%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : PUZ128+2 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n018.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 02:32:07 PM UTC 2026
% Result : Theorem 6.22s 1.22s
% Output : Proof 6.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 45
% Number of leaves : 3
% Syntax : Number of formulae : 160 ( 150 unt; 0 def)
% Number of atoms : 258 ( 177 equ)
% Maximal formula atoms : 16 ( 1 avg)
% Number of connectives : 142 ( 44 ~; 35 |; 63 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 23 ( 2 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of predicates : 6 ( 3 usr; 2 prp; 0-3 aty)
% Number of functors : 14 ( 14 usr; 12 con; 0-4 aty)
% Number of variables : 141 ( 2 sgn 10 !; 22 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f0,axiom,
? [A,B,C,D,E] :
( ~ ? [F] :
( qtd3 = F
& patricide(F) )
& qtd0 = E
& patricide(E)
& qtd2 = D
& relation(D,of,qtd3)
& parent(D)
& qtd0 = C
& relation(C,of,qtd2)
& parent(C)
& qtd1 = B
& relation(B,of,qtd2)
& parent(B)
& qtd1 = A
& relation(A,of,qtd0)
& parent(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',background) ).
fof(f0_nnf,plain,
? [A,B,C,D,E] :
( ! [F] :
( qtd3 != F
| ~ patricide(F) )
& qtd0 = E
& patricide(E)
& qtd2 = D
& relation(D,of,qtd3)
& parent(D)
& qtd0 = C
& relation(C,of,qtd2)
& parent(C)
& qtd1 = B
& relation(B,of,qtd2)
& parent(B)
& qtd1 = A
& relation(A,of,qtd0)
& parent(A) ),
inference(nnf_transformation,[status(thm)],[f0]) ).
fof(f0_sk,plain,
! [F] :
( ( qtd3 != F
| ~ patricide(F) )
& qtd0 = sk4
& patricide(sk4)
& qtd2 = sk3
& relation(sk3,of,qtd3)
& parent(sk3)
& qtd0 = sk2
& relation(sk2,of,qtd2)
& parent(sk2)
& qtd1 = sk1
& relation(sk1,of,qtd2)
& parent(sk1)
& qtd1 = sk0
& relation(sk0,of,qtd0)
& parent(sk0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0,sk1,sk2,sk3,sk4])],[f0_nnf]) ).
cnf(c14,plain,
( qtd3 != X5
| ~ patricide(X5) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(t15,plain,
ifeq(patricide(X1),true,ifeq(qtd3,X1,false,true),true) = true,
inference(equality_encoding,[status(esa)],[c14]) ).
cnf(t22,plain,
ifeq(patricide(X1),true,ifeq(qtd3,X1,false,true),true) = true,
inference(orient,[status(thm)],[t15]) ).
fof(f1,conjecture,
? [A,B,C,D] :
( qtd1 = A
& relation(A,of,B)
& B = C
& relation(C,of,D)
& ~ ? [E] :
( D = E
& patricide(E) )
& $true
& parent(C)
& patricide(B)
& parent(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove) ).
fof(f1_neg,negated_conjecture,
~ ? [A,B,C,D] :
( qtd1 = A
& relation(A,of,B)
& B = C
& relation(C,of,D)
& ~ ? [E] :
( D = E
& patricide(E) )
& $true
& parent(C)
& patricide(B)
& parent(A) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f1_nnf,plain,
! [A,B,C,D] :
( qtd1 != A
| ~ relation(A,of,B)
| B != C
| ~ relation(C,of,D)
| ? [E] :
( D = E
& patricide(E) )
| ~ $true
| ~ parent(C)
| ~ patricide(B)
| ~ parent(A) ),
inference(nnf_transformation,[status(thm)],[f1_neg]) ).
fof(f1_sk,plain,
! [A,B,C,D] :
( qtd1 != A
| ~ relation(A,of,B)
| B != C
| ~ relation(C,of,D)
| ( D = sk5(A,B,C,D)
& patricide(sk5(A,B,C,D)) )
| ~ $true
| ~ parent(C)
| ~ patricide(B)
| ~ parent(A) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk5])],[f1_nnf]) ).
cnf(c15,plain,
( qtd1 != X0
| ~ relation(X0,of,X1)
| X1 != X2
| ~ relation(X2,of,X3)
| patricide(sk5(X0,X1,X2,X3))
| ~ $true
| ~ parent(X2)
| ~ patricide(X1)
| ~ parent(X0) ),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(t16,plain,
ifeq(parent(X1),true,ifeq(patricide(X2),true,ifeq(parent(X3),true,ifeq(relation(X3,of,X4),true,ifeq(X2,X3,ifeq(relation(X1,of,X2),true,ifeq(qtd1,X1,patricide(sk5(X1,X2,X3,X4)),true),true),true),true),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c15]) ).
cnf(t19,plain,
ifeq(parent(X1),true,ifeq(patricide(X2),true,ifeq(parent(X3),true,ifeq(relation(X3,of,X4),true,ifeq(X2,X3,ifeq(relation(X1,of,X2),true,ifeq(qtd1,X1,patricide(sk5(X1,X2,X3,X4)),true),true),true),true),true),true),true) = true,
inference(orient,[status(thm)],[t16]) ).
cnf(c2,plain,
qtd1 = sk0,
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(t0,plain,
sk0 = qtd1,
inference(equality_encoding,[status(esa)],[c2]) ).
cnf(t71,plain,
qtd1 = sk0,
inference(orient,[status(thm)],[t0]) ).
cnf(t660,plain,
ifeq(parent(X1),true,ifeq(patricide(X2),true,ifeq(parent(X3),true,ifeq(relation(X3,of,X4),true,ifeq(X2,X3,ifeq(relation(X1,of,X2),true,ifeq(sk0,X1,patricide(sk5(X1,X2,X3,X4)),true),true),true),true),true),true),true) = true,
inference(step,[status(thm)],[t19,t71]) ).
cnf(t73,plain,
ifeq(parent(X1),true,ifeq(patricide(X2),true,ifeq(parent(X3),true,ifeq(relation(X3,of,X4),true,ifeq(X2,X3,ifeq(relation(X1,of,X2),true,ifeq(sk0,X1,patricide(sk5(X1,X2,X3,X4)),true),true),true),true),true),true),true) = true,
inference(rw,[status(thm)],[t660]) ).
cnf(c5,plain,
qtd1 = sk1,
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(t1,plain,
sk1 = qtd1,
inference(equality_encoding,[status(esa)],[c5]) ).
cnf(t661,plain,
sk1 = sk0,
inference(step,[status(thm)],[t1,t71]) ).
cnf(t74,plain,
sk0 = sk1,
inference(orient,[status(thm)],[t661]) ).
cnf(t674,plain,
ifeq(parent(X1),true,ifeq(patricide(X2),true,ifeq(parent(X3),true,ifeq(relation(X3,of,X4),true,ifeq(X2,X3,ifeq(relation(X1,of,X2),true,ifeq(sk1,X1,patricide(sk5(X1,X2,X3,X4)),true),true),true),true),true),true),true) = true,
inference(step,[status(thm)],[t73,t74]) ).
cnf(t92,plain,
ifeq(parent(X1),true,ifeq(patricide(X2),true,ifeq(parent(X3),true,ifeq(relation(X3,of,X4),true,ifeq(X2,X3,ifeq(relation(X1,of,X2),true,ifeq(sk1,X1,patricide(sk5(X1,X2,X3,X4)),true),true),true),true),true),true),true) = true,
inference(orient,[status(thm)],[t674]) ).
cnf(c10,plain,
relation(sk3,of,qtd3),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(t13,plain,
relation(sk3,of,qtd3) = true,
inference(equality_encoding,[status(esa)],[c10]) ).
cnf(t45,plain,
relation(sk3,of,qtd3) = true,
inference(orient,[status(thm)],[t13]) ).
cnf(t101,plain,
true = ifeq(parent(X1),true,ifeq(patricide(X2),true,ifeq(parent(sk3),true,ifeq(true,true,ifeq(X2,sk3,ifeq(relation(X1,of,X2),true,ifeq(sk1,X1,patricide(sk5(X1,X2,sk3,qtd3)),true),true),true),true),true),true),true),
inference(cp,[status(thm)],[t92,t45]) ).
cnf(c9,plain,
parent(sk3),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(t8,plain,
parent(sk3) = true,
inference(equality_encoding,[status(esa)],[c9]) ).
cnf(t33,plain,
parent(sk3) = true,
inference(orient,[status(thm)],[t8]) ).
cnf(t739,plain,
true = ifeq(parent(X1),true,ifeq(patricide(X2),true,ifeq(true,true,ifeq(true,true,ifeq(X2,sk3,ifeq(relation(X1,of,X2),true,ifeq(sk1,X1,patricide(sk5(X1,X2,sk3,qtd3)),true),true),true),true),true),true),true),
inference(step,[status(thm)],[t101,t33]) ).
cnf(t14,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t18,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t14]) ).
cnf(t740,plain,
true = ifeq(parent(X1),true,ifeq(patricide(X2),true,ifeq(true,true,ifeq(X2,sk3,ifeq(relation(X1,of,X2),true,ifeq(sk1,X1,patricide(sk5(X1,X2,sk3,qtd3)),true),true),true),true),true),true),
inference(step,[status(thm)],[t739,t18]) ).
cnf(t741,plain,
true = ifeq(parent(X1),true,ifeq(patricide(X2),true,ifeq(X2,sk3,ifeq(relation(X1,of,X2),true,ifeq(sk1,X1,patricide(sk5(X1,X2,sk3,qtd3)),true),true),true),true),true),
inference(step,[status(thm)],[t740,t18]) ).
cnf(t188,plain,
ifeq(parent(X1),true,ifeq(patricide(X2),true,ifeq(X2,sk3,ifeq(relation(X1,of,X2),true,ifeq(sk1,X1,patricide(sk5(X1,X2,sk3,qtd3)),true),true),true),true),true) = true,
inference(orient,[status(thm)],[t741]) ).
cnf(c3,plain,
parent(sk1),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(t6,plain,
parent(sk1) = true,
inference(equality_encoding,[status(esa)],[c3]) ).
cnf(t27,plain,
parent(sk1) = true,
inference(orient,[status(thm)],[t6]) ).
cnf(t191,plain,
true = ifeq(true,true,ifeq(patricide(X1),true,ifeq(X1,sk3,ifeq(relation(sk1,of,X1),true,ifeq(sk1,sk1,patricide(sk5(sk1,X1,sk3,qtd3)),true),true),true),true),true),
inference(cp,[status(thm)],[t188,t27]) ).
cnf(t749,plain,
true = ifeq(patricide(X1),true,ifeq(X1,sk3,ifeq(relation(sk1,of,X1),true,ifeq(sk1,sk1,patricide(sk5(sk1,X1,sk3,qtd3)),true),true),true),true),
inference(step,[status(thm)],[t191,t18]) ).
cnf(t750,plain,
true = ifeq(patricide(X1),true,ifeq(X1,sk3,ifeq(relation(sk1,of,X1),true,patricide(sk5(sk1,X1,sk3,qtd3)),true),true),true),
inference(step,[status(thm)],[t749,t18]) ).
cnf(t200,plain,
ifeq(patricide(X1),true,ifeq(X1,sk3,ifeq(relation(sk1,of,X1),true,patricide(sk5(sk1,X1,sk3,qtd3)),true),true),true) = true,
inference(orient,[status(thm)],[t750]) ).
cnf(c1,plain,
relation(sk0,of,qtd0),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(t10,plain,
relation(sk0,of,qtd0) = true,
inference(equality_encoding,[status(esa)],[c1]) ).
cnf(t36,plain,
relation(sk0,of,qtd0) = true,
inference(orient,[status(thm)],[t10]) ).
cnf(t664,plain,
relation(sk1,of,qtd0) = true,
inference(step,[status(thm)],[t36,t74]) ).
cnf(t77,plain,
relation(sk1,of,qtd0) = true,
inference(rw,[status(thm)],[t664]) ).
cnf(c8,plain,
qtd0 = sk2,
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(t2,plain,
sk2 = qtd0,
inference(equality_encoding,[status(esa)],[c8]) ).
cnf(t78,plain,
qtd0 = sk2,
inference(orient,[status(thm)],[t2]) ).
cnf(c13,plain,
qtd0 = sk4,
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(t4,plain,
sk4 = qtd0,
inference(equality_encoding,[status(esa)],[c13]) ).
cnf(t667,plain,
sk4 = sk2,
inference(step,[status(thm)],[t4,t78]) ).
cnf(t82,plain,
sk2 = sk4,
inference(orient,[status(thm)],[t667]) ).
cnf(t668,plain,
qtd0 = sk4,
inference(step,[status(thm)],[t78,t82]) ).
cnf(t83,plain,
qtd0 = sk4,
inference(orient,[status(thm)],[t668]) ).
cnf(t671,plain,
relation(sk1,of,sk4) = true,
inference(step,[status(thm)],[t77,t83]) ).
cnf(t87,plain,
relation(sk1,of,sk4) = true,
inference(orient,[status(thm)],[t671]) ).
cnf(t107,plain,
true = ifeq(parent(sk1),true,ifeq(patricide(sk4),true,ifeq(parent(X1),true,ifeq(relation(X1,of,X2),true,ifeq(sk4,X1,ifeq(true,true,ifeq(sk1,sk1,patricide(sk5(sk1,sk4,X1,X2)),true),true),true),true),true),true),true),
inference(cp,[status(thm)],[t92,t87]) ).
cnf(t675,plain,
true = ifeq(true,true,ifeq(patricide(sk4),true,ifeq(parent(X1),true,ifeq(relation(X1,of,X2),true,ifeq(sk4,X1,ifeq(true,true,ifeq(sk1,sk1,patricide(sk5(sk1,sk4,X1,X2)),true),true),true),true),true),true),true),
inference(step,[status(thm)],[t107,t27]) ).
cnf(t676,plain,
true = ifeq(patricide(sk4),true,ifeq(parent(X1),true,ifeq(relation(X1,of,X2),true,ifeq(sk4,X1,ifeq(true,true,ifeq(sk1,sk1,patricide(sk5(sk1,sk4,X1,X2)),true),true),true),true),true),true),
inference(step,[status(thm)],[t675,t18]) ).
cnf(c12,plain,
patricide(sk4),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(t9,plain,
patricide(sk4) = true,
inference(equality_encoding,[status(esa)],[c12]) ).
cnf(t48,plain,
patricide(sk4) = true,
inference(orient,[status(thm)],[t9]) ).
cnf(t677,plain,
true = ifeq(true,true,ifeq(parent(X1),true,ifeq(relation(X1,of,X2),true,ifeq(sk4,X1,ifeq(true,true,ifeq(sk1,sk1,patricide(sk5(sk1,sk4,X1,X2)),true),true),true),true),true),true),
inference(step,[status(thm)],[t676,t48]) ).
cnf(t678,plain,
true = ifeq(parent(X1),true,ifeq(relation(X1,of,X2),true,ifeq(sk4,X1,ifeq(true,true,ifeq(sk1,sk1,patricide(sk5(sk1,sk4,X1,X2)),true),true),true),true),true),
inference(step,[status(thm)],[t677,t18]) ).
cnf(t679,plain,
true = ifeq(parent(X1),true,ifeq(relation(X1,of,X2),true,ifeq(sk4,X1,ifeq(sk1,sk1,patricide(sk5(sk1,sk4,X1,X2)),true),true),true),true),
inference(step,[status(thm)],[t678,t18]) ).
cnf(t680,plain,
true = ifeq(parent(X1),true,ifeq(relation(X1,of,X2),true,ifeq(sk4,X1,patricide(sk5(sk1,sk4,X1,X2)),true),true),true),
inference(step,[status(thm)],[t679,t18]) ).
cnf(t110,plain,
ifeq(parent(X1),true,ifeq(relation(X1,of,X2),true,ifeq(sk4,X1,patricide(sk5(sk1,sk4,X1,X2)),true),true),true) = true,
inference(orient,[status(thm)],[t680]) ).
cnf(c7,plain,
relation(sk2,of,qtd2),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(t12,plain,
relation(sk2,of,qtd2) = true,
inference(equality_encoding,[status(esa)],[c7]) ).
cnf(t42,plain,
relation(sk2,of,qtd2) = true,
inference(orient,[status(thm)],[t12]) ).
cnf(c11,plain,
qtd2 = sk3,
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(t3,plain,
sk3 = qtd2,
inference(equality_encoding,[status(esa)],[c11]) ).
cnf(t79,plain,
qtd2 = sk3,
inference(orient,[status(thm)],[t3]) ).
cnf(t665,plain,
relation(sk2,of,sk3) = true,
inference(step,[status(thm)],[t42,t79]) ).
cnf(t80,plain,
relation(sk2,of,sk3) = true,
inference(rw,[status(thm)],[t665]) ).
cnf(t672,plain,
relation(sk4,of,sk3) = true,
inference(step,[status(thm)],[t80,t82]) ).
cnf(t88,plain,
relation(sk4,of,sk3) = true,
inference(orient,[status(thm)],[t672]) ).
cnf(t114,plain,
true = ifeq(parent(sk4),true,ifeq(true,true,ifeq(sk4,sk4,patricide(sk5(sk1,sk4,sk4,sk3)),true),true),true),
inference(cp,[status(thm)],[t110,t88]) ).
cnf(c6,plain,
parent(sk2),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(t7,plain,
parent(sk2) = true,
inference(equality_encoding,[status(esa)],[c6]) ).
cnf(t30,plain,
parent(sk2) = true,
inference(orient,[status(thm)],[t7]) ).
cnf(t670,plain,
parent(sk4) = true,
inference(step,[status(thm)],[t30,t82]) ).
cnf(t85,plain,
parent(sk4) = true,
inference(rw,[status(thm)],[t670]) ).
cnf(t86,plain,
parent(sk4) = true,
inference(orient,[status(thm)],[t85]) ).
cnf(t681,plain,
true = ifeq(true,true,ifeq(true,true,ifeq(sk4,sk4,patricide(sk5(sk1,sk4,sk4,sk3)),true),true),true),
inference(step,[status(thm)],[t114,t86]) ).
cnf(t682,plain,
true = ifeq(true,true,ifeq(sk4,sk4,patricide(sk5(sk1,sk4,sk4,sk3)),true),true),
inference(step,[status(thm)],[t681,t18]) ).
cnf(t683,plain,
true = ifeq(sk4,sk4,patricide(sk5(sk1,sk4,sk4,sk3)),true),
inference(step,[status(thm)],[t682,t18]) ).
cnf(t684,plain,
true = patricide(sk5(sk1,sk4,sk4,sk3)),
inference(step,[status(thm)],[t683,t18]) ).
cnf(t119,plain,
patricide(sk5(sk1,sk4,sk4,sk3)) = true,
inference(orient,[status(thm)],[t684]) ).
cnf(t201,plain,
true = ifeq(true,true,ifeq(sk5(sk1,sk4,sk4,sk3),sk3,ifeq(relation(sk1,of,sk5(sk1,sk4,sk4,sk3)),true,patricide(sk5(sk1,sk5(sk1,sk4,sk4,sk3),sk3,qtd3)),true),true),true),
inference(cp,[status(thm)],[t200,t119]) ).
cnf(t756,plain,
true = ifeq(sk5(sk1,sk4,sk4,sk3),sk3,ifeq(relation(sk1,of,sk5(sk1,sk4,sk4,sk3)),true,patricide(sk5(sk1,sk5(sk1,sk4,sk4,sk3),sk3,qtd3)),true),true),
inference(step,[status(thm)],[t201,t18]) ).
cnf(t214,plain,
ifeq(sk5(sk1,sk4,sk4,sk3),sk3,ifeq(relation(sk1,of,sk5(sk1,sk4,sk4,sk3)),true,patricide(sk5(sk1,sk5(sk1,sk4,sk4,sk3),sk3,qtd3)),true),true) = true,
inference(orient,[status(thm)],[t756]) ).
cnf(c16,plain,
( qtd1 != X0
| ~ relation(X0,of,X1)
| X1 != X2
| ~ relation(X2,of,X3)
| X3 = sk5(X0,X1,X2,X3)
| ~ $true
| ~ parent(X2)
| ~ patricide(X1)
| ~ parent(X0) ),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(t17,plain,
ifeq(parent(X1),true,ifeq(patricide(X2),true,ifeq(parent(X3),true,ifeq(relation(X3,of,X4),true,ifeq(X2,X3,ifeq(relation(X1,of,X2),true,ifeq(qtd1,X1,X4,sk5(X1,X2,X3,X4)),sk5(X1,X2,X3,X4)),sk5(X1,X2,X3,X4)),sk5(X1,X2,X3,X4)),sk5(X1,X2,X3,X4)),sk5(X1,X2,X3,X4)),sk5(X1,X2,X3,X4)) = sk5(X1,X2,X3,X4),
inference(equality_encoding,[status(esa)],[c16]) ).
cnf(t51,plain,
ifeq(parent(X1),true,ifeq(patricide(X2),true,ifeq(parent(X3),true,ifeq(relation(X3,of,X4),true,ifeq(X2,X3,ifeq(relation(X1,of,X2),true,ifeq(qtd1,X1,X4,sk5(X1,X2,X3,X4)),sk5(X1,X2,X3,X4)),sk5(X1,X2,X3,X4)),sk5(X1,X2,X3,X4)),sk5(X1,X2,X3,X4)),sk5(X1,X2,X3,X4)),sk5(X1,X2,X3,X4)) = sk5(X1,X2,X3,X4),
inference(orient,[status(thm)],[t17]) ).
cnf(t72,plain,
ifeq(parent(X1),true,ifeq(patricide(X2),true,ifeq(parent(X3),true,ifeq(relation(X3,of,X4),true,ifeq(X2,X3,ifeq(relation(X1,of,X2),true,ifeq(qtd1,X1,X4,sk5(X1,X2,X3,X4)),sk5(X1,X2,X3,X4)),sk5(X1,X2,X3,X4)),sk5(X1,X2,X3,X4)),sk5(X1,X2,X3,X4)),sk5(X1,X2,X3,X4)),sk5(X1,X2,X3,X4)) = sk5(X1,X2,X3,X4),
inference(rw,[status(thm)],[t51]) ).
cnf(t662,plain,
qtd1 = sk1,
inference(step,[status(thm)],[t71,t74]) ).
cnf(t75,plain,
qtd1 = sk1,
inference(orient,[status(thm)],[t662]) ).
cnf(t737,plain,
ifeq(parent(X1),true,ifeq(patricide(X2),true,ifeq(parent(X3),true,ifeq(relation(X3,of,X4),true,ifeq(X2,X3,ifeq(relation(X1,of,X2),true,ifeq(sk1,X1,X4,sk5(X1,X2,X3,X4)),sk5(X1,X2,X3,X4)),sk5(X1,X2,X3,X4)),sk5(X1,X2,X3,X4)),sk5(X1,X2,X3,X4)),sk5(X1,X2,X3,X4)),sk5(X1,X2,X3,X4)) = sk5(X1,X2,X3,X4),
inference(step,[status(thm)],[t72,t75]) ).
cnf(t168,plain,
ifeq(parent(X1),true,ifeq(patricide(X2),true,ifeq(parent(X3),true,ifeq(relation(X3,of,X4),true,ifeq(X2,X3,ifeq(relation(X1,of,X2),true,ifeq(sk1,X1,X4,sk5(X1,X2,X3,X4)),sk5(X1,X2,X3,X4)),sk5(X1,X2,X3,X4)),sk5(X1,X2,X3,X4)),sk5(X1,X2,X3,X4)),sk5(X1,X2,X3,X4)),sk5(X1,X2,X3,X4)) = sk5(X1,X2,X3,X4),
inference(orient,[status(thm)],[t737]) ).
cnf(t181,plain,
sk5(X1,X2,X2,X3) = ifeq(parent(X1),true,ifeq(patricide(X2),true,ifeq(parent(X2),true,ifeq(relation(X2,of,X3),true,ifeq(relation(X1,of,X2),true,ifeq(sk1,X1,X3,sk5(X1,X2,X2,X3)),sk5(X1,X2,X2,X3)),sk5(X1,X2,X2,X3)),sk5(X1,X2,X2,X3)),sk5(X1,X2,X2,X3)),sk5(X1,X2,X2,X3)),
inference(cp,[status(thm)],[t168,t18]) ).
cnf(t428,plain,
ifeq(parent(X1),true,ifeq(patricide(X2),true,ifeq(parent(X2),true,ifeq(relation(X2,of,X3),true,ifeq(relation(X1,of,X2),true,ifeq(sk1,X1,X3,sk5(X1,X2,X2,X3)),sk5(X1,X2,X2,X3)),sk5(X1,X2,X2,X3)),sk5(X1,X2,X2,X3)),sk5(X1,X2,X2,X3)),sk5(X1,X2,X2,X3)) = sk5(X1,X2,X2,X3),
inference(orient,[status(thm)],[t181]) ).
cnf(t445,plain,
sk5(sk1,X1,X1,X2) = ifeq(parent(sk1),true,ifeq(patricide(X1),true,ifeq(parent(X1),true,ifeq(relation(X1,of,X2),true,ifeq(relation(sk1,of,X1),true,X2,sk5(sk1,X1,X1,X2)),sk5(sk1,X1,X1,X2)),sk5(sk1,X1,X1,X2)),sk5(sk1,X1,X1,X2)),sk5(sk1,X1,X1,X2)),
inference(cp,[status(thm)],[t428,t18]) ).
cnf(t863,plain,
sk5(sk1,X1,X1,X2) = ifeq(true,true,ifeq(patricide(X1),true,ifeq(parent(X1),true,ifeq(relation(X1,of,X2),true,ifeq(relation(sk1,of,X1),true,X2,sk5(sk1,X1,X1,X2)),sk5(sk1,X1,X1,X2)),sk5(sk1,X1,X1,X2)),sk5(sk1,X1,X1,X2)),sk5(sk1,X1,X1,X2)),
inference(step,[status(thm)],[t445,t27]) ).
cnf(t864,plain,
sk5(sk1,X1,X1,X2) = ifeq(patricide(X1),true,ifeq(parent(X1),true,ifeq(relation(X1,of,X2),true,ifeq(relation(sk1,of,X1),true,X2,sk5(sk1,X1,X1,X2)),sk5(sk1,X1,X1,X2)),sk5(sk1,X1,X1,X2)),sk5(sk1,X1,X1,X2)),
inference(step,[status(thm)],[t863,t18]) ).
cnf(t446,plain,
ifeq(patricide(X1),true,ifeq(parent(X1),true,ifeq(relation(X1,of,X2),true,ifeq(relation(sk1,of,X1),true,X2,sk5(sk1,X1,X1,X2)),sk5(sk1,X1,X1,X2)),sk5(sk1,X1,X1,X2)),sk5(sk1,X1,X1,X2)) = sk5(sk1,X1,X1,X2),
inference(orient,[status(thm)],[t864]) ).
cnf(t452,plain,
sk5(sk1,sk4,sk4,sk3) = ifeq(patricide(sk4),true,ifeq(parent(sk4),true,ifeq(true,true,ifeq(relation(sk1,of,sk4),true,sk3,sk5(sk1,sk4,sk4,sk3)),sk5(sk1,sk4,sk4,sk3)),sk5(sk1,sk4,sk4,sk3)),sk5(sk1,sk4,sk4,sk3)),
inference(cp,[status(thm)],[t446,t88]) ).
cnf(t865,plain,
sk5(sk1,sk4,sk4,sk3) = ifeq(true,true,ifeq(parent(sk4),true,ifeq(true,true,ifeq(relation(sk1,of,sk4),true,sk3,sk5(sk1,sk4,sk4,sk3)),sk5(sk1,sk4,sk4,sk3)),sk5(sk1,sk4,sk4,sk3)),sk5(sk1,sk4,sk4,sk3)),
inference(step,[status(thm)],[t452,t48]) ).
cnf(t866,plain,
sk5(sk1,sk4,sk4,sk3) = ifeq(parent(sk4),true,ifeq(true,true,ifeq(relation(sk1,of,sk4),true,sk3,sk5(sk1,sk4,sk4,sk3)),sk5(sk1,sk4,sk4,sk3)),sk5(sk1,sk4,sk4,sk3)),
inference(step,[status(thm)],[t865,t18]) ).
cnf(t867,plain,
sk5(sk1,sk4,sk4,sk3) = ifeq(true,true,ifeq(true,true,ifeq(relation(sk1,of,sk4),true,sk3,sk5(sk1,sk4,sk4,sk3)),sk5(sk1,sk4,sk4,sk3)),sk5(sk1,sk4,sk4,sk3)),
inference(step,[status(thm)],[t866,t86]) ).
cnf(t868,plain,
sk5(sk1,sk4,sk4,sk3) = ifeq(true,true,ifeq(relation(sk1,of,sk4),true,sk3,sk5(sk1,sk4,sk4,sk3)),sk5(sk1,sk4,sk4,sk3)),
inference(step,[status(thm)],[t867,t18]) ).
cnf(t869,plain,
sk5(sk1,sk4,sk4,sk3) = ifeq(relation(sk1,of,sk4),true,sk3,sk5(sk1,sk4,sk4,sk3)),
inference(step,[status(thm)],[t868,t18]) ).
cnf(t870,plain,
sk5(sk1,sk4,sk4,sk3) = ifeq(true,true,sk3,sk5(sk1,sk4,sk4,sk3)),
inference(step,[status(thm)],[t869,t87]) ).
cnf(t871,plain,
sk5(sk1,sk4,sk4,sk3) = sk3,
inference(step,[status(thm)],[t870,t18]) ).
cnf(t458,plain,
sk5(sk1,sk4,sk4,sk3) = sk3,
inference(orient,[status(thm)],[t871]) ).
cnf(t884,plain,
ifeq(sk3,sk3,ifeq(relation(sk1,of,sk5(sk1,sk4,sk4,sk3)),true,patricide(sk5(sk1,sk5(sk1,sk4,sk4,sk3),sk3,qtd3)),true),true) = true,
inference(step,[status(thm)],[t214,t458]) ).
cnf(t885,plain,
ifeq(relation(sk1,of,sk5(sk1,sk4,sk4,sk3)),true,patricide(sk5(sk1,sk5(sk1,sk4,sk4,sk3),sk3,qtd3)),true) = true,
inference(step,[status(thm)],[t884,t18]) ).
cnf(t886,plain,
ifeq(relation(sk1,of,sk3),true,patricide(sk5(sk1,sk5(sk1,sk4,sk4,sk3),sk3,qtd3)),true) = true,
inference(step,[status(thm)],[t885,t458]) ).
cnf(c4,plain,
relation(sk1,of,qtd2),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(t11,plain,
relation(sk1,of,qtd2) = true,
inference(equality_encoding,[status(esa)],[c4]) ).
cnf(t39,plain,
relation(sk1,of,qtd2) = true,
inference(orient,[status(thm)],[t11]) ).
cnf(t666,plain,
relation(sk1,of,sk3) = true,
inference(step,[status(thm)],[t39,t79]) ).
cnf(t81,plain,
relation(sk1,of,sk3) = true,
inference(rw,[status(thm)],[t666]) ).
cnf(t89,plain,
relation(sk1,of,sk3) = true,
inference(orient,[status(thm)],[t81]) ).
cnf(t887,plain,
ifeq(true,true,patricide(sk5(sk1,sk5(sk1,sk4,sk4,sk3),sk3,qtd3)),true) = true,
inference(step,[status(thm)],[t886,t89]) ).
cnf(t888,plain,
patricide(sk5(sk1,sk5(sk1,sk4,sk4,sk3),sk3,qtd3)) = true,
inference(step,[status(thm)],[t887,t18]) ).
cnf(t889,plain,
patricide(sk5(sk1,sk3,sk3,qtd3)) = true,
inference(step,[status(thm)],[t888,t458]) ).
cnf(t489,plain,
patricide(sk5(sk1,sk3,sk3,qtd3)) = true,
inference(rw,[status(thm)],[t889]) ).
cnf(t585,plain,
patricide(sk5(sk1,sk3,sk3,qtd3)) = true,
inference(orient,[status(thm)],[t489]) ).
cnf(t586,plain,
true = ifeq(true,true,ifeq(qtd3,sk5(sk1,sk3,sk3,qtd3),false,true),true),
inference(cp,[status(thm)],[t22,t585]) ).
cnf(t1058,plain,
true = ifeq(qtd3,sk5(sk1,sk3,sk3,qtd3),false,true),
inference(step,[status(thm)],[t586,t18]) ).
cnf(t626,plain,
ifeq(qtd3,sk5(sk1,sk3,sk3,qtd3),false,true) = true,
inference(orient,[status(thm)],[t1058]) ).
cnf(t453,plain,
sk5(sk1,sk3,sk3,qtd3) = ifeq(patricide(sk3),true,ifeq(parent(sk3),true,ifeq(true,true,ifeq(relation(sk1,of,sk3),true,qtd3,sk5(sk1,sk3,sk3,qtd3)),sk5(sk1,sk3,sk3,qtd3)),sk5(sk1,sk3,sk3,qtd3)),sk5(sk1,sk3,sk3,qtd3)),
inference(cp,[status(thm)],[t446,t45]) ).
cnf(t111,plain,
true = ifeq(true,true,ifeq(relation(sk4,of,X1),true,ifeq(sk4,sk4,patricide(sk5(sk1,sk4,sk4,X1)),true),true),true),
inference(cp,[status(thm)],[t110,t86]) ).
cnf(t695,plain,
true = ifeq(relation(sk4,of,X1),true,ifeq(sk4,sk4,patricide(sk5(sk1,sk4,sk4,X1)),true),true),
inference(step,[status(thm)],[t111,t18]) ).
cnf(t696,plain,
true = ifeq(relation(sk4,of,X1),true,patricide(sk5(sk1,sk4,sk4,X1)),true),
inference(step,[status(thm)],[t695,t18]) ).
cnf(t126,plain,
ifeq(relation(sk4,of,X1),true,patricide(sk5(sk1,sk4,sk4,X1)),true) = true,
inference(orient,[status(thm)],[t696]) ).
cnf(t459,plain,
true = ifeq(relation(sk4,of,sk3),true,patricide(sk3),true),
inference(cp,[status(thm)],[t126,t458]) ).
cnf(t1016,plain,
true = ifeq(true,true,patricide(sk3),true),
inference(step,[status(thm)],[t459,t88]) ).
cnf(t1017,plain,
true = patricide(sk3),
inference(step,[status(thm)],[t1016,t18]) ).
cnf(t523,plain,
patricide(sk3) = true,
inference(orient,[status(thm)],[t1017]) ).
cnf(t1059,plain,
sk5(sk1,sk3,sk3,qtd3) = ifeq(true,true,ifeq(parent(sk3),true,ifeq(true,true,ifeq(relation(sk1,of,sk3),true,qtd3,sk5(sk1,sk3,sk3,qtd3)),sk5(sk1,sk3,sk3,qtd3)),sk5(sk1,sk3,sk3,qtd3)),sk5(sk1,sk3,sk3,qtd3)),
inference(step,[status(thm)],[t453,t523]) ).
cnf(t1060,plain,
sk5(sk1,sk3,sk3,qtd3) = ifeq(parent(sk3),true,ifeq(true,true,ifeq(relation(sk1,of,sk3),true,qtd3,sk5(sk1,sk3,sk3,qtd3)),sk5(sk1,sk3,sk3,qtd3)),sk5(sk1,sk3,sk3,qtd3)),
inference(step,[status(thm)],[t1059,t18]) ).
cnf(t1061,plain,
sk5(sk1,sk3,sk3,qtd3) = ifeq(true,true,ifeq(true,true,ifeq(relation(sk1,of,sk3),true,qtd3,sk5(sk1,sk3,sk3,qtd3)),sk5(sk1,sk3,sk3,qtd3)),sk5(sk1,sk3,sk3,qtd3)),
inference(step,[status(thm)],[t1060,t33]) ).
cnf(t1062,plain,
sk5(sk1,sk3,sk3,qtd3) = ifeq(true,true,ifeq(relation(sk1,of,sk3),true,qtd3,sk5(sk1,sk3,sk3,qtd3)),sk5(sk1,sk3,sk3,qtd3)),
inference(step,[status(thm)],[t1061,t18]) ).
cnf(t1063,plain,
sk5(sk1,sk3,sk3,qtd3) = ifeq(relation(sk1,of,sk3),true,qtd3,sk5(sk1,sk3,sk3,qtd3)),
inference(step,[status(thm)],[t1062,t18]) ).
cnf(t1064,plain,
sk5(sk1,sk3,sk3,qtd3) = ifeq(true,true,qtd3,sk5(sk1,sk3,sk3,qtd3)),
inference(step,[status(thm)],[t1063,t89]) ).
cnf(t1065,plain,
sk5(sk1,sk3,sk3,qtd3) = qtd3,
inference(step,[status(thm)],[t1064,t18]) ).
cnf(t631,plain,
sk5(sk1,sk3,sk3,qtd3) = qtd3,
inference(orient,[status(thm)],[t1065]) ).
cnf(t1066,plain,
ifeq(qtd3,qtd3,false,true) = true,
inference(step,[status(thm)],[t626,t631]) ).
cnf(t1067,plain,
false = true,
inference(step,[status(thm)],[t1066,t18]) ).
cnf(t653,plain,
false = true,
inference(rw,[status(thm)],[t1067]) ).
cnf(t655,plain,
false = true,
inference(orient,[status(thm)],[t653]) ).
cnf(goal_0,negated_conjecture,
true != false,
inference(equality_encoding,[status(esa)],[c14]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t655]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : PUZ128+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.09/0.36 % Computer : n018.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Thu Sep 24 07:01:48 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 6.22/1.22 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 6.22/1.22 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------