%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET664+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 : n020.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 08:36:46 AM UTC 2026
% Result : Theorem 0.16s 0.49s
% Output : CNFRefutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 8
% Syntax : Number of formulae : 39 ( 13 unt; 0 def)
% Number of atoms : 108 ( 17 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 109 ( 40 ~; 34 |; 11 &)
% ( 1 <=>; 23 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 6 con; 0-2 aty)
% Number of variables : 63 ( 8 sgn 20 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(p1,axiom,
! [B] :
( ilf_type(B,set_type)
=> ( subset(B,empty_set)
=> B = empty_set ) ),
file('theBenchmark.p',p1) ).
fof(p2,axiom,
! [B] :
( ilf_type(B,binary_relation_type)
=> ( ( range_of(B) = empty_set
| domain_of(B) = empty_set )
=> B = empty_set ) ),
file('theBenchmark.p',p2) ).
fof(p3,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',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(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(p28,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',p28) ).
fof(p33,axiom,
! [B] : ilf_type(B,set_type),
file('theBenchmark.p',p33) ).
fof(prove_relset_1_27,conjecture,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ! [D] :
( ilf_type(D,relation_type(C,B))
=> ( ilf_type(D,relation_type(C,empty_set))
=> D = empty_set ) ) ) ),
file('theBenchmark.p',prove_relset_1_27) ).
fof(prove_relset_1_27_neg,negated_conjecture,
~ ! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ! [D] :
( ilf_type(D,relation_type(C,B))
=> ( ilf_type(D,relation_type(C,empty_set))
=> D = empty_set ) ) ) ),
inference(assume_negation,[status(cth)],[prove_relset_1_27]) ).
cnf(c_39,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)],[p28]) ).
cnf(c_42,plain,
( ~ relation_like(A)
| ilf_type(A,binary_relation_type)
| ~ ilf_type(A,set_type) ),
inference(clausify,[status(thm)],[p13]) ).
cnf(c_50,plain,
( ~ ilf_type(A,subset_type(cross_product(B,C)))
| ~ ilf_type(C,set_type)
| ~ ilf_type(B,set_type)
| ilf_type(A,binary_relation_type)
| ~ ilf_type(A,set_type) ),
inference(resolve,[status(thm)],[c_42,c_39]) ).
cnf(c_80,plain,
( empty_set = A
| ~ subset(A,empty_set)
| ~ ilf_type(A,set_type) ),
inference(clausify,[status(thm)],[p1]) ).
cnf(c_82,plain,
( empty_set = A
| range_of(A) != empty_set
| ~ ilf_type(A,binary_relation_type) ),
inference(clausify,[status(thm)],[p2]) ).
cnf(c_84,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)],[p3]) ).
cnf(c_88,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_125,plain,
ilf_type(A,set_type),
inference(clausify,[status(thm)],[p33]) ).
fof(nnf_33,plain,
? [B] :
( ? [C] :
( ? [D] :
( D != empty_set
& ilf_type(D,relation_type(C,empty_set))
& ilf_type(D,relation_type(C,B)) )
& ilf_type(C,set_type) )
& ilf_type(B,set_type) ),
inference(fof_nnf,[status(thm)],[prove_relset_1_27_neg]) ).
fof(sk_prove_relset_1_27_neg,plain,
( sK0 != empty_set
& ilf_type(sK0,relation_type(sK1,empty_set))
& ilf_type(sK0,relation_type(sK1,sK2))
& ilf_type(sK1,set_type)
& ilf_type(sK2,set_type) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK1,sK0]),skolemize(B,sK2),skolemize(C,sK1),skolemize(D,sK0)],[nnf_33]) ).
cnf(c_126,negated_conjecture,
ilf_type(sK0,relation_type(sK1,sK2)),
inference(split_conjunct,[status(thm)],[sk_prove_relset_1_27_neg]) ).
cnf(c_127,negated_conjecture,
ilf_type(sK0,relation_type(sK1,empty_set)),
inference(split_conjunct,[status(thm)],[sk_prove_relset_1_27_neg]) ).
cnf(c_128,negated_conjecture,
sK0 != empty_set,
inference(split_conjunct,[status(thm)],[sk_prove_relset_1_27_neg]) ).
cnf(c_310,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_125,c_88]) ).
cnf(c_197,plain,
( ilf_type(A,subset_type(cross_product(B,C)))
| ~ ilf_type(A,relation_type(B,C)) ),
inference(resolve,[status(thm)],[c_125,c_310]) ).
cnf(c_311,plain,
( subset(range_of(B),A)
| ~ ilf_type(B,relation_type(C,A))
| ~ ilf_type(A,set_type) ),
inference(resolve,[status(thm)],[c_125,c_84]) ).
cnf(c_200,plain,
( subset(range_of(A),C)
| ~ ilf_type(A,relation_type(B,C)) ),
inference(resolve,[status(thm)],[c_125,c_311]) ).
cnf(c_202,plain,
( empty_set = A
| ~ subset(A,empty_set) ),
inference(resolve,[status(thm)],[c_125,c_80]) ).
cnf(c_312,plain,
( ~ ilf_type(A,subset_type(cross_product(B,C)))
| ~ ilf_type(C,set_type)
| ~ ilf_type(B,set_type)
| ilf_type(A,binary_relation_type) ),
inference(resolve,[status(thm)],[c_125,c_50]) ).
cnf(c_313,plain,
( ~ ilf_type(A,subset_type(cross_product(C,B)))
| ~ ilf_type(B,set_type)
| ilf_type(A,binary_relation_type) ),
inference(resolve,[status(thm)],[c_125,c_312]) ).
cnf(c_209,plain,
( ~ ilf_type(A,subset_type(cross_product(B,C)))
| ilf_type(A,binary_relation_type) ),
inference(resolve,[status(thm)],[c_125,c_313]) ).
cnf(c_245,plain,
ilf_type(sK0,subset_type(cross_product(sK1,sK2))),
inference(resolve,[status(thm)],[c_197,c_126]) ).
cnf(c_250,plain,
subset(range_of(sK0),empty_set),
inference(resolve,[status(thm)],[c_200,c_127]) ).
cnf(c_314,plain,
empty_set = range_of(sK0),
inference(resolve,[status(thm)],[c_250,c_202]) ).
cnf(c_292,plain,
range_of(sK0) = empty_set,
inference(copy,[status(thm)],[c_314]) ).
cnf(c_315,plain,
( empty_set = sK0
| ~ ilf_type(sK0,binary_relation_type) ),
inference(resolve,[status(thm)],[c_82,c_292]) ).
cnf(c_316,negated_conjecture,
empty_set != sK0,
inference(copy,[status(thm)],[c_128]) ).
cnf(c_307,negated_conjecture,
~ ilf_type(sK0,binary_relation_type),
inference(resolve,[status(thm)],[c_315,c_316]) ).
cnf(c_308,plain,
~ ilf_type(sK0,subset_type(cross_product(A,B))),
inference(resolve,[status(thm)],[c_209,c_307]) ).
cnf(c_309,plain,
$false,
inference(resolve,[status(thm)],[c_308,c_245]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SET664+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 : n020.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 08:04:04 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 1034921 was started by sandbox2 on n020,
% 0.16/0.43 % Sat Sep 26 08:04:04 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).
% 0.16/0.49
% 0.16/0.49 % SZS status Theorem for theBenchmark
% 0.16/0.49
% 0.16/0.49 % Proof 1 at 0.02 (+ 0.01) seconds.
% 0.16/0.49 % Length of proof is 29.
% 0.16/0.49 % Level of proof is 7.
% 0.16/0.49 % Maximum clause weight is 18.000.
% 0.16/0.49 % Given clauses 68.
% 0.16/0.49
% 0.16/0.49 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------