%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET658+3 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n012.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 08:36:45 AM UTC 2026
% Result : Theorem 0.03s 5.33s
% Output : CNFRefutation 0.03s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 4
% Syntax : Number of formulae : 17 ( 7 unt; 0 def)
% Number of atoms : 32 ( 0 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 27 ( 12 ~; 7 |; 2 &)
% ( 0 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 15 ( 1 sgn 6 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(p1,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,binary_relation_type)
=> ( subset(domain_of(C),B)
=> ilf_type(C,relation_type(B,range_of(C))) ) ) ),
file('theBenchmark.p',p1) ).
fof(p15,axiom,
! [B] :
( ilf_type(B,set_type)
=> subset(B,B) ),
file('theBenchmark.p',p15) ).
fof(p28,axiom,
! [B] : ilf_type(B,set_type),
file('theBenchmark.p',p28) ).
fof(prove_relset_1_20,conjecture,
! [B] :
( ilf_type(B,binary_relation_type)
=> ilf_type(B,relation_type(domain_of(B),range_of(B))) ),
file('theBenchmark.p',prove_relset_1_20) ).
fof(prove_relset_1_20_neg,negated_conjecture,
~ ! [B] :
( ilf_type(B,binary_relation_type)
=> ilf_type(B,relation_type(domain_of(B),range_of(B))) ),
inference(assume_negation,[status(cth)],[prove_relset_1_20]) ).
fof(nnf_29,plain,
? [B] :
( ~ ilf_type(B,relation_type(domain_of(B),range_of(B)))
& ilf_type(B,binary_relation_type) ),
inference(fof_nnf,[status(thm)],[prove_relset_1_20_neg]) ).
fof(sk_prove_relset_1_20_neg,plain,
( ~ ilf_type(sK0,relation_type(domain_of(sK0),range_of(sK0)))
& ilf_type(sK0,binary_relation_type) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(B,sK0)],[nnf_29]) ).
cnf(c_56,negated_conjecture,
~ ilf_type(sK0,relation_type(domain_of(sK0),range_of(sK0))),
inference(split_conjunct,[status(thm)],[sk_prove_relset_1_20_neg]) ).
cnf(c_57,negated_conjecture,
ilf_type(sK0,binary_relation_type),
inference(split_conjunct,[status(thm)],[sk_prove_relset_1_20_neg]) ).
cnf(c_58,plain,
ilf_type(A,set_type),
inference(clausify,[status(thm)],[p28]) ).
cnf(c_88,plain,
( subset(A,A)
| ~ ilf_type(A,set_type) ),
inference(clausify,[status(thm)],[p15]) ).
cnf(c_89,plain,
subset(A,A),
inference(resolve,[status(thm)],[c_58,c_88]) ).
cnf(c_122,plain,
( ilf_type(B,relation_type(A,range_of(B)))
| ~ subset(domain_of(B),A)
| ~ ilf_type(B,binary_relation_type)
| ~ ilf_type(A,set_type) ),
inference(clausify,[status(thm)],[p1]) ).
cnf(c_123,plain,
( ilf_type(A,relation_type(B,range_of(A)))
| ~ subset(domain_of(A),B)
| ~ ilf_type(A,binary_relation_type) ),
inference(resolve,[status(thm)],[c_58,c_122]) ).
cnf(c_180,plain,
( ilf_type(A,relation_type(domain_of(A),range_of(A)))
| ~ ilf_type(A,binary_relation_type) ),
inference(resolve,[status(thm)],[c_123,c_89]) ).
cnf(c_181,negated_conjecture,
~ ilf_type(sK0,binary_relation_type),
inference(resolve,[status(thm)],[c_180,c_56]) ).
cnf(c_179,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_57,c_181]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SET658+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.02 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.03/5.31 % Computer : n012.cluster.edu
% 0.03/5.31 % Model : x86_64 x86_64
% 0.03/5.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.03/5.31 % Memory : 8046.5625MB
% 0.03/5.31 % OS : Linux 6.8.0-71-generic
% 0.03/5.31 % CPULimit : 300
% 0.03/5.31 % WCLimit : 300
% 0.03/5.31 % DateTime : Sat Sep 26 08:03:11 UTC 2026
% 0.03/5.31 % CPUTime :
% 0.03/5.31 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.03/5.31 % Process 85453 was started by sandbox on n012,
% 0.03/5.31 % Sat Sep 26 08:03:11 2026
% 0.03/5.31 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.03/5.32
% 0.03/5.32 % From the command line: assign(max_seconds, 300).
% 0.03/5.33
% 0.03/5.33 % SZS status Theorem for theBenchmark
% 0.03/5.33
% 0.03/5.33 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.03/5.33 % Length of proof is 12.
% 0.03/5.33 % Level of proof is 3.
% 0.03/5.33 % Maximum clause weight is 13.000.
% 0.03/5.33 % Given clauses 32.
% 0.03/5.33
% 0.03/5.33 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------