(X3,X2),X3))),true),
inference(cp,[status(thm)],[t495,t1342]) ).
cnf(t231149,plain,
true = is_a_theorem(equivalent(equivalent(equivalent(X1,X1),X2),equivalent(equivalent(X3,X2),X3))),
inference(step,[status(thm)],[t1349,t5]) ).
cnf(t1388,plain,
is_a_theorem(equivalent(equivalent(equivalent(X1,X1),X2),equivalent(equivalent(X3,X2),X3))) = true,
inference(orient,[status(thm)],[t231149]) ).
cnf(t1389,plain,
true = ifeq(true,true,ifeq(is_a_theorem(equivalent(equivalent(X1,X1),X2)),true,is_a_theorem(equivalent(equivalent(X3,X2),X3)),true),true),
inference(cp,[status(thm)],[t9,t1388]) ).
cnf(t231173,plain,
true = ifeq(is_a_theorem(equivalent(equivalent(X1,X1),X2)),true,is_a_theorem(equivalent(equivalent(X3,X2),X3)),true),
inference(step,[status(thm)],[t1389,t5]) ).
cnf(t2374,plain,
ifeq(is_a_theorem(equivalent(equivalent(X1,X1),X2)),true,is_a_theorem(equivalent(equivalent(X3,X2),X3)),true) = true,
inference(orient,[status(thm)],[t231173]) ).
cnf(t500,plain,
true = ifeq(true,true,is_a_theorem(equivalent(equivalent(equivalent(X1,X1),X2),X2)),true),
inference(cp,[status(thm)],[t495,t470]) ).
cnf(t231124,plain,
true = is_a_theorem(equivalent(equivalent(equivalent(X1,X1),X2),X2)),
inference(step,[status(thm)],[t500,t5]) ).
cnf(t522,plain,
is_a_theorem(equivalent(equivalent(equivalent(X1,X1),X2),X2)) = true,
inference(orient,[status(thm)],[t231124]) ).
cnf(t526,plain,
true = ifeq(true,true,is_a_theorem(equivalent(X1,equivalent(equivalent(X1,X2),equivalent(equivalent(X3,X3),X2)))),true),
inference(cp,[status(thm)],[t19,t522]) ).
cnf(t231127,plain,
true = is_a_theorem(equivalent(X1,equivalent(equivalent(X1,X2),equivalent(equivalent(X3,X3),X2)))),
inference(step,[status(thm)],[t526,t5]) ).
cnf(t641,plain,
is_a_theorem(equivalent(X1,equivalent(equivalent(X1,X2),equivalent(equivalent(X3,X3),X2)))) = true,
inference(orient,[status(thm)],[t231127]) ).
cnf(t646,plain,
true = ifeq(true,true,is_a_theorem(equivalent(equivalent(equivalent(X1,X1),X2),equivalent(equivalent(X3,X3),X2))),true),
inference(cp,[status(thm)],[t495,t641]) ).
cnf(t231131,plain,
true = is_a_theorem(equivalent(equivalent(equivalent(X1,X1),X2),equivalent(equivalent(X3,X3),X2))),
inference(step,[status(thm)],[t646,t5]) ).
cnf(t759,plain,
is_a_theorem(equivalent(equivalent(equivalent(X1,X1),X2),equivalent(equivalent(X3,X3),X2))) = true,
inference(orient,[status(thm)],[t231131]) ).
cnf(t760,plain,
true = ifeq(true,true,ifeq(is_a_theorem(equivalent(equivalent(X1,X1),X2)),true,is_a_theorem(equivalent(equivalent(X3,X3),X2)),true),true),
inference(cp,[status(thm)],[t9,t759]) ).
cnf(t231163,plain,
true = ifeq(is_a_theorem(equivalent(equivalent(X1,X1),X2)),true,is_a_theorem(equivalent(equivalent(X3,X3),X2)),true),
inference(step,[status(thm)],[t760,t5]) ).
cnf(t1905,plain,
ifeq(is_a_theorem(equivalent(equivalent(X1,X1),X2)),true,is_a_theorem(equivalent(equivalent(X3,X3),X2)),true) = true,
inference(orient,[status(thm)],[t231163]) ).
cnf(t471,plain,
true = ifeq(true,true,ifeq(is_a_theorem(X1),true,is_a_theorem(equivalent(equivalent(X1,X2),X2)),true),true),
inference(cp,[status(thm)],[t9,t470]) ).
cnf(t231125,plain,
true = ifeq(is_a_theorem(X1),true,is_a_theorem(equivalent(equivalent(X1,X2),X2)),true),
inference(step,[status(thm)],[t471,t5]) ).
cnf(t547,plain,
ifeq(is_a_theorem(X1),true,is_a_theorem(equivalent(equivalent(X1,X2),X2)),true) = true,
inference(orient,[status(thm)],[t231125]) ).
cnf(t1230,plain,
true = ifeq(true,true,is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X1,X2),X1),X2),X3),X3)),true),
inference(cp,[status(thm)],[t547,t1224]) ).
cnf(t231147,plain,
true = is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X1,X2),X1),X2),X3),X3)),
inference(step,[status(thm)],[t1230,t5]) ).
cnf(t1303,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X1,X2),X1),X2),X3),X3)) = true,
inference(orient,[status(thm)],[t231147]) ).
cnf(t1914,plain,
true = ifeq(true,true,is_a_theorem(equivalent(equivalent(X1,X1),equivalent(equivalent(equivalent(X2,X3),X2),X3))),true),
inference(cp,[status(thm)],[t1905,t1303]) ).
cnf(t231166,plain,
true = is_a_theorem(equivalent(equivalent(X1,X1),equivalent(equivalent(equivalent(X2,X3),X2),X3))),
inference(step,[status(thm)],[t1914,t5]) ).
cnf(t2014,plain,
is_a_theorem(equivalent(equivalent(X1,X1),equivalent(equivalent(equivalent(X2,X3),X2),X3))) = true,
inference(orient,[status(thm)],[t231166]) ).
cnf(t2375,plain,
true = ifeq(true,true,is_a_theorem(equivalent(equivalent(X1,equivalent(equivalent(equivalent(X2,X3),X2),X3)),X1)),true),
inference(cp,[status(thm)],[t2374,t2014]) ).
cnf(t231174,plain,
true = is_a_theorem(equivalent(equivalent(X1,equivalent(equivalent(equivalent(X2,X3),X2),X3)),X1)),
inference(step,[status(thm)],[t2375,t5]) ).
cnf(t2404,plain,
is_a_theorem(equivalent(equivalent(X1,equivalent(equivalent(equivalent(X2,X3),X2),X3)),X1)) = true,
inference(orient,[status(thm)],[t231174]) ).
cnf(t2442,plain,
true = ifeq(true,true,is_a_theorem(equivalent(equivalent(X1,equivalent(equivalent(X1,X2),X3)),equivalent(X3,X2))),true),
inference(cp,[status(thm)],[t39,t2404]) ).
cnf(t231178,plain,
true = is_a_theorem(equivalent(equivalent(X1,equivalent(equivalent(X1,X2),X3)),equivalent(X3,X2))),
inference(step,[status(thm)],[t2442,t5]) ).
cnf(t2583,plain,
is_a_theorem(equivalent(equivalent(X1,equivalent(equivalent(X1,X2),X3)),equivalent(X3,X2))) = true,
inference(orient,[status(thm)],[t231178]) ).
cnf(t2584,plain,
true = ifeq(true,true,ifeq(is_a_theorem(equivalent(X1,equivalent(equivalent(X1,X2),X3))),true,is_a_theorem(equivalent(X3,X2)),true),true),
inference(cp,[status(thm)],[t9,t2583]) ).
cnf(t231224,plain,
true = ifeq(is_a_theorem(equivalent(X1,equivalent(equivalent(X1,X2),X3))),true,is_a_theorem(equivalent(X3,X2)),true),
inference(step,[status(thm)],[t2584,t5]) ).
cnf(t5376,plain,
ifeq(is_a_theorem(equivalent(X1,equivalent(equivalent(X1,X2),X3))),true,is_a_theorem(equivalent(X3,X2)),true) = true,
inference(orient,[status(thm)],[t231224]) ).
cnf(t2405,plain,
true = ifeq(true,true,ifeq(is_a_theorem(equivalent(X1,equivalent(equivalent(equivalent(X2,X3),X2),X3))),true,is_a_theorem(X1),true),true),
inference(cp,[status(thm)],[t9,t2404]) ).
cnf(t231194,plain,
true = ifeq(is_a_theorem(equivalent(X1,equivalent(equivalent(equivalent(X2,X3),X2),X3))),true,is_a_theorem(X1),true),
inference(step,[status(thm)],[t2405,t5]) ).
cnf(t3471,plain,
ifeq(is_a_theorem(equivalent(X1,equivalent(equivalent(equivalent(X2,X3),X2),X3))),true,is_a_theorem(X1),true) = true,
inference(orient,[status(thm)],[t231194]) ).
cnf(t1353,plain,
true = ifeq(true,true,is_a_theorem(equivalent(X1,equivalent(equivalent(X1,equivalent(equivalent(X2,X3),equivalent(equivalent(X4,X3),X4))),X2))),true),
inference(cp,[status(thm)],[t19,t1342]) ).
cnf(t231327,plain,
true = is_a_theorem(equivalent(X1,equivalent(equivalent(X1,equivalent(equivalent(X2,X3),equivalent(equivalent(X4,X3),X4))),X2))),
inference(step,[status(thm)],[t1353,t5]) ).
cnf(t15832,plain,
is_a_theorem(equivalent(X1,equivalent(equivalent(X1,equivalent(equivalent(X2,X3),equivalent(equivalent(X4,X3),X4))),X2))) = true,
inference(orient,[status(thm)],[t231327]) ).
cnf(t15910,plain,
true = ifeq(true,true,is_a_theorem(equivalent(equivalent(equivalent(X1,X2),equivalent(equivalent(X3,X2),X3)),X1)),true),
inference(cp,[status(thm)],[t3471,t15832]) ).
cnf(t231328,plain,
true = is_a_theorem(equivalent(equivalent(equivalent(X1,X2),equivalent(equivalent(X3,X2),X3)),X1)),
inference(step,[status(thm)],[t15910,t5]) ).
cnf(t15946,plain,
is_a_theorem(equivalent(equivalent(equivalent(X1,X2),equivalent(equivalent(X3,X2),X3)),X1)) = true,
inference(orient,[status(thm)],[t231328]) ).
cnf(t16038,plain,
true = ifeq(true,true,is_a_theorem(equivalent(equivalent(equivalent(X1,X2),equivalent(equivalent(X3,X1),X3)),X2)),true),
inference(cp,[status(thm)],[t154,t15946]) ).
cnf(t231329,plain,
true = is_a_theorem(equivalent(equivalent(equivalent(X1,X2),equivalent(equivalent(X3,X1),X3)),X2)),
inference(step,[status(thm)],[t16038,t5]) ).
cnf(t16050,plain,
is_a_theorem(equivalent(equivalent(equivalent(X1,X2),equivalent(equivalent(X3,X1),X3)),X2)) = true,
inference(orient,[status(thm)],[t231329]) ).
cnf(t16051,plain,
true = ifeq(true,true,ifeq(is_a_theorem(equivalent(equivalent(X1,X2),equivalent(equivalent(X3,X1),X3))),true,is_a_theorem(X2),true),true),
inference(cp,[status(thm)],[t9,t16050]) ).
cnf(t231340,plain,
true = ifeq(is_a_theorem(equivalent(equivalent(X1,X2),equivalent(equivalent(X3,X1),X3))),true,is_a_theorem(X2),true),
inference(step,[status(thm)],[t16051,t5]) ).
cnf(t17252,plain,
ifeq(is_a_theorem(equivalent(equivalent(X1,X2),equivalent(equivalent(X3,X1),X3))),true,is_a_theorem(X2),true) = true,
inference(orient,[status(thm)],[t231340]) ).
cnf(t17253,plain,
true = ifeq(true,true,is_a_theorem(equivalent(equivalent(X1,X2),equivalent(X2,X1))),true),
inference(cp,[status(thm)],[t17252,t2583]) ).
cnf(t231341,plain,
true = is_a_theorem(equivalent(equivalent(X1,X2),equivalent(X2,X1))),
inference(step,[status(thm)],[t17253,t5]) ).
cnf(t17442,plain,
is_a_theorem(equivalent(equivalent(X1,X2),equivalent(X2,X1))) = true,
inference(orient,[status(thm)],[t231341]) ).
cnf(t17443,plain,
true = ifeq(true,true,ifeq(is_a_theorem(equivalent(X1,X2)),true,is_a_theorem(equivalent(X2,X1)),true),true),
inference(cp,[status(thm)],[t9,t17442]) ).
cnf(t231342,plain,
true = ifeq(is_a_theorem(equivalent(X1,X2)),true,is_a_theorem(equivalent(X2,X1)),true),
inference(step,[status(thm)],[t17443,t5]) ).
cnf(t17533,plain,
ifeq(is_a_theorem(equivalent(X1,X2)),true,is_a_theorem(equivalent(X2,X1)),true) = true,
inference(orient,[status(thm)],[t231342]) ).
cnf(t17479,plain,
true = ifeq(true,true,is_a_theorem(equivalent(X1,equivalent(equivalent(X1,equivalent(X2,X3)),equivalent(X3,X2)))),true),
inference(cp,[status(thm)],[t19,t17442]) ).
cnf(t231347,plain,
true = is_a_theorem(equivalent(X1,equivalent(equivalent(X1,equivalent(X2,X3)),equivalent(X3,X2)))),
inference(step,[status(thm)],[t17479,t5]) ).
cnf(t18137,plain,
is_a_theorem(equivalent(X1,equivalent(equivalent(X1,equivalent(X2,X3)),equivalent(X3,X2)))) = true,
inference(orient,[status(thm)],[t231347]) ).
cnf(t18141,plain,
true = ifeq(true,true,is_a_theorem(equivalent(equivalent(equivalent(X1,equivalent(X2,X3)),equivalent(X3,X2)),X1)),true),
inference(cp,[status(thm)],[t17533,t18137]) ).
cnf(t231380,plain,
true = is_a_theorem(equivalent(equivalent(equivalent(X1,equivalent(X2,X3)),equivalent(X3,X2)),X1)),
inference(step,[status(thm)],[t18141,t5]) ).
cnf(t21795,plain,
is_a_theorem(equivalent(equivalent(equivalent(X1,equivalent(X2,X3)),equivalent(X3,X2)),X1)) = true,
inference(orient,[status(thm)],[t231380]) ).
cnf(t21796,plain,
true = ifeq(true,true,ifeq(is_a_theorem(equivalent(equivalent(X1,equivalent(X2,X3)),equivalent(X3,X2))),true,is_a_theorem(X1),true),true),
inference(cp,[status(thm)],[t9,t21795]) ).
cnf(t231585,plain,
true = ifeq(is_a_theorem(equivalent(equivalent(X1,equivalent(X2,X3)),equivalent(X3,X2))),true,is_a_theorem(X1),true),
inference(step,[status(thm)],[t21796,t5]) ).
cnf(t56972,plain,
ifeq(is_a_theorem(equivalent(equivalent(X1,equivalent(X2,X3)),equivalent(X3,X2))),true,is_a_theorem(X1),true) = true,
inference(orient,[status(thm)],[t231585]) ).
cnf(t613,plain,
true = ifeq(true,true,is_a_theorem(equivalent(X1,equivalent(equivalent(X1,equivalent(equivalent(X2,equivalent(equivalent(X3,X4),X4)),X3)),X2))),true),
inference(cp,[status(thm)],[t19,t606]) ).
cnf(t231248,plain,
true = is_a_theorem(equivalent(X1,equivalent(equivalent(X1,equivalent(equivalent(X2,equivalent(equivalent(X3,X4),X4)),X3)),X2))),
inference(step,[status(thm)],[t613,t5]) ).
cnf(t7632,plain,
is_a_theorem(equivalent(X1,equivalent(equivalent(X1,equivalent(equivalent(X2,equivalent(equivalent(X3,X4),X4)),X3)),X2))) = true,
inference(orient,[status(thm)],[t231248]) ).
cnf(t7688,plain,
true = ifeq(true,true,is_a_theorem(equivalent(equivalent(equivalent(X1,equivalent(equivalent(X2,X3),X3)),X2),X1)),true),
inference(cp,[status(thm)],[t3471,t7632]) ).
cnf(t231249,plain,
true = is_a_theorem(equivalent(equivalent(equivalent(X1,equivalent(equivalent(X2,X3),X3)),X2),X1)),
inference(step,[status(thm)],[t7688,t5]) ).
cnf(t7724,plain,
is_a_theorem(equivalent(equivalent(equivalent(X1,equivalent(equivalent(X2,X3),X3)),X2),X1)) = true,
inference(orient,[status(thm)],[t231249]) ).
cnf(t7725,plain,
true = ifeq(true,true,ifeq(is_a_theorem(equivalent(equivalent(X1,equivalent(equivalent(X2,X3),X3)),X2)),true,is_a_theorem(X1),true),true),
inference(cp,[status(thm)],[t9,t7724]) ).
cnf(t231252,plain,
true = ifeq(is_a_theorem(equivalent(equivalent(X1,equivalent(equivalent(X2,X3),X3)),X2)),true,is_a_theorem(X1),true),
inference(step,[status(thm)],[t7725,t5]) ).
cnf(t7999,plain,
ifeq(is_a_theorem(equivalent(equivalent(X1,equivalent(equivalent(X2,X3),X3)),X2)),true,is_a_theorem(X1),true) = true,
inference(orient,[status(thm)],[t231252]) ).
cnf(t21853,plain,
true = ifeq(true,true,is_a_theorem(equivalent(X1,equivalent(X2,equivalent(X1,X2)))),true),
inference(cp,[status(thm)],[t7999,t21795]) ).
cnf(t231381,plain,
true = is_a_theorem(equivalent(X1,equivalent(X2,equivalent(X1,X2)))),
inference(step,[status(thm)],[t21853,t5]) ).
cnf(t21914,plain,
is_a_theorem(equivalent(X1,equivalent(X2,equivalent(X1,X2)))) = true,
inference(orient,[status(thm)],[t231381]) ).
cnf(t21954,plain,
true = ifeq(true,true,is_a_theorem(equivalent(X1,equivalent(equivalent(X1,equivalent(X2,equivalent(X3,X2))),X3))),true),
inference(cp,[status(thm)],[t19,t21914]) ).
cnf(t231407,plain,
true = is_a_theorem(equivalent(X1,equivalent(equivalent(X1,equivalent(X2,equivalent(X3,X2))),X3))),
inference(step,[status(thm)],[t21954,t5]) ).
cnf(t25064,plain,
is_a_theorem(equivalent(X1,equivalent(equivalent(X1,equivalent(X2,equivalent(X3,X2))),X3))) = true,
inference(orient,[status(thm)],[t231407]) ).
cnf(t25068,plain,
true = ifeq(true,true,is_a_theorem(equivalent(equivalent(equivalent(X1,equivalent(X2,equivalent(X3,X2))),X3),X1)),true),
inference(cp,[status(thm)],[t17533,t25064]) ).
cnf(t231448,plain,
true = is_a_theorem(equivalent(equivalent(equivalent(X1,equivalent(X2,equivalent(X3,X2))),X3),X1)),
inference(step,[status(thm)],[t25068,t5]) ).
cnf(t29634,plain,
is_a_theorem(equivalent(equivalent(equivalent(X1,equivalent(X2,equivalent(X3,X2))),X3),X1)) = true,
inference(orient,[status(thm)],[t231448]) ).
cnf(t56973,plain,
true = ifeq(true,true,is_a_theorem(equivalent(equivalent(X1,X2),equivalent(X3,equivalent(equivalent(X2,X1),X3)))),true),
inference(cp,[status(thm)],[t56972,t29634]) ).
cnf(t231586,plain,
true = is_a_theorem(equivalent(equivalent(X1,X2),equivalent(X3,equivalent(equivalent(X2,X1),X3)))),
inference(step,[status(thm)],[t56973,t5]) ).
cnf(t57340,plain,
is_a_theorem(equivalent(equivalent(X1,X2),equivalent(X3,equivalent(equivalent(X2,X1),X3)))) = true,
inference(orient,[status(thm)],[t231586]) ).
cnf(t57390,plain,
true = ifeq(true,true,is_a_theorem(equivalent(equivalent(equivalent(X1,X2),equivalent(equivalent(X2,X1),X3)),X3)),true),
inference(cp,[status(thm)],[t5376,t57340]) ).
cnf(t231590,plain,
true = is_a_theorem(equivalent(equivalent(equivalent(X1,X2),equivalent(equivalent(X2,X1),X3)),X3)),
inference(step,[status(thm)],[t57390,t5]) ).
cnf(t57889,plain,
is_a_theorem(equivalent(equivalent(equivalent(X1,X2),equivalent(equivalent(X2,X1),X3)),X3)) = true,
inference(orient,[status(thm)],[t231590]) ).
cnf(t57890,plain,
true = ifeq(true,true,ifeq(is_a_theorem(equivalent(equivalent(X1,X2),equivalent(equivalent(X2,X1),X3))),true,is_a_theorem(X3),true),true),
inference(cp,[status(thm)],[t9,t57889]) ).
cnf(t231769,plain,
true = ifeq(is_a_theorem(equivalent(equivalent(X1,X2),equivalent(equivalent(X2,X1),X3))),true,is_a_theorem(X3),true),
inference(step,[status(thm)],[t57890,t5]) ).
cnf(t117981,plain,
ifeq(is_a_theorem(equivalent(equivalent(X1,X2),equivalent(equivalent(X2,X1),X3))),true,is_a_theorem(X3),true) = true,
inference(orient,[status(thm)],[t231769]) ).
cnf(t3474,plain,
true = ifeq(true,true,is_a_theorem(equivalent(X1,equivalent(equivalent(X2,X1),X2))),true),
inference(cp,[status(thm)],[t3471,t1342]) ).
cnf(t231197,plain,
true = is_a_theorem(equivalent(X1,equivalent(equivalent(X2,X1),X2))),
inference(step,[status(thm)],[t3474,t5]) ).
cnf(t3665,plain,
is_a_theorem(equivalent(X1,equivalent(equivalent(X2,X1),X2))) = true,
inference(orient,[status(thm)],[t231197]) ).
cnf(t3683,plain,
true = ifeq(true,true,is_a_theorem(equivalent(X1,equivalent(equivalent(X1,equivalent(equivalent(X2,X3),X2)),X3))),true),
inference(cp,[status(thm)],[t19,t3665]) ).
cnf(t231207,plain,
true = is_a_theorem(equivalent(X1,equivalent(equivalent(X1,equivalent(equivalent(X2,X3),X2)),X3))),
inference(step,[status(thm)],[t3683,t5]) ).
cnf(t4288,plain,
is_a_theorem(equivalent(X1,equivalent(equivalent(X1,equivalent(equivalent(X2,X3),X2)),X3))) = true,
inference(orient,[status(thm)],[t231207]) ).
cnf(t17537,plain,
true = ifeq(true,true,is_a_theorem(equivalent(equivalent(equivalent(X1,equivalent(equivalent(X2,X3),X2)),X3),X1)),true),
inference(cp,[status(thm)],[t17533,t4288]) ).
cnf(t231348,plain,
true = is_a_theorem(equivalent(equivalent(equivalent(X1,equivalent(equivalent(X2,X3),X2)),X3),X1)),
inference(step,[status(thm)],[t17537,t5]) ).
cnf(t18253,plain,
is_a_theorem(equivalent(equivalent(equivalent(X1,equivalent(equivalent(X2,X3),X2)),X3),X1)) = true,
inference(orient,[status(thm)],[t231348]) ).
cnf(t18254,plain,
true = ifeq(true,true,ifeq(is_a_theorem(equivalent(equivalent(X1,equivalent(equivalent(X2,X3),X2)),X3)),true,is_a_theorem(X1),true),true),
inference(cp,[status(thm)],[t9,t18253]) ).
cnf(t231547,plain,
true = ifeq(is_a_theorem(equivalent(equivalent(X1,equivalent(equivalent(X2,X3),X2)),X3)),true,is_a_theorem(X1),true),
inference(step,[status(thm)],[t18254,t5]) ).
cnf(t42866,plain,
ifeq(is_a_theorem(equivalent(equivalent(X1,equivalent(equivalent(X2,X3),X2)),X3)),true,is_a_theorem(X1),true) = true,
inference(orient,[status(thm)],[t231547]) ).
cnf(h0,plain,
is_a_theorem(equivalent(V0,equivalent(equivalent(V0,equivalent(V1,equivalent(equivalent(V1,V2),V3))),equivalent(V3,V2)))) = true,
inference(hyper_resolution,[status(thm)],[hi0,hi1,hi1]) ).
cnf(t4,plain,
is_a_theorem(equivalent(X1,equivalent(equivalent(X1,equivalent(equivalent(X2,equivalent(X3,equivalent(equivalent(X3,X4),X5))),equivalent(X5,X4))),X2))) = true,
inference(hyper_resolution,[status(thm)],[hi0,hi1,h0]) ).
cnf(t7,plain,
is_a_theorem(equivalent(X1,equivalent(equivalent(X1,equivalent(equivalent(X2,equivalent(X3,equivalent(equivalent(X3,X4),X5))),equivalent(X5,X4))),X2))) = true,
inference(orient,[status(thm)],[t4]) ).
cnf(t15,plain,
true = ifeq(is_a_theorem(equivalent(equivalent(X1,equivalent(equivalent(X1,equivalent(equivalent(X2,equivalent(X3,equivalent(equivalent(X3,X4),X5))),equivalent(X5,X4))),X2)),Y5)),true,ifeq(true,true,is_a_theorem(Y5),true),true),
inference(cp,[status(thm)],[t9,t7]) ).
cnf(t231100,plain,
true = ifeq(is_a_theorem(equivalent(equivalent(X1,equivalent(equivalent(X1,equivalent(equivalent(X2,equivalent(X3,equivalent(equivalent(X3,X4),X5))),equivalent(X5,X4))),X2)),Y5)),true,is_a_theorem(Y5),true),
inference(step,[status(thm)],[t15,t5]) ).
cnf(t77,plain,
ifeq(is_a_theorem(equivalent(equivalent(X1,equivalent(equivalent(X1,equivalent(equivalent(X2,equivalent(X3,equivalent(equivalent(X3,X4),X5))),equivalent(X5,X4))),X2)),Y5)),true,is_a_theorem(Y5),true) = true,
inference(orient,[status(thm)],[t231100]) ).
cnf(t2450,plain,
true = ifeq(true,true,is_a_theorem(equivalent(equivalent(equivalent(X1,equivalent(X2,equivalent(equivalent(X2,X3),X4))),equivalent(X4,X3)),X1)),true),
inference(cp,[status(thm)],[t77,t2404]) ).
cnf(t231862,plain,
true = is_a_theorem(equivalent(equivalent(equivalent(X1,equivalent(X2,equivalent(equivalent(X2,X3),X4))),equivalent(X4,X3)),X1)),
inference(step,[status(thm)],[t2450,t5]) ).
cnf(t151862,plain,
is_a_theorem(equivalent(equivalent(equivalent(X1,equivalent(X2,equivalent(equivalent(X2,X3),X4))),equivalent(X4,X3)),X1)) = true,
inference(orient,[status(thm)],[t231862]) ).
cnf(t152146,plain,
true = ifeq(true,true,is_a_theorem(equivalent(X1,equivalent(X2,equivalent(equivalent(X2,X3),equivalent(X3,X1))))),true),
inference(cp,[status(thm)],[t42866,t151862]) ).
cnf(t231866,plain,
true = is_a_theorem(equivalent(X1,equivalent(X2,equivalent(equivalent(X2,X3),equivalent(X3,X1))))),
inference(step,[status(thm)],[t152146,t5]) ).
cnf(t153221,plain,
is_a_theorem(equivalent(X1,equivalent(X2,equivalent(equivalent(X2,X3),equivalent(X3,X1))))) = true,
inference(orient,[status(thm)],[t231866]) ).
cnf(t153266,plain,
true = ifeq(true,true,is_a_theorem(equivalent(equivalent(equivalent(X1,X2),X3),equivalent(X3,equivalent(X2,X1)))),true),
inference(cp,[status(thm)],[t117981,t153221]) ).
cnf(t231891,plain,
true = is_a_theorem(equivalent(equivalent(equivalent(X1,X2),X3),equivalent(X3,equivalent(X2,X1)))),
inference(step,[status(thm)],[t153266,t5]) ).
cnf(t161645,plain,
is_a_theorem(equivalent(equivalent(equivalent(X1,X2),X3),equivalent(X3,equivalent(X2,X1)))) = true,
inference(orient,[status(thm)],[t231891]) ).
cnf(t161646,plain,
true = ifeq(true,true,ifeq(is_a_theorem(equivalent(equivalent(X1,X2),X3)),true,is_a_theorem(equivalent(X3,equivalent(X2,X1))),true),true),
inference(cp,[status(thm)],[t9,t161645]) ).
cnf(t232019,plain,
true = ifeq(is_a_theorem(equivalent(equivalent(X1,X2),X3)),true,is_a_theorem(equivalent(X3,equivalent(X2,X1))),true),
inference(step,[status(thm)],[t161646,t5]) ).
cnf(t209711,plain,
ifeq(is_a_theorem(equivalent(equivalent(X1,X2),X3)),true,is_a_theorem(equivalent(X3,equivalent(X2,X1))),true) = true,
inference(orient,[status(thm)],[t232019]) ).
cnf(t29635,plain,
true = ifeq(true,true,ifeq(is_a_theorem(equivalent(equivalent(X1,equivalent(X2,equivalent(X3,X2))),X3)),true,is_a_theorem(X1),true),true),
inference(cp,[status(thm)],[t9,t29634]) ).
cnf(t231643,plain,
true = ifeq(is_a_theorem(equivalent(equivalent(X1,equivalent(X2,equivalent(X3,X2))),X3)),true,is_a_theorem(X1),true),
inference(step,[status(thm)],[t29635,t5]) ).
cnf(t78326,plain,
ifeq(is_a_theorem(equivalent(equivalent(X1,equivalent(X2,equivalent(X3,X2))),X3)),true,is_a_theorem(X1),true) = true,
inference(orient,[status(thm)],[t231643]) ).
cnf(t15947,plain,
true = ifeq(true,true,ifeq(is_a_theorem(equivalent(equivalent(X1,X2),equivalent(equivalent(X3,X2),X3))),true,is_a_theorem(X1),true),true),
inference(cp,[status(thm)],[t9,t15946]) ).
cnf(t231332,plain,
true = ifeq(is_a_theorem(equivalent(equivalent(X1,X2),equivalent(equivalent(X3,X2),X3))),true,is_a_theorem(X1),true),
inference(step,[status(thm)],[t15947,t5]) ).
cnf(t16353,plain,
ifeq(is_a_theorem(equivalent(equivalent(X1,X2),equivalent(equivalent(X3,X2),X3))),true,is_a_theorem(X1),true) = true,
inference(orient,[status(thm)],[t231332]) ).
cnf(t21918,plain,
true = ifeq(true,true,is_a_theorem(equivalent(equivalent(X1,equivalent(X2,X1)),X2)),true),
inference(cp,[status(thm)],[t17533,t21914]) ).
cnf(t231382,plain,
true = is_a_theorem(equivalent(equivalent(X1,equivalent(X2,X1)),X2)),
inference(step,[status(thm)],[t21918,t5]) ).
cnf(t22008,plain,
is_a_theorem(equivalent(equivalent(X1,equivalent(X2,X1)),X2)) = true,
inference(orient,[status(thm)],[t231382]) ).
cnf(t22045,plain,
true = ifeq(true,true,is_a_theorem(equivalent(X1,equivalent(equivalent(X1,X2),equivalent(X3,equivalent(X2,X3))))),true),
inference(cp,[status(thm)],[t19,t22008]) ).
cnf(t231412,plain,
true = is_a_theorem(equivalent(X1,equivalent(equivalent(X1,X2),equivalent(X3,equivalent(X2,X3))))),
inference(step,[status(thm)],[t22045,t5]) ).
cnf(t25625,plain,
is_a_theorem(equivalent(X1,equivalent(equivalent(X1,X2),equivalent(X3,equivalent(X2,X3))))) = true,
inference(orient,[status(thm)],[t231412]) ).
cnf(t25629,plain,
true = ifeq(true,true,is_a_theorem(equivalent(equivalent(equivalent(X1,X2),equivalent(X3,equivalent(X2,X3))),X1)),true),
inference(cp,[status(thm)],[t17533,t25625]) ).
cnf(t231450,plain,
true = is_a_theorem(equivalent(equivalent(equivalent(X1,X2),equivalent(X3,equivalent(X2,X3))),X1)),
inference(step,[status(thm)],[t25629,t5]) ).
cnf(t29866,plain,
is_a_theorem(equivalent(equivalent(equivalent(X1,X2),equivalent(X3,equivalent(X2,X3))),X1)) = true,
inference(orient,[status(thm)],[t231450]) ).
cnf(t29889,plain,
true = ifeq(true,true,is_a_theorem(equivalent(equivalent(equivalent(X1,equivalent(X2,equivalent(X3,X2))),X1),X3)),true),
inference(cp,[status(thm)],[t16353,t29866]) ).
cnf(t231465,plain,
true = is_a_theorem(equivalent(equivalent(equivalent(X1,equivalent(X2,equivalent(X3,X2))),X1),X3)),
inference(step,[status(thm)],[t29889,t5]) ).
cnf(t31497,plain,
is_a_theorem(equivalent(equivalent(equivalent(X1,equivalent(X2,equivalent(X3,X2))),X1),X3)) = true,
inference(orient,[status(thm)],[t231465]) ).
cnf(t78329,plain,
true = ifeq(true,true,is_a_theorem(equivalent(equivalent(X1,equivalent(X2,X1)),equivalent(X3,equivalent(X2,X3)))),true),
inference(cp,[status(thm)],[t78326,t31497]) ).
cnf(t231645,plain,
true = is_a_theorem(equivalent(equivalent(X1,equivalent(X2,X1)),equivalent(X3,equivalent(X2,X3)))),
inference(step,[status(thm)],[t78329,t5]) ).
cnf(t78928,plain,
is_a_theorem(equivalent(equivalent(X1,equivalent(X2,X1)),equivalent(X3,equivalent(X2,X3)))) = true,
inference(orient,[status(thm)],[t231645]) ).
cnf(t78992,plain,
true = ifeq(true,true,is_a_theorem(equivalent(equivalent(X1,equivalent(equivalent(X2,equivalent(X1,X2)),X3)),X3)),true),
inference(cp,[status(thm)],[t5376,t78928]) ).
cnf(t231654,plain,
true = is_a_theorem(equivalent(equivalent(X1,equivalent(equivalent(X2,equivalent(X1,X2)),X3)),X3)),
inference(step,[status(thm)],[t78992,t5]) ).
cnf(t80804,plain,
is_a_theorem(equivalent(equivalent(X1,equivalent(equivalent(X2,equivalent(X1,X2)),X3)),X3)) = true,
inference(orient,[status(thm)],[t231654]) ).
cnf(t80805,plain,
true = ifeq(true,true,ifeq(is_a_theorem(equivalent(X1,equivalent(equivalent(X2,equivalent(X1,X2)),X3))),true,is_a_theorem(X3),true),true),
inference(cp,[status(thm)],[t9,t80804]) ).
cnf(t231782,plain,
true = ifeq(is_a_theorem(equivalent(X1,equivalent(equivalent(X2,equivalent(X1,X2)),X3))),true,is_a_theorem(X3),true),
inference(step,[status(thm)],[t80805,t5]) ).
cnf(t122248,plain,
ifeq(is_a_theorem(equivalent(X1,equivalent(equivalent(X2,equivalent(X1,X2)),X3))),true,is_a_theorem(X3),true) = true,
inference(orient,[status(thm)],[t231782]) ).
cnf(t153390,plain,
true = ifeq(true,true,is_a_theorem(equivalent(equivalent(equivalent(X1,equivalent(X2,X1)),X3),equivalent(X3,X2))),true),
inference(cp,[status(thm)],[t122248,t153221]) ).
cnf(t231898,plain,
true = is_a_theorem(equivalent(equivalent(equivalent(X1,equivalent(X2,X1)),X3),equivalent(X3,X2))),
inference(step,[status(thm)],[t153390,t5]) ).
cnf(t163778,plain,
is_a_theorem(equivalent(equivalent(equivalent(X1,equivalent(X2,X1)),X3),equivalent(X3,X2))) = true,
inference(orient,[status(thm)],[t231898]) ).
cnf(t163779,plain,
true = ifeq(true,true,ifeq(is_a_theorem(equivalent(equivalent(X1,equivalent(X2,X1)),X3)),true,is_a_theorem(equivalent(X3,X2)),true),true),
inference(cp,[status(thm)],[t9,t163778]) ).
cnf(t232060,plain,
true = ifeq(is_a_theorem(equivalent(equivalent(X1,equivalent(X2,X1)),X3)),true,is_a_theorem(equivalent(X3,X2)),true),
inference(step,[status(thm)],[t163779,t5]) ).
cnf(t227411,plain,
ifeq(is_a_theorem(equivalent(equivalent(X1,equivalent(X2,X1)),X3)),true,is_a_theorem(equivalent(X3,X2)),true) = true,
inference(orient,[status(thm)],[t232060]) ).
cnf(t119,plain,
true = ifeq(true,true,is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X1,X2),X3),X2),X1),X3),equivalent(X4,equivalent(equivalent(X4,X5),Y5))),equivalent(Y5,X5))),true),
inference(cp,[status(thm)],[t23,t110]) ).
cnf(t231112,plain,
true = is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X1,X2),X3),X2),X1),X3),equivalent(X4,equivalent(equivalent(X4,X5),Y5))),equivalent(Y5,X5))),
inference(step,[status(thm)],[t119,t5]) ).
cnf(t254,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X1,X2),X3),X2),X1),X3),equivalent(X4,equivalent(equivalent(X4,X5),Y5))),equivalent(Y5,X5))) = true,
inference(orient,[status(thm)],[t231112]) ).
cnf(t227461,plain,
true = ifeq(true,true,is_a_theorem(equivalent(equivalent(X1,X2),equivalent(equivalent(equivalent(X2,X3),X1),X3))),true),
inference(cp,[status(thm)],[t227411,t254]) ).
cnf(t232062,plain,
true = is_a_theorem(equivalent(equivalent(X1,X2),equivalent(equivalent(equivalent(X2,X3),X1),X3))),
inference(step,[status(thm)],[t227461,t5]) ).
cnf(t228648,plain,
is_a_theorem(equivalent(equivalent(X1,X2),equivalent(equivalent(equivalent(X2,X3),X1),X3))) = true,
inference(orient,[status(thm)],[t232062]) ).
cnf(t228652,plain,
true = ifeq(true,true,is_a_theorem(equivalent(equivalent(equivalent(equivalent(X1,X2),X3),X2),equivalent(X3,X1))),true),
inference(cp,[status(thm)],[t17533,t228648]) ).
cnf(t232065,plain,
true = is_a_theorem(equivalent(equivalent(equivalent(equivalent(X1,X2),X3),X2),equivalent(X3,X1))),
inference(step,[status(thm)],[t228652,t5]) ).
cnf(t229724,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(X1,X2),X3),X2),equivalent(X3,X1))) = true,
inference(orient,[status(thm)],[t232065]) ).
cnf(t229728,plain,
true = ifeq(true,true,is_a_theorem(equivalent(equivalent(X1,X2),equivalent(X3,equivalent(equivalent(X2,X3),X1)))),true),
inference(cp,[status(thm)],[t209711,t229724]) ).
cnf(t232068,plain,
true = is_a_theorem(equivalent(equivalent(X1,X2),equivalent(X3,equivalent(equivalent(X2,X3),X1)))),
inference(step,[status(thm)],[t229728,t5]) ).
cnf(t230759,plain,
is_a_theorem(equivalent(equivalent(X1,X2),equivalent(X3,equivalent(equivalent(X2,X3),X1)))) = true,
inference(orient,[status(thm)],[t232068]) ).
cnf(f2,negated_conjecture,
~ is_a_theorem(equivalent(equivalent(a,b),equivalent(c,equivalent(equivalent(b,c),a)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_yrm) ).
fof(f2_nnf,plain,
~ is_a_theorem(equivalent(equivalent(a,b),equivalent(c,equivalent(equivalent(b,c),a)))),
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
~ is_a_theorem(equivalent(equivalent(a,b),equivalent(c,equivalent(equivalent(b,c),a)))),
inference(skolemisation,[status(esa)],[f2_nnf]) ).
cnf(c2,plain,
~ is_a_theorem(equivalent(equivalent(a,b),equivalent(c,equivalent(equivalent(b,c),a)))),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(goal_0,negated_conjecture,
is_a_theorem(equivalent(equivalent(a,b),equivalent(c,equivalent(equivalent(b,c),a)))) != true,
inference(equality_encoding,[status(esa)],[c2]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t230759]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL016-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.10/0.37 % Computer : n005.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Wed Sep 23 21:37:17 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 71.46/10.94 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 71.46/10.94 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------