%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET642+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 : n006.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 08:36:42 AM UTC 2026
% Result : Theorem 0.09s 5.39s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 4
% Syntax : Number of formulae : 23 ( 8 unt; 0 def)
% Number of atoms : 77 ( 0 equ)
% Maximal formula atoms : 6 ( 3 avg)
% Number of connectives : 85 ( 31 ~; 25 |; 10 &)
% ( 0 <=>; 19 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 5 con; 0-2 aty)
% Number of variables : 51 ( 1 sgn 16 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(p1,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ! [D] :
( ilf_type(D,set_type)
=> ! [E] :
( ilf_type(E,relation_type(C,D))
=> ( subset(B,E)
=> subset(B,cross_product(C,D)) ) ) ) ) ),
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)
=> ( subset(B,cross_product(C,D))
=> ilf_type(B,relation_type(C,D)) ) ) ) ),
file('theBenchmark.p',p2) ).
fof(p19,axiom,
! [B] : ilf_type(B,set_type),
file('theBenchmark.p',p19) ).
fof(prove_relset_1_4,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(C,D))
=> ( subset(B,E)
=> ilf_type(B,relation_type(C,D)) ) ) ) ) ),
file('theBenchmark.p',prove_relset_1_4) ).
fof(prove_relset_1_4_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(C,D))
=> ( subset(B,E)
=> ilf_type(B,relation_type(C,D)) ) ) ) ) ),
inference(assume_negation,[status(cth)],[prove_relset_1_4]) ).
fof(nnf_20,plain,
? [B] :
( ? [C] :
( ? [D] :
( ? [E] :
( ~ ilf_type(B,relation_type(C,D))
& subset(B,E)
& ilf_type(E,relation_type(C,D)) )
& ilf_type(D,set_type) )
& ilf_type(C,set_type) )
& ilf_type(B,set_type) ),
inference(fof_nnf,[status(thm)],[prove_relset_1_4_neg]) ).
fof(sk_prove_relset_1_4_neg,plain,
( ~ ilf_type(sK0,relation_type(sK1,sK2))
& subset(sK0,sK3)
& ilf_type(sK3,relation_type(sK1,sK2))
& ilf_type(sK2,set_type)
& ilf_type(sK1,set_type)
& ilf_type(sK0,set_type) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3]),skolemize(B,sK0),skolemize(C,sK1),skolemize(D,sK2),skolemize(E,sK3)],[nnf_20]) ).
cnf(c_36,negated_conjecture,
~ ilf_type(sK0,relation_type(sK1,sK2)),
inference(split_conjunct,[status(thm)],[sk_prove_relset_1_4_neg]) ).
cnf(c_37,negated_conjecture,
subset(sK0,sK3),
inference(split_conjunct,[status(thm)],[sk_prove_relset_1_4_neg]) ).
cnf(c_38,negated_conjecture,
ilf_type(sK3,relation_type(sK1,sK2)),
inference(split_conjunct,[status(thm)],[sk_prove_relset_1_4_neg]) ).
cnf(c_42,plain,
ilf_type(A,set_type),
inference(clausify,[status(thm)],[p19]) ).
cnf(c_87,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)],[p2]) ).
cnf(c_141,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_42,c_87]) ).
cnf(c_142,plain,
( ilf_type(B,relation_type(C,A))
| ~ subset(B,cross_product(C,A))
| ~ ilf_type(A,set_type) ),
inference(resolve,[status(thm)],[c_42,c_141]) ).
cnf(c_88,plain,
( ilf_type(A,relation_type(B,C))
| ~ subset(A,cross_product(B,C)) ),
inference(resolve,[status(thm)],[c_42,c_142]) ).
cnf(c_89,plain,
( subset(A,cross_product(B,C))
| ~ subset(A,D)
| ~ ilf_type(D,relation_type(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,
( subset(D,cross_product(A,B))
| ~ subset(D,C)
| ~ ilf_type(C,relation_type(A,B))
| ~ ilf_type(B,set_type)
| ~ ilf_type(A,set_type) ),
inference(resolve,[status(thm)],[c_42,c_89]) ).
cnf(c_144,plain,
( subset(D,cross_product(C,A))
| ~ subset(D,B)
| ~ ilf_type(B,relation_type(C,A))
| ~ ilf_type(A,set_type) ),
inference(resolve,[status(thm)],[c_42,c_143]) ).
cnf(c_90,plain,
( subset(D,cross_product(B,C))
| ~ subset(D,A)
| ~ ilf_type(A,relation_type(B,C)) ),
inference(resolve,[status(thm)],[c_42,c_144]) ).
cnf(c_128,negated_conjecture,
~ subset(sK0,cross_product(sK1,sK2)),
inference(resolve,[status(thm)],[c_88,c_36]) ).
cnf(c_145,negated_conjecture,
( subset(sK0,cross_product(A,B))
| ~ ilf_type(sK3,relation_type(A,B)) ),
inference(resolve,[status(thm)],[c_90,c_37]) ).
cnf(c_146,negated_conjecture,
~ ilf_type(sK3,relation_type(sK1,sK2)),
inference(resolve,[status(thm)],[c_145,c_128]) ).
cnf(c_140,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_38,c_146]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET642+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/5.36 % Computer : n006.cluster.edu
% 0.09/5.36 % Model : x86_64 x86_64
% 0.09/5.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/5.36 % Memory : 8046.5625MB
% 0.09/5.36 % OS : Linux 6.8.0-71-generic
% 0.09/5.36 % CPULimit : 300
% 0.09/5.36 % WCLimit : 300
% 0.09/5.36 % DateTime : Sat Sep 26 08:02:19 UTC 2026
% 0.09/5.36 % CPUTime :
% 0.09/5.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/5.37 % Process 779921 was started by sandbox2 on n006,
% 0.09/5.37 % Sat Sep 26 08:02:19 2026
% 0.09/5.37 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.09/5.37
% 0.09/5.37 % From the command line: assign(max_seconds, 300).
% 0.09/5.39
% 0.09/5.39 % SZS status Theorem for theBenchmark
% 0.09/5.39
% 0.09/5.39 % Proof 1 at 0.01 (+ 0.00) seconds.
% 0.09/5.39 % Length of proof is 14.
% 0.09/5.39 % Level of proof is 4.
% 0.09/5.39 % Maximum clause weight is 13.000.
% 0.09/5.39 % Given clauses 31.
% 0.09/5.39
% 0.09/5.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------