%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET589+3 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n009.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 08:36:32 AM UTC 2026
% Result : Theorem 0.07s 5.37s
% Output : CNFRefutation 0.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 4
% Syntax : Number of formulae : 18 ( 7 unt; 0 def)
% Number of atoms : 35 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 27 ( 10 ~; 5 |; 7 &)
% ( 0 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 34 ( 0 sgn 17 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(transitivity_of_subset,axiom,
! [B,C,D] :
( ( subset(C,D)
& subset(B,C) )
=> subset(B,D) ),
file('theBenchmark.p',transitivity_of_subset) ).
fof(difference_subset1,axiom,
! [B,C,D] :
( subset(B,C)
=> subset(difference(B,D),difference(C,D)) ),
file('theBenchmark.p',difference_subset1) ).
fof(difference_subset2,axiom,
! [B,C,D] :
( subset(B,C)
=> subset(difference(D,C),difference(D,B)) ),
file('theBenchmark.p',difference_subset2) ).
fof(prove_th48,conjecture,
! [B,C,D,E] :
( ( subset(D,E)
& subset(B,C) )
=> subset(difference(B,E),difference(C,D)) ),
file('theBenchmark.p',prove_th48) ).
fof(prove_th48_neg,negated_conjecture,
~ ! [B,C,D,E] :
( ( subset(D,E)
& subset(B,C) )
=> subset(difference(B,E),difference(C,D)) ),
inference(assume_negation,[status(cth)],[prove_th48]) ).
cnf(c_8,plain,
( subset(A,C)
| ~ subset(B,C)
| ~ subset(A,B) ),
inference(clausify,[status(thm)],[transitivity_of_subset]) ).
cnf(c_9,plain,
( subset(difference(A,C),difference(B,C))
| ~ subset(A,B) ),
inference(clausify,[status(thm)],[difference_subset1]) ).
cnf(c_10,plain,
( subset(difference(C,B),difference(C,A))
| ~ subset(A,B) ),
inference(clausify,[status(thm)],[difference_subset2]) ).
fof(nnf_7,plain,
? [B,C,D,E] :
( ~ subset(difference(B,E),difference(C,D))
& subset(D,E)
& subset(B,C) ),
inference(fof_nnf,[status(thm)],[prove_th48_neg]) ).
fof(sk_prove_th48_neg,plain,
( ~ subset(difference(sK0,sK3),difference(sK1,sK2))
& subset(sK2,sK3)
& subset(sK0,sK1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3]),skolemize(B,sK0),skolemize(C,sK1),skolemize(D,sK2),skolemize(E,sK3)],[nnf_7]) ).
cnf(c_18,negated_conjecture,
subset(sK0,sK1),
inference(split_conjunct,[status(thm)],[sk_prove_th48_neg]) ).
cnf(c_19,negated_conjecture,
subset(sK2,sK3),
inference(split_conjunct,[status(thm)],[sk_prove_th48_neg]) ).
cnf(c_20,negated_conjecture,
~ subset(difference(sK0,sK3),difference(sK1,sK2)),
inference(split_conjunct,[status(thm)],[sk_prove_th48_neg]) ).
cnf(c_26,plain,
subset(difference(sK0,A),difference(sK1,A)),
inference(resolve,[status(thm)],[c_18,c_9]) ).
cnf(c_29,plain,
subset(difference(A,sK3),difference(A,sK2)),
inference(resolve,[status(thm)],[c_19,c_10]) ).
cnf(c_70,plain,
( subset(A,difference(sK1,B))
| ~ subset(A,difference(sK0,B)) ),
inference(resolve,[status(thm)],[c_8,c_26]) ).
cnf(c_71,negated_conjecture,
~ subset(difference(sK0,sK3),difference(sK0,sK2)),
inference(resolve,[status(thm)],[c_70,c_20]) ).
cnf(c_69,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_29,c_71]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET589+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.07/5.35 % Computer : n009.cluster.edu
% 0.07/5.35 % Model : x86_64 x86_64
% 0.07/5.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/5.35 % Memory : 8046.5625MB
% 0.07/5.35 % OS : Linux 6.8.0-71-generic
% 0.07/5.35 % CPULimit : 300
% 0.07/5.35 % WCLimit : 300
% 0.07/5.35 % DateTime : Sat Sep 26 07:57:50 UTC 2026
% 0.07/5.35 % CPUTime :
% 0.07/5.35 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.07/5.35 % Process 3761075 was started by sandbox2 on n009,
% 0.07/5.35 % Sat Sep 26 07:57:50 2026
% 0.07/5.35 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.07/5.36
% 0.07/5.36 % From the command line: assign(max_seconds, 300).
% 0.07/5.37
% 0.07/5.37 % SZS status Theorem for theBenchmark
% 0.07/5.37
% 0.07/5.37 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.07/5.37 % Length of proof is 13.
% 0.07/5.37 % Level of proof is 3.
% 0.07/5.37 % Maximum clause weight is 10.000.
% 0.07/5.37 % Given clauses 29.
% 0.07/5.37
% 0.07/5.37 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------