%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET643+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 : n007.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 08:36:43 AM UTC 2026
% Result : Theorem 0.14s 10.41s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 4
% Syntax : Number of formulae : 17 ( 6 unt; 0 def)
% Number of atoms : 41 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 39 ( 15 ~; 11 |; 4 &)
% ( 0 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 28 ( 1 sgn 9 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(p1,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ! [D] :
( ilf_type(D,set_type)
=> ( subset(B,cross_product(C,D))
=> ilf_type(B,relation_type(C,D)) ) ) ) ),
file('theBenchmark.p',p1) ).
fof(p10,axiom,
! [B] :
( ilf_type(B,set_type)
=> subset(B,B) ),
file('theBenchmark.p',p10) ).
fof(p19,axiom,
! [B] : ilf_type(B,set_type),
file('theBenchmark.p',p19) ).
fof(prove_relset_1_5,conjecture,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ilf_type(cross_product(B,C),relation_type(B,C)) ) ),
file('theBenchmark.p',prove_relset_1_5) ).
fof(prove_relset_1_5_neg,negated_conjecture,
~ ! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ilf_type(cross_product(B,C),relation_type(B,C)) ) ),
inference(assume_negation,[status(cth)],[prove_relset_1_5]) ).
fof(nnf_20,plain,
? [B] :
( ? [C] :
( ~ ilf_type(cross_product(B,C),relation_type(B,C))
& ilf_type(C,set_type) )
& ilf_type(B,set_type) ),
inference(fof_nnf,[status(thm)],[prove_relset_1_5_neg]) ).
fof(sk_prove_relset_1_5_neg,plain,
( ~ ilf_type(cross_product(sK0,sK1),relation_type(sK0,sK1))
& ilf_type(sK1,set_type)
& ilf_type(sK0,set_type) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(B,sK0),skolemize(C,sK1)],[nnf_20]) ).
cnf(c_36,negated_conjecture,
~ ilf_type(cross_product(sK0,sK1),relation_type(sK0,sK1)),
inference(split_conjunct,[status(thm)],[sk_prove_relset_1_5_neg]) ).
cnf(c_39,plain,
ilf_type(A,set_type),
inference(clausify,[status(thm)],[p19]) ).
cnf(c_61,plain,
( subset(A,A)
| ~ ilf_type(A,set_type) ),
inference(clausify,[status(thm)],[p10]) ).
cnf(c_62,plain,
subset(A,A),
inference(resolve,[status(thm)],[c_39,c_61]) ).
cnf(c_94,plain,
( ilf_type(A,relation_type(B,C))
| ~ subset(A,cross_product(B,C))
| ~ ilf_type(C,set_type)
| ~ ilf_type(B,set_type)
| ~ ilf_type(A,set_type) ),
inference(clausify,[status(thm)],[p1]) ).
cnf(c_143,plain,
( ilf_type(C,relation_type(A,B))
| ~ subset(C,cross_product(A,B))
| ~ ilf_type(B,set_type)
| ~ ilf_type(A,set_type) ),
inference(resolve,[status(thm)],[c_39,c_94]) ).
cnf(c_144,plain,
( ilf_type(B,relation_type(C,A))
| ~ subset(B,cross_product(C,A))
| ~ ilf_type(A,set_type) ),
inference(resolve,[status(thm)],[c_39,c_143]) ).
cnf(c_95,plain,
( ilf_type(A,relation_type(B,C))
| ~ subset(A,cross_product(B,C)) ),
inference(resolve,[status(thm)],[c_39,c_144]) ).
cnf(c_141,plain,
ilf_type(cross_product(A,B),relation_type(A,B)),
inference(resolve,[status(thm)],[c_95,c_62]) ).
cnf(c_142,plain,
$false,
inference(resolve,[status(thm)],[c_141,c_36]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET643+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/10.38 % Computer : n007.cluster.edu
% 0.09/10.38 % Model : x86_64 x86_64
% 0.09/10.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/10.38 % Memory : 8046.5625MB
% 0.09/10.38 % OS : Linux 6.8.0-71-generic
% 0.09/10.38 % CPULimit : 300
% 0.09/10.38 % WCLimit : 300
% 0.09/10.38 % DateTime : Sat Sep 26 08:00:35 UTC 2026
% 0.09/10.38 % CPUTime :
% 0.09/10.39 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/10.39 % Process 3223275 was started by sandbox2 on n007,
% 0.09/10.39 % Sat Sep 26 08:00:35 2026
% 0.09/10.39 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.09/10.39
% 0.09/10.39 % From the command line: assign(max_seconds, 300).
% 0.14/10.41
% 0.14/10.41 % SZS status Theorem for theBenchmark
% 0.14/10.41
% 0.14/10.41 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.14/10.41 % Length of proof is 12.
% 0.14/10.41 % Level of proof is 4.
% 0.14/10.41 % Maximum clause weight is 10.000.
% 0.14/10.41 % Given clauses 26.
% 0.14/10.41
% 0.14/10.41 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------