%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET585+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 : n004.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 0.09s 5.37s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 4
% Syntax : Number of formulae : 14 ( 11 unt; 0 def)
% Number of atoms : 19 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 13 ( 8 ~; 3 |; 1 &)
% ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 26 ( 3 sgn 13 !; 3 ?)
% 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(subset_of_union,axiom,
! [B,C] : subset(B,union(B,C)),
file('theBenchmark.p',subset_of_union) ).
fof(intersection_is_subset,axiom,
! [B,C] : subset(intersection(B,C),B),
file('theBenchmark.p',intersection_is_subset) ).
fof(prove_intersection_subset_of_union,conjecture,
! [B,C,D] : subset(intersection(B,C),union(B,D)),
file('theBenchmark.p',prove_intersection_subset_of_union) ).
fof(prove_intersection_subset_of_union_neg,negated_conjecture,
~ ! [B,C,D] : subset(intersection(B,C),union(B,D)),
inference(assume_negation,[status(cth)],[prove_intersection_subset_of_union]) ).
cnf(c_12,plain,
( subset(A,C)
| ~ subset(B,C)
| ~ subset(A,B) ),
inference(clausify,[status(thm)],[transitivity_of_subset]) ).
cnf(c_13,plain,
subset(A,union(A,B)),
inference(clausify,[status(thm)],[subset_of_union]) ).
cnf(c_14,plain,
subset(intersection(A,B),A),
inference(clausify,[status(thm)],[intersection_is_subset]) ).
fof(nnf_11,plain,
? [B,C,D] : ~ subset(intersection(B,C),union(B,D)),
inference(fof_nnf,[status(thm)],[prove_intersection_subset_of_union_neg]) ).
fof(sk_prove_intersection_subset_of_union_neg,plain,
~ subset(intersection(sK0,sK1),union(sK0,sK2)),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(B,sK0),skolemize(C,sK1),skolemize(D,sK2)],[nnf_11]) ).
cnf(c_31,negated_conjecture,
~ subset(intersection(sK0,sK1),union(sK0,sK2)),
inference(split_conjunct,[status(thm)],[sk_prove_intersection_subset_of_union_neg]) ).
cnf(c_87,plain,
( subset(A,union(B,C))
| ~ subset(A,B) ),
inference(resolve,[status(thm)],[c_12,c_13]) ).
cnf(c_88,negated_conjecture,
~ subset(intersection(sK0,sK1),sK0),
inference(resolve,[status(thm)],[c_87,c_31]) ).
cnf(c_86,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_14,c_88]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET585+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/5.35 % Computer : n004.cluster.edu
% 0.09/5.35 % Model : x86_64 x86_64
% 0.09/5.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/5.35 % Memory : 8046.5625MB
% 0.09/5.35 % OS : Linux 6.8.0-71-generic
% 0.09/5.35 % CPULimit : 300
% 0.09/5.35 % WCLimit : 300
% 0.09/5.35 % DateTime : Sat Sep 26 07:57:43 UTC 2026
% 0.09/5.35 % CPUTime :
% 0.09/5.35 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/5.35 % Process 1173360 was started by sandbox2 on n004,
% 0.09/5.35 % Sat Sep 26 07:57:43 2026
% 0.09/5.35 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.09/5.36
% 0.09/5.36 % From the command line: assign(max_seconds, 300).
% 0.09/5.37
% 0.09/5.37 % SZS status Theorem for theBenchmark
% 0.09/5.37
% 0.09/5.37 % Proof 1 at 0.01 (+ 0.00) seconds.
% 0.09/5.37 % Length of proof is 9.
% 0.09/5.37 % Level of proof is 2.
% 0.09/5.37 % Maximum clause weight is 9.000.
% 0.09/5.37 % Given clauses 20.
% 0.09/5.37
% 0.09/5.37 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------