%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : LCL896+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 : n014.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 42.53s 6.64s
% Output : Proof 42.53s
% Verified :
% SZS Type : Refutation
% Derivation depth : 39
% Number of leaves : 12
% Syntax : Number of formulae : 141 ( 120 unt; 0 def)
% Number of atoms : 174 ( 115 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 : 6 ( 2 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 : 303 ( 36 sgn 73 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
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(t166,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)],[t166]) ).
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(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/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(hi3,axiom,
qtd2(X0,X0) = true,
inference(equality_encoding,[status(esa)],[c3]) ).
cnf(t21,plain,
qtd2(qtd0(X1,qtd3(X1,X2)),X2) = true,
inference(hyper_resolution,[status(thm)],[hi7,hi3]) ).
cnf(t375,plain,
qtd2(qtd0(X1,qtd3(X1,X2)),X2) = true,
inference(orient,[status(thm)],[t21]) ).
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/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(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]) ).
cnf(hi5,axiom,
ifeq(qtd2(X0,X1),true,ifeq(qtd2(X1,X0),true,X0,X1),X1) = X1,
inference(equality_encoding,[status(esa)],[c5]) ).
cnf(t53,plain,
qtd3(X1,qtd0(X1,qtd3(X1,X2))) = qtd3(X1,X2),
inference(hyper_resolution,[status(thm)],[hi5,h3,h24]) ).
cnf(t259,plain,
qtd3(X1,qtd0(X1,qtd3(X1,X2))) = qtd3(X1,X2),
inference(orient,[status(thm)],[t53]) ).
fof(f11,axiom,
! [A,B,C] : qtd0(qtd0(A,qtd3(A,B)),qtd3(qtd0(A,qtd3(A,B)),C)) = qtd0(A,qtd3(A,qtd0(B,qtd3(B,C)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos_12) ).
fof(f11_nnf,plain,
! [A,B,C] : qtd0(qtd0(A,qtd3(A,B)),qtd3(qtd0(A,qtd3(A,B)),C)) = qtd0(A,qtd3(A,qtd0(B,qtd3(B,C)))),
inference(nnf_transformation,[status(thm)],[f11]) ).
fof(f11_sk,plain,
! [A,B,C] : qtd0(qtd0(A,qtd3(A,B)),qtd3(qtd0(A,qtd3(A,B)),C)) = qtd0(A,qtd3(A,qtd0(B,qtd3(B,C)))),
inference(skolemisation,[status(esa)],[f11_nnf]) ).
cnf(c12,plain,
qtd0(qtd0(X0,qtd3(X0,X1)),qtd3(qtd0(X0,qtd3(X0,X1)),X2)) = qtd0(X0,qtd3(X0,qtd0(X1,qtd3(X1,X2)))),
inference(cnf_transformation,[status(esa)],[f11_sk]) ).
cnf(t242,plain,
qtd0(qtd0(X1,qtd3(X1,X2)),qtd3(qtd0(X1,qtd3(X1,X2)),X3)) = qtd0(X1,qtd3(X1,qtd0(X2,qtd3(X2,X3)))),
inference(equality_encoding,[status(esa)],[c12]) ).
cnf(t274,plain,
qtd0(qtd0(X1,qtd3(X1,X2)),qtd3(qtd0(X1,qtd3(X1,X2)),X3)) = qtd0(X1,qtd3(X1,qtd0(X2,qtd3(X2,X3)))),
inference(orient,[status(thm)],[t242]) ).
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(t46,plain,
qtd0(qtd0(X1,X2),X3) = qtd0(X1,qtd0(X2,X3)),
inference(equality_encoding,[status(esa)],[c0]) ).
cnf(t285,plain,
qtd0(qtd0(X1,X2),X3) = qtd0(X1,qtd0(X2,X3)),
inference(orient,[status(thm)],[t46]) ).
cnf(t19709,plain,
qtd0(X1,qtd0(qtd3(X1,X2),qtd3(qtd0(X1,qtd3(X1,X2)),X3))) = qtd0(X1,qtd3(X1,qtd0(X2,qtd3(X2,X3)))),
inference(step,[status(thm)],[t274,t285]) ).
cnf(t292,plain,
qtd0(X1,qtd0(qtd3(X1,X2),qtd3(qtd0(X1,qtd3(X1,X2)),X3))) = qtd0(X1,qtd3(X1,qtd0(X2,qtd3(X2,X3)))),
inference(rw,[status(thm)],[t19709]) ).
cnf(t4798,plain,
qtd0(X1,qtd0(qtd3(X1,X2),qtd3(qtd0(X1,qtd3(X1,X2)),X3))) = qtd0(X1,qtd3(X1,qtd0(X2,qtd3(X2,X3)))),
inference(orient,[status(thm)],[t292]) ).
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(t2,plain,
qtd2(X1,qtd1) = true,
inference(equality_encoding,[status(esa)],[c8]) ).
cnf(t326,plain,
qtd2(X1,qtd1) = true,
inference(orient,[status(thm)],[t2]) ).
cnf(t328,plain,
X1 = ifeq(qtd2(qtd1,X1),true,ifeq(true,true,qtd1,X1),X1),
inference(cp,[status(thm)],[t258,t326]) ).
cnf(t4,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t257,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t4]) ).
cnf(t19722,plain,
X1 = ifeq(qtd2(qtd1,X1),true,qtd1,X1),
inference(step,[status(thm)],[t328,t257]) ).
cnf(t762,plain,
ifeq(qtd2(qtd1,X1),true,qtd1,X1) = X1,
inference(orient,[status(thm)],[t19722]) ).
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(t168,plain,
ifeq(qtd2(X1,X2),true,qtd2(qtd3(X2,X3),qtd3(X1,X3)),true) = true,
inference(equality_encoding,[status(esa)],[c10]) ).
cnf(t467,plain,
ifeq(qtd2(X1,X2),true,qtd2(qtd3(X2,X3),qtd3(X1,X3)),true) = true,
inference(orient,[status(thm)],[t168]) ).
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(h41,plain,
qtd2(qtd0(V0,qtd3(V0,V1)),qtd3(V2,qtd0(V2,V1))) = true,
inference(hyper_resolution,[status(thm)],[hi4,h2,h3]) ).
cnf(t116,plain,
qtd2(qtd0(X1,qtd0(X2,qtd3(X2,X3))),qtd0(X1,X3)) = true,
inference(hyper_resolution,[status(thm)],[hi7,h41]) ).
cnf(t396,plain,
qtd2(qtd0(X1,qtd0(X2,qtd3(X2,X3))),qtd0(X1,X3)) = true,
inference(orient,[status(thm)],[t116]) ).
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(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(t64,plain,
qtd3(X1,qtd3(X2,qtd0(X2,qtd0(X1,qtd1)))) = qtd1,
inference(hyper_resolution,[status(thm)],[hi5,h11,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(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(t19698,plain,
qtd3(X1,qtd3(X2,qtd0(X2,X1))) = qtd1,
inference(step,[status(thm)],[t64,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(h4,plain,
qtd2(qtd3(V0,V1),qtd3(V0,qtd1)) = true,
inference(hyper_resolution,[status(thm)],[hi11,hi8]) ).
cnf(h8,plain,
qtd2(qtd3(V0,qtd3(V1,V2)),qtd3(V0,qtd3(V1,V2))) = true,
inference(hyper_resolution,[status(thm)],[hi11,h0]) ).
cnf(h72,plain,
qtd2(qtd3(V0,qtd3(V1,V2)),qtd3(V0,qtd1)) = true,
inference(hyper_resolution,[status(thm)],[hi4,h8,h4]) ).
cnf(t141,plain,
qtd3(X1,qtd3(X2,qtd0(X2,qtd0(X1,qtd1)))) = qtd3(X1,qtd1),
inference(hyper_resolution,[status(thm)],[hi5,h72,h489]) ).
cnf(t19697,plain,
qtd3(X1,qtd3(X2,qtd0(X2,X1))) = qtd3(X1,qtd1),
inference(step,[status(thm)],[t141,t256]) ).
cnf(t260,plain,
qtd3(X1,qtd3(X2,qtd0(X2,X1))) = qtd3(X1,qtd1),
inference(orient,[status(thm)],[t19697]) ).
cnf(t19699,plain,
qtd3(X1,qtd1) = qtd1,
inference(step,[status(thm)],[t19698,t260]) ).
cnf(t263,plain,
qtd3(X1,qtd1) = qtd1,
inference(orient,[status(thm)],[t19699]) ).
cnf(t400,plain,
true = qtd2(qtd0(X1,qtd0(X2,qtd1)),qtd0(X1,qtd1)),
inference(cp,[status(thm)],[t396,t263]) ).
cnf(t19712,plain,
true = qtd2(qtd0(X1,X2),qtd0(X1,qtd1)),
inference(step,[status(thm)],[t400,t256]) ).
cnf(t19713,plain,
true = qtd2(qtd0(X1,X2),X1),
inference(step,[status(thm)],[t19712,t256]) ).
cnf(t655,plain,
qtd2(qtd0(X1,X2),X1) = true,
inference(orient,[status(thm)],[t19713]) ).
cnf(t666,plain,
true = ifeq(true,true,qtd2(qtd3(X1,X2),qtd3(qtd0(X1,X3),X2)),true),
inference(cp,[status(thm)],[t467,t655]) ).
cnf(t19739,plain,
true = qtd2(qtd3(X1,X2),qtd3(qtd0(X1,X3),X2)),
inference(step,[status(thm)],[t666,t257]) ).
cnf(t1021,plain,
qtd2(qtd3(X1,X2),qtd3(qtd0(X1,X3),X2)) = true,
inference(orient,[status(thm)],[t19739]) ).
cnf(h33,plain,
qtd2(qtd3(V0,V1),qtd3(V0,qtd3(V2,qtd0(V2,V1)))) = true,
inference(hyper_resolution,[status(thm)],[hi11,h3]) ).
cnf(h403,plain,
qtd2(qtd3(V0,V1),qtd3(V0,qtd3(V2,qtd0(V2,qtd1)))) = true,
inference(hyper_resolution,[status(thm)],[hi4,h4,h33]) ).
cnf(h78,plain,
qtd2(qtd3(V0,V1),qtd3(V2,qtd0(V2,qtd1))) = true,
inference(hyper_resolution,[status(thm)],[hi4,h11,h3]) ).
cnf(t142,plain,
qtd3(X1,qtd3(X2,qtd0(X2,qtd1))) = qtd3(X1,qtd0(X1,qtd1)),
inference(hyper_resolution,[status(thm)],[hi5,h78,h403]) ).
cnf(t19705,plain,
qtd3(X1,qtd3(X2,X2)) = qtd3(X1,qtd0(X1,qtd1)),
inference(step,[status(thm)],[t142,t256]) ).
cnf(h7,plain,
qtd2(V0,qtd3(V1,qtd1)) = true,
inference(hyper_resolution,[status(thm)],[hi6,hi8]) ).
cnf(h401,plain,
qtd2(V0,qtd3(V1,qtd3(V2,qtd0(V2,qtd1)))) = true,
inference(hyper_resolution,[status(thm)],[hi4,h7,h33]) ).
cnf(h45,plain,
qtd2(qtd3(V0,qtd3(V1,V2)),qtd3(V0,qtd3(V1,qtd1))) = true,
inference(hyper_resolution,[status(thm)],[hi11,h4]) ).
cnf(t144,plain,
qtd3(X1,qtd3(X2,qtd0(X2,qtd1))) = qtd3(X1,qtd3(X2,qtd1)),
inference(hyper_resolution,[status(thm)],[hi5,h45,h401]) ).
cnf(t19702,plain,
qtd3(X1,qtd3(X2,X2)) = qtd3(X1,qtd3(X2,qtd1)),
inference(step,[status(thm)],[t144,t256]) ).
cnf(t19703,plain,
qtd3(X1,qtd3(X2,X2)) = qtd3(X1,qtd1),
inference(step,[status(thm)],[t19702,t263]) ).
cnf(t19704,plain,
qtd3(X1,qtd3(X2,X2)) = qtd1,
inference(step,[status(thm)],[t19703,t263]) ).
cnf(t267,plain,
qtd3(X1,qtd3(X2,X2)) = qtd1,
inference(orient,[status(thm)],[t19704]) ).
cnf(t19706,plain,
qtd1 = qtd3(X1,qtd0(X1,qtd1)),
inference(step,[status(thm)],[t19705,t267]) ).
cnf(t19707,plain,
qtd1 = qtd3(X1,X1),
inference(step,[status(thm)],[t19706,t256]) ).
cnf(t269,plain,
qtd3(X1,X1) = qtd1,
inference(orient,[status(thm)],[t19707]) ).
cnf(t1022,plain,
true = qtd2(qtd1,qtd3(qtd0(X1,X2),X1)),
inference(cp,[status(thm)],[t1021,t269]) ).
cnf(t1041,plain,
qtd2(qtd1,qtd3(qtd0(X1,X2),X1)) = true,
inference(orient,[status(thm)],[t1022]) ).
cnf(t1047,plain,
qtd3(qtd0(X1,X2),X1) = ifeq(true,true,qtd1,qtd3(qtd0(X1,X2),X1)),
inference(cp,[status(thm)],[t762,t1041]) ).
cnf(t19740,plain,
qtd3(qtd0(X1,X2),X1) = qtd1,
inference(step,[status(thm)],[t1047,t257]) ).
cnf(t1056,plain,
qtd3(qtd0(X1,X2),X1) = qtd1,
inference(orient,[status(thm)],[t19740]) ).
cnf(t4826,plain,
qtd0(X1,qtd3(X1,qtd0(X2,qtd3(X2,X1)))) = qtd0(X1,qtd0(qtd3(X1,X2),qtd1)),
inference(cp,[status(thm)],[t4798,t1056]) ).
cnf(t19810,plain,
qtd0(X1,qtd3(X1,qtd0(X2,qtd3(X2,X1)))) = qtd0(X1,qtd3(X1,X2)),
inference(step,[status(thm)],[t4826,t256]) ).
cnf(t5099,plain,
qtd0(X1,qtd3(X1,qtd0(X2,qtd3(X2,X1)))) = qtd0(X1,qtd3(X1,X2)),
inference(orient,[status(thm)],[t19810]) ).
cnf(t5197,plain,
qtd3(X1,qtd0(X2,qtd3(X2,X1))) = qtd3(X1,qtd0(X1,qtd3(X1,X2))),
inference(cp,[status(thm)],[t259,t5099]) ).
cnf(t19811,plain,
qtd3(X1,qtd0(X2,qtd3(X2,X1))) = qtd3(X1,X2),
inference(step,[status(thm)],[t5197,t259]) ).
cnf(t5300,plain,
qtd3(X1,qtd0(X2,qtd3(X2,X1))) = qtd3(X1,X2),
inference(orient,[status(thm)],[t19811]) ).
cnf(t5349,plain,
true = qtd2(qtd0(X1,qtd3(X1,X2)),qtd0(X2,qtd3(X2,X1))),
inference(cp,[status(thm)],[t375,t5300]) ).
cnf(t19051,plain,
qtd2(qtd0(X1,qtd3(X1,X2)),qtd0(X2,qtd3(X2,X1))) = true,
inference(orient,[status(thm)],[t5349]) ).
cnf(t19143,plain,
qtd0(X1,qtd3(X1,X2)) = ifeq(true,true,ifeq(qtd2(qtd0(X1,qtd3(X1,X2)),qtd0(X2,qtd3(X2,X1))),true,qtd0(X2,qtd3(X2,X1)),qtd0(X1,qtd3(X1,X2))),qtd0(X1,qtd3(X1,X2))),
inference(cp,[status(thm)],[t258,t19051]) ).
cnf(t20056,plain,
qtd0(X1,qtd3(X1,X2)) = ifeq(qtd2(qtd0(X1,qtd3(X1,X2)),qtd0(X2,qtd3(X2,X1))),true,qtd0(X2,qtd3(X2,X1)),qtd0(X1,qtd3(X1,X2))),
inference(step,[status(thm)],[t19143,t257]) ).
cnf(t20057,plain,
qtd0(X1,qtd3(X1,X2)) = ifeq(true,true,qtd0(X2,qtd3(X2,X1)),qtd0(X1,qtd3(X1,X2))),
inference(step,[status(thm)],[t20056,t19051]) ).
cnf(t20058,plain,
qtd0(X1,qtd3(X1,X2)) = qtd0(X2,qtd3(X2,X1)),
inference(step,[status(thm)],[t20057,t257]) ).
cnf(t19153,plain,
qtd0(X1,qtd3(X1,X2)) = qtd0(X2,qtd3(X2,X1)),
inference(orient,[status(thm)],[t20058]) ).
fof(f12,conjecture,
! [X17,X18] : qtd0(X17,qtd3(X17,X18)) = qtd0(X18,qtd3(X18,X17)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals_13) ).
fof(f12_neg,negated_conjecture,
~ ! [X17,X18] : qtd0(X17,qtd3(X17,X18)) = qtd0(X18,qtd3(X18,X17)),
inference(negated_conjecture,[status(cth)],[f12]) ).
fof(f12_nnf,plain,
? [X17,X18] : qtd0(X17,qtd3(X17,X18)) != qtd0(X18,qtd3(X18,X17)),
inference(nnf_transformation,[status(thm)],[f12_neg]) ).
fof(f12_sk,plain,
qtd0(sk0,qtd3(sk0,sk1)) != qtd0(sk1,qtd3(sk1,sk0)),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0,sk1])],[f12_nnf]) ).
cnf(c13,plain,
qtd0(sk0,qtd3(sk0,sk1)) != qtd0(sk1,qtd3(sk1,sk0)),
inference(cnf_transformation,[status(esa)],[f12_sk]) ).
cnf(goal_0,negated_conjecture,
qtd0(sk1,qtd3(sk1,sk0)) != qtd0(sk0,qtd3(sk0,sk1)),
inference(equality_encoding,[status(esa)],[c13]) ).
cnf(g0_0,plain,
qtd0(sk1,qtd3(sk1,sk0)) != qtd0(sk1,qtd3(sk1,sk0)),
inference(rw,[status(thm)],[goal_0,t19153]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : LCL896+1 : TPTP v9.3.1. Released v5.5.0.
% 0.00/0.06 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.18/0.44 % Computer : n014.cluster.edu
% 0.18/0.44 % Model : x86_64 x86_64
% 0.18/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.44 % Memory : 8046.5625MB
% 0.18/0.44 % OS : Linux 6.8.0-71-generic
% 0.18/0.45 % CPULimit : 300
% 0.18/0.45 % WCLimit : 300
% 0.18/0.45 % DateTime : Thu Sep 24 00:39:18 UTC 2026
% 0.18/0.45 % CPUTime :
% 0.18/0.45 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 42.53/6.64 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 42.53/6.64 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------