%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET653+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 : 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 08:36:44 AM UTC 2026
% Result : Theorem 0.16s 0.47s
% Output : CNFRefutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 5
% Syntax : Number of formulae : 29 ( 9 unt; 0 def)
% Number of atoms : 99 ( 0 equ)
% Maximal formula atoms : 6 ( 3 avg)
% Number of connectives : 112 ( 42 ~; 36 |; 12 &)
% ( 0 <=>; 22 =>; 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 : 8 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 63 ( 5 sgn 19 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(p1,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ! [D] :
( ilf_type(D,set_type)
=> ( ( subset(C,D)
& subset(B,C) )
=> subset(B,D) ) ) ) ),
file('theBenchmark.p',p1) ).
fof(p2,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',p2) ).
fof(p3,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(B,D))
=> ( subset(domain_of(E),C)
=> ilf_type(E,relation_type(C,D)) ) ) ) ) ),
file('theBenchmark.p',p3) ).
fof(p22,axiom,
! [B] : ilf_type(B,set_type),
file('theBenchmark.p',p22) ).
fof(prove_relset_1_15,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(B,D))
=> ( subset(B,C)
=> ilf_type(E,relation_type(C,D)) ) ) ) ) ),
file('theBenchmark.p',prove_relset_1_15) ).
fof(prove_relset_1_15_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(B,D))
=> ( subset(B,C)
=> ilf_type(E,relation_type(C,D)) ) ) ) ) ),
inference(assume_negation,[status(cth)],[prove_relset_1_15]) ).
fof(nnf_23,plain,
? [B] :
( ? [C] :
( ? [D] :
( ? [E] :
( ~ ilf_type(E,relation_type(C,D))
& subset(B,C)
& ilf_type(E,relation_type(B,D)) )
& ilf_type(D,set_type) )
& ilf_type(C,set_type) )
& ilf_type(B,set_type) ),
inference(fof_nnf,[status(thm)],[prove_relset_1_15_neg]) ).
fof(sk_prove_relset_1_15_neg,plain,
( ~ ilf_type(sK0,relation_type(sK1,sK2))
& subset(sK3,sK1)
& ilf_type(sK0,relation_type(sK3,sK2))
& ilf_type(sK2,set_type)
& ilf_type(sK1,set_type)
& ilf_type(sK3,set_type) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3,sK1,sK2,sK0]),skolemize(B,sK3),skolemize(C,sK1),skolemize(D,sK2),skolemize(E,sK0)],[nnf_23]) ).
cnf(c_39,negated_conjecture,
~ ilf_type(sK0,relation_type(sK1,sK2)),
inference(split_conjunct,[status(thm)],[sk_prove_relset_1_15_neg]) ).
cnf(c_40,negated_conjecture,
subset(sK3,sK1),
inference(split_conjunct,[status(thm)],[sk_prove_relset_1_15_neg]) ).
cnf(c_41,negated_conjecture,
ilf_type(sK0,relation_type(sK3,sK2)),
inference(split_conjunct,[status(thm)],[sk_prove_relset_1_15_neg]) ).
cnf(c_45,plain,
ilf_type(A,set_type),
inference(clausify,[status(thm)],[p22]) ).
cnf(c_90,plain,
( ilf_type(D,relation_type(B,C))
| ~ subset(domain_of(D),B)
| ~ ilf_type(D,relation_type(A,C))
| ~ ilf_type(C,set_type)
| ~ ilf_type(B,set_type)
| ~ ilf_type(A,set_type) ),
inference(clausify,[status(thm)],[p3]) ).
cnf(c_162,plain,
( ilf_type(C,relation_type(A,B))
| ~ subset(domain_of(C),A)
| ~ ilf_type(C,relation_type(D,B))
| ~ ilf_type(B,set_type)
| ~ ilf_type(A,set_type) ),
inference(resolve,[status(thm)],[c_45,c_90]) ).
cnf(c_163,plain,
( ilf_type(B,relation_type(D,A))
| ~ subset(domain_of(B),D)
| ~ ilf_type(B,relation_type(C,A))
| ~ ilf_type(A,set_type) ),
inference(resolve,[status(thm)],[c_45,c_162]) ).
cnf(c_91,plain,
( ilf_type(A,relation_type(D,C))
| ~ subset(domain_of(A),D)
| ~ ilf_type(A,relation_type(B,C)) ),
inference(resolve,[status(thm)],[c_45,c_163]) ).
cnf(c_94,plain,
( subset(domain_of(C),A)
| ~ ilf_type(C,relation_type(A,B))
| ~ ilf_type(B,set_type)
| ~ ilf_type(A,set_type) ),
inference(clausify,[status(thm)],[p2]) ).
cnf(c_164,plain,
( subset(domain_of(B),C)
| ~ ilf_type(B,relation_type(C,A))
| ~ ilf_type(A,set_type) ),
inference(resolve,[status(thm)],[c_45,c_94]) ).
cnf(c_95,plain,
( subset(domain_of(A),B)
| ~ ilf_type(A,relation_type(B,C)) ),
inference(resolve,[status(thm)],[c_45,c_164]) ).
cnf(c_96,plain,
( subset(A,C)
| ~ subset(B,C)
| ~ subset(A,B)
| ~ ilf_type(C,set_type)
| ~ ilf_type(B,set_type)
| ~ ilf_type(A,set_type) ),
inference(clausify,[status(thm)],[p1]) ).
cnf(c_165,plain,
( subset(C,B)
| ~ subset(A,B)
| ~ subset(C,A)
| ~ ilf_type(B,set_type)
| ~ ilf_type(A,set_type) ),
inference(resolve,[status(thm)],[c_45,c_96]) ).
cnf(c_166,plain,
( subset(B,A)
| ~ subset(C,A)
| ~ subset(B,C)
| ~ ilf_type(A,set_type) ),
inference(resolve,[status(thm)],[c_45,c_165]) ).
cnf(c_97,plain,
( subset(A,C)
| ~ subset(B,C)
| ~ subset(A,B) ),
inference(resolve,[status(thm)],[c_45,c_166]) ).
cnf(c_167,negated_conjecture,
( ilf_type(sK0,relation_type(A,sK2))
| ~ subset(domain_of(sK0),A) ),
inference(resolve,[status(thm)],[c_91,c_41]) ).
cnf(c_139,negated_conjecture,
~ subset(domain_of(sK0),sK1),
inference(resolve,[status(thm)],[c_167,c_39]) ).
cnf(c_143,plain,
subset(domain_of(sK0),sK3),
inference(resolve,[status(thm)],[c_95,c_41]) ).
cnf(c_168,negated_conjecture,
( subset(A,sK1)
| ~ subset(A,sK3) ),
inference(resolve,[status(thm)],[c_97,c_40]) ).
cnf(c_169,negated_conjecture,
~ subset(domain_of(sK0),sK3),
inference(resolve,[status(thm)],[c_168,c_139]) ).
cnf(c_161,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_143,c_169]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SET653+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.16/0.44 % Computer : n006.cluster.edu
% 0.16/0.44 % Model : x86_64 x86_64
% 0.16/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.44 % Memory : 8046.5625MB
% 0.16/0.44 % OS : Linux 6.8.0-71-generic
% 0.16/0.44 % CPULimit : 300
% 0.16/0.44 % WCLimit : 300
% 0.16/0.44 % DateTime : Sat Sep 26 08:03:25 UTC 2026
% 0.16/0.45 % CPUTime :
% 0.16/0.45 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.16/0.45 % Process 781712 was started by sandbox on n006,
% 0.16/0.45 % Sat Sep 26 08:03:25 2026
% 0.16/0.45 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.16/0.45
% 0.16/0.45 % From the command line: assign(max_seconds, 300).
% 0.16/0.47
% 0.16/0.47 % SZS status Theorem for theBenchmark
% 0.16/0.47
% 0.16/0.47 % Proof 1 at 0.01 (+ 0.00) seconds.
% 0.16/0.47 % Length of proof is 18.
% 0.16/0.47 % Level of proof is 4.
% 0.16/0.47 % Maximum clause weight is 24.000.
% 0.16/0.47 % Given clauses 35.
% 0.16/0.47
% 0.16/0.47 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------