%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET583+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 : n005.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 08:36:31 AM UTC 2026
% Result : Theorem 0.15s 0.39s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 2
% Syntax : Number of formulae : 13 ( 5 unt; 0 def)
% Number of atoms : 27 ( 9 equ)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 23 ( 9 ~; 4 |; 7 &)
% ( 1 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 2 ( 2 usr; 2 con; 0-0 aty)
% Number of variables : 10 ( 0 sgn 6 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(equal_defn,axiom,
! [B,C] :
( B = C
<=> ( subset(C,B)
& subset(B,C) ) ),
file('theBenchmark.p',equal_defn) ).
fof(prove_extensionality,conjecture,
! [B,C] :
( ( subset(C,B)
& subset(B,C) )
=> B = C ),
file('theBenchmark.p',prove_extensionality) ).
fof(prove_extensionality_neg,negated_conjecture,
~ ! [B,C] :
( ( subset(C,B)
& subset(B,C) )
=> B = C ),
inference(assume_negation,[status(cth)],[prove_extensionality]) ).
cnf(c_7,plain,
( ~ subset(A,B)
| ~ subset(B,A)
| A = B ),
inference(clausify,[status(thm)],[equal_defn]) ).
fof(nnf_4,plain,
? [B,C] :
( C != B
& subset(C,B)
& subset(B,C) ),
inference(fof_nnf,[status(thm)],[prove_extensionality_neg]) ).
fof(sk_prove_extensionality_neg,plain,
( sK1 != sK0
& subset(sK1,sK0)
& subset(sK0,sK1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(B,sK0),skolemize(C,sK1)],[nnf_4]) ).
cnf(c_12,negated_conjecture,
subset(sK0,sK1),
inference(split_conjunct,[status(thm)],[sk_prove_extensionality_neg]) ).
cnf(c_13,negated_conjecture,
subset(sK1,sK0),
inference(split_conjunct,[status(thm)],[sk_prove_extensionality_neg]) ).
cnf(c_14,negated_conjecture,
sK1 != sK0,
inference(split_conjunct,[status(thm)],[sk_prove_extensionality_neg]) ).
cnf(c_17,negated_conjecture,
( ~ subset(sK1,sK0)
| sK0 = sK1 ),
inference(resolve,[status(thm)],[c_12,c_7]) ).
cnf(c_18,negated_conjecture,
( ~ subset(sK1,sK0)
| sK1 = sK0 ),
inference(copy,[status(thm)],[c_17]) ).
cnf(c_19,negated_conjecture,
~ subset(sK1,sK0),
inference(resolve,[status(thm)],[c_14,c_18]) ).
cnf(c_16,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_13,c_19]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET583+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.37 % Computer : n005.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Sat Sep 26 07:57:18 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.11/0.37 % Process 1627648 was started by sandbox on n005,
% 0.11/0.37 % Sat Sep 26 07:57:18 2026
% 0.11/0.37 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.11/0.38
% 0.11/0.38 % From the command line: assign(max_seconds, 300).
% 0.15/0.39
% 0.15/0.39 % SZS status Theorem for theBenchmark
% 0.15/0.39
% 0.15/0.39 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.15/0.39 % Length of proof is 7.
% 0.15/0.39 % Level of proof is 2.
% 0.15/0.39 % Maximum clause weight is 9.000.
% 0.15/0.39 % Given clauses 8.
% 0.15/0.39
% 0.15/0.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------