%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET651+3 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n026.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 : Sun Sep 27 08:36:44 AM UTC 2026
% Result : Theorem 0.38s 0.63s
% Output : CNFRefutation 0.38s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 15
% Syntax : Number of formulae : 97 ( 21 unt; 0 def)
% Number of atoms : 335 ( 0 equ)
% Maximal formula atoms : 18 ( 3 avg)
% Number of connectives : 402 ( 164 ~; 160 |; 26 &)
% ( 6 <=>; 46 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 6 con; 0-2 aty)
% Number of variables : 198 ( 11 sgn 56 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(p1,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ! [D] :
( ilf_type(D,set_type)
=> ( ( subset(C,D)
& subset(B,C) )
=> subset(B,D) ) ) ) ),
file('theBenchmark.p',p1) ).
fof(p2,axiom,
! [B] :
( ilf_type(B,binary_relation_type)
=> subset(B,cross_product(domain_of(B),range_of(B))) ),
file('theBenchmark.p',p2) ).
fof(p3,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ! [D] :
( ilf_type(D,set_type)
=> ! [E] :
( ilf_type(E,set_type)
=> ( ( subset(D,E)
& subset(B,C) )
=> subset(cross_product(B,D),cross_product(C,E)) ) ) ) ) ),
file('theBenchmark.p',p3) ).
fof(p4,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ( ! [E] :
( ilf_type(E,relation_type(B,C))
=> ilf_type(E,subset_type(cross_product(B,C))) )
& ! [D] :
( ilf_type(D,subset_type(cross_product(B,C)))
=> ilf_type(D,relation_type(B,C)) ) ) ) ),
file('theBenchmark.p',p4) ).
fof(p6,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ! [D] :
( ilf_type(D,relation_type(B,C))
=> ( subset(range_of(D),C)
& subset(domain_of(D),B) ) ) ) ),
file('theBenchmark.p',p6) ).
fof(p9,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ( subset(B,C)
<=> ! [D] :
( ilf_type(D,set_type)
=> ( member(D,B)
=> member(D,C) ) ) ) ) ),
file('theBenchmark.p',p9) ).
fof(p13,axiom,
! [B] :
( ilf_type(B,set_type)
=> ( ilf_type(B,binary_relation_type)
<=> ( ilf_type(B,set_type)
& relation_like(B) ) ) ),
file('theBenchmark.p',p13) ).
fof(p15,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ( ilf_type(C,subset_type(B))
<=> ilf_type(C,member_type(power_set(B))) ) ) ),
file('theBenchmark.p',p15) ).
fof(p18,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ( member(B,power_set(C))
<=> ! [D] :
( ilf_type(D,set_type)
=> ( member(D,B)
=> member(D,C) ) ) ) ) ),
file('theBenchmark.p',p18) ).
fof(p19,axiom,
! [B] :
( ilf_type(B,set_type)
=> ( ilf_type(power_set(B),set_type)
& ~ empty(power_set(B)) ) ),
file('theBenchmark.p',p19) ).
fof(p20,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ( ilf_type(C,set_type)
& ~ empty(C) )
=> ( ilf_type(B,member_type(C))
<=> member(B,C) ) ) ),
file('theBenchmark.p',p20) ).
fof(p23,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ! [D] :
( ilf_type(D,subset_type(cross_product(B,C)))
=> relation_like(D) ) ) ),
file('theBenchmark.p',p23) ).
fof(p24,axiom,
! [B] :
( ilf_type(B,set_type)
=> ( empty(B)
<=> ! [C] :
( ilf_type(C,set_type)
=> ~ member(C,B) ) ) ),
file('theBenchmark.p',p24) ).
fof(p26,axiom,
! [B] : ilf_type(B,set_type),
file('theBenchmark.p',p26) ).
fof(prove_relset_1_13,conjecture,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ! [D] :
( ilf_type(D,set_type)
=> ! [E] :
( ilf_type(E,relation_type(B,D))
=> ( subset(domain_of(E),C)
=> ilf_type(E,relation_type(C,D)) ) ) ) ) ),
file('theBenchmark.p',prove_relset_1_13) ).
fof(prove_relset_1_13_neg,negated_conjecture,
~ ! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ! [D] :
( ilf_type(D,set_type)
=> ! [E] :
( ilf_type(E,relation_type(B,D))
=> ( subset(domain_of(E),C)
=> ilf_type(E,relation_type(C,D)) ) ) ) ) ),
inference(assume_negation,[status(cth)],[prove_relset_1_13]) ).
cnf(c_28,plain,
( ~ relation_like(A)
| ilf_type(A,binary_relation_type)
| ~ ilf_type(A,set_type) ),
inference(clausify,[status(thm)],[p13]) ).
cnf(c_36,plain,
( relation_like(C)
| ~ ilf_type(C,subset_type(cross_product(A,B)))
| ~ ilf_type(B,set_type)
| ~ ilf_type(A,set_type) ),
inference(clausify,[status(thm)],[p23]) ).
cnf(c_42,plain,
( ilf_type(C,binary_relation_type)
| ~ ilf_type(C,set_type)
| ~ ilf_type(C,subset_type(cross_product(A,B)))
| ~ ilf_type(B,set_type)
| ~ ilf_type(A,set_type) ),
inference(resolve,[status(thm)],[c_36,c_28]) ).
fof(nnf_27,plain,
? [B] :
( ? [C] :
( ? [D] :
( ? [E] :
( ~ ilf_type(E,relation_type(C,D))
& subset(domain_of(E),C)
& ilf_type(E,relation_type(B,D)) )
& ilf_type(D,set_type) )
& ilf_type(C,set_type) )
& ilf_type(B,set_type) ),
inference(fof_nnf,[status(thm)],[prove_relset_1_13_neg]) ).
fof(sk_prove_relset_1_13_neg,plain,
( ~ ilf_type(sK0,relation_type(sK1,sK2))
& subset(domain_of(sK0),sK1)
& ilf_type(sK0,relation_type(sK3,sK2))
& ilf_type(sK2,set_type)
& ilf_type(sK1,set_type)
& ilf_type(sK3,set_type) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3,sK1,sK2,sK0]),skolemize(B,sK3),skolemize(C,sK1),skolemize(D,sK2),skolemize(E,sK0)],[nnf_27]) ).
cnf(c_54,negated_conjecture,
~ ilf_type(sK0,relation_type(sK1,sK2)),
inference(split_conjunct,[status(thm)],[sk_prove_relset_1_13_neg]) ).
cnf(c_55,negated_conjecture,
subset(domain_of(sK0),sK1),
inference(split_conjunct,[status(thm)],[sk_prove_relset_1_13_neg]) ).
cnf(c_56,negated_conjecture,
ilf_type(sK0,relation_type(sK3,sK2)),
inference(split_conjunct,[status(thm)],[sk_prove_relset_1_13_neg]) ).
cnf(c_60,plain,
ilf_type(A,set_type),
inference(clausify,[status(thm)],[p26]) ).
cnf(c_64,plain,
( ~ member(B,A)
| ~ ilf_type(B,set_type)
| ~ empty(A)
| ~ ilf_type(A,set_type) ),
inference(clausify,[status(thm)],[p24]) ).
cnf(c_1181,plain,
( ~ member(B,A)
| ~ ilf_type(B,set_type)
| ~ empty(A) ),
inference(resolve,[status(thm)],[c_60,c_64]) ).
cnf(c_65,plain,
( ~ member(B,A)
| ~ empty(A) ),
inference(resolve,[status(thm)],[c_60,c_1181]) ).
cnf(c_68,plain,
( ~ member(A,B)
| ilf_type(A,member_type(B))
| ~ ilf_type(B,set_type)
| empty(B)
| ~ ilf_type(A,set_type) ),
inference(clausify,[status(thm)],[p20]) ).
cnf(c_1182,plain,
( ~ member(B,A)
| ilf_type(B,member_type(A))
| ~ ilf_type(A,set_type)
| empty(A) ),
inference(resolve,[status(thm)],[c_60,c_68]) ).
cnf(c_69,plain,
( ~ member(B,A)
| ilf_type(B,member_type(A))
| empty(A) ),
inference(resolve,[status(thm)],[c_60,c_1182]) ).
cnf(c_70,plain,
( member(A,B)
| ~ ilf_type(A,member_type(B))
| ~ ilf_type(B,set_type)
| empty(B)
| ~ ilf_type(A,set_type) ),
inference(clausify,[status(thm)],[p20]) ).
cnf(c_1183,plain,
( member(B,A)
| ~ ilf_type(B,member_type(A))
| ~ ilf_type(A,set_type)
| empty(A) ),
inference(resolve,[status(thm)],[c_60,c_70]) ).
cnf(c_71,plain,
( member(B,A)
| ~ ilf_type(B,member_type(A))
| empty(A) ),
inference(resolve,[status(thm)],[c_60,c_1183]) ).
cnf(c_73,plain,
( ~ empty(power_set(A))
| ~ ilf_type(A,set_type) ),
inference(clausify,[status(thm)],[p19]) ).
cnf(c_74,plain,
~ empty(power_set(A)),
inference(resolve,[status(thm)],[c_60,c_73]) ).
fof(nnf_18,plain,
! [B] :
( ! [C] :
( ( ( ? [D] :
( ~ member(D,C)
& member(D,B)
& ilf_type(D,set_type) )
| member(B,power_set(C)) )
& ( ! [X0] :
( member(X0,C)
| ~ member(X0,B)
| ~ ilf_type(X0,set_type) )
| ~ member(B,power_set(C)) ) )
| ~ ilf_type(C,set_type) )
| ~ ilf_type(B,set_type) ),
inference(fof_nnf,[status(thm)],[p18]) ).
fof(sk_p18_sk,plain,
! [B] :
( ! [C] :
( ( ( ( ~ member(sK4(B,C),C)
& member(sK4(B,C),B)
& ilf_type(sK4(B,C),set_type) )
| member(B,power_set(C)) )
& ( ! [X0] :
( member(X0,C)
| ~ member(X0,B)
| ~ ilf_type(X0,set_type) )
| ~ member(B,power_set(C)) ) )
| ~ ilf_type(C,set_type) )
| ~ ilf_type(B,set_type) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(D,sK4(B,C))],[nnf_18]) ).
fof(sk_p18,plain,
( ! [VAR_0,VAR_1] :
( ~ member(sK4(VAR_0,VAR_1),VAR_1)
| member(VAR_0,power_set(VAR_1))
| ~ ilf_type(VAR_1,set_type)
| ~ ilf_type(VAR_0,set_type) )
& ! [VAR_0,VAR_1] :
( member(sK4(VAR_0,VAR_1),VAR_0)
| member(VAR_0,power_set(VAR_1))
| ~ ilf_type(VAR_1,set_type)
| ~ ilf_type(VAR_0,set_type) )
& ! [VAR_0,VAR_1] :
( ilf_type(sK4(VAR_0,VAR_1),set_type)
| member(VAR_0,power_set(VAR_1))
| ~ ilf_type(VAR_1,set_type)
| ~ ilf_type(VAR_0,set_type) )
& ! [VAR_0,VAR_1,VAR_2] :
( member(VAR_2,VAR_1)
| ~ member(VAR_2,VAR_0)
| ~ ilf_type(VAR_2,set_type)
| ~ member(VAR_0,power_set(VAR_1))
| ~ ilf_type(VAR_1,set_type)
| ~ ilf_type(VAR_0,set_type) ) ),
inference(cnf_transformation,[status(thm)],[sk_p18_sk]) ).
cnf(c_75,plain,
( ~ member(sK4(A,B),B)
| member(A,power_set(B))
| ~ ilf_type(B,set_type)
| ~ ilf_type(A,set_type) ),
inference(split_conjunct,[status(thm)],[sk_p18]) ).
cnf(c_1184,plain,
( ~ member(sK4(B,A),A)
| member(B,power_set(A))
| ~ ilf_type(A,set_type) ),
inference(resolve,[status(thm)],[c_60,c_75]) ).
cnf(c_76,plain,
( ~ member(sK4(A,B),B)
| member(A,power_set(B)) ),
inference(resolve,[status(thm)],[c_60,c_1184]) ).
cnf(c_77,plain,
( member(sK4(A,B),A)
| member(A,power_set(B))
| ~ ilf_type(B,set_type)
| ~ ilf_type(A,set_type) ),
inference(split_conjunct,[status(thm)],[sk_p18]) ).
cnf(c_1185,plain,
( member(sK4(B,A),B)
| member(B,power_set(A))
| ~ ilf_type(A,set_type) ),
inference(resolve,[status(thm)],[c_60,c_77]) ).
cnf(c_78,plain,
( member(sK4(A,B),A)
| member(A,power_set(B)) ),
inference(resolve,[status(thm)],[c_60,c_1185]) ).
cnf(c_86,plain,
( ~ ilf_type(B,member_type(power_set(A)))
| ilf_type(B,subset_type(A))
| ~ ilf_type(B,set_type)
| ~ ilf_type(A,set_type) ),
inference(clausify,[status(thm)],[p15]) ).
cnf(c_1186,plain,
( ~ ilf_type(A,member_type(power_set(B)))
| ilf_type(A,subset_type(B))
| ~ ilf_type(A,set_type) ),
inference(resolve,[status(thm)],[c_60,c_86]) ).
cnf(c_87,plain,
( ~ ilf_type(A,member_type(power_set(B)))
| ilf_type(A,subset_type(B)) ),
inference(resolve,[status(thm)],[c_60,c_1186]) ).
cnf(c_98,plain,
( member(C,B)
| ~ member(C,A)
| ~ ilf_type(C,set_type)
| ~ subset(A,B)
| ~ ilf_type(B,set_type)
| ~ ilf_type(A,set_type) ),
inference(clausify,[status(thm)],[p9]) ).
cnf(c_1187,plain,
( member(C,A)
| ~ member(C,B)
| ~ ilf_type(C,set_type)
| ~ subset(B,A)
| ~ ilf_type(A,set_type) ),
inference(resolve,[status(thm)],[c_60,c_98]) ).
cnf(c_1188,plain,
( member(C,B)
| ~ member(C,A)
| ~ ilf_type(C,set_type)
| ~ subset(A,B) ),
inference(resolve,[status(thm)],[c_60,c_1187]) ).
cnf(c_99,plain,
( member(C,B)
| ~ member(C,A)
| ~ subset(A,B) ),
inference(resolve,[status(thm)],[c_60,c_1188]) ).
cnf(c_105,plain,
( subset(range_of(C),B)
| ~ ilf_type(C,relation_type(A,B))
| ~ ilf_type(B,set_type)
| ~ ilf_type(A,set_type) ),
inference(clausify,[status(thm)],[p6]) ).
cnf(c_1189,plain,
( subset(range_of(B),A)
| ~ ilf_type(B,relation_type(C,A))
| ~ ilf_type(A,set_type) ),
inference(resolve,[status(thm)],[c_60,c_105]) ).
cnf(c_106,plain,
( subset(range_of(A),C)
| ~ ilf_type(A,relation_type(B,C)) ),
inference(resolve,[status(thm)],[c_60,c_1189]) ).
cnf(c_111,plain,
( ilf_type(C,subset_type(cross_product(A,B)))
| ~ ilf_type(C,relation_type(A,B))
| ~ ilf_type(B,set_type)
| ~ ilf_type(A,set_type) ),
inference(clausify,[status(thm)],[p4]) ).
cnf(c_1190,plain,
( ilf_type(B,subset_type(cross_product(C,A)))
| ~ ilf_type(B,relation_type(C,A))
| ~ ilf_type(A,set_type) ),
inference(resolve,[status(thm)],[c_60,c_111]) ).
cnf(c_112,plain,
( ilf_type(A,subset_type(cross_product(B,C)))
| ~ ilf_type(A,relation_type(B,C)) ),
inference(resolve,[status(thm)],[c_60,c_1190]) ).
cnf(c_113,plain,
( ilf_type(C,relation_type(A,B))
| ~ ilf_type(C,subset_type(cross_product(A,B)))
| ~ ilf_type(B,set_type)
| ~ ilf_type(A,set_type) ),
inference(clausify,[status(thm)],[p4]) ).
cnf(c_1191,plain,
( ilf_type(B,relation_type(C,A))
| ~ ilf_type(B,subset_type(cross_product(C,A)))
| ~ ilf_type(A,set_type) ),
inference(resolve,[status(thm)],[c_60,c_113]) ).
cnf(c_114,plain,
( ilf_type(A,relation_type(B,C))
| ~ ilf_type(A,subset_type(cross_product(B,C))) ),
inference(resolve,[status(thm)],[c_60,c_1191]) ).
cnf(c_115,plain,
( subset(cross_product(A,C),cross_product(B,D))
| ~ subset(C,D)
| ~ subset(A,B)
| ~ ilf_type(D,set_type)
| ~ ilf_type(C,set_type)
| ~ ilf_type(B,set_type)
| ~ ilf_type(A,set_type) ),
inference(clausify,[status(thm)],[p3]) ).
cnf(c_1192,plain,
( subset(cross_product(D,B),cross_product(A,C))
| ~ subset(B,C)
| ~ subset(D,A)
| ~ ilf_type(C,set_type)
| ~ ilf_type(B,set_type)
| ~ ilf_type(A,set_type) ),
inference(resolve,[status(thm)],[c_60,c_115]) ).
cnf(c_1193,plain,
( subset(cross_product(C,A),cross_product(D,B))
| ~ subset(A,B)
| ~ subset(C,D)
| ~ ilf_type(B,set_type)
| ~ ilf_type(A,set_type) ),
inference(resolve,[status(thm)],[c_60,c_1192]) ).
cnf(c_1194,plain,
( subset(cross_product(B,D),cross_product(C,A))
| ~ subset(D,A)
| ~ subset(B,C)
| ~ ilf_type(A,set_type) ),
inference(resolve,[status(thm)],[c_60,c_1193]) ).
cnf(c_116,plain,
( subset(cross_product(A,C),cross_product(B,D))
| ~ subset(C,D)
| ~ subset(A,B) ),
inference(resolve,[status(thm)],[c_60,c_1194]) ).
cnf(c_117,plain,
( subset(A,cross_product(domain_of(A),range_of(A)))
| ~ ilf_type(A,binary_relation_type) ),
inference(clausify,[status(thm)],[p2]) ).
cnf(c_118,plain,
( subset(A,C)
| ~ subset(B,C)
| ~ subset(A,B)
| ~ ilf_type(C,set_type)
| ~ ilf_type(B,set_type)
| ~ ilf_type(A,set_type) ),
inference(clausify,[status(thm)],[p1]) ).
cnf(c_1195,plain,
( subset(C,B)
| ~ subset(A,B)
| ~ subset(C,A)
| ~ ilf_type(B,set_type)
| ~ ilf_type(A,set_type) ),
inference(resolve,[status(thm)],[c_60,c_118]) ).
cnf(c_1196,plain,
( subset(B,A)
| ~ subset(C,A)
| ~ subset(B,C)
| ~ ilf_type(A,set_type) ),
inference(resolve,[status(thm)],[c_60,c_1195]) ).
cnf(c_119,plain,
( subset(A,C)
| ~ subset(B,C)
| ~ subset(A,B) ),
inference(resolve,[status(thm)],[c_60,c_1196]) ).
cnf(c_1197,plain,
( ilf_type(B,binary_relation_type)
| ~ ilf_type(B,set_type)
| ~ ilf_type(B,subset_type(cross_product(C,A)))
| ~ ilf_type(A,set_type) ),
inference(resolve,[status(thm)],[c_60,c_42]) ).
cnf(c_1198,plain,
( ilf_type(A,binary_relation_type)
| ~ ilf_type(A,set_type)
| ~ ilf_type(A,subset_type(cross_product(B,C))) ),
inference(resolve,[status(thm)],[c_60,c_1197]) ).
cnf(c_146,plain,
( ilf_type(A,binary_relation_type)
| ~ ilf_type(A,subset_type(cross_product(B,C))) ),
inference(resolve,[status(thm)],[c_60,c_1198]) ).
cnf(c_153,plain,
( ilf_type(sK4(A,B),member_type(A))
| empty(A)
| member(A,power_set(B)) ),
inference(resolve,[status(thm)],[c_78,c_69]) ).
cnf(c_154,plain,
( ~ empty(A)
| member(A,power_set(B)) ),
inference(resolve,[status(thm)],[c_78,c_65]) ).
cnf(c_166,plain,
subset(range_of(sK0),sK2),
inference(resolve,[status(thm)],[c_106,c_56]) ).
cnf(c_171,plain,
ilf_type(sK0,subset_type(cross_product(sK3,sK2))),
inference(resolve,[status(thm)],[c_112,c_56]) ).
cnf(c_173,negated_conjecture,
~ ilf_type(sK0,subset_type(cross_product(sK1,sK2))),
inference(resolve,[status(thm)],[c_114,c_54]) ).
cnf(c_176,plain,
( subset(cross_product(domain_of(sK0),A),cross_product(sK1,B))
| ~ subset(A,B) ),
inference(resolve,[status(thm)],[c_116,c_55]) ).
cnf(c_201,plain,
~ ilf_type(sK0,member_type(power_set(cross_product(sK1,sK2)))),
inference(resolve,[status(thm)],[c_87,c_173]) ).
cnf(c_1199,plain,
( ~ member(A,power_set(B))
| ilf_type(A,member_type(power_set(B))) ),
inference(resolve,[status(thm)],[c_69,c_74]) ).
cnf(c_202,plain,
~ member(sK0,power_set(cross_product(sK1,sK2))),
inference(resolve,[status(thm)],[c_1199,c_201]) ).
cnf(c_203,plain,
~ member(sK4(sK0,cross_product(sK1,sK2)),cross_product(sK1,sK2)),
inference(resolve,[status(thm)],[c_76,c_202]) ).
cnf(c_247,plain,
~ empty(sK0),
inference(resolve,[status(thm)],[c_154,c_202]) ).
cnf(c_1200,plain,
( ilf_type(sK4(sK0,cross_product(sK1,sK2)),member_type(sK0))
| empty(sK0) ),
inference(resolve,[status(thm)],[c_153,c_202]) ).
cnf(c_252,plain,
ilf_type(sK4(sK0,cross_product(sK1,sK2)),member_type(sK0)),
inference(resolve,[status(thm)],[c_247,c_1200]) ).
cnf(c_331,plain,
ilf_type(sK0,binary_relation_type),
inference(resolve,[status(thm)],[c_171,c_146]) ).
cnf(c_333,plain,
subset(sK0,cross_product(domain_of(sK0),range_of(sK0))),
inference(resolve,[status(thm)],[c_331,c_117]) ).
cnf(c_1201,plain,
( member(sK4(sK0,cross_product(sK1,sK2)),sK0)
| empty(sK0) ),
inference(resolve,[status(thm)],[c_252,c_71]) ).
cnf(c_1140,plain,
member(sK4(sK0,cross_product(sK1,sK2)),sK0),
inference(resolve,[status(thm)],[c_247,c_1201]) ).
cnf(c_1202,plain,
( member(sK4(sK0,cross_product(sK1,sK2)),A)
| ~ subset(sK0,A) ),
inference(resolve,[status(thm)],[c_99,c_1140]) ).
cnf(c_1148,plain,
~ subset(sK0,cross_product(sK1,sK2)),
inference(resolve,[status(thm)],[c_1202,c_203]) ).
cnf(c_1170,plain,
subset(cross_product(domain_of(sK0),range_of(sK0)),cross_product(sK1,sK2)),
inference(resolve,[status(thm)],[c_176,c_166]) ).
cnf(c_1203,plain,
( subset(sK0,A)
| ~ subset(cross_product(domain_of(sK0),range_of(sK0)),A) ),
inference(resolve,[status(thm)],[c_119,c_333]) ).
cnf(c_1204,plain,
~ subset(cross_product(domain_of(sK0),range_of(sK0)),cross_product(sK1,sK2)),
inference(resolve,[status(thm)],[c_1203,c_1148]) ).
cnf(c_1180,plain,
$false,
inference(resolve,[status(thm)],[c_1170,c_1204]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SET651+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.16/0.43 % Computer : n026.cluster.edu
% 0.16/0.43 % Model : x86_64 x86_64
% 0.16/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.43 % Memory : 8046.5625MB
% 0.16/0.43 % OS : Linux 6.8.0-71-generic
% 0.16/0.43 % CPULimit : 300
% 0.16/0.43 % WCLimit : 300
% 0.16/0.43 % DateTime : Sat Sep 26 08:05:26 UTC 2026
% 0.16/0.43 % CPUTime :
% 0.16/0.43 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.16/0.43 % Process 490948 was started by sandbox2 on n026,
% 0.16/0.43 % Sat Sep 26 08:05:26 2026
% 0.16/0.43 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.16/0.45
% 0.16/0.45 % From the command line: assign(max_seconds, 300).
% 0.38/0.63
% 0.38/0.63 % SZS status Theorem for theBenchmark
% 0.38/0.63
% 0.38/0.63 % Proof 1 at 0.10 (+ 0.07) seconds.
% 0.38/0.63 % Length of proof is 67.
% 0.38/0.63 % Level of proof is 10.
% 0.38/0.63 % Maximum clause weight is 18.000.
% 0.38/0.63 % Given clauses 178.
% 0.38/0.63
% 0.38/0.63 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------