%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET899+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 08:37:14 AM UTC 2026
% Result : Theorem 0.14s 0.39s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 2
% Syntax : Number of formulae : 12 ( 5 unt; 0 def)
% Number of atoms : 25 ( 0 equ)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 23 ( 10 ~; 6 |; 4 &)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 16 ( 0 sgn 9 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(l3_zfmisc_1,axiom,
! [A,B,C] :
( subset(A,B)
=> ( subset(A,set_difference(B,singleton(C)))
| in(C,A) ) ),
file('theBenchmark.p',l3_zfmisc_1) ).
fof(t40_zfmisc_1,conjecture,
! [A,B,C] :
( subset(A,B)
=> ( subset(A,set_difference(B,singleton(C)))
| in(C,A) ) ),
file('theBenchmark.p',t40_zfmisc_1) ).
fof(t40_zfmisc_1_neg,negated_conjecture,
~ ! [A,B,C] :
( subset(A,B)
=> ( subset(A,set_difference(B,singleton(C)))
| in(C,A) ) ),
inference(assume_negation,[status(cth)],[t40_zfmisc_1]) ).
fof(nnf_6,plain,
? [A,B,C] :
( ~ subset(A,set_difference(B,singleton(C)))
& ~ in(C,A)
& subset(A,B) ),
inference(fof_nnf,[status(thm)],[t40_zfmisc_1_neg]) ).
fof(sk_t40_zfmisc_1_neg,plain,
( ~ subset(sK0,set_difference(sK1,singleton(sK2)))
& ~ in(sK2,sK0)
& subset(sK0,sK1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(A,sK0),skolemize(B,sK1),skolemize(C,sK2)],[nnf_6]) ).
cnf(c_9,negated_conjecture,
~ subset(sK0,set_difference(sK1,singleton(sK2))),
inference(split_conjunct,[status(thm)],[sk_t40_zfmisc_1_neg]) ).
cnf(c_10,negated_conjecture,
~ in(sK2,sK0),
inference(split_conjunct,[status(thm)],[sk_t40_zfmisc_1_neg]) ).
cnf(c_11,negated_conjecture,
subset(sK0,sK1),
inference(split_conjunct,[status(thm)],[sk_t40_zfmisc_1_neg]) ).
cnf(c_12,plain,
( subset(A,set_difference(B,singleton(C)))
| in(C,A)
| ~ subset(A,B) ),
inference(clausify,[status(thm)],[l3_zfmisc_1]) ).
cnf(c_18,negated_conjecture,
( subset(sK0,set_difference(A,singleton(sK2)))
| ~ subset(sK0,A) ),
inference(resolve,[status(thm)],[c_12,c_10]) ).
cnf(c_19,negated_conjecture,
~ subset(sK0,sK1),
inference(resolve,[status(thm)],[c_18,c_9]) ).
cnf(c_17,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_11,c_19]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET899+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n018.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sat Sep 26 08:26:53 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 4188959 was started by sandbox on n018,
% 0.09/0.36 % Sat Sep 26 08:26:53 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).
% 0.14/0.39
% 0.14/0.39 % SZS status Theorem for theBenchmark
% 0.14/0.39
% 0.14/0.39 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.14/0.39 % Length of proof is 7.
% 0.14/0.39 % Level of proof is 2.
% 0.14/0.39 % Maximum clause weight is 12.000.
% 0.14/0.39 % Given clauses 4.
% 0.14/0.39
% 0.14/0.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------