%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET638+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 : n026.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 08:36:42 AM UTC 2026
% Result : Theorem 0.14s 0.42s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 6
% Syntax : Number of formulae : 26 ( 20 unt; 0 def)
% Number of atoms : 36 ( 19 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 15 ( 5 ~; 1 |; 6 &)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 34 ( 2 sgn 16 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(intersection_is_subset,axiom,
! [B,C] : subset(intersection(B,C),B),
file('theBenchmark.p',intersection_is_subset) ).
fof(subset_intersection,axiom,
! [B,C] :
( subset(B,C)
=> intersection(B,C) = B ),
file('theBenchmark.p',subset_intersection) ).
fof(union_empty_set,axiom,
! [B] : union(B,empty_set) = B,
file('theBenchmark.p',union_empty_set) ).
fof(intersection_distributes_over_union,axiom,
! [B,C,D] : intersection(B,union(C,D)) = union(intersection(B,C),intersection(B,D)),
file('theBenchmark.p',intersection_distributes_over_union) ).
fof(commutativity_of_intersection,axiom,
! [B,C] : intersection(B,C) = intersection(C,B),
file('theBenchmark.p',commutativity_of_intersection) ).
fof(prove_th120,conjecture,
! [B,C,D] :
( ( intersection(B,D) = empty_set
& subset(B,union(C,D)) )
=> subset(B,C) ),
file('theBenchmark.p',prove_th120) ).
fof(prove_th120_neg,negated_conjecture,
~ ! [B,C,D] :
( ( intersection(B,D) = empty_set
& subset(B,union(C,D)) )
=> subset(B,C) ),
inference(assume_negation,[status(cth)],[prove_th120]) ).
fof(nnf_15,plain,
? [B,C,D] :
( ~ subset(B,C)
& intersection(B,D) = empty_set
& subset(B,union(C,D)) ),
inference(fof_nnf,[status(thm)],[prove_th120_neg]) ).
fof(sk_prove_th120_neg,plain,
( ~ subset(sK0,sK1)
& intersection(sK0,sK2) = empty_set
& subset(sK0,union(sK1,sK2)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(B,sK0),skolemize(C,sK1),skolemize(D,sK2)],[nnf_15]) ).
cnf(c_19,negated_conjecture,
~ subset(sK0,sK1),
inference(split_conjunct,[status(thm)],[sk_prove_th120_neg]) ).
cnf(c_20,negated_conjecture,
intersection(sK0,sK2) = empty_set,
inference(split_conjunct,[status(thm)],[sk_prove_th120_neg]) ).
cnf(c_21,negated_conjecture,
empty_set = intersection(sK0,sK2),
inference(copy,[status(thm)],[c_20]) ).
cnf(c_22,negated_conjecture,
subset(sK0,union(sK1,sK2)),
inference(split_conjunct,[status(thm)],[sk_prove_th120_neg]) ).
cnf(c_28,plain,
intersection(A,B) = intersection(B,A),
inference(clausify,[status(thm)],[commutativity_of_intersection]) ).
cnf(c_44,plain,
union(intersection(A,B),intersection(A,C)) = intersection(A,union(B,C)),
inference(clausify,[status(thm)],[intersection_distributes_over_union]) ).
cnf(c_45,plain,
union(A,empty_set) = A,
inference(clausify,[status(thm)],[union_empty_set]) ).
cnf(c_46,plain,
union(A,intersection(sK0,sK2)) = A,
inference(paramod,[status(thm)],[c_21,c_45]) ).
cnf(c_47,plain,
( intersection(A,B) = A
| ~ subset(A,B) ),
inference(clausify,[status(thm)],[subset_intersection]) ).
cnf(c_48,plain,
subset(intersection(A,B),A),
inference(clausify,[status(thm)],[intersection_is_subset]) ).
cnf(c_219,plain,
intersection(sK0,A) = intersection(sK0,union(A,sK2)),
inference(paramod,[status(thm)],[c_46,c_44]) ).
cnf(c_112,plain,
intersection(sK0,union(A,sK2)) = intersection(sK0,A),
inference(copy,[status(thm)],[c_219]) ).
cnf(c_220,negated_conjecture,
intersection(sK0,union(sK1,sK2)) = sK0,
inference(resolve,[status(thm)],[c_47,c_22]) ).
cnf(c_115,negated_conjecture,
intersection(sK0,sK1) = sK0,
inference(paramod,[status(thm)],[c_112,c_220]) ).
cnf(c_118,plain,
subset(intersection(A,B),B),
inference(paramod,[status(thm)],[c_28,c_48]) ).
cnf(c_221,plain,
subset(sK0,sK1),
inference(paramod,[status(thm)],[c_115,c_118]) ).
cnf(c_218,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_19,c_221]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET638+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n026.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sat Sep 26 08:04:55 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.36 % Process 490110 was started by sandbox2 on n026,
% 0.09/0.36 % Sat Sep 26 08:04:55 2026
% 0.09/0.36 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.09/0.37
% 0.09/0.37 % From the command line: assign(max_seconds, 300).
% 0.14/0.42
% 0.14/0.42 % SZS status Theorem for theBenchmark
% 0.14/0.42
% 0.14/0.42 % Proof 1 at 0.02 (+ 0.02) seconds.
% 0.14/0.42 % Length of proof is 20.
% 0.14/0.42 % Level of proof is 6.
% 0.14/0.42 % Maximum clause weight is 13.000.
% 0.14/0.42 % Given clauses 44.
% 0.14/0.42
% 0.14/0.42 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------