%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET685+3 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 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 : Sun Sep 27 08:36:49 AM UTC 2026
% Result : Theorem 0.23s 0.54s
% Output : CNFRefutation 0.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 9
% Syntax : Number of formulae : 76 ( 14 unt; 0 def)
% Number of atoms : 338 ( 6 equ)
% Maximal formula atoms : 22 ( 4 avg)
% Number of connectives : 442 ( 180 ~; 166 |; 58 &)
% ( 5 <=>; 33 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 16 ( 16 usr; 8 con; 0-4 aty)
% Number of variables : 183 ( 12 sgn 57 !; 10 ?)
% Comments :
%------------------------------------------------------------------------------
fof(p1,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ! [D] :
( ilf_type(D,binary_relation_type)
=> ( member(C,image(D,B))
<=> ? [E] :
( member(E,B)
& member(ordered_pair(E,C),D)
& ilf_type(E,set_type) ) ) ) ) ),
file('theBenchmark.p',p1) ).
fof(p2,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)
=> ! [F] :
( ilf_type(F,relation_type(B,C))
=> ( member(ordered_pair(D,E),F)
=> ( member(E,C)
& member(D,B) ) ) ) ) ) ) ),
file('theBenchmark.p',p2) ).
fof(p5,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',p5) ).
fof(p7,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',p7) ).
fof(p15,axiom,
! [B] :
( ilf_type(B,set_type)
=> ( ilf_type(B,binary_relation_type)
<=> ( ilf_type(B,set_type)
& relation_like(B) ) ) ),
file('theBenchmark.p',p15) ).
fof(p24,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',p24) ).
fof(p25,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ! [D] :
( ilf_type(D,relation_type(B,C))
=> ! [E] :
( ilf_type(E,set_type)
=> image4(B,C,D,E) = image(D,E) ) ) ) ),
file('theBenchmark.p',p25) ).
fof(p27,axiom,
! [B] : ilf_type(B,set_type),
file('theBenchmark.p',p27) ).
fof(prove_relset_1_52,conjecture,
! [B] :
( ( ilf_type(B,set_type)
& ~ empty(B) )
=> ! [C] :
( ( ilf_type(C,set_type)
& ~ empty(C) )
=> ! [D] :
( ( ilf_type(D,set_type)
& ~ empty(D) )
=> ! [E] :
( ilf_type(E,relation_type(D,B))
=> ! [F] :
( ilf_type(F,member_type(B))
=> ( member(F,image4(D,B,E,C))
<=> ? [G] :
( member(G,C)
& member(ordered_pair(G,F),E)
& ilf_type(G,member_type(D)) ) ) ) ) ) ) ),
file('theBenchmark.p',prove_relset_1_52) ).
fof(prove_relset_1_52_neg,negated_conjecture,
~ ! [B] :
( ( ilf_type(B,set_type)
& ~ empty(B) )
=> ! [C] :
( ( ilf_type(C,set_type)
& ~ empty(C) )
=> ! [D] :
( ( ilf_type(D,set_type)
& ~ empty(D) )
=> ! [E] :
( ilf_type(E,relation_type(D,B))
=> ! [F] :
( ilf_type(F,member_type(B))
=> ( member(F,image4(D,B,E,C))
<=> ? [G] :
( member(G,C)
& member(ordered_pair(G,F),E)
& ilf_type(G,member_type(D)) ) ) ) ) ) ) ),
inference(assume_negation,[status(cth)],[prove_relset_1_52]) ).
cnf(c_29,plain,
( ~ relation_like(A)
| ilf_type(A,binary_relation_type)
| ~ ilf_type(A,set_type) ),
inference(clausify,[status(thm)],[p15]) ).
cnf(c_38,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)],[p24]) ).
cnf(c_39,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_38,c_29]) ).
fof(nnf_28,plain,
? [B] :
( ? [C] :
( ? [D] :
( ? [E] :
( ? [F] :
( ( ! [G] :
( ~ member(G,C)
| ~ member(ordered_pair(G,F),E)
| ~ ilf_type(G,member_type(D)) )
| ~ member(F,image4(D,B,E,C)) )
& ( ? [X0] :
( member(X0,C)
& member(ordered_pair(X0,F),E)
& ilf_type(X0,member_type(D)) )
| member(F,image4(D,B,E,C)) )
& ilf_type(F,member_type(B)) )
& ilf_type(E,relation_type(D,B)) )
& ilf_type(D,set_type)
& ~ empty(D) )
& ilf_type(C,set_type)
& ~ empty(C) )
& ilf_type(B,set_type)
& ~ empty(B) ),
inference(fof_nnf,[status(thm)],[prove_relset_1_52_neg]) ).
fof(sk_prove_relset_1_52_neg_sk,plain,
( ( ! [G] :
( ~ member(G,sK4)
| ~ member(ordered_pair(G,sK0),sK3)
| ~ ilf_type(G,member_type(sK1)) )
| ~ member(sK0,image4(sK1,sK2,sK3,sK4)) )
& ( ( member(sK5,sK4)
& member(ordered_pair(sK5,sK0),sK3)
& ilf_type(sK5,member_type(sK1)) )
| member(sK0,image4(sK1,sK2,sK3,sK4)) )
& ilf_type(sK0,member_type(sK2))
& ilf_type(sK3,relation_type(sK1,sK2))
& ilf_type(sK1,set_type)
& ~ empty(sK1)
& ilf_type(sK4,set_type)
& ~ empty(sK4)
& ilf_type(sK2,set_type)
& ~ empty(sK2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK4,sK1,sK3,sK0,sK5]),skolemize(B,sK2),skolemize(C,sK4),skolemize(D,sK1),skolemize(E,sK3),skolemize(F,sK0),skolemize(X0,sK5)],[nnf_28]) ).
fof(sk_prove_relset_1_52_neg,plain,
( ! [VAR_0] :
( ~ member(VAR_0,sK4)
| ~ member(ordered_pair(VAR_0,sK0),sK3)
| ~ ilf_type(VAR_0,member_type(sK1))
| ~ member(sK0,image4(sK1,sK2,sK3,sK4)) )
& ( member(sK5,sK4)
| member(sK0,image4(sK1,sK2,sK3,sK4)) )
& ( member(ordered_pair(sK5,sK0),sK3)
| member(sK0,image4(sK1,sK2,sK3,sK4)) )
& ( ilf_type(sK5,member_type(sK1))
| member(sK0,image4(sK1,sK2,sK3,sK4)) )
& ilf_type(sK0,member_type(sK2))
& ilf_type(sK3,relation_type(sK1,sK2))
& ilf_type(sK1,set_type)
& ~ empty(sK1)
& ilf_type(sK4,set_type)
& ~ empty(sK4)
& ilf_type(sK2,set_type)
& ~ empty(sK2) ),
inference(cnf_transformation,[status(thm)],[sk_prove_relset_1_52_neg_sk]) ).
cnf(c_55,negated_conjecture,
( ~ member(A,sK4)
| ~ member(ordered_pair(A,sK0),sK3)
| ~ ilf_type(A,member_type(sK1))
| ~ member(sK0,image4(sK1,sK2,sK3,sK4)) ),
inference(split_conjunct,[status(thm)],[sk_prove_relset_1_52_neg]) ).
cnf(c_56,negated_conjecture,
( member(sK5,sK4)
| member(sK0,image4(sK1,sK2,sK3,sK4)) ),
inference(split_conjunct,[status(thm)],[sk_prove_relset_1_52_neg]) ).
cnf(c_57,negated_conjecture,
( member(ordered_pair(sK5,sK0),sK3)
| member(sK0,image4(sK1,sK2,sK3,sK4)) ),
inference(split_conjunct,[status(thm)],[sk_prove_relset_1_52_neg]) ).
cnf(c_60,negated_conjecture,
ilf_type(sK3,relation_type(sK1,sK2)),
inference(split_conjunct,[status(thm)],[sk_prove_relset_1_52_neg]) ).
cnf(c_62,negated_conjecture,
~ empty(sK1),
inference(split_conjunct,[status(thm)],[sk_prove_relset_1_52_neg]) ).
cnf(c_67,plain,
ilf_type(A,set_type),
inference(clausify,[status(thm)],[p27]) ).
cnf(c_70,plain,
( image4(A,B,C,D) = image(C,D)
| ~ ilf_type(D,set_type)
| ~ ilf_type(C,relation_type(A,B))
| ~ ilf_type(B,set_type)
| ~ ilf_type(A,set_type) ),
inference(clausify,[status(thm)],[p25]) ).
cnf(c_568,plain,
( image4(C,A,B,D) = image(B,D)
| ~ ilf_type(D,set_type)
| ~ ilf_type(B,relation_type(C,A))
| ~ ilf_type(A,set_type) ),
inference(resolve,[status(thm)],[c_67,c_70]) ).
cnf(c_569,plain,
( image4(B,C,A,D) = image(A,D)
| ~ ilf_type(D,set_type)
| ~ ilf_type(A,relation_type(B,C)) ),
inference(resolve,[status(thm)],[c_67,c_568]) ).
cnf(c_71,plain,
( image4(B,C,A,D) = image(A,D)
| ~ ilf_type(A,relation_type(B,C)) ),
inference(resolve,[status(thm)],[c_67,c_569]) ).
cnf(c_111,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)],[p7]) ).
cnf(c_570,plain,
( ~ member(B,A)
| ilf_type(B,member_type(A))
| ~ ilf_type(A,set_type)
| empty(A) ),
inference(resolve,[status(thm)],[c_67,c_111]) ).
cnf(c_112,plain,
( ~ member(B,A)
| ilf_type(B,member_type(A))
| empty(A) ),
inference(resolve,[status(thm)],[c_67,c_570]) ).
cnf(c_117,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)],[p5]) ).
cnf(c_571,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_67,c_117]) ).
cnf(c_118,plain,
( ilf_type(A,subset_type(cross_product(B,C)))
| ~ ilf_type(A,relation_type(B,C)) ),
inference(resolve,[status(thm)],[c_67,c_571]) ).
cnf(c_128,plain,
( member(C,A)
| ~ member(ordered_pair(C,D),E)
| ~ ilf_type(E,relation_type(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)],[p2]) ).
cnf(c_572,plain,
( member(B,E)
| ~ member(ordered_pair(B,C),D)
| ~ ilf_type(D,relation_type(E,A))
| ~ ilf_type(C,set_type)
| ~ ilf_type(B,set_type)
| ~ ilf_type(A,set_type) ),
inference(resolve,[status(thm)],[c_67,c_128]) ).
cnf(c_573,plain,
( member(A,D)
| ~ member(ordered_pair(A,B),C)
| ~ ilf_type(C,relation_type(D,E))
| ~ ilf_type(B,set_type)
| ~ ilf_type(A,set_type) ),
inference(resolve,[status(thm)],[c_67,c_572]) ).
cnf(c_574,plain,
( member(E,C)
| ~ member(ordered_pair(E,A),B)
| ~ ilf_type(B,relation_type(C,D))
| ~ ilf_type(A,set_type) ),
inference(resolve,[status(thm)],[c_67,c_573]) ).
cnf(c_129,plain,
( member(D,B)
| ~ member(ordered_pair(D,E),A)
| ~ ilf_type(A,relation_type(B,C)) ),
inference(resolve,[status(thm)],[c_67,c_574]) ).
fof(nnf_1,plain,
! [B] :
( ! [C] :
( ! [D] :
( ( ( ! [E] :
( ~ member(E,B)
| ~ member(ordered_pair(E,C),D)
| ~ ilf_type(E,set_type) )
| member(C,image(D,B)) )
& ( ? [X0] :
( member(X0,B)
& member(ordered_pair(X0,C),D)
& ilf_type(X0,set_type) )
| ~ member(C,image(D,B)) ) )
| ~ ilf_type(D,binary_relation_type) )
| ~ ilf_type(C,set_type) )
| ~ ilf_type(B,set_type) ),
inference(fof_nnf,[status(thm)],[p1]) ).
fof(sk_p1_sk,plain,
! [B] :
( ! [C] :
( ! [D] :
( ( ( ! [E] :
( ~ member(E,B)
| ~ member(ordered_pair(E,C),D)
| ~ ilf_type(E,set_type) )
| member(C,image(D,B)) )
& ( ( member(sK6(B,C,D),B)
& member(ordered_pair(sK6(B,C,D),C),D)
& ilf_type(sK6(B,C,D),set_type) )
| ~ member(C,image(D,B)) ) )
| ~ ilf_type(D,binary_relation_type) )
| ~ ilf_type(C,set_type) )
| ~ ilf_type(B,set_type) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(X0,sK6(B,C,D))],[nnf_1]) ).
fof(sk_p1,plain,
( ! [VAR_0,VAR_1,VAR_2,VAR_3] :
( ~ member(VAR_3,VAR_0)
| ~ member(ordered_pair(VAR_3,VAR_1),VAR_2)
| ~ ilf_type(VAR_3,set_type)
| member(VAR_1,image(VAR_2,VAR_0))
| ~ ilf_type(VAR_2,binary_relation_type)
| ~ ilf_type(VAR_1,set_type)
| ~ ilf_type(VAR_0,set_type) )
& ! [VAR_0,VAR_1,VAR_2] :
( member(sK6(VAR_0,VAR_1,VAR_2),VAR_0)
| ~ member(VAR_1,image(VAR_2,VAR_0))
| ~ ilf_type(VAR_2,binary_relation_type)
| ~ ilf_type(VAR_1,set_type)
| ~ ilf_type(VAR_0,set_type) )
& ! [VAR_0,VAR_1,VAR_2] :
( member(ordered_pair(sK6(VAR_0,VAR_1,VAR_2),VAR_1),VAR_2)
| ~ member(VAR_1,image(VAR_2,VAR_0))
| ~ ilf_type(VAR_2,binary_relation_type)
| ~ ilf_type(VAR_1,set_type)
| ~ ilf_type(VAR_0,set_type) )
& ! [VAR_0,VAR_1,VAR_2] :
( ilf_type(sK6(VAR_0,VAR_1,VAR_2),set_type)
| ~ member(VAR_1,image(VAR_2,VAR_0))
| ~ ilf_type(VAR_2,binary_relation_type)
| ~ ilf_type(VAR_1,set_type)
| ~ ilf_type(VAR_0,set_type) ) ),
inference(cnf_transformation,[status(thm)],[sk_p1_sk]) ).
cnf(c_130,plain,
( ~ member(D,A)
| ~ member(ordered_pair(D,B),C)
| ~ ilf_type(D,set_type)
| member(B,image(C,A))
| ~ ilf_type(C,binary_relation_type)
| ~ ilf_type(B,set_type)
| ~ ilf_type(A,set_type) ),
inference(split_conjunct,[status(thm)],[sk_p1]) ).
cnf(c_575,plain,
( ~ member(D,C)
| ~ member(ordered_pair(D,A),B)
| ~ ilf_type(D,set_type)
| member(A,image(B,C))
| ~ ilf_type(B,binary_relation_type)
| ~ ilf_type(A,set_type) ),
inference(resolve,[status(thm)],[c_67,c_130]) ).
cnf(c_576,plain,
( ~ member(D,C)
| ~ member(ordered_pair(D,B),A)
| ~ ilf_type(D,set_type)
| member(B,image(A,C))
| ~ ilf_type(A,binary_relation_type) ),
inference(resolve,[status(thm)],[c_67,c_575]) ).
cnf(c_131,plain,
( ~ member(D,C)
| ~ member(ordered_pair(D,B),A)
| member(B,image(A,C))
| ~ ilf_type(A,binary_relation_type) ),
inference(resolve,[status(thm)],[c_67,c_576]) ).
cnf(c_132,plain,
( member(sK6(A,B,C),A)
| ~ member(B,image(C,A))
| ~ ilf_type(C,binary_relation_type)
| ~ ilf_type(B,set_type)
| ~ ilf_type(A,set_type) ),
inference(split_conjunct,[status(thm)],[sk_p1]) ).
cnf(c_577,plain,
( member(sK6(C,A,B),C)
| ~ member(A,image(B,C))
| ~ ilf_type(B,binary_relation_type)
| ~ ilf_type(A,set_type) ),
inference(resolve,[status(thm)],[c_67,c_132]) ).
cnf(c_133,plain,
( member(sK6(C,B,A),C)
| ~ member(B,image(A,C))
| ~ ilf_type(A,binary_relation_type) ),
inference(resolve,[status(thm)],[c_67,c_577]) ).
cnf(c_134,plain,
( member(ordered_pair(sK6(A,B,C),B),C)
| ~ member(B,image(C,A))
| ~ ilf_type(C,binary_relation_type)
| ~ ilf_type(B,set_type)
| ~ ilf_type(A,set_type) ),
inference(split_conjunct,[status(thm)],[sk_p1]) ).
cnf(c_578,plain,
( member(ordered_pair(sK6(C,A,B),A),B)
| ~ member(A,image(B,C))
| ~ ilf_type(B,binary_relation_type)
| ~ ilf_type(A,set_type) ),
inference(resolve,[status(thm)],[c_67,c_134]) ).
cnf(c_135,plain,
( member(ordered_pair(sK6(C,B,A),B),A)
| ~ member(B,image(A,C))
| ~ ilf_type(A,binary_relation_type) ),
inference(resolve,[status(thm)],[c_67,c_578]) ).
cnf(c_579,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_67,c_39]) ).
cnf(c_580,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_67,c_579]) ).
cnf(c_164,plain,
( ilf_type(A,binary_relation_type)
| ~ ilf_type(A,subset_type(cross_product(B,C))) ),
inference(resolve,[status(thm)],[c_67,c_580]) ).
cnf(c_168,plain,
image4(sK1,sK2,sK3,A) = image(sK3,A),
inference(resolve,[status(thm)],[c_71,c_60]) ).
cnf(c_171,negated_conjecture,
( member(ordered_pair(sK5,sK0),sK3)
| member(sK0,image(sK3,sK4)) ),
inference(paramod,[status(thm)],[c_168,c_57]) ).
cnf(c_172,negated_conjecture,
( member(sK5,sK4)
| member(sK0,image(sK3,sK4)) ),
inference(paramod,[status(thm)],[c_168,c_56]) ).
cnf(c_173,negated_conjecture,
( ~ member(A,sK4)
| ~ member(ordered_pair(A,sK0),sK3)
| ~ ilf_type(A,member_type(sK1))
| ~ member(sK0,image(sK3,sK4)) ),
inference(paramod,[status(thm)],[c_168,c_55]) ).
cnf(c_213,plain,
ilf_type(sK3,subset_type(cross_product(sK1,sK2))),
inference(resolve,[status(thm)],[c_118,c_60]) ).
cnf(c_221,plain,
( member(A,sK1)
| ~ member(ordered_pair(A,B),sK3) ),
inference(resolve,[status(thm)],[c_129,c_60]) ).
cnf(c_329,plain,
( ~ member(sK5,A)
| member(sK0,image(sK3,A))
| ~ ilf_type(sK3,binary_relation_type)
| member(sK0,image(sK3,sK4)) ),
inference(resolve,[status(thm)],[c_171,c_131]) ).
cnf(c_336,plain,
( ~ member(sK5,sK4)
| ~ ilf_type(sK3,binary_relation_type)
| member(sK0,image(sK3,sK4)) ),
inference(factor,[status(thm)],[c_329]) ).
cnf(c_460,plain,
ilf_type(sK3,binary_relation_type),
inference(resolve,[status(thm)],[c_213,c_164]) ).
cnf(c_466,plain,
( ~ member(sK5,sK4)
| member(sK0,image(sK3,sK4)) ),
inference(resolve,[status(thm)],[c_460,c_336]) ).
cnf(c_581,negated_conjecture,
( member(sK0,image(sK3,sK4))
| member(sK0,image(sK3,sK4)) ),
inference(resolve,[status(thm)],[c_466,c_172]) ).
cnf(c_474,negated_conjecture,
member(sK0,image(sK3,sK4)),
inference(copy,[status(thm)],[c_581]) ).
cnf(c_484,negated_conjecture,
( ~ member(A,sK4)
| ~ member(ordered_pair(A,sK0),sK3)
| ~ ilf_type(A,member_type(sK1)) ),
inference(resolve,[status(thm)],[c_474,c_173]) ).
cnf(c_582,plain,
( member(ordered_pair(sK6(sK4,sK0,sK3),sK0),sK3)
| ~ ilf_type(sK3,binary_relation_type) ),
inference(resolve,[status(thm)],[c_474,c_135]) ).
cnf(c_489,plain,
member(ordered_pair(sK6(sK4,sK0,sK3),sK0),sK3),
inference(resolve,[status(thm)],[c_460,c_582]) ).
cnf(c_583,plain,
( member(sK6(sK4,sK0,sK3),sK4)
| ~ ilf_type(sK3,binary_relation_type) ),
inference(resolve,[status(thm)],[c_474,c_133]) ).
cnf(c_490,plain,
member(sK6(sK4,sK0,sK3),sK4),
inference(resolve,[status(thm)],[c_460,c_583]) ).
cnf(c_584,negated_conjecture,
( ~ member(ordered_pair(sK6(sK4,sK0,sK3),sK0),sK3)
| ~ ilf_type(sK6(sK4,sK0,sK3),member_type(sK1)) ),
inference(resolve,[status(thm)],[c_490,c_484]) ).
cnf(c_551,negated_conjecture,
~ ilf_type(sK6(sK4,sK0,sK3),member_type(sK1)),
inference(resolve,[status(thm)],[c_489,c_584]) ).
cnf(c_585,negated_conjecture,
( ~ member(A,sK1)
| ilf_type(A,member_type(sK1)) ),
inference(resolve,[status(thm)],[c_112,c_62]) ).
cnf(c_560,negated_conjecture,
~ member(sK6(sK4,sK0,sK3),sK1),
inference(resolve,[status(thm)],[c_585,c_551]) ).
cnf(c_566,plain,
~ member(ordered_pair(sK6(sK4,sK0,sK3),A),sK3),
inference(resolve,[status(thm)],[c_221,c_560]) ).
cnf(c_567,plain,
$false,
inference(resolve,[status(thm)],[c_566,c_489]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SET685+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.07 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.18/0.45 % Computer : n018.cluster.edu
% 0.18/0.45 % Model : x86_64 x86_64
% 0.18/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.45 % Memory : 8046.5625MB
% 0.18/0.45 % OS : Linux 6.8.0-71-generic
% 0.18/0.45 % CPULimit : 300
% 0.18/0.45 % WCLimit : 300
% 0.18/0.45 % DateTime : Sat Sep 26 08:07:52 UTC 2026
% 0.18/0.46 % CPUTime :
% 0.18/0.46 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.18/0.46 % Process 4145504 was started by sandbox on n018,
% 0.18/0.46 % Sat Sep 26 08:07:52 2026
% 0.18/0.46 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.18/0.48
% 0.18/0.48 % From the command line: assign(max_seconds, 300).
% 0.23/0.54
% 0.23/0.54 % SZS status Theorem for theBenchmark
% 0.23/0.54
% 0.23/0.54 % Proof 1 at 0.04 (+ 0.01) seconds.
% 0.23/0.54 % Length of proof is 51.
% 0.23/0.54 % Level of proof is 13.
% 0.23/0.54 % Maximum clause weight is 33.000.
% 0.23/0.54 % Given clauses 138.
% 0.23/0.54
% 0.23/0.54 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------