%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET605+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 : 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 08:36:35 AM UTC 2026
% Result : Theorem 0.11s 0.40s
% Output : CNFRefutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 3
% Syntax : Number of formulae : 11 ( 9 unt; 0 def)
% Number of atoms : 13 ( 7 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 8 ( 6 ~; 1 |; 0 &)
% ( 1 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 14 ( 1 sgn 8 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(subset_of_union,axiom,
! [B,C] : subset(B,union(B,C)),
file('theBenchmark.p',subset_of_union) ).
fof(difference_empty_set,axiom,
! [B,C] :
( difference(B,C) = empty_set
<=> subset(B,C) ),
file('theBenchmark.p',difference_empty_set) ).
fof(prove_th76,conjecture,
! [B,C] : difference(B,union(B,C)) = empty_set,
file('theBenchmark.p',prove_th76) ).
fof(prove_th76_neg,negated_conjecture,
~ ! [B,C] : difference(B,union(B,C)) = empty_set,
inference(assume_negation,[status(cth)],[prove_th76]) ).
fof(nnf_12,plain,
? [B,C] : difference(B,union(B,C)) != empty_set,
inference(fof_nnf,[status(thm)],[prove_th76_neg]) ).
fof(sk_prove_th76_neg,plain,
difference(sK0,union(sK0,sK1)) != empty_set,
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(B,sK0),skolemize(C,sK1)],[nnf_12]) ).
cnf(c_16,negated_conjecture,
difference(sK0,union(sK0,sK1)) != empty_set,
inference(split_conjunct,[status(thm)],[sk_prove_th76_neg]) ).
cnf(c_36,plain,
( ~ subset(A,B)
| difference(A,B) = empty_set ),
inference(clausify,[status(thm)],[difference_empty_set]) ).
cnf(c_38,plain,
subset(A,union(A,B)),
inference(clausify,[status(thm)],[subset_of_union]) ).
cnf(c_89,negated_conjecture,
~ subset(sK0,union(sK0,sK1)),
inference(resolve,[status(thm)],[c_36,c_16]) ).
cnf(c_88,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_38,c_89]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET605+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 : n007.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 07:57:09 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.38 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.11/0.38 % Process 3212406 was started by sandbox on n007,
% 0.11/0.38 % Sat Sep 26 07:57:09 2026
% 0.11/0.38 % 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).
% 0.11/0.40
% 0.11/0.40 % SZS status Theorem for theBenchmark
% 0.11/0.40
% 0.11/0.40 % Proof 1 at 0.00 (+ 0.01) seconds.
% 0.11/0.40 % Length of proof is 7.
% 0.11/0.40 % Level of proof is 2.
% 0.11/0.40 % Maximum clause weight is 8.000.
% 0.11/0.40 % Given clauses 22.
% 0.11/0.40
% 0.11/0.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------