%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET639+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 : n001.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 0.09s 0.40s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 3
% Syntax : Number of formulae : 18 ( 12 unt; 0 def)
% Number of atoms : 28 ( 20 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 19 ( 9 ~; 1 |; 6 &)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 14 ( 0 sgn 8 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(subset_intersection,axiom,
! [B,C] :
( subset(B,C)
=> intersection(B,C) = B ),
file('theBenchmark.p',subset_intersection) ).
fof(commutativity_of_intersection,axiom,
! [B,C] : intersection(B,C) = intersection(C,B),
file('theBenchmark.p',commutativity_of_intersection) ).
fof(prove_th121,conjecture,
! [B,C] :
( ( intersection(C,B) = empty_set
& subset(B,C) )
=> B = empty_set ),
file('theBenchmark.p',prove_th121) ).
fof(prove_th121_neg,negated_conjecture,
~ ! [B,C] :
( ( intersection(C,B) = empty_set
& subset(B,C) )
=> B = empty_set ),
inference(assume_negation,[status(cth)],[prove_th121]) ).
fof(nnf_10,plain,
? [B,C] :
( empty_set != B
& intersection(C,B) = empty_set
& subset(B,C) ),
inference(fof_nnf,[status(thm)],[prove_th121_neg]) ).
fof(sk_prove_th121_neg,plain,
( empty_set != sK0
& intersection(sK1,sK0) = empty_set
& subset(sK0,sK1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(B,sK0),skolemize(C,sK1)],[nnf_10]) ).
cnf(c_14,negated_conjecture,
empty_set != sK0,
inference(split_conjunct,[status(thm)],[sk_prove_th121_neg]) ).
cnf(c_15,negated_conjecture,
sK0 != empty_set,
inference(copy,[status(thm)],[c_14]) ).
cnf(c_16,negated_conjecture,
intersection(sK1,sK0) = empty_set,
inference(split_conjunct,[status(thm)],[sk_prove_th121_neg]) ).
cnf(c_17,negated_conjecture,
empty_set = intersection(sK1,sK0),
inference(copy,[status(thm)],[c_16]) ).
cnf(c_18,negated_conjecture,
subset(sK0,sK1),
inference(split_conjunct,[status(thm)],[sk_prove_th121_neg]) ).
cnf(c_24,plain,
intersection(A,B) = intersection(B,A),
inference(clausify,[status(thm)],[commutativity_of_intersection]) ).
cnf(c_36,plain,
( intersection(A,B) = A
| ~ subset(A,B) ),
inference(clausify,[status(thm)],[subset_intersection]) ).
cnf(c_77,negated_conjecture,
sK0 != intersection(sK1,sK0),
inference(paramod,[status(thm)],[c_17,c_15]) ).
cnf(c_78,negated_conjecture,
sK0 != intersection(sK0,sK1),
inference(paramod,[status(thm)],[c_24,c_77]) ).
cnf(c_37,negated_conjecture,
intersection(sK0,sK1) != sK0,
inference(copy,[status(thm)],[c_78]) ).
cnf(c_79,negated_conjecture,
intersection(sK0,sK1) = sK0,
inference(resolve,[status(thm)],[c_36,c_18]) ).
cnf(c_76,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_37,c_79]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET639+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.37 % Computer : n001.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Sat Sep 26 08:07:57 UTC 2026
% 0.09/0.38 % CPUTime :
% 0.09/0.38 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.38 % Process 1328549 was started by sandbox on n001,
% 0.09/0.38 % Sat Sep 26 08:07:57 2026
% 0.09/0.38 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.09/0.38
% 0.09/0.38 % From the command line: assign(max_seconds, 300).
% 0.09/0.40
% 0.09/0.40 % SZS status Theorem for theBenchmark
% 0.09/0.40
% 0.09/0.40 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.09/0.40 % Length of proof is 12.
% 0.09/0.40 % Level of proof is 4.
% 0.09/0.40 % Maximum clause weight is 8.000.
% 0.09/0.40 % Given clauses 19.
% 0.09/0.40
% 0.09/0.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------