%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : LCL898+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 : n015.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 02:03:18 PM UTC 2026
% Result : Theorem 52.84s 11.09s
% Output : Proof 52.84s
% Verified :
% SZS Type : Refutation
% Derivation depth : 47
% Number of leaves : 16
% Syntax : Number of formulae : 226 ( 201 unt; 0 def)
% Number of atoms : 263 ( 196 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 70 ( 33 ~; 27 |; 4 &)
% ( 1 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 5 con; 0-4 aty)
% Number of variables : 464 ( 26 sgn 91 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f11,axiom,
! [A,B] : qtd0(A,qtd3(A,B)) = qtd0(B,qtd3(B,A)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_12) ).
fof(f11_nnf,plain,
! [A,B] : qtd0(A,qtd3(A,B)) = qtd0(B,qtd3(B,A)),
inference(nnf_transformation,[status(thm)],[f11]) ).
fof(f11_sk,plain,
! [A,B] : qtd0(A,qtd3(A,B)) = qtd0(B,qtd3(B,A)),
inference(skolemisation,[status(esa)],[f11_nnf]) ).
cnf(c12,plain,
qtd0(X0,qtd3(X0,X1)) = qtd0(X1,qtd3(X1,X0)),
inference(cnf_transformation,[status(esa)],[f11_sk]) ).
cnf(t33,plain,
qtd0(X1,qtd3(X1,X2)) = qtd0(X2,qtd3(X2,X1)),
inference(equality_encoding,[status(esa)],[c12]) ).
cnf(t311,plain,
qtd0(X1,qtd3(X1,X2)) = qtd0(X2,qtd3(X2,X1)),
inference(orient,[status(thm)],[t33]) ).
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(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]) ).
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(h2,plain,
qtd2(qtd0(V0,qtd3(V0,V1)),V1) = true,
inference(hyper_resolution,[status(thm)],[hi7,hi3]) ).
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(h24,plain,
qtd2(qtd3(V0,qtd0(V1,qtd3(V1,V2))),qtd3(V0,V2)) = true,
inference(hyper_resolution,[status(thm)],[hi11,h2]) ).
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]) ).
cnf(h3,plain,
qtd2(V0,qtd3(V1,qtd0(V1,V0))) = true,
inference(hyper_resolution,[status(thm)],[hi6,hi3]) ).
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(hi5,axiom,
ifeq(qtd2(X0,X1),true,ifeq(qtd2(X1,X0),true,X0,X1),X1) = X1,
inference(equality_encoding,[status(esa)],[c5]) ).
cnf(t43,plain,
qtd3(X1,qtd0(X1,qtd3(X1,X2))) = qtd3(X1,X2),
inference(hyper_resolution,[status(thm)],[hi5,h3,h24]) ).
cnf(t260,plain,
qtd3(X1,qtd0(X1,qtd3(X1,X2))) = qtd3(X1,X2),
inference(orient,[status(thm)],[t43]) ).
cnf(t322,plain,
qtd3(X1,X2) = qtd3(X1,qtd0(X2,qtd3(X2,X1))),
inference(cp,[status(thm)],[t260,t311]) ).
cnf(t1562,plain,
qtd3(X1,qtd0(X2,qtd3(X2,X1))) = qtd3(X1,X2),
inference(orient,[status(thm)],[t322]) ).
fof(f12,axiom,
! [A] : qtd3(qtd3(A,qtd4),qtd4) = A,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_13) ).
fof(f12_nnf,plain,
! [A] : qtd3(qtd3(A,qtd4),qtd4) = A,
inference(nnf_transformation,[status(thm)],[f12]) ).
fof(f12_sk,plain,
! [A] : qtd3(qtd3(A,qtd4),qtd4) = A,
inference(skolemisation,[status(esa)],[f12_nnf]) ).
cnf(c13,plain,
qtd3(qtd3(X0,qtd4),qtd4) = X0,
inference(cnf_transformation,[status(esa)],[f12_sk]) ).
cnf(t10,plain,
qtd3(qtd3(X1,qtd4),qtd4) = X1,
inference(equality_encoding,[status(esa)],[c13]) ).
cnf(t256,plain,
qtd3(qtd3(X1,qtd4),qtd4) = X1,
inference(orient,[status(thm)],[t10]) ).
cnf(t134,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)],[t134]) ).
cnf(t13,plain,
qtd2(X1,qtd3(X2,qtd0(X2,X1))) = true,
inference(hyper_resolution,[status(thm)],[hi6,hi3]) ).
cnf(t386,plain,
qtd2(X1,qtd3(X2,qtd0(X2,X1))) = true,
inference(orient,[status(thm)],[t13]) ).
fof(f0,axiom,
! [A,B,C] : qtd0(qtd0(A,B),C) = qtd0(A,qtd0(B,C)),
file('/export/starexec/sandbox/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(t36,plain,
qtd0(qtd0(X1,X2),X3) = qtd0(X1,qtd0(X2,X3)),
inference(equality_encoding,[status(esa)],[c0]) ).
cnf(t325,plain,
qtd0(qtd0(X1,X2),X3) = qtd0(X1,qtd0(X2,X3)),
inference(orient,[status(thm)],[t36]) ).
cnf(t389,plain,
true = qtd2(X1,qtd3(qtd0(X2,X3),qtd0(X2,qtd0(X3,X1)))),
inference(cp,[status(thm)],[t386,t325]) ).
cnf(t8471,plain,
qtd2(X1,qtd3(qtd0(X2,X3),qtd0(X2,qtd0(X3,X1)))) = true,
inference(orient,[status(thm)],[t389]) ).
cnf(t15,plain,
qtd2(qtd0(X1,qtd3(X1,X2)),X2) = true,
inference(hyper_resolution,[status(thm)],[hi7,hi3]) ).
cnf(t531,plain,
qtd2(qtd0(X1,qtd3(X1,X2)),X2) = true,
inference(orient,[status(thm)],[t15]) ).
fof(f13,axiom,
! [A] : qtd0(A,qtd4) = qtd4,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_14) ).
fof(f13_nnf,plain,
! [A] : qtd0(A,qtd4) = qtd4,
inference(nnf_transformation,[status(thm)],[f13]) ).
fof(f13_sk,plain,
! [A] : qtd0(A,qtd4) = qtd4,
inference(skolemisation,[status(esa)],[f13_nnf]) ).
cnf(c14,plain,
qtd0(X0,qtd4) = qtd4,
inference(cnf_transformation,[status(esa)],[f13_sk]) ).
cnf(t1,plain,
qtd0(X1,qtd4) = qtd4,
inference(equality_encoding,[status(esa)],[c14]) ).
cnf(t341,plain,
qtd0(X1,qtd4) = qtd4,
inference(orient,[status(thm)],[t1]) ).
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(t300,plain,
qtd0(X1,X2) = qtd0(X2,X1),
inference(orient,[status(thm)],[t6]) ).
cnf(t342,plain,
qtd4 = qtd0(qtd4,X1),
inference(cp,[status(thm)],[t341,t300]) ).
cnf(t971,plain,
qtd0(qtd4,X1) = qtd4,
inference(orient,[status(thm)],[t342]) ).
cnf(t978,plain,
true = qtd2(qtd4,X1),
inference(cp,[status(thm)],[t531,t971]) ).
cnf(t1008,plain,
qtd2(qtd4,X1) = true,
inference(orient,[status(thm)],[t978]) ).
cnf(t1009,plain,
X1 = ifeq(true,true,ifeq(qtd2(X1,qtd4),true,qtd4,X1),X1),
inference(cp,[status(thm)],[t259,t1008]) ).
cnf(t5,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t258,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t5]) ).
cnf(t86262,plain,
X1 = ifeq(qtd2(X1,qtd4),true,qtd4,X1),
inference(step,[status(thm)],[t1009,t258]) ).
cnf(t1205,plain,
ifeq(qtd2(X1,qtd4),true,qtd4,X1) = X1,
inference(orient,[status(thm)],[t86262]) ).
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(t109,plain,
qtd2(qtd0(qtd0(X1,qtd3(X1,X2)),qtd3(X2,X3)),X3) = true,
inference(hyper_resolution,[status(thm)],[hi7,h25]) ).
cnf(t86243,plain,
qtd2(qtd0(X1,qtd0(qtd3(X1,X2),qtd3(X2,X3))),X3) = true,
inference(step,[status(thm)],[t109,t325]) ).
cnf(t634,plain,
qtd2(qtd0(X1,qtd0(qtd3(X1,X2),qtd3(X2,X3))),X3) = true,
inference(orient,[status(thm)],[t86243]) ).
cnf(t1206,plain,
qtd0(X1,qtd0(qtd3(X1,X2),qtd3(X2,qtd4))) = ifeq(true,true,qtd4,qtd0(X1,qtd0(qtd3(X1,X2),qtd3(X2,qtd4)))),
inference(cp,[status(thm)],[t1205,t634]) ).
cnf(t86309,plain,
qtd0(X1,qtd0(qtd3(X1,X2),qtd3(X2,qtd4))) = qtd4,
inference(step,[status(thm)],[t1206,t258]) ).
cnf(t2256,plain,
qtd0(X1,qtd0(qtd3(X1,X2),qtd3(X2,qtd4))) = qtd4,
inference(orient,[status(thm)],[t86309]) ).
cnf(t2268,plain,
qtd4 = qtd0(X1,qtd0(qtd3(X1,qtd3(X2,qtd4)),X2)),
inference(cp,[status(thm)],[t2256,t256]) ).
cnf(t86338,plain,
qtd4 = qtd0(X1,qtd0(X2,qtd3(X1,qtd3(X2,qtd4)))),
inference(step,[status(thm)],[t2268,t300]) ).
cnf(t4164,plain,
qtd0(X1,qtd0(X2,qtd3(X1,qtd3(X2,qtd4)))) = qtd4,
inference(orient,[status(thm)],[t86338]) ).
cnf(t8496,plain,
true = qtd2(qtd3(X1,qtd3(X2,qtd4)),qtd3(qtd0(X1,X2),qtd4)),
inference(cp,[status(thm)],[t8471,t4164]) ).
cnf(t76094,plain,
qtd2(qtd3(X1,qtd3(X2,qtd4)),qtd3(qtd0(X1,X2),qtd4)) = true,
inference(orient,[status(thm)],[t8496]) ).
cnf(t76184,plain,
qtd3(qtd0(X1,X2),qtd4) = ifeq(true,true,ifeq(qtd2(qtd3(qtd0(X1,X2),qtd4),qtd3(X1,qtd3(X2,qtd4))),true,qtd3(X1,qtd3(X2,qtd4)),qtd3(qtd0(X1,X2),qtd4)),qtd3(qtd0(X1,X2),qtd4)),
inference(cp,[status(thm)],[t259,t76094]) ).
cnf(t86918,plain,
qtd3(qtd0(X1,X2),qtd4) = ifeq(qtd2(qtd3(qtd0(X1,X2),qtd4),qtd3(X1,qtd3(X2,qtd4))),true,qtd3(X1,qtd3(X2,qtd4)),qtd3(qtd0(X1,X2),qtd4)),
inference(step,[status(thm)],[t76184,t258]) ).
cnf(t90,plain,
qtd2(X1,qtd3(X2,qtd3(X3,qtd0(X3,qtd0(X2,X1))))) = true,
inference(hyper_resolution,[status(thm)],[hi6,h3]) ).
cnf(t374,plain,
qtd2(X1,qtd3(X2,qtd3(X3,qtd0(X3,qtd0(X2,X1))))) = true,
inference(orient,[status(thm)],[t90]) ).
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(h40,plain,
qtd2(V0,qtd3(V1,qtd0(V1,qtd3(V2,qtd0(V2,V0))))) = true,
inference(hyper_resolution,[status(thm)],[hi4,h3,h3]) ).
cnf(h548,plain,
qtd2(qtd0(V0,V1),qtd0(V0,qtd3(V2,qtd0(V2,V1)))) = true,
inference(hyper_resolution,[status(thm)],[hi7,h40]) ).
fof(f8,axiom,
! [X8,X9,X10] :
( qtd2(X8,X9)
=> qtd2(qtd0(X8,X10),qtd0(X9,X10)) ),
file('/export/starexec/sandbox/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(h1,plain,
qtd2(qtd0(V0,V1),qtd0(V0,V1)) = true,
inference(hyper_resolution,[status(thm)],[hi9,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(h22,plain,
qtd2(qtd0(qtd0(V0,V1),V2),qtd0(qtd0(V0,V1),V2)) = true,
inference(hyper_resolution,[status(thm)],[hi9,h1]) ).
cnf(h357,plain,
qtd2(qtd0(qtd0(V0,V1),qtd3(qtd0(V0,V1),qtd0(V2,V3))),qtd0(V2,V3)) = true,
inference(hyper_resolution,[status(thm)],[hi4,h22,h30]) ).
cnf(t202,plain,
qtd0(qtd0(X1,X2),qtd3(qtd0(X1,X2),qtd0(qtd0(X1,X2),X3))) = qtd0(qtd0(X1,X2),X3),
inference(hyper_resolution,[status(thm)],[hi5,h357,h548]) ).
cnf(t86239,plain,
qtd0(X1,qtd0(X2,qtd3(qtd0(X1,X2),qtd0(qtd0(X1,X2),X3)))) = qtd0(qtd0(X1,X2),X3),
inference(step,[status(thm)],[t202,t325]) ).
cnf(t86240,plain,
qtd0(X1,qtd0(X2,qtd3(qtd0(X1,X2),qtd0(X1,qtd0(X2,X3))))) = qtd0(qtd0(X1,X2),X3),
inference(step,[status(thm)],[t86239,t325]) ).
cnf(t86241,plain,
qtd0(X1,qtd0(X2,qtd3(qtd0(X1,X2),qtd0(X1,qtd0(X2,X3))))) = qtd0(X1,qtd0(X2,X3)),
inference(step,[status(thm)],[t86240,t325]) ).
cnf(t350,plain,
qtd0(X1,qtd0(X2,qtd3(qtd0(X1,X2),qtd0(X1,qtd0(X2,X3))))) = qtd0(X1,qtd0(X2,X3)),
inference(orient,[status(thm)],[t86241]) ).
cnf(t361,plain,
qtd0(X1,qtd0(X2,qtd4)) = qtd0(X1,qtd0(X2,qtd3(qtd0(X1,X2),qtd0(X1,qtd4)))),
inference(cp,[status(thm)],[t350,t341]) ).
cnf(t86275,plain,
qtd0(X1,qtd4) = qtd0(X1,qtd0(X2,qtd3(qtd0(X1,X2),qtd0(X1,qtd4)))),
inference(step,[status(thm)],[t361,t341]) ).
cnf(t86276,plain,
qtd4 = qtd0(X1,qtd0(X2,qtd3(qtd0(X1,X2),qtd0(X1,qtd4)))),
inference(step,[status(thm)],[t86275,t341]) ).
cnf(t86277,plain,
qtd4 = qtd0(X1,qtd0(X2,qtd3(qtd0(X1,X2),qtd4))),
inference(step,[status(thm)],[t86276,t341]) ).
cnf(t1593,plain,
qtd0(X1,qtd0(X2,qtd3(qtd0(X1,X2),qtd4))) = qtd4,
inference(orient,[status(thm)],[t86277]) ).
cnf(t1600,plain,
qtd4 = qtd0(X1,qtd0(X2,qtd3(qtd0(X2,X1),qtd4))),
inference(cp,[status(thm)],[t1593,t300]) ).
cnf(t3075,plain,
qtd0(X1,qtd0(X2,qtd3(qtd0(X2,X1),qtd4))) = qtd4,
inference(orient,[status(thm)],[t1600]) ).
cnf(t3137,plain,
true = qtd2(qtd3(qtd0(X1,X2),qtd4),qtd3(X1,qtd3(X2,qtd4))),
inference(cp,[status(thm)],[t374,t3075]) ).
cnf(t28538,plain,
qtd2(qtd3(qtd0(X1,X2),qtd4),qtd3(X1,qtd3(X2,qtd4))) = true,
inference(orient,[status(thm)],[t3137]) ).
cnf(t86919,plain,
qtd3(qtd0(X1,X2),qtd4) = ifeq(true,true,qtd3(X1,qtd3(X2,qtd4)),qtd3(qtd0(X1,X2),qtd4)),
inference(step,[status(thm)],[t86918,t28538]) ).
cnf(t86920,plain,
qtd3(qtd0(X1,X2),qtd4) = qtd3(X1,qtd3(X2,qtd4)),
inference(step,[status(thm)],[t86919,t258]) ).
cnf(t76195,plain,
qtd3(qtd0(X1,X2),qtd4) = qtd3(X1,qtd3(X2,qtd4)),
inference(orient,[status(thm)],[t86920]) ).
cnf(t76249,plain,
qtd0(X1,X2) = qtd3(qtd3(X1,qtd3(X2,qtd4)),qtd4),
inference(cp,[status(thm)],[t256,t76195]) ).
cnf(t76738,plain,
qtd3(qtd3(X1,qtd3(X2,qtd4)),qtd4) = qtd0(X1,X2),
inference(orient,[status(thm)],[t76249]) ).
cnf(t76805,plain,
qtd0(X1,qtd3(X2,qtd3(X3,qtd4))) = qtd3(qtd3(X1,qtd0(X2,X3)),qtd4),
inference(cp,[status(thm)],[t76738,t76738]) ).
cnf(t81023,plain,
qtd0(X1,qtd3(X2,qtd3(X3,qtd4))) = qtd3(qtd3(X1,qtd0(X2,X3)),qtd4),
inference(orient,[status(thm)],[t76805]) ).
cnf(t81137,plain,
qtd3(qtd3(X1,qtd4),X2) = qtd3(qtd3(X1,qtd4),qtd3(qtd3(X2,qtd0(X2,X1)),qtd4)),
inference(cp,[status(thm)],[t1562,t81023]) ).
cnf(t4226,plain,
true = qtd2(qtd3(X1,qtd3(X2,qtd4)),qtd3(X2,qtd3(X1,qtd4))),
inference(cp,[status(thm)],[t374,t4164]) ).
cnf(t37286,plain,
qtd2(qtd3(X1,qtd3(X2,qtd4)),qtd3(X2,qtd3(X1,qtd4))) = true,
inference(orient,[status(thm)],[t4226]) ).
cnf(t37304,plain,
qtd3(X1,qtd3(X2,qtd4)) = ifeq(true,true,ifeq(qtd2(qtd3(X1,qtd3(X2,qtd4)),qtd3(X2,qtd3(X1,qtd4))),true,qtd3(X2,qtd3(X1,qtd4)),qtd3(X1,qtd3(X2,qtd4))),qtd3(X1,qtd3(X2,qtd4))),
inference(cp,[status(thm)],[t259,t37286]) ).
cnf(t86641,plain,
qtd3(X1,qtd3(X2,qtd4)) = ifeq(qtd2(qtd3(X1,qtd3(X2,qtd4)),qtd3(X2,qtd3(X1,qtd4))),true,qtd3(X2,qtd3(X1,qtd4)),qtd3(X1,qtd3(X2,qtd4))),
inference(step,[status(thm)],[t37304,t258]) ).
cnf(t86642,plain,
qtd3(X1,qtd3(X2,qtd4)) = ifeq(true,true,qtd3(X2,qtd3(X1,qtd4)),qtd3(X1,qtd3(X2,qtd4))),
inference(step,[status(thm)],[t86641,t37286]) ).
cnf(t86643,plain,
qtd3(X1,qtd3(X2,qtd4)) = qtd3(X2,qtd3(X1,qtd4)),
inference(step,[status(thm)],[t86642,t258]) ).
cnf(t37315,plain,
qtd3(X1,qtd3(X2,qtd4)) = qtd3(X2,qtd3(X1,qtd4)),
inference(orient,[status(thm)],[t86643]) ).
cnf(t37332,plain,
qtd3(qtd3(X1,qtd4),qtd3(X2,qtd4)) = qtd3(X2,X1),
inference(cp,[status(thm)],[t37315,t256]) ).
cnf(t37592,plain,
qtd3(qtd3(X1,qtd4),qtd3(X2,qtd4)) = qtd3(X2,X1),
inference(orient,[status(thm)],[t37332]) ).
cnf(t87127,plain,
qtd3(qtd3(X1,qtd4),X2) = qtd3(qtd3(X2,qtd0(X2,X1)),X1),
inference(step,[status(thm)],[t81137,t37592]) ).
cnf(t81358,plain,
qtd3(qtd3(X1,qtd0(X1,X2)),X2) = qtd3(qtd3(X2,qtd4),X1),
inference(orient,[status(thm)],[t87127]) ).
cnf(t76789,plain,
qtd0(qtd3(X1,qtd4),X2) = qtd3(qtd3(X2,X1),qtd4),
inference(cp,[status(thm)],[t76738,t37592]) ).
cnf(t77061,plain,
qtd0(qtd3(X1,qtd4),X2) = qtd3(qtd3(X2,X1),qtd4),
inference(orient,[status(thm)],[t76789]) ).
cnf(t81373,plain,
qtd3(qtd3(X1,qtd4),qtd3(X2,qtd4)) = qtd3(qtd3(qtd3(X2,qtd4),qtd3(qtd3(X1,X2),qtd4)),X1),
inference(cp,[status(thm)],[t81358,t77061]) ).
cnf(t87128,plain,
qtd3(X2,X1) = qtd3(qtd3(qtd3(X2,qtd4),qtd3(qtd3(X1,X2),qtd4)),X1),
inference(step,[status(thm)],[t81373,t37592]) ).
cnf(t87129,plain,
qtd3(X2,X1) = qtd3(qtd3(qtd3(X1,X2),X2),X1),
inference(step,[status(thm)],[t87128,t37592]) ).
cnf(t81690,plain,
qtd3(qtd3(qtd3(X1,X2),X2),X1) = qtd3(X2,X1),
inference(orient,[status(thm)],[t87129]) ).
cnf(t81866,plain,
qtd0(X1,qtd3(X1,qtd3(qtd3(X1,X2),X2))) = qtd0(qtd3(qtd3(X1,X2),X2),qtd3(X2,X1)),
inference(cp,[status(thm)],[t311,t81690]) ).
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(t3,plain,
qtd2(X1,qtd1) = true,
inference(equality_encoding,[status(esa)],[c8]) ).
cnf(t434,plain,
qtd2(X1,qtd1) = true,
inference(orient,[status(thm)],[t3]) ).
cnf(t436,plain,
X1 = ifeq(qtd2(qtd1,X1),true,ifeq(true,true,qtd1,X1),X1),
inference(cp,[status(thm)],[t259,t434]) ).
cnf(t86260,plain,
X1 = ifeq(qtd2(qtd1,X1),true,qtd1,X1),
inference(step,[status(thm)],[t436,t258]) ).
cnf(t1194,plain,
ifeq(qtd2(qtd1,X1),true,qtd1,X1) = X1,
inference(orient,[status(thm)],[t86260]) ).
cnf(t137,plain,
ifeq(qtd2(X1,X2),true,qtd2(qtd3(X3,X1),qtd3(X3,X2)),true) = true,
inference(equality_encoding,[status(esa)],[c11]) ).
cnf(t654,plain,
ifeq(qtd2(X1,X2),true,qtd2(qtd3(X3,X1),qtd3(X3,X2)),true) = true,
inference(orient,[status(thm)],[t137]) ).
cnf(hi8,axiom,
qtd2(X0,qtd1) = true,
inference(equality_encoding,[status(esa)],[c8]) ).
cnf(h7,plain,
qtd2(V0,qtd3(V1,qtd1)) = true,
inference(hyper_resolution,[status(thm)],[hi6,hi8]) ).
cnf(t48,plain,
qtd3(X1,qtd0(X1,qtd3(X2,qtd1))) = qtd3(X2,qtd1),
inference(hyper_resolution,[status(thm)],[hi5,h7,h3]) ).
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]) ).
cnf(h19,plain,
qtd2(qtd3(V0,V1),qtd1) = true,
inference(hyper_resolution,[status(thm)],[hi4,h0,hi8]) ).
cnf(t54,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/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(t257,plain,
qtd0(X1,qtd1) = X1,
inference(orient,[status(thm)],[t0]) ).
cnf(t86212,plain,
qtd3(X1,qtd3(X2,qtd0(X2,X1))) = qtd1,
inference(step,[status(thm)],[t54,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(t126,plain,
qtd3(X1,qtd3(X2,qtd0(X2,qtd0(X1,qtd1)))) = qtd3(X1,qtd1),
inference(hyper_resolution,[status(thm)],[hi5,h123,h483]) ).
cnf(t86211,plain,
qtd3(X1,qtd3(X2,qtd0(X2,X1))) = qtd3(X1,qtd1),
inference(step,[status(thm)],[t126,t257]) ).
cnf(t274,plain,
qtd3(X1,qtd3(X2,qtd0(X2,X1))) = qtd3(X1,qtd1),
inference(orient,[status(thm)],[t86211]) ).
cnf(t86213,plain,
qtd3(X1,qtd1) = qtd1,
inference(step,[status(thm)],[t86212,t274]) ).
cnf(t276,plain,
qtd3(X1,qtd1) = qtd1,
inference(orient,[status(thm)],[t86213]) ).
cnf(t86228,plain,
qtd3(X1,qtd0(X1,qtd1)) = qtd3(X2,qtd1),
inference(step,[status(thm)],[t48,t276]) ).
cnf(t86229,plain,
qtd3(X1,X1) = qtd3(X2,qtd1),
inference(step,[status(thm)],[t86228,t257]) ).
cnf(t86230,plain,
qtd3(X1,X1) = qtd1,
inference(step,[status(thm)],[t86229,t276]) ).
cnf(t290,plain,
qtd3(X1,X1) = qtd1,
inference(orient,[status(thm)],[t86230]) ).
cnf(t677,plain,
true = ifeq(qtd2(X1,X2),true,qtd2(qtd1,qtd3(X1,X2)),true),
inference(cp,[status(thm)],[t654,t290]) ).
cnf(t10488,plain,
ifeq(qtd2(X1,X2),true,qtd2(qtd1,qtd3(X1,X2)),true) = true,
inference(orient,[status(thm)],[t677]) ).
cnf(t382,plain,
true = qtd2(X1,qtd3(X2,qtd3(X3,qtd0(X3,qtd0(X1,X2))))),
inference(cp,[status(thm)],[t374,t300]) ).
cnf(t8393,plain,
qtd2(X1,qtd3(X2,qtd3(X3,qtd0(X3,qtd0(X1,X2))))) = true,
inference(orient,[status(thm)],[t382]) ).
cnf(t327,plain,
qtd0(X1,qtd0(X2,X3)) = qtd0(X3,qtd0(X1,X2)),
inference(cp,[status(thm)],[t325,t300]) ).
cnf(t1791,plain,
qtd0(X1,qtd0(X2,X3)) = qtd0(X3,qtd0(X1,X2)),
inference(orient,[status(thm)],[t327]) ).
cnf(t2258,plain,
qtd4 = qtd0(qtd3(X1,qtd4),qtd0(X2,qtd3(X2,X1))),
inference(cp,[status(thm)],[t2256,t1791]) ).
cnf(t3965,plain,
qtd0(qtd3(X1,qtd4),qtd0(X2,qtd3(X2,X1))) = qtd4,
inference(orient,[status(thm)],[t2258]) ).
cnf(t8405,plain,
true = qtd2(X1,qtd3(qtd3(X1,X2),qtd3(qtd3(X2,qtd4),qtd4))),
inference(cp,[status(thm)],[t8393,t3965]) ).
cnf(t86398,plain,
true = qtd2(X1,qtd3(qtd3(X1,X2),X2)),
inference(step,[status(thm)],[t8405,t256]) ).
cnf(t8458,plain,
qtd2(X1,qtd3(qtd3(X1,X2),X2)) = true,
inference(orient,[status(thm)],[t86398]) ).
cnf(t10497,plain,
true = ifeq(true,true,qtd2(qtd1,qtd3(X1,qtd3(qtd3(X1,X2),X2))),true),
inference(cp,[status(thm)],[t10488,t8458]) ).
cnf(t86405,plain,
true = qtd2(qtd1,qtd3(X1,qtd3(qtd3(X1,X2),X2))),
inference(step,[status(thm)],[t10497,t258]) ).
cnf(t10558,plain,
qtd2(qtd1,qtd3(X1,qtd3(qtd3(X1,X2),X2))) = true,
inference(orient,[status(thm)],[t86405]) ).
cnf(t10561,plain,
qtd3(X1,qtd3(qtd3(X1,X2),X2)) = ifeq(true,true,qtd1,qtd3(X1,qtd3(qtd3(X1,X2),X2))),
inference(cp,[status(thm)],[t1194,t10558]) ).
cnf(t86406,plain,
qtd3(X1,qtd3(qtd3(X1,X2),X2)) = qtd1,
inference(step,[status(thm)],[t10561,t258]) ).
cnf(t10570,plain,
qtd3(X1,qtd3(qtd3(X1,X2),X2)) = qtd1,
inference(orient,[status(thm)],[t86406]) ).
cnf(t87130,plain,
qtd0(X1,qtd1) = qtd0(qtd3(qtd3(X1,X2),X2),qtd3(X2,X1)),
inference(step,[status(thm)],[t81866,t10570]) ).
cnf(t87131,plain,
X1 = qtd0(qtd3(qtd3(X1,X2),X2),qtd3(X2,X1)),
inference(step,[status(thm)],[t87130,t257]) ).
cnf(t87132,plain,
X1 = qtd0(qtd3(X2,X1),qtd3(qtd3(X1,X2),X2)),
inference(step,[status(thm)],[t87131,t300]) ).
cnf(t82197,plain,
qtd0(qtd3(X1,X2),qtd3(qtd3(X2,X1),X1)) = X2,
inference(orient,[status(thm)],[t87132]) ).
cnf(t82214,plain,
qtd3(qtd3(X1,X2),X2) = qtd0(qtd1,qtd3(qtd3(qtd3(qtd3(X1,X2),X2),X1),X1)),
inference(cp,[status(thm)],[t82197,t10570]) ).
cnf(t301,plain,
qtd0(qtd1,X1) = X1,
inference(cp,[status(thm)],[t300,t257]) ).
cnf(t929,plain,
qtd0(qtd1,X1) = X1,
inference(orient,[status(thm)],[t301]) ).
cnf(t87144,plain,
qtd3(qtd3(X1,X2),X2) = qtd3(qtd3(qtd3(qtd3(X1,X2),X2),X1),X1),
inference(step,[status(thm)],[t82214,t929]) ).
cnf(t87145,plain,
qtd3(qtd3(X1,X2),X2) = qtd3(qtd3(X2,X1),X1),
inference(step,[status(thm)],[t87144,t81690]) ).
cnf(t85903,plain,
qtd3(qtd3(X1,X2),X2) = qtd3(qtd3(X2,X1),X1),
inference(orient,[status(thm)],[t87145]) ).
fof(f14,conjecture,
! [X17,X18] : qtd3(qtd3(X17,X18),X18) = qtd3(qtd3(X18,X17),X17),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals_15) ).
fof(f14_neg,negated_conjecture,
~ ! [X17,X18] : qtd3(qtd3(X17,X18),X18) = qtd3(qtd3(X18,X17),X17),
inference(negated_conjecture,[status(cth)],[f14]) ).
fof(f14_nnf,plain,
? [X17,X18] : qtd3(qtd3(X17,X18),X18) != qtd3(qtd3(X18,X17),X17),
inference(nnf_transformation,[status(thm)],[f14_neg]) ).
fof(f14_sk,plain,
qtd3(qtd3(sk0,sk1),sk1) != qtd3(qtd3(sk1,sk0),sk0),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0,sk1])],[f14_nnf]) ).
cnf(c15,plain,
qtd3(qtd3(sk0,sk1),sk1) != qtd3(qtd3(sk1,sk0),sk0),
inference(cnf_transformation,[status(esa)],[f14_sk]) ).
cnf(goal_0,negated_conjecture,
qtd3(qtd3(sk1,sk0),sk0) != qtd3(qtd3(sk0,sk1),sk1),
inference(equality_encoding,[status(esa)],[c15]) ).
cnf(g0_0,plain,
qtd3(qtd3(sk1,sk0),sk0) != qtd3(qtd3(sk1,sk0),sk0),
inference(rw,[status(thm)],[goal_0,t85903]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL898+1 : TPTP v9.3.1. Released v5.5.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.09/0.37 % Computer : n015.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Thu Sep 24 00:43:25 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 52.84/11.09 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 52.84/11.09 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------