%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET627+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 : 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 08:36:40 AM UTC 2026
% Result : Theorem 0.08s 0.37s
% Output : CNFRefutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 4
% Syntax : Number of formulae : 17 ( 10 unt; 0 def)
% Number of atoms : 38 ( 0 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 40 ( 19 ~; 12 |; 7 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-2 aty)
% Number of variables : 29 ( 2 sgn 20 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(empty_set_defn,axiom,
! [B] : ~ member(B,empty_set),
file('theBenchmark.p',empty_set_defn) ).
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_th104,conjecture,
! [B] : disjoint(B,empty_set),
file('theBenchmark.p',prove_th104) ).
fof(prove_th104_neg,negated_conjecture,
~ ! [B] : disjoint(B,empty_set),
inference(assume_negation,[status(cth)],[prove_th104]) ).
cnf(c_7,plain,
( intersect(A,B)
| disjoint(A,B) ),
inference(clausify,[status(thm)],[disjoint_defn]) ).
fof(nnf_6,plain,
? [B] : ~ disjoint(B,empty_set),
inference(fof_nnf,[status(thm)],[prove_th104_neg]) ).
fof(sk_prove_th104_neg,plain,
~ disjoint(sK0,empty_set),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(B,sK0)],[nnf_6]) ).
cnf(c_9,negated_conjecture,
~ disjoint(sK0,empty_set),
inference(split_conjunct,[status(thm)],[sk_prove_th104_neg]) ).
cnf(c_13,plain,
~ member(A,empty_set),
inference(clausify,[status(thm)],[empty_set_defn]) ).
fof(nnf_2,plain,
! [B,C] :
( ( ! [D] :
( ~ member(D,C)
| ~ member(D,B) )
| intersect(B,C) )
& ( ? [X0] :
( member(X0,C)
& member(X0,B) )
| ~ intersect(B,C) ) ),
inference(fof_nnf,[status(thm)],[intersect_defn]) ).
fof(sk_intersect_defn_sk,plain,
! [B,C] :
( ( ! [D] :
( ~ member(D,C)
| ~ member(D,B) )
| intersect(B,C) )
& ( ( member(sK1(B,C),C)
& member(sK1(B,C),B) )
| ~ intersect(B,C) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(X0,sK1(B,C))],[nnf_2]) ).
fof(sk_intersect_defn,plain,
( ! [VAR_0,VAR_1,VAR_2] :
( ~ member(VAR_2,VAR_1)
| ~ member(VAR_2,VAR_0)
| intersect(VAR_0,VAR_1) )
& ! [VAR_0,VAR_1] :
( member(sK1(VAR_0,VAR_1),VAR_1)
| ~ intersect(VAR_0,VAR_1) )
& ! [VAR_0,VAR_1] :
( member(sK1(VAR_0,VAR_1),VAR_0)
| ~ intersect(VAR_0,VAR_1) ) ),
inference(cnf_transformation,[status(thm)],[sk_intersect_defn_sk]) ).
cnf(c_15,plain,
( member(sK1(A,B),B)
| ~ intersect(A,B) ),
inference(split_conjunct,[status(thm)],[sk_intersect_defn]) ).
cnf(c_18,negated_conjecture,
intersect(sK0,empty_set),
inference(resolve,[status(thm)],[c_9,c_7]) ).
cnf(c_20,plain,
~ intersect(A,empty_set),
inference(resolve,[status(thm)],[c_15,c_13]) ).
cnf(c_21,plain,
$false,
inference(resolve,[status(thm)],[c_20,c_18]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET627+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n004.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Sat Sep 26 08:01:51 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.08/0.36 % Process 1183410 was started by sandbox on n004,
% 0.08/0.36 % Sat Sep 26 08:01:51 2026
% 0.08/0.36 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.08/0.36
% 0.08/0.36 % From the command line: assign(max_seconds, 300).
% 0.08/0.37
% 0.08/0.37 % SZS status Theorem for theBenchmark
% 0.08/0.37
% 0.08/0.37 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.08/0.37 % Length of proof is 11.
% 0.08/0.37 % Level of proof is 3.
% 0.08/0.37 % Maximum clause weight is 8.000.
% 0.08/0.37 % Given clauses 4.
% 0.08/0.37
% 0.08/0.37 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------