%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET947+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 : n002.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 08:37:20 AM UTC 2026
% Result : Theorem 0.12s 0.39s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 4
% Syntax : Number of formulae : 21 ( 10 unt; 0 def)
% Number of atoms : 48 ( 2 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 47 ( 20 ~; 16 |; 6 &)
% ( 3 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 1 con; 0-2 aty)
% Number of variables : 36 ( 0 sgn 23 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(d1_zfmisc_1,axiom,
! [A,B] :
( B = powerset(A)
<=> ! [C] :
( in(C,B)
<=> subset(C,A) ) ),
file('theBenchmark.p',d1_zfmisc_1) ).
fof(d3_tarski,axiom,
! [A,B] :
( subset(A,B)
<=> ! [C] :
( in(C,A)
=> in(C,B) ) ),
file('theBenchmark.p',d3_tarski) ).
fof(l50_zfmisc_1,axiom,
! [A,B] :
( in(A,B)
=> subset(A,union(B)) ),
file('theBenchmark.p',l50_zfmisc_1) ).
fof(t100_zfmisc_1,conjecture,
! [A] : subset(A,powerset(union(A))),
file('theBenchmark.p',t100_zfmisc_1) ).
fof(t100_zfmisc_1_neg,negated_conjecture,
~ ! [A] : subset(A,powerset(union(A))),
inference(assume_negation,[status(cth)],[t100_zfmisc_1]) ).
cnf(c_11,plain,
( ~ subset(C,A)
| in(C,B)
| powerset(A) != B ),
inference(clausify,[status(thm)],[d1_zfmisc_1]) ).
fof(nnf_3,plain,
! [A,B] :
( ( ? [C] :
( ~ in(C,B)
& in(C,A) )
| subset(A,B) )
& ( ! [X0] :
( in(X0,B)
| ~ in(X0,A) )
| ~ subset(A,B) ) ),
inference(fof_nnf,[status(thm)],[d3_tarski]) ).
fof(sk_d3_tarski_sk,plain,
! [A,B] :
( ( ( ~ in(sK0(A,B),B)
& in(sK0(A,B),A) )
| subset(A,B) )
& ( ! [X0] :
( in(X0,B)
| ~ in(X0,A) )
| ~ subset(A,B) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(C,sK0(A,B))],[nnf_3]) ).
fof(sk_d3_tarski,plain,
( ! [VAR_0,VAR_1] :
( ~ in(sK0(VAR_0,VAR_1),VAR_1)
| subset(VAR_0,VAR_1) )
& ! [VAR_0,VAR_1] :
( in(sK0(VAR_0,VAR_1),VAR_0)
| subset(VAR_0,VAR_1) )
& ! [VAR_0,VAR_1,VAR_2] :
( in(VAR_2,VAR_1)
| ~ in(VAR_2,VAR_0)
| ~ subset(VAR_0,VAR_1) ) ),
inference(cnf_transformation,[status(thm)],[sk_d3_tarski_sk]) ).
cnf(c_15,plain,
( in(sK0(A,B),A)
| subset(A,B) ),
inference(split_conjunct,[status(thm)],[sk_d3_tarski]) ).
cnf(c_16,plain,
( ~ in(sK0(A,B),B)
| subset(A,B) ),
inference(split_conjunct,[status(thm)],[sk_d3_tarski]) ).
cnf(c_17,plain,
( subset(A,union(B))
| ~ in(A,B) ),
inference(clausify,[status(thm)],[l50_zfmisc_1]) ).
fof(nnf_8,plain,
? [A] : ~ subset(A,powerset(union(A))),
inference(fof_nnf,[status(thm)],[t100_zfmisc_1_neg]) ).
fof(sk_t100_zfmisc_1_neg,plain,
~ subset(sK1,powerset(union(sK1))),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(A,sK1)],[nnf_8]) ).
cnf(c_21,negated_conjecture,
~ subset(sK1,powerset(union(sK1))),
inference(split_conjunct,[status(thm)],[sk_t100_zfmisc_1_neg]) ).
cnf(c_29,plain,
in(sK0(sK1,powerset(union(sK1))),sK1),
inference(resolve,[status(thm)],[c_21,c_15]) ).
cnf(c_30,negated_conjecture,
~ in(sK0(sK1,powerset(union(sK1))),powerset(union(sK1))),
inference(resolve,[status(thm)],[c_16,c_21]) ).
cnf(c_67,plain,
subset(sK0(sK1,powerset(union(sK1))),union(sK1)),
inference(resolve,[status(thm)],[c_29,c_17]) ).
cnf(c_106,plain,
( ~ subset(A,B)
| in(A,powerset(B)) ),
inference(xxres,[status(thm)],[c_11]) ).
cnf(c_107,plain,
~ subset(sK0(sK1,powerset(union(sK1))),union(sK1)),
inference(resolve,[status(thm)],[c_106,c_30]) ).
cnf(c_105,plain,
$false,
inference(resolve,[status(thm)],[c_67,c_107]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET947+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.36 % Computer : n002.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Sat Sep 26 08:29:50 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.12/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.12/0.37 % Process 1257329 was started by sandbox on n002,
% 0.12/0.37 % Sat Sep 26 08:29:50 2026
% 0.12/0.37 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.12/0.37
% 0.12/0.37 % From the command line: assign(max_seconds, 300).
% 0.12/0.39
% 0.12/0.39 % SZS status Theorem for theBenchmark
% 0.12/0.39
% 0.12/0.39 % Proof 1 at 0.01 (+ 0.00) seconds.
% 0.12/0.39 % Length of proof is 13.
% 0.12/0.39 % Level of proof is 4.
% 0.12/0.39 % Maximum clause weight is 29.000.
% 0.12/0.39 % Given clauses 41.
% 0.12/0.39
% 0.12/0.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------