%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SEU094+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/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 08:45:00 AM UTC 2026
% Result : Theorem 0.14s 0.44s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 6
% Syntax : Number of formulae : 41 ( 8 unt; 0 def)
% Number of atoms : 118 ( 0 equ)
% Maximal formula atoms : 11 ( 2 avg)
% Number of connectives : 121 ( 44 ~; 52 |; 16 &)
% ( 3 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-1 aty)
% Number of variables : 34 ( 0 sgn 19 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(l22_finset_1,axiom,
! [A] :
( ( ! [B] :
( in(B,A)
=> finite(B) )
& finite(A) )
=> finite(union(A)) ),
file('theBenchmark.p',l22_finset_1) ).
fof(t100_zfmisc_1,axiom,
! [A] : subset(A,powerset(union(A))),
file('theBenchmark.p',t100_zfmisc_1) ).
fof(t13_finset_1,axiom,
! [A,B] :
( ( finite(B)
& subset(A,B) )
=> finite(A) ),
file('theBenchmark.p',t13_finset_1) ).
fof(t24_finset_1,axiom,
! [A] :
( finite(A)
<=> finite(powerset(A)) ),
file('theBenchmark.p',t24_finset_1) ).
fof(t92_zfmisc_1,axiom,
! [A,B] :
( in(A,B)
=> subset(A,union(B)) ),
file('theBenchmark.p',t92_zfmisc_1) ).
fof(t25_finset_1,conjecture,
! [A] :
( ( ! [B] :
( in(B,A)
=> finite(B) )
& finite(A) )
<=> finite(union(A)) ),
file('theBenchmark.p',t25_finset_1) ).
fof(t25_finset_1_neg,negated_conjecture,
~ ! [A] :
( ( ! [B] :
( in(B,A)
=> finite(B) )
& finite(A) )
<=> finite(union(A)) ),
inference(assume_negation,[status(cth)],[t25_finset_1]) ).
cnf(c_122,plain,
( finite(A)
| ~ finite(B)
| ~ subset(A,B) ),
inference(clausify,[status(thm)],[t13_finset_1]) ).
cnf(c_123,plain,
subset(A,powerset(union(A))),
inference(clausify,[status(thm)],[t100_zfmisc_1]) ).
cnf(c_127,plain,
( subset(A,union(B))
| ~ in(A,B) ),
inference(clausify,[status(thm)],[t92_zfmisc_1]) ).
cnf(c_128,plain,
( finite(A)
| ~ finite(union(B))
| ~ in(A,B) ),
inference(resolve,[status(thm)],[c_127,c_122]) ).
cnf(c_133,plain,
( finite(A)
| ~ finite(powerset(union(A))) ),
inference(resolve,[status(thm)],[c_122,c_123]) ).
fof(nnf_58,plain,
? [A] :
( ( ~ finite(union(A))
| ? [B] :
( ~ finite(B)
& in(B,A) )
| ~ finite(A) )
& ( finite(union(A))
| ( ! [X0] :
( finite(X0)
| ~ in(X0,A) )
& finite(A) ) ) ),
inference(fof_nnf,[status(thm)],[t25_finset_1_neg]) ).
fof(sk_t25_finset_1_neg_sk,plain,
( ( ~ finite(union(sK0))
| ( ~ finite(sK1)
& in(sK1,sK0) )
| ~ finite(sK0) )
& ( finite(union(sK0))
| ( ! [X0] :
( finite(X0)
| ~ in(X0,sK0) )
& finite(sK0) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(A,sK0),skolemize(B,sK1)],[nnf_58]) ).
fof(sk_t25_finset_1_neg,plain,
( ( ~ finite(union(sK0))
| ~ finite(sK1)
| ~ finite(sK0) )
& ( ~ finite(union(sK0))
| in(sK1,sK0)
| ~ finite(sK0) )
& ! [VAR_0] :
( finite(union(sK0))
| finite(VAR_0)
| ~ in(VAR_0,sK0) )
& ( finite(union(sK0))
| finite(sK0) ) ),
inference(cnf_transformation,[status(thm)],[sk_t25_finset_1_neg_sk]) ).
cnf(c_134,negated_conjecture,
( ~ finite(union(sK0))
| ~ finite(sK1)
| ~ finite(sK0) ),
inference(split_conjunct,[status(thm)],[sk_t25_finset_1_neg]) ).
cnf(c_135,negated_conjecture,
( ~ finite(union(sK0))
| in(sK1,sK0)
| ~ finite(sK0) ),
inference(split_conjunct,[status(thm)],[sk_t25_finset_1_neg]) ).
cnf(c_136,negated_conjecture,
( finite(union(sK0))
| finite(A)
| ~ in(A,sK0) ),
inference(split_conjunct,[status(thm)],[sk_t25_finset_1_neg]) ).
cnf(c_137,negated_conjecture,
( finite(union(sK0))
| finite(sK0) ),
inference(split_conjunct,[status(thm)],[sk_t25_finset_1_neg]) ).
cnf(c_145,plain,
( finite(powerset(A))
| ~ finite(A) ),
inference(clausify,[status(thm)],[t24_finset_1]) ).
fof(nnf_19,plain,
! [A] :
( finite(union(A))
| ? [B] :
( ~ finite(B)
& in(B,A) )
| ~ finite(A) ),
inference(fof_nnf,[status(thm)],[l22_finset_1]) ).
fof(sk_l22_finset_1_sk,plain,
! [A] :
( finite(union(A))
| ( ~ finite(sK2(A))
& in(sK2(A),A) )
| ~ finite(A) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(B,sK2(A))],[nnf_19]) ).
fof(sk_l22_finset_1,plain,
( ! [VAR_0] :
( finite(union(VAR_0))
| ~ finite(sK2(VAR_0))
| ~ finite(VAR_0) )
& ! [VAR_0] :
( finite(union(VAR_0))
| in(sK2(VAR_0),VAR_0)
| ~ finite(VAR_0) ) ),
inference(cnf_transformation,[status(thm)],[sk_l22_finset_1_sk]) ).
cnf(c_179,plain,
( finite(union(A))
| ~ finite(sK2(A))
| ~ finite(A) ),
inference(split_conjunct,[status(thm)],[sk_l22_finset_1]) ).
cnf(c_180,plain,
( finite(union(A))
| in(sK2(A),A)
| ~ finite(A) ),
inference(split_conjunct,[status(thm)],[sk_l22_finset_1]) ).
cnf(c_198,plain,
( finite(sK0)
| finite(powerset(union(sK0))) ),
inference(resolve,[status(thm)],[c_145,c_137]) ).
cnf(c_1071,plain,
( finite(sK0)
| finite(sK0) ),
inference(resolve,[status(thm)],[c_198,c_133]) ).
cnf(c_328,plain,
finite(sK0),
inference(copy,[status(thm)],[c_1071]) ).
cnf(c_329,negated_conjecture,
( ~ finite(union(sK0))
| in(sK1,sK0) ),
inference(resolve,[status(thm)],[c_328,c_135]) ).
cnf(c_330,negated_conjecture,
( ~ finite(union(sK0))
| ~ finite(sK1) ),
inference(resolve,[status(thm)],[c_328,c_134]) ).
cnf(c_340,plain,
( finite(union(sK0))
| in(sK2(sK0),sK0) ),
inference(resolve,[status(thm)],[c_328,c_180]) ).
cnf(c_341,plain,
( finite(union(sK0))
| ~ finite(sK2(sK0)) ),
inference(resolve,[status(thm)],[c_328,c_179]) ).
cnf(c_1072,negated_conjecture,
( finite(union(sK0))
| finite(sK2(sK0))
| finite(union(sK0)) ),
inference(resolve,[status(thm)],[c_340,c_136]) ).
cnf(c_1021,negated_conjecture,
( finite(sK2(sK0))
| finite(union(sK0)) ),
inference(copy,[status(thm)],[c_1072]) ).
cnf(c_1073,plain,
( finite(union(sK0))
| finite(union(sK0)) ),
inference(resolve,[status(thm)],[c_1021,c_341]) ).
cnf(c_1057,plain,
finite(union(sK0)),
inference(copy,[status(thm)],[c_1073]) ).
cnf(c_1058,negated_conjecture,
~ finite(sK1),
inference(resolve,[status(thm)],[c_1057,c_330]) ).
cnf(c_1059,negated_conjecture,
in(sK1,sK0),
inference(resolve,[status(thm)],[c_1057,c_329]) ).
cnf(c_1074,negated_conjecture,
( finite(sK1)
| ~ finite(union(sK0)) ),
inference(resolve,[status(thm)],[c_1059,c_128]) ).
cnf(c_1075,negated_conjecture,
finite(sK1),
inference(resolve,[status(thm)],[c_1057,c_1074]) ).
cnf(c_1070,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_1058,c_1075]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU094+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n018.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Sat Sep 26 08:38:06 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.36 % Process 24287 was started by sandbox on n018,
% 0.09/0.36 % Sat Sep 26 08:38:06 2026
% 0.09/0.36 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.14/0.37
% 0.14/0.37 % From the command line: assign(max_seconds, 300).
% 0.14/0.44
% 0.14/0.44 % SZS status Theorem for theBenchmark
% 0.14/0.44
% 0.14/0.44 % Proof 1 at 0.04 (+ 0.02) seconds.
% 0.14/0.44 % Length of proof is 29.
% 0.14/0.44 % Level of proof is 8.
% 0.14/0.44 % Maximum clause weight is 21.000.
% 0.14/0.44 % Given clauses 280.
% 0.14/0.44
% 0.14/0.44 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------