%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET676+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 : 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 08:36:47 AM UTC 2026
% Result : Theorem 0.16s 0.46s
% Output : CNFRefutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 4
% Syntax : Number of formulae : 17 ( 6 unt; 0 def)
% Number of atoms : 35 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 32 ( 14 ~; 9 |; 2 &)
% ( 1 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 21 ( 1 sgn 7 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(p1,axiom,
! [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',p1) ).
fof(p4,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ( ilf_type(C,identity_relation_of_type(B))
<=> ilf_type(C,relation_type(B,B)) ) ) ),
file('theBenchmark.p',p4) ).
fof(p19,axiom,
! [B] : ilf_type(B,set_type),
file('theBenchmark.p',p19) ).
fof(prove_relset_1_41,conjecture,
! [B] :
( ilf_type(B,set_type)
=> ilf_type(cross_product(B,B),identity_relation_of_type(B)) ),
file('theBenchmark.p',prove_relset_1_41) ).
fof(prove_relset_1_41_neg,negated_conjecture,
~ ! [B] :
( ilf_type(B,set_type)
=> ilf_type(cross_product(B,B),identity_relation_of_type(B)) ),
inference(assume_negation,[status(cth)],[prove_relset_1_41]) ).
fof(nnf_20,plain,
? [B] :
( ~ ilf_type(cross_product(B,B),identity_relation_of_type(B))
& ilf_type(B,set_type) ),
inference(fof_nnf,[status(thm)],[prove_relset_1_41_neg]) ).
fof(sk_prove_relset_1_41_neg,plain,
( ~ ilf_type(cross_product(sK0,sK0),identity_relation_of_type(sK0))
& ilf_type(sK0,set_type) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(B,sK0)],[nnf_20]) ).
cnf(c_36,negated_conjecture,
~ ilf_type(cross_product(sK0,sK0),identity_relation_of_type(sK0)),
inference(split_conjunct,[status(thm)],[sk_prove_relset_1_41_neg]) ).
cnf(c_38,plain,
ilf_type(A,set_type),
inference(clausify,[status(thm)],[p19]) ).
cnf(c_75,plain,
( ~ ilf_type(B,relation_type(A,A))
| ilf_type(B,identity_relation_of_type(A))
| ~ ilf_type(B,set_type)
| ~ ilf_type(A,set_type) ),
inference(clausify,[status(thm)],[p4]) ).
cnf(c_126,plain,
( ~ ilf_type(A,relation_type(B,B))
| ilf_type(A,identity_relation_of_type(B))
| ~ ilf_type(A,set_type) ),
inference(resolve,[status(thm)],[c_38,c_75]) ).
cnf(c_76,plain,
( ~ ilf_type(A,relation_type(B,B))
| ilf_type(A,identity_relation_of_type(B)) ),
inference(resolve,[status(thm)],[c_38,c_126]) ).
cnf(c_90,plain,
( ilf_type(cross_product(A,B),relation_type(A,B))
| ~ ilf_type(B,set_type)
| ~ ilf_type(A,set_type) ),
inference(clausify,[status(thm)],[p1]) ).
cnf(c_127,plain,
( ilf_type(cross_product(B,A),relation_type(B,A))
| ~ ilf_type(A,set_type) ),
inference(resolve,[status(thm)],[c_38,c_90]) ).
cnf(c_91,plain,
ilf_type(cross_product(A,B),relation_type(A,B)),
inference(resolve,[status(thm)],[c_38,c_127]) ).
cnf(c_128,negated_conjecture,
~ ilf_type(cross_product(sK0,sK0),relation_type(sK0,sK0)),
inference(resolve,[status(thm)],[c_76,c_36]) ).
cnf(c_125,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_91,c_128]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SET676+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.16/0.42 % Computer : n018.cluster.edu
% 0.16/0.42 % Model : x86_64 x86_64
% 0.16/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.42 % Memory : 8046.5625MB
% 0.16/0.42 % OS : Linux 6.8.0-71-generic
% 0.16/0.42 % CPULimit : 300
% 0.16/0.42 % WCLimit : 300
% 0.16/0.42 % DateTime : Sat Sep 26 08:06:37 UTC 2026
% 0.16/0.42 % CPUTime :
% 0.16/0.43 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.16/0.43 % Process 4141880 was started by sandbox2 on n018,
% 0.16/0.43 % Sat Sep 26 08:06:37 2026
% 0.16/0.43 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.16/0.44
% 0.16/0.44 % From the command line: assign(max_seconds, 300).
% 0.16/0.46
% 0.16/0.46 % SZS status Theorem for theBenchmark
% 0.16/0.46
% 0.16/0.46 % Proof 1 at 0.01 (+ 0.00) seconds.
% 0.16/0.46 % Length of proof is 11.
% 0.16/0.46 % Level of proof is 3.
% 0.16/0.46 % Maximum clause weight is 9.000.
% 0.16/0.46 % Given clauses 19.
% 0.16/0.46
% 0.16/0.46 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------