%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SEU263+1 : TPTP v9.3.1. Released v3.3.0.
% 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 08:45:37 AM UTC 2026
% Result : Theorem 0.15s 0.41s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 9
% Syntax : Number of formulae : 34 ( 9 unt; 0 def)
% Number of atoms : 68 ( 0 equ)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 55 ( 21 ~; 15 |; 7 &)
% ( 2 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 70 ( 7 sgn 31 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(cc1_relset_1,axiom,
! [A,B,C] :
( element(C,powerset(cartesian_product2(A,B)))
=> relation(C) ),
file('theBenchmark.p',cc1_relset_1) ).
fof(d1_relset_1,axiom,
! [A,B,C] :
( relation_of2(C,A,B)
<=> subset(C,cartesian_product2(A,B)) ),
file('theBenchmark.p',d1_relset_1) ).
fof(dt_m2_relset_1,axiom,
! [A,B,C] :
( relation_of2_as_subset(C,A,B)
=> element(C,powerset(cartesian_product2(A,B))) ),
file('theBenchmark.p',dt_m2_relset_1) ).
fof(redefinition_m2_relset_1,axiom,
! [A,B,C] :
( relation_of2_as_subset(C,A,B)
<=> relation_of2(C,A,B) ),
file('theBenchmark.p',redefinition_m2_relset_1) ).
fof(t119_zfmisc_1,axiom,
! [A,B,C,D] :
( ( subset(C,D)
& subset(A,B) )
=> subset(cartesian_product2(A,C),cartesian_product2(B,D)) ),
file('theBenchmark.p',t119_zfmisc_1) ).
fof(t12_relset_1,axiom,
! [A,B,C] :
( relation_of2_as_subset(C,A,B)
=> ( subset(relation_rng(C),B)
& subset(relation_dom(C),A) ) ),
file('theBenchmark.p',t12_relset_1) ).
fof(t1_xboole_1,axiom,
! [A,B,C] :
( ( subset(B,C)
& subset(A,B) )
=> subset(A,C) ),
file('theBenchmark.p',t1_xboole_1) ).
fof(t21_relat_1,axiom,
! [A] :
( relation(A)
=> subset(A,cartesian_product2(relation_dom(A),relation_rng(A))) ),
file('theBenchmark.p',t21_relat_1) ).
fof(t14_relset_1,conjecture,
! [A,B,C,D] :
( relation_of2_as_subset(D,C,A)
=> ( subset(relation_rng(D),B)
=> relation_of2_as_subset(D,C,B) ) ),
file('theBenchmark.p',t14_relset_1) ).
fof(t14_relset_1_neg,negated_conjecture,
~ ! [A,B,C,D] :
( relation_of2_as_subset(D,C,A)
=> ( subset(relation_rng(D),B)
=> relation_of2_as_subset(D,C,B) ) ),
inference(assume_negation,[status(cth)],[t14_relset_1]) ).
cnf(c_21,plain,
( element(A,powerset(cartesian_product2(B,C)))
| ~ relation_of2_as_subset(A,B,C) ),
inference(clausify,[status(thm)],[dt_m2_relset_1]) ).
cnf(c_22,plain,
( relation(A)
| ~ element(A,powerset(cartesian_product2(B,C))) ),
inference(clausify,[status(thm)],[cc1_relset_1]) ).
cnf(c_26,plain,
( subset(A,cartesian_product2(relation_dom(A),relation_rng(A)))
| ~ relation(A) ),
inference(clausify,[status(thm)],[t21_relat_1]) ).
cnf(c_27,plain,
( relation(A)
| ~ relation_of2_as_subset(A,B,C) ),
inference(resolve,[status(thm)],[c_21,c_22]) ).
cnf(c_30,plain,
( ~ subset(A,cartesian_product2(B,C))
| relation_of2(A,B,C) ),
inference(clausify,[status(thm)],[d1_relset_1]) ).
cnf(c_34,plain,
( ~ relation_of2(A,B,C)
| relation_of2_as_subset(A,B,C) ),
inference(clausify,[status(thm)],[redefinition_m2_relset_1]) ).
cnf(c_37,plain,
( ~ subset(A,cartesian_product2(B,C))
| relation_of2_as_subset(A,B,C) ),
inference(resolve,[status(thm)],[c_34,c_30]) ).
fof(nnf_20,plain,
? [A,B,C,D] :
( ~ relation_of2_as_subset(D,C,B)
& subset(relation_rng(D),B)
& relation_of2_as_subset(D,C,A) ),
inference(fof_nnf,[status(thm)],[t14_relset_1_neg]) ).
fof(sk_t14_relset_1_neg,plain,
( ~ relation_of2_as_subset(sK0,sK1,sK2)
& subset(relation_rng(sK0),sK2)
& relation_of2_as_subset(sK0,sK1,sK3) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK3,sK2]),skolemize(A,sK3),skolemize(B,sK2),skolemize(C,sK1),skolemize(D,sK0)],[nnf_20]) ).
cnf(c_38,negated_conjecture,
~ relation_of2_as_subset(sK0,sK1,sK2),
inference(split_conjunct,[status(thm)],[sk_t14_relset_1_neg]) ).
cnf(c_39,negated_conjecture,
relation_of2_as_subset(sK0,sK1,sK3),
inference(split_conjunct,[status(thm)],[sk_t14_relset_1_neg]) ).
cnf(c_41,plain,
( subset(relation_dom(A),B)
| ~ relation_of2_as_subset(A,B,C) ),
inference(clausify,[status(thm)],[t12_relset_1]) ).
cnf(c_43,plain,
( ~ relation_of2_as_subset(A,B,C)
| subset(A,cartesian_product2(relation_dom(A),relation_rng(A))) ),
inference(resolve,[status(thm)],[c_26,c_27]) ).
cnf(c_45,negated_conjecture,
subset(sK0,cartesian_product2(relation_dom(sK0),relation_rng(sK0))),
inference(resolve,[status(thm)],[c_43,c_39]) ).
cnf(c_52,negated_conjecture,
subset(relation_dom(sK0),sK1),
inference(resolve,[status(thm)],[c_41,c_39]) ).
cnf(c_57,negated_conjecture,
~ subset(sK0,cartesian_product2(sK1,sK2)),
inference(resolve,[status(thm)],[c_38,c_37]) ).
cnf(c_62,plain,
( subset(cartesian_product2(A,C),cartesian_product2(B,D))
| ~ subset(C,D)
| ~ subset(A,B) ),
inference(clausify,[status(thm)],[t119_zfmisc_1]) ).
cnf(c_63,plain,
( subset(A,C)
| ~ subset(B,C)
| ~ subset(A,B) ),
inference(clausify,[status(thm)],[t1_xboole_1]) ).
cnf(c_64,negated_conjecture,
subset(relation_rng(sK0),sK2),
inference(split_conjunct,[status(thm)],[sk_t14_relset_1_neg]) ).
cnf(c_350,negated_conjecture,
( subset(sK0,A)
| ~ subset(cartesian_product2(relation_dom(sK0),relation_rng(sK0)),A) ),
inference(resolve,[status(thm)],[c_63,c_45]) ).
cnf(c_336,negated_conjecture,
~ subset(cartesian_product2(relation_dom(sK0),relation_rng(sK0)),cartesian_product2(sK1,sK2)),
inference(resolve,[status(thm)],[c_350,c_57]) ).
cnf(c_351,negated_conjecture,
( subset(cartesian_product2(relation_dom(sK0),A),cartesian_product2(sK1,B))
| ~ subset(A,B) ),
inference(resolve,[status(thm)],[c_62,c_52]) ).
cnf(c_348,negated_conjecture,
subset(cartesian_product2(relation_dom(sK0),relation_rng(sK0)),cartesian_product2(sK1,sK2)),
inference(resolve,[status(thm)],[c_351,c_64]) ).
cnf(c_349,plain,
$false,
inference(resolve,[status(thm)],[c_348,c_336]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU263+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.37 % Computer : n007.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sat Sep 26 08:59:10 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.37 % Process 3359923 was started by sandbox2 on n007,
% 0.10/0.37 % Sat Sep 26 08:59:10 2026
% 0.10/0.37 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.10/0.38
% 0.10/0.38 % From the command line: assign(max_seconds, 300).
% 0.15/0.41
% 0.15/0.41 % SZS status Theorem for theBenchmark
% 0.15/0.41
% 0.15/0.41 % Proof 1 at 0.01 (+ 0.01) seconds.
% 0.15/0.41 % Length of proof is 29.
% 0.15/0.41 % Level of proof is 6.
% 0.15/0.41 % Maximum clause weight is 13.000.
% 0.15/0.41 % Given clauses 21.
% 0.15/0.41
% 0.15/0.41 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------