%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : LCL899+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 : n002.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 31.49s 9.92s
% Output : Proof 31.49s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 13
% Syntax : Number of formulae : 116 ( 91 unt; 0 def)
% Number of atoms : 153 ( 86 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 : 221 ( 25 sgn 77 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f12,axiom,
! [A,B] : qtd3(qtd3(A,B),B) = qtd3(qtd3(B,A),A),
file('/export/starexec/sandbox/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(t76,plain,
qtd3(qtd3(X1,X2),X2) = qtd3(qtd3(X2,X1),X1),
inference(equality_encoding,[status(esa)],[c13]) ).
cnf(t329,plain,
qtd3(qtd3(X1,X2),X2) = qtd3(qtd3(X2,X1),X1),
inference(orient,[status(thm)],[t76]) ).
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(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(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(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(h7,plain,
qtd2(V0,qtd3(V1,qtd1)) = true,
inference(hyper_resolution,[status(thm)],[hi6,hi8]) ).
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(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]) ).
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(h0,plain,
qtd2(qtd3(V0,V1),qtd3(V0,V1)) = true,
inference(hyper_resolution,[status(thm)],[hi11,hi3]) ).
cnf(h11,plain,
qtd2(qtd3(V0,V1),qtd1) = true,
inference(hyper_resolution,[status(thm)],[hi4,h0,hi8]) ).
cnf(h24,plain,
qtd2(qtd3(V0,qtd0(V1,qtd3(V1,V2))),qtd3(V0,V2)) = true,
inference(hyper_resolution,[status(thm)],[hi11,h2]) ).
cnf(h217,plain,
qtd2(qtd3(V0,qtd0(V1,qtd3(V1,V2))),qtd1) = true,
inference(hyper_resolution,[status(thm)],[hi4,h24,h11]) ).
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(t130,plain,
qtd3(qtd0(X1,qtd3(X1,X2)),qtd0(X2,qtd3(X2,qtd1))) = qtd1,
inference(hyper_resolution,[status(thm)],[hi5,h217,h542]) ).
cnf(h36,plain,
qtd2(V0,qtd3(V1,qtd3(V2,qtd0(V2,qtd0(V1,V0))))) = true,
inference(hyper_resolution,[status(thm)],[hi6,h3]) ).
cnf(t54,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/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(t1065,plain,
qtd3(X1,qtd3(X2,qtd0(X2,X1))) = qtd1,
inference(step,[status(thm)],[t54,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(t127,plain,
qtd3(X1,qtd3(X2,qtd0(X2,qtd0(X1,qtd1)))) = qtd3(X1,qtd1),
inference(hyper_resolution,[status(thm)],[hi5,h66,h489]) ).
cnf(t1064,plain,
qtd3(X1,qtd3(X2,qtd0(X2,X1))) = qtd3(X1,qtd1),
inference(step,[status(thm)],[t127,t256]) ).
cnf(t272,plain,
qtd3(X1,qtd3(X2,qtd0(X2,X1))) = qtd3(X1,qtd1),
inference(orient,[status(thm)],[t1064]) ).
cnf(t1066,plain,
qtd3(X1,qtd1) = qtd1,
inference(step,[status(thm)],[t1065,t272]) ).
cnf(t274,plain,
qtd3(X1,qtd1) = qtd1,
inference(orient,[status(thm)],[t1066]) ).
cnf(t1078,plain,
qtd3(qtd0(X1,qtd3(X1,X2)),qtd0(X2,qtd1)) = qtd1,
inference(step,[status(thm)],[t130,t274]) ).
cnf(t1079,plain,
qtd3(qtd0(X1,qtd3(X1,X2)),X2) = qtd1,
inference(step,[status(thm)],[t1078,t256]) ).
cnf(t366,plain,
qtd3(qtd0(X1,qtd3(X1,X2)),X2) = qtd1,
inference(orient,[status(thm)],[t1079]) ).
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(t398,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(t374,plain,
qtd0(X1,X2) = qtd0(X2,X1),
inference(orient,[status(thm)],[t6]) ).
cnf(t399,plain,
qtd4 = qtd0(qtd4,X1),
inference(cp,[status(thm)],[t398,t374]) ).
cnf(t933,plain,
qtd0(qtd4,X1) = qtd4,
inference(orient,[status(thm)],[t399]) ).
cnf(t940,plain,
qtd1 = qtd3(qtd4,X1),
inference(cp,[status(thm)],[t366,t933]) ).
cnf(t1042,plain,
qtd3(qtd4,X1) = qtd1,
inference(orient,[status(thm)],[t940]) ).
cnf(t375,plain,
qtd0(qtd1,X1) = X1,
inference(cp,[status(thm)],[t374,t256]) ).
cnf(t893,plain,
qtd0(qtd1,X1) = X1,
inference(orient,[status(thm)],[t375]) ).
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(t33,plain,
qtd0(X1,qtd3(X1,qtd0(X1,X2))) = qtd0(X1,X2),
inference(hyper_resolution,[status(thm)],[hi5,h30,h548]) ).
cnf(t382,plain,
qtd0(X1,qtd3(X1,qtd0(X1,X2))) = qtd0(X1,X2),
inference(orient,[status(thm)],[t33]) ).
cnf(t894,plain,
qtd3(qtd1,qtd0(qtd1,X1)) = qtd0(qtd1,X1),
inference(cp,[status(thm)],[t893,t382]) ).
cnf(t1085,plain,
qtd3(qtd1,X1) = qtd0(qtd1,X1),
inference(step,[status(thm)],[t894,t893]) ).
cnf(t1086,plain,
qtd3(qtd1,X1) = X1,
inference(step,[status(thm)],[t1085,t893]) ).
cnf(t961,plain,
qtd3(qtd1,X1) = X1,
inference(orient,[status(thm)],[t1086]) ).
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,
qtd3(qtd3(qtd4,sk0),sk0) != sk0,
inference(rw,[status(thm)],[goal_0,t329]) ).
cnf(g0_1,plain,
qtd3(qtd1,sk0) != sk0,
inference(rw,[status(thm)],[g0_0,t1042]) ).
cnf(g0_2,plain,
sk0 != sk0,
inference(rw,[status(thm)],[g0_1,t961]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL899+1 : TPTP v9.3.1. Released v5.5.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.11/5.36 % Computer : n002.cluster.edu
% 0.11/5.36 % Model : x86_64 x86_64
% 0.11/5.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/5.36 % Memory : 8046.5625MB
% 0.11/5.36 % OS : Linux 6.8.0-71-generic
% 0.11/5.37 % CPULimit : 300
% 0.11/5.37 % WCLimit : 300
% 0.11/5.37 % DateTime : Thu Sep 24 00:42:54 UTC 2026
% 0.11/5.37 % CPUTime :
% 0.11/5.37 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 31.49/9.92 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 31.49/9.92 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------