%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET573+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 : n012.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 08:36:29 AM UTC 2026
% Result : Theorem 0.02s 0.31s
% Output : CNFRefutation 0.02s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 3
% Syntax : Number of formulae : 15 ( 6 unt; 0 def)
% Number of atoms : 30 ( 0 equ)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 25 ( 10 ~; 4 |; 7 &)
% ( 2 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 3 con; 0-0 aty)
% Number of variables : 20 ( 0 sgn 10 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(intersect_defn,axiom,
! [B,C] :
( intersect(B,C)
<=> ? [D] :
( member(D,C)
& member(D,B) ) ),
file('theBenchmark.p',intersect_defn) ).
fof(disjoint_defn,axiom,
! [B,C] :
( disjoint(B,C)
<=> ~ intersect(B,C) ),
file('theBenchmark.p',disjoint_defn) ).
fof(prove_th12,conjecture,
! [B,C,D] :
( ( disjoint(C,D)
& member(B,C) )
=> ~ member(B,D) ),
file('theBenchmark.p',prove_th12) ).
fof(prove_th12_neg,negated_conjecture,
~ ! [B,C,D] :
( ( disjoint(C,D)
& member(B,C) )
=> ~ member(B,D) ),
inference(assume_negation,[status(cth)],[prove_th12]) ).
cnf(c_6,plain,
( ~ intersect(A,B)
| ~ disjoint(A,B) ),
inference(clausify,[status(thm)],[disjoint_defn]) ).
fof(nnf_4,plain,
? [B,C,D] :
( member(B,D)
& disjoint(C,D)
& member(B,C) ),
inference(fof_nnf,[status(thm)],[prove_th12_neg]) ).
fof(sk_prove_th12_neg,plain,
( member(sK2,sK1)
& disjoint(sK0,sK1)
& member(sK2,sK0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK0,sK1]),skolemize(B,sK2),skolemize(C,sK0),skolemize(D,sK1)],[nnf_4]) ).
cnf(c_7,negated_conjecture,
disjoint(sK0,sK1),
inference(split_conjunct,[status(thm)],[sk_prove_th12_neg]) ).
cnf(c_8,negated_conjecture,
~ intersect(sK0,sK1),
inference(resolve,[status(thm)],[c_7,c_6]) ).
cnf(c_9,negated_conjecture,
member(sK2,sK1),
inference(split_conjunct,[status(thm)],[sk_prove_th12_neg]) ).
cnf(c_10,negated_conjecture,
member(sK2,sK0),
inference(split_conjunct,[status(thm)],[sk_prove_th12_neg]) ).
cnf(c_12,plain,
( ~ member(C,B)
| ~ member(C,A)
| intersect(A,B) ),
inference(clausify,[status(thm)],[intersect_defn]) ).
cnf(c_20,negated_conjecture,
( ~ member(sK2,A)
| intersect(sK0,A) ),
inference(resolve,[status(thm)],[c_12,c_10]) ).
cnf(c_18,negated_conjecture,
intersect(sK0,sK1),
inference(resolve,[status(thm)],[c_20,c_9]) ).
cnf(c_19,plain,
$false,
inference(resolve,[status(thm)],[c_18,c_8]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SET573+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.02 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.02/0.29 % Computer : n012.cluster.edu
% 0.02/0.29 % Model : x86_64 x86_64
% 0.02/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.02/0.29 % Memory : 8046.5625MB
% 0.02/0.29 % OS : Linux 6.8.0-71-generic
% 0.02/0.29 % CPULimit : 300
% 0.02/0.29 % WCLimit : 300
% 0.02/0.29 % DateTime : Sat Sep 26 07:56:19 UTC 2026
% 0.02/0.29 % CPUTime :
% 0.02/0.29 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.02/0.29 % Process 69402 was started by sandbox2 on n012,
% 0.02/0.29 % Sat Sep 26 07:56:19 2026
% 0.02/0.29 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.02/0.30
% 0.02/0.30 % From the command line: assign(max_seconds, 300).
% 0.02/0.31
% 0.02/0.31 % SZS status Theorem for theBenchmark
% 0.02/0.31
% 0.02/0.31 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.02/0.31 % Length of proof is 11.
% 0.02/0.31 % Level of proof is 3.
% 0.02/0.31 % Maximum clause weight is 9.000.
% 0.02/0.31 % Given clauses 5.
% 0.02/0.31
% 0.02/0.31 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------