%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET680+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 : 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 : Sun Sep 27 08:36:48 AM UTC 2026
% Result : Theorem 0.08s 0.45s
% Output : CNFRefutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 10
% Syntax : Number of formulae : 64 ( 13 unt; 0 def)
% Number of atoms : 257 ( 5 equ)
% Maximal formula atoms : 13 ( 4 avg)
% Number of connectives : 318 ( 125 ~; 113 |; 42 &)
% ( 5 <=>; 33 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 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; 7 con; 0-3 aty)
% Number of variables : 143 ( 15 sgn 48 !; 9 ?)
% Comments :
%------------------------------------------------------------------------------
fof(p1,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,binary_relation_type)
=> ( member(B,domain_of(C))
<=> ? [D] :
( member(ordered_pair(B,D),C)
& ilf_type(D,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,binary_relation_type)
=> ( member(ordered_pair(B,C),D)
=> ( member(C,range_of(D))
& member(B,domain_of(D)) ) ) ) ) ),
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)
=> ! [F] :
( ilf_type(F,relation_type(B,C))
=> ( member(ordered_pair(D,E),F)
=> ( member(E,C)
& member(D,B) ) ) ) ) ) ) ),
file('theBenchmark.p',p3) ).
fof(p6,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',p6) ).
fof(p8,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',p8) ).
fof(p17,axiom,
! [B] :
( ilf_type(B,set_type)
=> ( ilf_type(B,binary_relation_type)
<=> ( ilf_type(B,set_type)
& relation_like(B) ) ) ),
file('theBenchmark.p',p17) ).
fof(p26,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',p26) ).
fof(p27,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ! [D] :
( ilf_type(D,relation_type(B,C))
=> domain(B,C,D) = domain_of(D) ) ) ),
file('theBenchmark.p',p27) ).
fof(p31,axiom,
! [B] : ilf_type(B,set_type),
file('theBenchmark.p',p31) ).
fof(prove_relset_1_47,conjecture,
! [B] :
( ( ilf_type(B,set_type)
& ~ empty(B) )
=> ! [C] :
( ( ilf_type(C,set_type)
& ~ empty(C) )
=> ! [D] :
( ilf_type(D,relation_type(B,C))
=> ! [E] :
( ilf_type(E,member_type(B))
=> ( member(E,domain(B,C,D))
<=> ? [F] :
( member(ordered_pair(E,F),D)
& ilf_type(F,member_type(C)) ) ) ) ) ) ),
file('theBenchmark.p',prove_relset_1_47) ).
fof(prove_relset_1_47_neg,negated_conjecture,
~ ! [B] :
( ( ilf_type(B,set_type)
& ~ empty(B) )
=> ! [C] :
( ( ilf_type(C,set_type)
& ~ empty(C) )
=> ! [D] :
( ilf_type(D,relation_type(B,C))
=> ! [E] :
( ilf_type(E,member_type(B))
=> ( member(E,domain(B,C,D))
<=> ? [F] :
( member(ordered_pair(E,F),D)
& ilf_type(F,member_type(C)) ) ) ) ) ) ),
inference(assume_negation,[status(cth)],[prove_relset_1_47]) ).
cnf(c_33,plain,
( ~ relation_like(A)
| ilf_type(A,binary_relation_type)
| ~ ilf_type(A,set_type) ),
inference(clausify,[status(thm)],[p17]) ).
cnf(c_42,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)],[p26]) ).
cnf(c_43,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_42,c_33]) ).
fof(nnf_32,plain,
? [B] :
( ? [C] :
( ? [D] :
( ? [E] :
( ( ! [F] :
( ~ member(ordered_pair(E,F),D)
| ~ ilf_type(F,member_type(C)) )
| ~ member(E,domain(B,C,D)) )
& ( ? [X0] :
( member(ordered_pair(E,X0),D)
& ilf_type(X0,member_type(C)) )
| member(E,domain(B,C,D)) )
& ilf_type(E,member_type(B)) )
& ilf_type(D,relation_type(B,C)) )
& ilf_type(C,set_type)
& ~ empty(C) )
& ilf_type(B,set_type)
& ~ empty(B) ),
inference(fof_nnf,[status(thm)],[prove_relset_1_47_neg]) ).
fof(sk_prove_relset_1_47_neg_sk,plain,
( ( ! [F] :
( ~ member(ordered_pair(sK0,F),sK3)
| ~ ilf_type(F,member_type(sK2)) )
| ~ member(sK0,domain(sK1,sK2,sK3)) )
& ( ( member(ordered_pair(sK0,sK4),sK3)
& ilf_type(sK4,member_type(sK2)) )
| member(sK0,domain(sK1,sK2,sK3)) )
& ilf_type(sK0,member_type(sK1))
& ilf_type(sK3,relation_type(sK1,sK2))
& ilf_type(sK2,set_type)
& ~ empty(sK2)
& ilf_type(sK1,set_type)
& ~ empty(sK1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2,sK3,sK0,sK4]),skolemize(B,sK1),skolemize(C,sK2),skolemize(D,sK3),skolemize(E,sK0),skolemize(X0,sK4)],[nnf_32]) ).
fof(sk_prove_relset_1_47_neg,plain,
( ! [VAR_0] :
( ~ member(ordered_pair(sK0,VAR_0),sK3)
| ~ ilf_type(VAR_0,member_type(sK2))
| ~ member(sK0,domain(sK1,sK2,sK3)) )
& ( member(ordered_pair(sK0,sK4),sK3)
| member(sK0,domain(sK1,sK2,sK3)) )
& ( ilf_type(sK4,member_type(sK2))
| member(sK0,domain(sK1,sK2,sK3)) )
& ilf_type(sK0,member_type(sK1))
& ilf_type(sK3,relation_type(sK1,sK2))
& ilf_type(sK2,set_type)
& ~ empty(sK2)
& ilf_type(sK1,set_type)
& ~ empty(sK1) ),
inference(cnf_transformation,[status(thm)],[sk_prove_relset_1_47_neg_sk]) ).
cnf(c_59,negated_conjecture,
( ~ member(ordered_pair(sK0,A),sK3)
| ~ ilf_type(A,member_type(sK2))
| ~ member(sK0,domain(sK1,sK2,sK3)) ),
inference(split_conjunct,[status(thm)],[sk_prove_relset_1_47_neg]) ).
cnf(c_60,negated_conjecture,
( member(ordered_pair(sK0,sK4),sK3)
| member(sK0,domain(sK1,sK2,sK3)) ),
inference(split_conjunct,[status(thm)],[sk_prove_relset_1_47_neg]) ).
cnf(c_63,negated_conjecture,
ilf_type(sK3,relation_type(sK1,sK2)),
inference(split_conjunct,[status(thm)],[sk_prove_relset_1_47_neg]) ).
cnf(c_65,negated_conjecture,
~ empty(sK2),
inference(split_conjunct,[status(thm)],[sk_prove_relset_1_47_neg]) ).
cnf(c_68,plain,
ilf_type(A,set_type),
inference(clausify,[status(thm)],[p31]) ).
cnf(c_75,plain,
( domain(A,B,C) = domain_of(C)
| ~ ilf_type(C,relation_type(A,B))
| ~ ilf_type(B,set_type)
| ~ ilf_type(A,set_type) ),
inference(clausify,[status(thm)],[p27]) ).
cnf(c_457,plain,
( domain(C,A,B) = domain_of(B)
| ~ ilf_type(B,relation_type(C,A))
| ~ ilf_type(A,set_type) ),
inference(resolve,[status(thm)],[c_68,c_75]) ).
cnf(c_76,plain,
( domain(B,C,A) = domain_of(A)
| ~ ilf_type(A,relation_type(B,C)) ),
inference(resolve,[status(thm)],[c_68,c_457]) ).
cnf(c_115,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)],[p8]) ).
cnf(c_458,plain,
( ~ member(B,A)
| ilf_type(B,member_type(A))
| ~ ilf_type(A,set_type)
| empty(A) ),
inference(resolve,[status(thm)],[c_68,c_115]) ).
cnf(c_116,plain,
( ~ member(B,A)
| ilf_type(B,member_type(A))
| empty(A) ),
inference(resolve,[status(thm)],[c_68,c_458]) ).
cnf(c_121,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)],[p6]) ).
cnf(c_459,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_68,c_121]) ).
cnf(c_122,plain,
( ilf_type(A,subset_type(cross_product(B,C)))
| ~ ilf_type(A,relation_type(B,C)) ),
inference(resolve,[status(thm)],[c_68,c_459]) ).
cnf(c_130,plain,
( member(D,B)
| ~ 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)],[p3]) ).
cnf(c_460,plain,
( member(C,A)
| ~ 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_68,c_130]) ).
cnf(c_461,plain,
( member(B,E)
| ~ 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_68,c_460]) ).
cnf(c_462,plain,
( member(A,D)
| ~ member(ordered_pair(E,A),B)
| ~ ilf_type(B,relation_type(C,D))
| ~ ilf_type(A,set_type) ),
inference(resolve,[status(thm)],[c_68,c_461]) ).
cnf(c_131,plain,
( member(E,C)
| ~ member(ordered_pair(D,E),A)
| ~ ilf_type(A,relation_type(B,C)) ),
inference(resolve,[status(thm)],[c_68,c_462]) ).
cnf(c_136,plain,
( member(A,domain_of(C))
| ~ member(ordered_pair(A,B),C)
| ~ ilf_type(C,binary_relation_type)
| ~ ilf_type(B,set_type)
| ~ ilf_type(A,set_type) ),
inference(clausify,[status(thm)],[p2]) ).
cnf(c_463,plain,
( member(C,domain_of(B))
| ~ member(ordered_pair(C,A),B)
| ~ ilf_type(B,binary_relation_type)
| ~ ilf_type(A,set_type) ),
inference(resolve,[status(thm)],[c_68,c_136]) ).
cnf(c_137,plain,
( member(B,domain_of(A))
| ~ member(ordered_pair(B,C),A)
| ~ ilf_type(A,binary_relation_type) ),
inference(resolve,[status(thm)],[c_68,c_463]) ).
fof(nnf_1,plain,
! [B] :
( ! [C] :
( ( ( ! [D] :
( ~ member(ordered_pair(B,D),C)
| ~ ilf_type(D,set_type) )
| member(B,domain_of(C)) )
& ( ? [X0] :
( member(ordered_pair(B,X0),C)
& ilf_type(X0,set_type) )
| ~ member(B,domain_of(C)) ) )
| ~ ilf_type(C,binary_relation_type) )
| ~ ilf_type(B,set_type) ),
inference(fof_nnf,[status(thm)],[p1]) ).
fof(sk_p1_sk,plain,
! [B] :
( ! [C] :
( ( ( ! [D] :
( ~ member(ordered_pair(B,D),C)
| ~ ilf_type(D,set_type) )
| member(B,domain_of(C)) )
& ( ( member(ordered_pair(B,sK5(B,C)),C)
& ilf_type(sK5(B,C),set_type) )
| ~ member(B,domain_of(C)) ) )
| ~ ilf_type(C,binary_relation_type) )
| ~ ilf_type(B,set_type) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(X0,sK5(B,C))],[nnf_1]) ).
fof(sk_p1,plain,
( ! [VAR_0,VAR_1,VAR_2] :
( ~ member(ordered_pair(VAR_0,VAR_2),VAR_1)
| ~ ilf_type(VAR_2,set_type)
| member(VAR_0,domain_of(VAR_1))
| ~ ilf_type(VAR_1,binary_relation_type)
| ~ ilf_type(VAR_0,set_type) )
& ! [VAR_0,VAR_1] :
( member(ordered_pair(VAR_0,sK5(VAR_0,VAR_1)),VAR_1)
| ~ member(VAR_0,domain_of(VAR_1))
| ~ ilf_type(VAR_1,binary_relation_type)
| ~ ilf_type(VAR_0,set_type) )
& ! [VAR_0,VAR_1] :
( ilf_type(sK5(VAR_0,VAR_1),set_type)
| ~ member(VAR_0,domain_of(VAR_1))
| ~ ilf_type(VAR_1,binary_relation_type)
| ~ ilf_type(VAR_0,set_type) ) ),
inference(cnf_transformation,[status(thm)],[sk_p1_sk]) ).
cnf(c_139,plain,
( member(ordered_pair(A,sK5(A,B)),B)
| ~ member(A,domain_of(B))
| ~ ilf_type(B,binary_relation_type)
| ~ ilf_type(A,set_type) ),
inference(split_conjunct,[status(thm)],[sk_p1]) ).
cnf(c_140,plain,
( member(ordered_pair(B,sK5(B,A)),A)
| ~ member(B,domain_of(A))
| ~ ilf_type(A,binary_relation_type) ),
inference(resolve,[status(thm)],[c_68,c_139]) ).
cnf(c_464,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_68,c_43]) ).
cnf(c_465,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_68,c_464]) ).
cnf(c_169,plain,
( ilf_type(A,binary_relation_type)
| ~ ilf_type(A,subset_type(cross_product(B,C))) ),
inference(resolve,[status(thm)],[c_68,c_465]) ).
cnf(c_175,plain,
domain(sK1,sK2,sK3) = domain_of(sK3),
inference(resolve,[status(thm)],[c_76,c_63]) ).
cnf(c_178,negated_conjecture,
( member(ordered_pair(sK0,sK4),sK3)
| member(sK0,domain_of(sK3)) ),
inference(paramod,[status(thm)],[c_175,c_60]) ).
cnf(c_179,negated_conjecture,
( ~ member(ordered_pair(sK0,A),sK3)
| ~ ilf_type(A,member_type(sK2))
| ~ member(sK0,domain_of(sK3)) ),
inference(paramod,[status(thm)],[c_175,c_59]) ).
cnf(c_220,plain,
ilf_type(sK3,subset_type(cross_product(sK1,sK2))),
inference(resolve,[status(thm)],[c_122,c_63]) ).
cnf(c_466,negated_conjecture,
( member(sK0,domain_of(sK3))
| ~ ilf_type(sK3,binary_relation_type)
| member(sK0,domain_of(sK3)) ),
inference(resolve,[status(thm)],[c_178,c_137]) ).
cnf(c_307,negated_conjecture,
( ~ ilf_type(sK3,binary_relation_type)
| member(sK0,domain_of(sK3)) ),
inference(copy,[status(thm)],[c_466]) ).
cnf(c_315,plain,
ilf_type(sK3,binary_relation_type),
inference(resolve,[status(thm)],[c_220,c_169]) ).
cnf(c_317,negated_conjecture,
member(sK0,domain_of(sK3)),
inference(resolve,[status(thm)],[c_315,c_307]) ).
cnf(c_319,negated_conjecture,
( ~ member(ordered_pair(sK0,A),sK3)
| ~ ilf_type(A,member_type(sK2)) ),
inference(resolve,[status(thm)],[c_317,c_179]) ).
cnf(c_467,plain,
( member(ordered_pair(sK0,sK5(sK0,sK3)),sK3)
| ~ ilf_type(sK3,binary_relation_type) ),
inference(resolve,[status(thm)],[c_317,c_140]) ).
cnf(c_324,plain,
member(ordered_pair(sK0,sK5(sK0,sK3)),sK3),
inference(resolve,[status(thm)],[c_315,c_467]) ).
cnf(c_422,plain,
~ ilf_type(sK5(sK0,sK3),member_type(sK2)),
inference(resolve,[status(thm)],[c_324,c_319]) ).
cnf(c_468,negated_conjecture,
( ~ member(A,sK2)
| ilf_type(A,member_type(sK2)) ),
inference(resolve,[status(thm)],[c_116,c_65]) ).
cnf(c_449,negated_conjecture,
~ member(sK5(sK0,sK3),sK2),
inference(resolve,[status(thm)],[c_468,c_422]) ).
cnf(c_469,plain,
( member(sK5(sK0,sK3),B)
| ~ ilf_type(sK3,relation_type(A,B)) ),
inference(resolve,[status(thm)],[c_131,c_324]) ).
cnf(c_455,plain,
~ ilf_type(sK3,relation_type(A,sK2)),
inference(resolve,[status(thm)],[c_469,c_449]) ).
cnf(c_456,plain,
$false,
inference(resolve,[status(thm)],[c_455,c_63]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET680+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.37 % Computer : n014.cluster.edu
% 0.08/0.37 % Model : x86_64 x86_64
% 0.08/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.37 % Memory : 8046.5625MB
% 0.08/0.37 % OS : Linux 6.8.0-71-generic
% 0.08/0.37 % CPULimit : 300
% 0.08/0.37 % WCLimit : 300
% 0.08/0.37 % DateTime : Sat Sep 26 08:05:03 UTC 2026
% 0.08/0.37 % CPUTime :
% 0.08/0.38 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.08/0.38 % Process 2591297 was started by sandbox2 on n014,
% 0.08/0.38 % Sat Sep 26 08:05:03 2026
% 0.08/0.38 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.08/0.39
% 0.08/0.39 % From the command line: assign(max_seconds, 300).
% 0.08/0.45
% 0.08/0.45 % SZS status Theorem for theBenchmark
% 0.08/0.45
% 0.08/0.45 % Proof 1 at 0.03 (+ 0.01) seconds.
% 0.08/0.45 % Length of proof is 44.
% 0.08/0.45 % Level of proof is 11.
% 0.08/0.45 % Maximum clause weight is 18.000.
% 0.08/0.45 % Given clauses 100.
% 0.08/0.45
% 0.08/0.45 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------