%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : LCL901+1 : TPTP v9.3.1. Released v5.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n007.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 20.85s 9.72s
% Output : Proof 20.85s
% Verified :
% SZS Type : Refutation
% Derivation depth : 54
% Number of leaves : 15
% Syntax : Number of formulae : 185 ( 160 unt; 0 def)
% Number of atoms : 222 ( 155 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 72 ( 35 ~; 27 |; 4 &)
% ( 1 <=>; 5 =>; 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 : 380 ( 49 sgn 86 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f12,axiom,
! [A,B] : qtd3(qtd3(A,B),B) = qtd3(qtd3(B,A),A),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos_13) ).
fof(f12_nnf,plain,
! [A,B] : qtd3(qtd3(A,B),B) = qtd3(qtd3(B,A),A),
inference(nnf_transformation,[status(thm)],[f12]) ).
fof(f12_sk,plain,
! [A,B] : qtd3(qtd3(A,B),B) = qtd3(qtd3(B,A),A),
inference(skolemisation,[status(esa)],[f12_nnf]) ).
cnf(c13,plain,
qtd3(qtd3(X0,X1),X1) = qtd3(qtd3(X1,X0),X0),
inference(cnf_transformation,[status(esa)],[f12_sk]) ).
cnf(t88,plain,
qtd3(qtd3(X1,X2),X2) = qtd3(qtd3(X2,X1),X1),
inference(equality_encoding,[status(esa)],[c13]) ).
cnf(t281,plain,
qtd3(qtd3(X1,X2),X2) = qtd3(qtd3(X2,X1),X1),
inference(orient,[status(thm)],[t88]) ).
fof(f5,axiom,
! [X3,X4] :
( ( qtd2(X4,X3)
& qtd2(X3,X4) )
=> X3 = X4 ),
file('/export/starexec/sandbox2/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(t156,plain,
ifeq(qtd2(X1,X2),true,ifeq(qtd2(X2,X1),true,X1,X2),X2) = X2,
inference(equality_encoding,[status(esa)],[c5]) ).
cnf(t259,plain,
ifeq(qtd2(X1,X2),true,ifeq(qtd2(X2,X1),true,X1,X2),X2) = X2,
inference(orient,[status(thm)],[t156]) ).
fof(f6,axiom,
! [X5,X6,X7] :
( qtd2(qtd0(X5,X6),X7)
<=> qtd2(X6,qtd3(X5,X7)) ),
file('/export/starexec/sandbox2/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(t161,plain,
ifeq(qtd2(qtd0(X1,X2),X3),true,qtd2(X2,qtd3(X1,X3)),true) = true,
inference(equality_encoding,[status(esa)],[c6]) ).
cnf(t717,plain,
ifeq(qtd2(qtd0(X1,X2),X3),true,qtd2(X2,qtd3(X1,X3)),true) = true,
inference(orient,[status(thm)],[t161]) ).
fof(f3,axiom,
! [A] : qtd2(A,A),
file('/export/starexec/sandbox2/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(t3,plain,
qtd2(X1,X1) = true,
inference(equality_encoding,[status(esa)],[c3]) ).
cnf(t331,plain,
qtd2(X1,X1) = true,
inference(orient,[status(thm)],[t3]) ).
cnf(t720,plain,
true = ifeq(true,true,qtd2(X1,qtd3(X2,qtd0(X2,X1))),true),
inference(cp,[status(thm)],[t717,t331]) ).
cnf(t6,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t258,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t6]) ).
cnf(t5091,plain,
true = qtd2(X1,qtd3(X2,qtd0(X2,X1))),
inference(step,[status(thm)],[t720,t258]) ).
cnf(t919,plain,
qtd2(X1,qtd3(X2,qtd0(X2,X1))) = true,
inference(orient,[status(thm)],[t5091]) ).
fof(f9,axiom,
! [X11,X12,X13] :
( qtd2(X11,X12)
=> qtd2(qtd3(X12,X13),qtd3(X11,X13)) ),
file('/export/starexec/sandbox2/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]) ).
fof(f7,axiom,
! [A] : qtd2(A,qtd1),
file('/export/starexec/sandbox2/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(h5,plain,
qtd2(qtd3(qtd1,V0),qtd3(V1,V0)) = true,
inference(hyper_resolution,[status(thm)],[hi10,hi8]) ).
fof(f8,axiom,
! [X8,X9,X10] :
( qtd2(X8,X9)
=> qtd2(qtd0(X8,X10),qtd0(X9,X10)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos_09) ).
fof(f8_nnf,plain,
! [X8,X9,X10] :
( qtd2(qtd0(X8,X10),qtd0(X9,X10))
| ~ qtd2(X8,X9) ),
inference(nnf_transformation,[status(thm)],[f8]) ).
fof(f8_sk,plain,
! [X8,X9,X10] :
( qtd2(qtd0(X8,X10),qtd0(X9,X10))
| ~ qtd2(X8,X9) ),
inference(skolemisation,[status(esa)],[f8_nnf]) ).
cnf(c9,plain,
( qtd2(qtd0(X0,X2),qtd0(X1,X2))
| ~ qtd2(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
cnf(hi9,axiom,
ifeq(qtd2(X0,X1),true,qtd2(qtd0(X0,X2),qtd0(X1,X2)),true) = true,
inference(equality_encoding,[status(esa)],[c9]) ).
cnf(t121,plain,
qtd2(qtd0(qtd3(qtd1,X1),X2),qtd0(qtd3(X3,X1),X2)) = true,
inference(hyper_resolution,[status(thm)],[hi9,h5]) ).
cnf(t514,plain,
qtd2(qtd0(qtd3(qtd1,X1),X2),qtd0(qtd3(X3,X1),X2)) = true,
inference(orient,[status(thm)],[t121]) ).
cnf(hi6,axiom,
ifeq(qtd2(qtd0(X0,X1),X2),true,qtd2(X1,qtd3(X0,X2)),true) = true,
inference(equality_encoding,[status(esa)],[c6]) ).
cnf(hi3,axiom,
qtd2(X0,X0) = true,
inference(equality_encoding,[status(esa)],[c3]) ).
cnf(h3,plain,
qtd2(V0,qtd3(V1,qtd0(V1,V0))) = true,
inference(hyper_resolution,[status(thm)],[hi6,hi3]) ).
fof(f4,axiom,
! [X0,X1,X2] :
( ( qtd2(X1,X2)
& qtd2(X0,X1) )
=> qtd2(X0,X2) ),
file('/export/starexec/sandbox2/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(h40,plain,
qtd2(V0,qtd3(V1,qtd0(V1,qtd3(V2,qtd0(V2,V0))))) = true,
inference(hyper_resolution,[status(thm)],[hi4,h3,h3]) ).
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(h548,plain,
qtd2(qtd0(V0,V1),qtd0(V0,qtd3(V2,qtd0(V2,V1)))) = true,
inference(hyper_resolution,[status(thm)],[hi7,h40]) ).
cnf(h1,plain,
qtd2(qtd0(V0,V1),qtd0(V0,V1)) = true,
inference(hyper_resolution,[status(thm)],[hi9,hi3]) ).
cnf(h2,plain,
qtd2(qtd0(V0,qtd3(V0,V1)),V1) = true,
inference(hyper_resolution,[status(thm)],[hi7,hi3]) ).
cnf(h30,plain,
qtd2(qtd0(V0,qtd3(V0,qtd0(V1,V2))),qtd0(V1,V2)) = true,
inference(hyper_resolution,[status(thm)],[hi4,h2,h1]) ).
cnf(h7,plain,
qtd2(V0,qtd3(V1,qtd1)) = true,
inference(hyper_resolution,[status(thm)],[hi6,hi8]) ).
cnf(h10,plain,
qtd2(qtd0(V0,V1),qtd0(qtd3(V2,qtd1),V1)) = true,
inference(hyper_resolution,[status(thm)],[hi9,h7]) ).
cnf(h359,plain,
qtd2(qtd0(V0,qtd3(qtd3(V1,qtd1),qtd0(V2,V3))),qtd0(V2,V3)) = true,
inference(hyper_resolution,[status(thm)],[hi4,h10,h30]) ).
cnf(hi5,axiom,
ifeq(qtd2(X0,X1),true,ifeq(qtd2(X1,X0),true,X0,X1),X1) = X1,
inference(equality_encoding,[status(esa)],[c5]) ).
cnf(t209,plain,
qtd0(qtd3(X1,qtd1),qtd3(qtd3(X1,qtd1),qtd0(qtd3(X1,qtd1),X2))) = qtd0(qtd3(X1,qtd1),X2),
inference(hyper_resolution,[status(thm)],[hi5,h359,h548]) ).
cnf(h36,plain,
qtd2(V0,qtd3(V1,qtd3(V2,qtd0(V2,qtd0(V1,V0))))) = true,
inference(hyper_resolution,[status(thm)],[hi6,h3]) ).
fof(f10,axiom,
! [X14,X15,X16] :
( qtd2(X14,X15)
=> qtd2(qtd3(X16,X14),qtd3(X16,X15)) ),
file('/export/starexec/sandbox2/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(h0,plain,
qtd2(qtd3(V0,V1),qtd3(V0,V1)) = true,
inference(hyper_resolution,[status(thm)],[hi11,hi3]) ).
cnf(h19,plain,
qtd2(qtd3(V0,V1),qtd1) = true,
inference(hyper_resolution,[status(thm)],[hi4,h0,hi8]) ).
cnf(t67,plain,
qtd3(X1,qtd3(X2,qtd0(X2,qtd0(X1,qtd1)))) = qtd1,
inference(hyper_resolution,[status(thm)],[hi5,h19,h36]) ).
fof(f2,axiom,
! [A] : qtd0(A,qtd1) = A,
file('/export/starexec/sandbox2/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(t1,plain,
qtd0(X1,qtd1) = X1,
inference(equality_encoding,[status(esa)],[c2]) ).
cnf(t257,plain,
qtd0(X1,qtd1) = X1,
inference(orient,[status(thm)],[t1]) ).
cnf(t5021,plain,
qtd3(X1,qtd3(X2,qtd0(X2,X1))) = qtd1,
inference(step,[status(thm)],[t67,t257]) ).
cnf(h483,plain,
qtd2(qtd3(V0,V1),qtd3(V2,qtd3(V3,qtd0(V3,qtd0(V2,qtd1))))) = true,
inference(hyper_resolution,[status(thm)],[hi4,h19,h36]) ).
cnf(h4,plain,
qtd2(qtd3(V0,V1),qtd3(V0,qtd1)) = true,
inference(hyper_resolution,[status(thm)],[hi11,hi8]) ).
cnf(h15,plain,
qtd2(qtd3(V0,qtd3(V1,V2)),qtd3(V0,qtd3(V1,V2))) = true,
inference(hyper_resolution,[status(thm)],[hi11,h0]) ).
cnf(h123,plain,
qtd2(qtd3(V0,qtd3(V1,V2)),qtd3(V0,qtd1)) = true,
inference(hyper_resolution,[status(thm)],[hi4,h15,h4]) ).
cnf(t148,plain,
qtd3(X1,qtd3(X2,qtd0(X2,qtd0(X1,qtd1)))) = qtd3(X1,qtd1),
inference(hyper_resolution,[status(thm)],[hi5,h123,h483]) ).
cnf(t5020,plain,
qtd3(X1,qtd3(X2,qtd0(X2,X1))) = qtd3(X1,qtd1),
inference(step,[status(thm)],[t148,t257]) ).
cnf(t268,plain,
qtd3(X1,qtd3(X2,qtd0(X2,X1))) = qtd3(X1,qtd1),
inference(orient,[status(thm)],[t5020]) ).
cnf(t5022,plain,
qtd3(X1,qtd1) = qtd1,
inference(step,[status(thm)],[t5021,t268]) ).
cnf(t269,plain,
qtd3(X1,qtd1) = qtd1,
inference(orient,[status(thm)],[t5022]) ).
cnf(t5048,plain,
qtd0(qtd1,qtd3(qtd3(X1,qtd1),qtd0(qtd3(X1,qtd1),X2))) = qtd0(qtd3(X1,qtd1),X2),
inference(step,[status(thm)],[t209,t269]) ).
cnf(t5049,plain,
qtd0(qtd1,qtd3(qtd1,qtd0(qtd3(X1,qtd1),X2))) = qtd0(qtd3(X1,qtd1),X2),
inference(step,[status(thm)],[t5048,t269]) ).
cnf(t5050,plain,
qtd0(qtd1,qtd3(qtd1,qtd0(qtd1,X2))) = qtd0(qtd3(X1,qtd1),X2),
inference(step,[status(thm)],[t5049,t269]) ).
cnf(t5051,plain,
qtd0(qtd1,qtd3(qtd1,qtd0(qtd1,X2))) = qtd0(qtd1,X2),
inference(step,[status(thm)],[t5050,t269]) ).
cnf(t326,plain,
qtd0(qtd1,qtd3(qtd1,qtd0(qtd1,X1))) = qtd0(qtd1,X1),
inference(orient,[status(thm)],[t5051]) ).
fof(f1,axiom,
! [A,B] : qtd0(A,B) = qtd0(B,A),
file('/export/starexec/sandbox2/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(t7,plain,
qtd0(X1,X2) = qtd0(X2,X1),
inference(equality_encoding,[status(esa)],[c1]) ).
cnf(t298,plain,
qtd0(X1,X2) = qtd0(X2,X1),
inference(orient,[status(thm)],[t7]) ).
cnf(t299,plain,
qtd0(qtd1,X1) = X1,
inference(cp,[status(thm)],[t298,t257]) ).
cnf(t745,plain,
qtd0(qtd1,X1) = X1,
inference(orient,[status(thm)],[t299]) ).
cnf(t5064,plain,
qtd3(qtd1,qtd0(qtd1,X1)) = qtd0(qtd1,X1),
inference(step,[status(thm)],[t326,t745]) ).
cnf(t5065,plain,
qtd3(qtd1,X1) = qtd0(qtd1,X1),
inference(step,[status(thm)],[t5064,t745]) ).
cnf(t5066,plain,
qtd3(qtd1,X1) = X1,
inference(step,[status(thm)],[t5065,t745]) ).
cnf(t765,plain,
qtd3(qtd1,X1) = X1,
inference(rw,[status(thm)],[t5066]) ).
cnf(t807,plain,
qtd3(qtd1,X1) = X1,
inference(orient,[status(thm)],[t765]) ).
cnf(t5075,plain,
qtd2(qtd0(X1,X2),qtd0(qtd3(X3,X1),X2)) = true,
inference(step,[status(thm)],[t514,t807]) ).
cnf(t815,plain,
qtd2(qtd0(X1,X2),qtd0(qtd3(X3,X1),X2)) = true,
inference(rw,[status(thm)],[t5075]) ).
cnf(t1477,plain,
qtd2(qtd0(X1,X2),qtd0(qtd3(X3,X1),X2)) = true,
inference(orient,[status(thm)],[t815]) ).
fof(f13,axiom,
! [A] : qtd0(A,A) = A,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos_14) ).
fof(f13_nnf,plain,
! [A] : qtd0(A,A) = A,
inference(nnf_transformation,[status(thm)],[f13]) ).
fof(f13_sk,plain,
! [A] : qtd0(A,A) = A,
inference(skolemisation,[status(esa)],[f13_nnf]) ).
cnf(c14,plain,
qtd0(X0,X0) = X0,
inference(cnf_transformation,[status(esa)],[f13_sk]) ).
cnf(t0,plain,
qtd0(X1,X1) = X1,
inference(equality_encoding,[status(esa)],[c14]) ).
cnf(t256,plain,
qtd0(X1,X1) = X1,
inference(orient,[status(thm)],[t0]) ).
cnf(t1478,plain,
true = qtd2(X1,qtd0(qtd3(X2,X1),X1)),
inference(cp,[status(thm)],[t1477,t256]) ).
cnf(t5125,plain,
true = qtd2(X1,qtd0(X1,qtd3(X2,X1))),
inference(step,[status(thm)],[t1478,t298]) ).
cnf(t1501,plain,
qtd2(X1,qtd0(X1,qtd3(X2,X1))) = true,
inference(orient,[status(thm)],[t5125]) ).
cnf(t1505,plain,
qtd0(X1,qtd3(X2,X1)) = ifeq(true,true,ifeq(qtd2(qtd0(X1,qtd3(X2,X1)),X1),true,X1,qtd0(X1,qtd3(X2,X1))),qtd0(X1,qtd3(X2,X1))),
inference(cp,[status(thm)],[t259,t1501]) ).
cnf(t5126,plain,
qtd0(X1,qtd3(X2,X1)) = ifeq(qtd2(qtd0(X1,qtd3(X2,X1)),X1),true,X1,qtd0(X1,qtd3(X2,X1))),
inference(step,[status(thm)],[t1505,t258]) ).
cnf(h44,plain,
qtd2(V0,qtd3(V1,qtd0(V1,qtd1))) = true,
inference(hyper_resolution,[status(thm)],[hi4,hi8,h3]) ).
cnf(t16,plain,
qtd2(qtd0(X1,X2),qtd0(X1,qtd1)) = true,
inference(hyper_resolution,[status(thm)],[hi7,h44]) ).
cnf(t5057,plain,
qtd2(qtd0(X1,X2),X1) = true,
inference(step,[status(thm)],[t16,t257]) ).
cnf(t446,plain,
qtd2(qtd0(X1,X2),X1) = true,
inference(orient,[status(thm)],[t5057]) ).
cnf(t5127,plain,
qtd0(X1,qtd3(X2,X1)) = ifeq(true,true,X1,qtd0(X1,qtd3(X2,X1))),
inference(step,[status(thm)],[t5126,t446]) ).
cnf(t5128,plain,
qtd0(X1,qtd3(X2,X1)) = X1,
inference(step,[status(thm)],[t5127,t258]) ).
cnf(t1513,plain,
qtd0(X1,qtd3(X2,X1)) = X1,
inference(orient,[status(thm)],[t5128]) ).
cnf(t1516,plain,
X1 = qtd0(X1,qtd3(qtd3(X1,X2),X2)),
inference(cp,[status(thm)],[t1513,t281]) ).
cnf(t1559,plain,
qtd0(X1,qtd3(qtd3(X1,X2),X2)) = X1,
inference(orient,[status(thm)],[t1516]) ).
cnf(h25,plain,
qtd2(qtd3(V0,V1),qtd3(qtd0(V2,qtd3(V2,V0)),V1)) = true,
inference(hyper_resolution,[status(thm)],[hi10,h2]) ).
cnf(h39,plain,
qtd2(V0,qtd3(V1,qtd0(V1,qtd3(V2,qtd1)))) = true,
inference(hyper_resolution,[status(thm)],[hi4,h7,h3]) ).
cnf(h542,plain,
qtd2(V0,qtd3(qtd0(V1,qtd3(V1,V2)),qtd0(V2,qtd3(V3,qtd1)))) = true,
inference(hyper_resolution,[status(thm)],[hi4,h39,h25]) ).
cnf(h24,plain,
qtd2(qtd3(V0,qtd0(V1,qtd3(V1,V2))),qtd3(V0,V2)) = true,
inference(hyper_resolution,[status(thm)],[hi11,h2]) ).
cnf(h214,plain,
qtd2(qtd3(V0,qtd0(V1,qtd3(V1,V2))),qtd1) = true,
inference(hyper_resolution,[status(thm)],[hi4,h24,h19]) ).
cnf(t151,plain,
qtd3(qtd0(X1,qtd3(X1,X2)),qtd0(X2,qtd3(X2,qtd1))) = qtd1,
inference(hyper_resolution,[status(thm)],[hi5,h214,h542]) ).
cnf(t5043,plain,
qtd3(qtd0(X1,qtd3(X1,X2)),qtd0(X2,qtd1)) = qtd1,
inference(step,[status(thm)],[t151,t269]) ).
cnf(t5044,plain,
qtd3(qtd0(X1,qtd3(X1,X2)),X2) = qtd1,
inference(step,[status(thm)],[t5043,t257]) ).
cnf(t293,plain,
qtd3(qtd0(X1,qtd3(X1,X2)),X2) = qtd1,
inference(orient,[status(thm)],[t5044]) ).
cnf(t1563,plain,
qtd0(X1,qtd3(X1,X2)) = qtd0(qtd0(X1,qtd3(X1,X2)),qtd3(qtd1,X2)),
inference(cp,[status(thm)],[t1559,t293]) ).
fof(f0,axiom,
! [A,B,C] : qtd0(qtd0(A,B),C) = qtd0(A,qtd0(B,C)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos_01) ).
fof(f0_nnf,plain,
! [A,B,C] : qtd0(qtd0(A,B),C) = qtd0(A,qtd0(B,C)),
inference(nnf_transformation,[status(thm)],[f0]) ).
fof(f0_sk,plain,
! [A,B,C] : qtd0(qtd0(A,B),C) = qtd0(A,qtd0(B,C)),
inference(skolemisation,[status(esa)],[f0_nnf]) ).
cnf(c0,plain,
qtd0(qtd0(X0,X1),X2) = qtd0(X0,qtd0(X1,X2)),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(t40,plain,
qtd0(qtd0(X1,X2),X3) = qtd0(X1,qtd0(X2,X3)),
inference(equality_encoding,[status(esa)],[c0]) ).
cnf(t306,plain,
qtd0(qtd0(X1,X2),X3) = qtd0(X1,qtd0(X2,X3)),
inference(orient,[status(thm)],[t40]) ).
cnf(t5132,plain,
qtd0(X1,qtd3(X1,X2)) = qtd0(X1,qtd0(qtd3(X1,X2),qtd3(qtd1,X2))),
inference(step,[status(thm)],[t1563,t306]) ).
cnf(t5133,plain,
qtd0(X1,qtd3(X1,X2)) = qtd0(X1,qtd0(qtd3(X1,X2),X2)),
inference(step,[status(thm)],[t5132,t807]) ).
cnf(t5134,plain,
qtd0(X1,qtd3(X1,X2)) = qtd0(X1,qtd0(X2,qtd3(X1,X2))),
inference(step,[status(thm)],[t5133,t298]) ).
cnf(t5135,plain,
qtd0(X1,qtd3(X1,X2)) = qtd0(X1,X2),
inference(step,[status(thm)],[t5134,t1513]) ).
cnf(t1787,plain,
qtd0(X1,qtd3(X1,X2)) = qtd0(X1,X2),
inference(orient,[status(thm)],[t5135]) ).
cnf(t1821,plain,
true = qtd2(qtd3(X1,X2),qtd3(X1,qtd0(X1,X2))),
inference(cp,[status(thm)],[t919,t1787]) ).
cnf(t4889,plain,
qtd2(qtd3(X1,X2),qtd3(X1,qtd0(X1,X2))) = true,
inference(orient,[status(thm)],[t1821]) ).
cnf(t4918,plain,
qtd3(X1,qtd0(X1,X2)) = ifeq(true,true,ifeq(qtd2(qtd3(X1,qtd0(X1,X2)),qtd3(X1,X2)),true,qtd3(X1,X2),qtd3(X1,qtd0(X1,X2))),qtd3(X1,qtd0(X1,X2))),
inference(cp,[status(thm)],[t259,t4889]) ).
cnf(t5174,plain,
qtd3(X1,qtd0(X1,X2)) = ifeq(qtd2(qtd3(X1,qtd0(X1,X2)),qtd3(X1,X2)),true,qtd3(X1,X2),qtd3(X1,qtd0(X1,X2))),
inference(step,[status(thm)],[t4918,t258]) ).
cnf(h6,plain,
qtd2(qtd0(V0,V1),qtd0(qtd1,V1)) = true,
inference(hyper_resolution,[status(thm)],[hi9,hi8]) ).
cnf(t125,plain,
qtd2(qtd3(X1,qtd0(X2,X3)),qtd3(X1,qtd0(qtd1,X3))) = true,
inference(hyper_resolution,[status(thm)],[hi11,h6]) ).
cnf(t356,plain,
qtd2(qtd3(X1,qtd0(X2,X3)),qtd3(X1,qtd0(qtd1,X3))) = true,
inference(orient,[status(thm)],[t125]) ).
cnf(t5062,plain,
qtd2(qtd3(X1,qtd0(X2,X3)),qtd3(X1,X3)) = true,
inference(step,[status(thm)],[t356,t745]) ).
cnf(t763,plain,
qtd2(qtd3(X1,qtd0(X2,X3)),qtd3(X1,X3)) = true,
inference(rw,[status(thm)],[t5062]) ).
cnf(t1413,plain,
qtd2(qtd3(X1,qtd0(X2,X3)),qtd3(X1,X3)) = true,
inference(orient,[status(thm)],[t763]) ).
cnf(t5175,plain,
qtd3(X1,qtd0(X1,X2)) = ifeq(true,true,qtd3(X1,X2),qtd3(X1,qtd0(X1,X2))),
inference(step,[status(thm)],[t5174,t1413]) ).
cnf(t5176,plain,
qtd3(X1,qtd0(X1,X2)) = qtd3(X1,X2),
inference(step,[status(thm)],[t5175,t258]) ).
cnf(t4925,plain,
qtd3(X1,qtd0(X1,X2)) = qtd3(X1,X2),
inference(orient,[status(thm)],[t5176]) ).
cnf(t4929,plain,
qtd3(X1,qtd3(X1,X2)) = qtd3(X1,qtd0(X1,X2)),
inference(cp,[status(thm)],[t4925,t1787]) ).
cnf(t5177,plain,
qtd3(X1,qtd3(X1,X2)) = qtd3(X1,X2),
inference(step,[status(thm)],[t4929,t4925]) ).
cnf(t4996,plain,
qtd3(X1,qtd3(X1,X2)) = qtd3(X1,X2),
inference(orient,[status(thm)],[t5177]) ).
cnf(t61,plain,
qtd3(X1,qtd0(X1,qtd3(X2,qtd1))) = qtd3(X2,qtd1),
inference(hyper_resolution,[status(thm)],[hi5,h7,h3]) ).
cnf(t5037,plain,
qtd3(X1,qtd0(X1,qtd1)) = qtd3(X2,qtd1),
inference(step,[status(thm)],[t61,t269]) ).
cnf(t5038,plain,
qtd3(X1,X1) = qtd3(X2,qtd1),
inference(step,[status(thm)],[t5037,t257]) ).
cnf(t5039,plain,
qtd3(X1,X1) = qtd1,
inference(step,[status(thm)],[t5038,t269]) ).
cnf(t280,plain,
qtd3(X1,X1) = qtd1,
inference(orient,[status(thm)],[t5039]) ).
fof(f14,conjecture,
! [X17] : qtd3(qtd3(qtd3(X17,qtd4),X17),X17) = qtd1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals_15) ).
fof(f14_neg,negated_conjecture,
~ ! [X17] : qtd3(qtd3(qtd3(X17,qtd4),X17),X17) = qtd1,
inference(negated_conjecture,[status(cth)],[f14]) ).
fof(f14_nnf,plain,
? [X17] : qtd3(qtd3(qtd3(X17,qtd4),X17),X17) != qtd1,
inference(nnf_transformation,[status(thm)],[f14_neg]) ).
fof(f14_sk,plain,
qtd3(qtd3(qtd3(sk0,qtd4),sk0),sk0) != qtd1,
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0])],[f14_nnf]) ).
cnf(c15,plain,
qtd3(qtd3(qtd3(sk0,qtd4),sk0),sk0) != qtd1,
inference(cnf_transformation,[status(esa)],[f14_sk]) ).
cnf(goal_0,negated_conjecture,
qtd3(qtd3(qtd3(sk0,qtd4),sk0),sk0) != qtd1,
inference(equality_encoding,[status(esa)],[c15]) ).
cnf(g0_0,plain,
qtd3(qtd3(qtd3(sk0,qtd4),sk0),sk0) != qtd3(qtd3(sk0,qtd3(sk0,qtd4)),qtd3(sk0,qtd4)),
inference(rw,[status(thm)],[goal_0,t281]) ).
cnf(g0_1,plain,
qtd3(qtd3(qtd3(sk0,qtd4),sk0),sk0) != qtd3(qtd3(sk0,qtd4),qtd3(sk0,qtd4)),
inference(rw,[status(thm)],[g0_0,t4996]) ).
cnf(g0_2,plain,
qtd3(qtd3(qtd3(sk0,qtd4),sk0),sk0) != qtd1,
inference(rw,[status(thm)],[g0_1,t280]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL901+1 : TPTP v9.3.1. Released v5.5.0.
% 0.00/0.03 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.08/0.35 % Computer : n007.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 : Thu Sep 24 00:37:52 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.35 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 20.85/9.72 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 20.85/9.72 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------