%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : LCL902+1 : TPTP v9.3.1. Released v5.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n019.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 02:03:19 PM UTC 2026
% Result : Theorem 34.23s 4.87s
% Output : Proof 34.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 13
% Syntax : Number of formulae : 137 ( 116 unt; 0 def)
% Number of atoms : 170 ( 111 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 63 ( 30 ~; 24 |; 4 &)
% ( 1 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-4 aty)
% Number of variables : 237 ( 26 sgn 65 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f5,axiom,
! [X3,X4] :
( ( qtd2(X4,X3)
& qtd2(X3,X4) )
=> X3 = X4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_06) ).
fof(f5_nnf,plain,
! [X3,X4] :
( X3 = X4
| ~ qtd2(X4,X3)
| ~ qtd2(X3,X4) ),
inference(nnf_transformation,[status(thm)],[f5]) ).
fof(f5_sk,plain,
! [X3,X4] :
( X3 = X4
| ~ qtd2(X4,X3)
| ~ qtd2(X3,X4) ),
inference(skolemisation,[status(esa)],[f5_nnf]) ).
cnf(c5,plain,
( X0 = X1
| ~ qtd2(X1,X0)
| ~ qtd2(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
cnf(t168,plain,
ifeq(qtd2(X1,X2),true,ifeq(qtd2(X2,X1),true,X1,X2),X2) = X2,
inference(equality_encoding,[status(esa)],[c5]) ).
cnf(t258,plain,
ifeq(qtd2(X1,X2),true,ifeq(qtd2(X2,X1),true,X1,X2),X2) = X2,
inference(orient,[status(thm)],[t168]) ).
fof(f6,axiom,
! [X5,X6,X7] :
( qtd2(qtd0(X5,X6),X7)
<=> qtd2(X6,qtd3(X5,X7)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_07) ).
fof(f6_nnf,plain,
! [X5,X6,X7] :
( ( ~ qtd2(X6,qtd3(X5,X7))
| qtd2(qtd0(X5,X6),X7) )
& ( qtd2(X6,qtd3(X5,X7))
| ~ qtd2(qtd0(X5,X6),X7) ) ),
inference(nnf_transformation,[status(thm)],[f6]) ).
fof(f6_sk,plain,
! [X5,X6,X7] :
( ( ~ qtd2(X6,qtd3(X5,X7))
| qtd2(qtd0(X5,X6),X7) )
& ( qtd2(X6,qtd3(X5,X7))
| ~ qtd2(qtd0(X5,X6),X7) ) ),
inference(skolemisation,[status(esa)],[f6_nnf]) ).
cnf(c6,plain,
( qtd2(X1,qtd3(X0,X2))
| ~ qtd2(qtd0(X0,X1),X2) ),
inference(cnf_transformation,[status(esa)],[f6_sk]) ).
cnf(hi6,axiom,
ifeq(qtd2(qtd0(X0,X1),X2),true,qtd2(X1,qtd3(X0,X2)),true) = true,
inference(equality_encoding,[status(esa)],[c6]) ).
fof(f3,axiom,
! [A] : qtd2(A,A),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_04) ).
fof(f3_nnf,plain,
! [A] : qtd2(A,A),
inference(nnf_transformation,[status(thm)],[f3]) ).
fof(f3_sk,plain,
! [A] : qtd2(A,A),
inference(skolemisation,[status(esa)],[f3_nnf]) ).
cnf(c3,plain,
qtd2(X0,X0),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(hi3,axiom,
qtd2(X0,X0) = true,
inference(equality_encoding,[status(esa)],[c3]) ).
cnf(t20,plain,
qtd2(X1,qtd3(X2,qtd0(X2,X1))) = true,
inference(hyper_resolution,[status(thm)],[hi6,hi3]) ).
cnf(t310,plain,
qtd2(X1,qtd3(X2,qtd0(X2,X1))) = true,
inference(orient,[status(thm)],[t20]) ).
fof(f1,axiom,
! [A,B] : qtd0(A,B) = qtd0(B,A),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_02) ).
fof(f1_nnf,plain,
! [A,B] : qtd0(A,B) = qtd0(B,A),
inference(nnf_transformation,[status(thm)],[f1]) ).
fof(f1_sk,plain,
! [A,B] : qtd0(A,B) = qtd0(B,A),
inference(skolemisation,[status(esa)],[f1_nnf]) ).
cnf(c1,plain,
qtd0(X0,X1) = qtd0(X1,X0),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(t6,plain,
qtd0(X1,X2) = qtd0(X2,X1),
inference(equality_encoding,[status(esa)],[c1]) ).
cnf(t287,plain,
qtd0(X1,X2) = qtd0(X2,X1),
inference(orient,[status(thm)],[t6]) ).
cnf(t313,plain,
true = qtd2(X1,qtd3(X2,qtd0(X1,X2))),
inference(cp,[status(thm)],[t310,t287]) ).
cnf(t883,plain,
qtd2(X1,qtd3(X2,qtd0(X1,X2))) = true,
inference(orient,[status(thm)],[t313]) ).
cnf(c7,plain,
( ~ qtd2(X1,qtd3(X0,X2))
| qtd2(qtd0(X0,X1),X2) ),
inference(cnf_transformation,[status(esa)],[f6_sk]) ).
cnf(hi7,axiom,
ifeq(qtd2(X0,qtd3(X1,X2)),true,qtd2(qtd0(X1,X0),X2),true) = true,
inference(equality_encoding,[status(esa)],[c7]) ).
cnf(t22,plain,
qtd2(qtd0(X1,qtd3(X1,X2)),X2) = true,
inference(hyper_resolution,[status(thm)],[hi7,hi3]) ).
cnf(t400,plain,
qtd2(qtd0(X1,qtd3(X1,X2)),X2) = true,
inference(orient,[status(thm)],[t22]) ).
fof(f11,axiom,
! [A] : qtd0(A,qtd4) = qtd4,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_12) ).
fof(f11_nnf,plain,
! [A] : qtd0(A,qtd4) = qtd4,
inference(nnf_transformation,[status(thm)],[f11]) ).
fof(f11_sk,plain,
! [A] : qtd0(A,qtd4) = qtd4,
inference(skolemisation,[status(esa)],[f11_nnf]) ).
cnf(c12,plain,
qtd0(X0,qtd4) = qtd4,
inference(cnf_transformation,[status(esa)],[f11_sk]) ).
cnf(t1,plain,
qtd0(X1,qtd4) = qtd4,
inference(equality_encoding,[status(esa)],[c12]) ).
cnf(t297,plain,
qtd0(X1,qtd4) = qtd4,
inference(orient,[status(thm)],[t1]) ).
cnf(t298,plain,
qtd4 = qtd0(qtd4,X1),
inference(cp,[status(thm)],[t297,t287]) ).
cnf(t703,plain,
qtd0(qtd4,X1) = qtd4,
inference(orient,[status(thm)],[t298]) ).
cnf(t709,plain,
true = qtd2(qtd4,X1),
inference(cp,[status(thm)],[t400,t703]) ).
cnf(t730,plain,
qtd2(qtd4,X1) = true,
inference(orient,[status(thm)],[t709]) ).
cnf(t731,plain,
X1 = ifeq(true,true,ifeq(qtd2(X1,qtd4),true,qtd4,X1),X1),
inference(cp,[status(thm)],[t258,t730]) ).
cnf(t5,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t257,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t5]) ).
cnf(t1105,plain,
X1 = ifeq(qtd2(X1,qtd4),true,qtd4,X1),
inference(step,[status(thm)],[t731,t257]) ).
cnf(t957,plain,
ifeq(qtd2(X1,qtd4),true,qtd4,X1) = X1,
inference(orient,[status(thm)],[t1105]) ).
cnf(h2,plain,
qtd2(qtd0(V0,qtd3(V0,V1)),V1) = true,
inference(hyper_resolution,[status(thm)],[hi7,hi3]) ).
fof(f4,axiom,
! [X0,X1,X2] :
( ( qtd2(X1,X2)
& qtd2(X0,X1) )
=> qtd2(X0,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_05) ).
fof(f4_nnf,plain,
! [X0,X1,X2] :
( qtd2(X0,X2)
| ~ qtd2(X1,X2)
| ~ qtd2(X0,X1) ),
inference(nnf_transformation,[status(thm)],[f4]) ).
fof(f4_sk,plain,
! [X0,X1,X2] :
( qtd2(X0,X2)
| ~ qtd2(X1,X2)
| ~ qtd2(X0,X1) ),
inference(skolemisation,[status(esa)],[f4_nnf]) ).
cnf(c4,plain,
( qtd2(X0,X2)
| ~ qtd2(X1,X2)
| ~ qtd2(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(hi4,axiom,
ifeq(qtd2(X0,X1),true,ifeq(qtd2(X1,X2),true,qtd2(X0,X2),true),true) = true,
inference(equality_encoding,[status(esa)],[c4]) ).
cnf(t124,plain,
qtd2(qtd0(X1,qtd3(X1,qtd0(X2,qtd3(X2,X3)))),X3) = true,
inference(hyper_resolution,[status(thm)],[hi4,h2,h2]) ).
cnf(t413,plain,
qtd2(qtd0(X1,qtd3(X1,qtd0(X2,qtd3(X2,X3)))),X3) = true,
inference(orient,[status(thm)],[t124]) ).
cnf(t728,plain,
true = qtd2(qtd0(X1,qtd3(X1,qtd4)),X2),
inference(cp,[status(thm)],[t413,t703]) ).
cnf(t948,plain,
qtd2(qtd0(X1,qtd3(X1,qtd4)),X2) = true,
inference(orient,[status(thm)],[t728]) ).
cnf(t958,plain,
qtd0(X1,qtd3(X1,qtd4)) = ifeq(true,true,qtd4,qtd0(X1,qtd3(X1,qtd4))),
inference(cp,[status(thm)],[t957,t948]) ).
cnf(t1106,plain,
qtd0(X1,qtd3(X1,qtd4)) = qtd4,
inference(step,[status(thm)],[t958,t257]) ).
cnf(t964,plain,
qtd0(X1,qtd3(X1,qtd4)) = qtd4,
inference(orient,[status(thm)],[t1106]) ).
cnf(t967,plain,
true = qtd2(X1,qtd3(qtd3(X1,qtd4),qtd4)),
inference(cp,[status(thm)],[t883,t964]) ).
cnf(t1030,plain,
qtd2(X1,qtd3(qtd3(X1,qtd4),qtd4)) = true,
inference(orient,[status(thm)],[t967]) ).
cnf(t1031,plain,
qtd3(qtd3(X1,qtd4),qtd4) = ifeq(true,true,ifeq(qtd2(qtd3(qtd3(X1,qtd4),qtd4),X1),true,X1,qtd3(qtd3(X1,qtd4),qtd4)),qtd3(qtd3(X1,qtd4),qtd4)),
inference(cp,[status(thm)],[t258,t1030]) ).
cnf(t1110,plain,
qtd3(qtd3(X1,qtd4),qtd4) = ifeq(qtd2(qtd3(qtd3(X1,qtd4),qtd4),X1),true,X1,qtd3(qtd3(X1,qtd4),qtd4)),
inference(step,[status(thm)],[t1031,t257]) ).
fof(f10,axiom,
! [X14,X15,X16] :
( qtd2(X14,X15)
=> qtd2(qtd3(X16,X14),qtd3(X16,X15)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_11) ).
fof(f10_nnf,plain,
! [X14,X15,X16] :
( qtd2(qtd3(X16,X14),qtd3(X16,X15))
| ~ qtd2(X14,X15) ),
inference(nnf_transformation,[status(thm)],[f10]) ).
fof(f10_sk,plain,
! [X14,X15,X16] :
( qtd2(qtd3(X16,X14),qtd3(X16,X15))
| ~ qtd2(X14,X15) ),
inference(skolemisation,[status(esa)],[f10_nnf]) ).
cnf(c11,plain,
( qtd2(qtd3(X2,X0),qtd3(X2,X1))
| ~ qtd2(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f10_sk]) ).
cnf(hi11,axiom,
ifeq(qtd2(X0,X1),true,qtd2(qtd3(X2,X0),qtd3(X2,X1)),true) = true,
inference(equality_encoding,[status(esa)],[c11]) ).
cnf(t138,plain,
qtd2(qtd3(X1,qtd0(X2,qtd3(X2,X3))),qtd3(X1,X3)) = true,
inference(hyper_resolution,[status(thm)],[hi11,h2]) ).
cnf(t364,plain,
qtd2(qtd3(X1,qtd0(X2,qtd3(X2,X3))),qtd3(X1,X3)) = true,
inference(orient,[status(thm)],[t138]) ).
cnf(t721,plain,
true = qtd2(qtd3(X1,qtd4),qtd3(X1,X2)),
inference(cp,[status(thm)],[t364,t703]) ).
cnf(t937,plain,
qtd2(qtd3(X1,qtd4),qtd3(X1,X2)) = true,
inference(orient,[status(thm)],[t721]) ).
fof(f12,axiom,
! [A] : qtd3(qtd3(qtd3(A,qtd4),A),A) = qtd1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_13) ).
fof(f12_nnf,plain,
! [A] : qtd3(qtd3(qtd3(A,qtd4),A),A) = qtd1,
inference(nnf_transformation,[status(thm)],[f12]) ).
fof(f12_sk,plain,
! [A] : qtd3(qtd3(qtd3(A,qtd4),A),A) = qtd1,
inference(skolemisation,[status(esa)],[f12_nnf]) ).
cnf(c13,plain,
qtd3(qtd3(qtd3(X0,qtd4),X0),X0) = qtd1,
inference(cnf_transformation,[status(esa)],[f12_sk]) ).
cnf(t50,plain,
qtd3(qtd3(qtd3(X1,qtd4),X1),X1) = qtd1,
inference(equality_encoding,[status(esa)],[c13]) ).
cnf(t282,plain,
qtd3(qtd3(qtd3(X1,qtd4),X1),X1) = qtd1,
inference(orient,[status(thm)],[t50]) ).
cnf(t402,plain,
true = qtd2(qtd0(qtd3(qtd3(X1,qtd4),X1),qtd1),X1),
inference(cp,[status(thm)],[t400,t282]) ).
fof(f2,axiom,
! [A] : qtd0(A,qtd1) = A,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_03) ).
fof(f2_nnf,plain,
! [A] : qtd0(A,qtd1) = A,
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
! [A] : qtd0(A,qtd1) = A,
inference(skolemisation,[status(esa)],[f2_nnf]) ).
cnf(c2,plain,
qtd0(X0,qtd1) = X0,
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(t0,plain,
qtd0(X1,qtd1) = X1,
inference(equality_encoding,[status(esa)],[c2]) ).
cnf(t256,plain,
qtd0(X1,qtd1) = X1,
inference(orient,[status(thm)],[t0]) ).
cnf(t1100,plain,
true = qtd2(qtd3(qtd3(X1,qtd4),X1),X1),
inference(step,[status(thm)],[t402,t256]) ).
cnf(t900,plain,
qtd2(qtd3(qtd3(X1,qtd4),X1),X1) = true,
inference(orient,[status(thm)],[t1100]) ).
cnf(t901,plain,
X1 = ifeq(true,true,ifeq(qtd2(X1,qtd3(qtd3(X1,qtd4),X1)),true,qtd3(qtd3(X1,qtd4),X1),X1),X1),
inference(cp,[status(thm)],[t258,t900]) ).
cnf(t1101,plain,
X1 = ifeq(qtd2(X1,qtd3(qtd3(X1,qtd4),X1)),true,qtd3(qtd3(X1,qtd4),X1),X1),
inference(step,[status(thm)],[t901,t257]) ).
fof(f9,axiom,
! [X11,X12,X13] :
( qtd2(X11,X12)
=> qtd2(qtd3(X12,X13),qtd3(X11,X13)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_10) ).
fof(f9_nnf,plain,
! [X11,X12,X13] :
( qtd2(qtd3(X12,X13),qtd3(X11,X13))
| ~ qtd2(X11,X12) ),
inference(nnf_transformation,[status(thm)],[f9]) ).
fof(f9_sk,plain,
! [X11,X12,X13] :
( qtd2(qtd3(X12,X13),qtd3(X11,X13))
| ~ qtd2(X11,X12) ),
inference(skolemisation,[status(esa)],[f9_nnf]) ).
cnf(c10,plain,
( qtd2(qtd3(X1,X2),qtd3(X0,X2))
| ~ qtd2(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f9_sk]) ).
cnf(hi10,axiom,
ifeq(qtd2(X0,X1),true,qtd2(qtd3(X1,X2),qtd3(X0,X2)),true) = true,
inference(equality_encoding,[status(esa)],[c10]) ).
cnf(h25,plain,
qtd2(qtd3(V0,V1),qtd3(qtd0(V2,qtd3(V2,V0)),V1)) = true,
inference(hyper_resolution,[status(thm)],[hi10,h2]) ).
cnf(h3,plain,
qtd2(V0,qtd3(V1,qtd0(V1,V0))) = true,
inference(hyper_resolution,[status(thm)],[hi6,hi3]) ).
cnf(t114,plain,
qtd2(X1,qtd3(qtd0(X2,qtd3(X2,X3)),qtd0(X3,X1))) = true,
inference(hyper_resolution,[status(thm)],[hi4,h3,h25]) ).
cnf(t332,plain,
qtd2(X1,qtd3(qtd0(X2,qtd3(X2,X3)),qtd0(X3,X1))) = true,
inference(orient,[status(thm)],[t114]) ).
cnf(t288,plain,
qtd0(qtd1,X1) = X1,
inference(cp,[status(thm)],[t287,t256]) ).
cnf(t668,plain,
qtd0(qtd1,X1) = X1,
inference(orient,[status(thm)],[t288]) ).
cnf(t681,plain,
true = qtd2(X1,qtd3(qtd0(X2,qtd3(X2,qtd1)),X1)),
inference(cp,[status(thm)],[t332,t668]) ).
cnf(h36,plain,
qtd2(V0,qtd3(V1,qtd3(V2,qtd0(V2,qtd0(V1,V0))))) = true,
inference(hyper_resolution,[status(thm)],[hi6,h3]) ).
cnf(h0,plain,
qtd2(qtd3(V0,V1),qtd3(V0,V1)) = true,
inference(hyper_resolution,[status(thm)],[hi11,hi3]) ).
fof(f7,axiom,
! [A] : qtd2(A,qtd1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_08) ).
fof(f7_nnf,plain,
! [A] : qtd2(A,qtd1),
inference(nnf_transformation,[status(thm)],[f7]) ).
fof(f7_sk,plain,
! [A] : qtd2(A,qtd1),
inference(skolemisation,[status(esa)],[f7_nnf]) ).
cnf(c8,plain,
qtd2(X0,qtd1),
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
cnf(hi8,axiom,
qtd2(X0,qtd1) = true,
inference(equality_encoding,[status(esa)],[c8]) ).
cnf(h11,plain,
qtd2(qtd3(V0,V1),qtd1) = true,
inference(hyper_resolution,[status(thm)],[hi4,h0,hi8]) ).
cnf(hi5,axiom,
ifeq(qtd2(X0,X1),true,ifeq(qtd2(X1,X0),true,X0,X1),X1) = X1,
inference(equality_encoding,[status(esa)],[c5]) ).
cnf(t69,plain,
qtd3(X1,qtd3(X2,qtd0(X2,qtd0(X1,qtd1)))) = qtd1,
inference(hyper_resolution,[status(thm)],[hi5,h11,h36]) ).
cnf(t1074,plain,
qtd3(X1,qtd3(X2,qtd0(X2,X1))) = qtd1,
inference(step,[status(thm)],[t69,t256]) ).
cnf(h489,plain,
qtd2(qtd3(V0,V1),qtd3(V2,qtd3(V3,qtd0(V3,qtd0(V2,qtd1))))) = true,
inference(hyper_resolution,[status(thm)],[hi4,h11,h36]) ).
cnf(h66,plain,
qtd2(qtd3(V0,qtd3(V1,V2)),qtd3(V0,qtd1)) = true,
inference(hyper_resolution,[status(thm)],[hi11,h11]) ).
cnf(t145,plain,
qtd3(X1,qtd3(X2,qtd0(X2,qtd0(X1,qtd1)))) = qtd3(X1,qtd1),
inference(hyper_resolution,[status(thm)],[hi5,h66,h489]) ).
cnf(t1073,plain,
qtd3(X1,qtd3(X2,qtd0(X2,X1))) = qtd3(X1,qtd1),
inference(step,[status(thm)],[t145,t256]) ).
cnf(t272,plain,
qtd3(X1,qtd3(X2,qtd0(X2,X1))) = qtd3(X1,qtd1),
inference(orient,[status(thm)],[t1073]) ).
cnf(t1075,plain,
qtd3(X1,qtd1) = qtd1,
inference(step,[status(thm)],[t1074,t272]) ).
cnf(t274,plain,
qtd3(X1,qtd1) = qtd1,
inference(orient,[status(thm)],[t1075]) ).
cnf(t1096,plain,
true = qtd2(X1,qtd3(qtd0(X2,qtd1),X1)),
inference(step,[status(thm)],[t681,t274]) ).
cnf(t1097,plain,
true = qtd2(X1,qtd3(X2,X1)),
inference(step,[status(thm)],[t1096,t256]) ).
cnf(t848,plain,
qtd2(X1,qtd3(X2,X1)) = true,
inference(orient,[status(thm)],[t1097]) ).
cnf(t1102,plain,
X1 = ifeq(true,true,qtd3(qtd3(X1,qtd4),X1),X1),
inference(step,[status(thm)],[t1101,t848]) ).
cnf(t1103,plain,
X1 = qtd3(qtd3(X1,qtd4),X1),
inference(step,[status(thm)],[t1102,t257]) ).
cnf(t911,plain,
qtd3(qtd3(X1,qtd4),X1) = X1,
inference(orient,[status(thm)],[t1103]) ).
cnf(t939,plain,
true = qtd2(qtd3(qtd3(X1,qtd4),qtd4),X1),
inference(cp,[status(thm)],[t937,t911]) ).
cnf(t998,plain,
qtd2(qtd3(qtd3(X1,qtd4),qtd4),X1) = true,
inference(orient,[status(thm)],[t939]) ).
cnf(t1111,plain,
qtd3(qtd3(X1,qtd4),qtd4) = ifeq(true,true,X1,qtd3(qtd3(X1,qtd4),qtd4)),
inference(step,[status(thm)],[t1110,t998]) ).
cnf(t1112,plain,
qtd3(qtd3(X1,qtd4),qtd4) = X1,
inference(step,[status(thm)],[t1111,t257]) ).
cnf(t1040,plain,
qtd3(qtd3(X1,qtd4),qtd4) = X1,
inference(orient,[status(thm)],[t1112]) ).
fof(f13,conjecture,
! [X17] : qtd3(qtd3(X17,qtd4),qtd4) = X17,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals_14) ).
fof(f13_neg,negated_conjecture,
~ ! [X17] : qtd3(qtd3(X17,qtd4),qtd4) = X17,
inference(negated_conjecture,[status(cth)],[f13]) ).
fof(f13_nnf,plain,
? [X17] : qtd3(qtd3(X17,qtd4),qtd4) != X17,
inference(nnf_transformation,[status(thm)],[f13_neg]) ).
fof(f13_sk,plain,
qtd3(qtd3(sk0,qtd4),qtd4) != sk0,
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0])],[f13_nnf]) ).
cnf(c14,plain,
qtd3(qtd3(sk0,qtd4),qtd4) != sk0,
inference(cnf_transformation,[status(esa)],[f13_sk]) ).
cnf(goal_0,negated_conjecture,
qtd3(qtd3(sk0,qtd4),qtd4) != sk0,
inference(equality_encoding,[status(esa)],[c14]) ).
cnf(g0_0,plain,
sk0 != sk0,
inference(rw,[status(thm)],[goal_0,t1040]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : LCL902+1 : TPTP v9.3.1. Released v5.5.0.
% 0.00/0.07 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.16/0.43 % Computer : n019.cluster.edu
% 0.16/0.43 % Model : x86_64 x86_64
% 0.16/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.43 % Memory : 8046.5625MB
% 0.16/0.43 % OS : Linux 6.8.0-71-generic
% 0.16/0.43 % CPULimit : 300
% 0.16/0.43 % WCLimit : 300
% 0.16/0.43 % DateTime : Thu Sep 24 00:40:04 UTC 2026
% 0.16/0.43 % CPUTime :
% 0.16/0.43 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 34.23/4.87 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 34.23/4.87 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------