%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET631+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 : n016.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 0.16s 0.44s
% Output : CNFRefutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 4
% Syntax : Number of formulae : 24 ( 8 unt; 0 def)
% Number of atoms : 56 ( 0 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 57 ( 25 ~; 17 |; 10 &)
% ( 2 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 44 ( 1 sgn 26 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(difference_defn,axiom,
! [B,C,D] :
( member(D,difference(B,C))
<=> ( ~ member(D,C)
& member(D,B) ) ),
file('theBenchmark.p',difference_defn) ).
fof(intersect_defn,axiom,
! [B,C] :
( intersect(B,C)
<=> ? [D] :
( member(D,C)
& member(D,B) ) ),
file('theBenchmark.p',intersect_defn) ).
fof(symmetry_of_intersect,axiom,
! [B,C] :
( intersect(B,C)
=> intersect(C,B) ),
file('theBenchmark.p',symmetry_of_intersect) ).
fof(prove_th113,conjecture,
! [B,C,D] :
( intersect(B,difference(C,D))
=> intersect(B,C) ),
file('theBenchmark.p',prove_th113) ).
fof(prove_th113_neg,negated_conjecture,
~ ! [B,C,D] :
( intersect(B,difference(C,D))
=> intersect(B,C) ),
inference(assume_negation,[status(cth)],[prove_th113]) ).
cnf(c_5,plain,
( member(A,B)
| ~ member(A,difference(B,C)) ),
inference(clausify,[status(thm)],[difference_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(sK0(B,C),C)
& member(sK0(B,C),B) )
| ~ intersect(B,C) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0(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(sK0(VAR_0,VAR_1),VAR_1)
| ~ intersect(VAR_0,VAR_1) )
& ! [VAR_0,VAR_1] :
( member(sK0(VAR_0,VAR_1),VAR_0)
| ~ intersect(VAR_0,VAR_1) ) ),
inference(cnf_transformation,[status(thm)],[sk_intersect_defn_sk]) ).
cnf(c_8,plain,
( member(sK0(A,B),A)
| ~ intersect(A,B) ),
inference(split_conjunct,[status(thm)],[sk_intersect_defn]) ).
cnf(c_9,plain,
( member(sK0(A,B),B)
| ~ intersect(A,B) ),
inference(split_conjunct,[status(thm)],[sk_intersect_defn]) ).
cnf(c_10,plain,
( ~ member(C,B)
| ~ member(C,A)
| intersect(A,B) ),
inference(split_conjunct,[status(thm)],[sk_intersect_defn]) ).
cnf(c_11,plain,
( intersect(B,A)
| ~ intersect(A,B) ),
inference(clausify,[status(thm)],[symmetry_of_intersect]) ).
fof(nnf_4,plain,
? [B,C,D] :
( ~ intersect(B,C)
& intersect(B,difference(C,D)) ),
inference(fof_nnf,[status(thm)],[prove_th113_neg]) ).
fof(sk_prove_th113_neg,plain,
( ~ intersect(sK1,sK2)
& intersect(sK1,difference(sK2,sK3)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2,sK3]),skolemize(B,sK1),skolemize(C,sK2),skolemize(D,sK3)],[nnf_4]) ).
cnf(c_12,negated_conjecture,
intersect(sK1,difference(sK2,sK3)),
inference(split_conjunct,[status(thm)],[sk_prove_th113_neg]) ).
cnf(c_13,negated_conjecture,
~ intersect(sK1,sK2),
inference(split_conjunct,[status(thm)],[sk_prove_th113_neg]) ).
cnf(c_16,plain,
member(sK0(sK1,difference(sK2,sK3)),difference(sK2,sK3)),
inference(resolve,[status(thm)],[c_12,c_9]) ).
cnf(c_17,plain,
member(sK0(sK1,difference(sK2,sK3)),sK1),
inference(resolve,[status(thm)],[c_12,c_8]) ).
cnf(c_18,negated_conjecture,
~ intersect(sK2,sK1),
inference(resolve,[status(thm)],[c_11,c_13]) ).
cnf(c_44,plain,
( ~ member(A,sK1)
| ~ member(A,sK2) ),
inference(resolve,[status(thm)],[c_10,c_18]) ).
cnf(c_25,plain,
~ member(sK0(sK1,difference(sK2,sK3)),sK2),
inference(resolve,[status(thm)],[c_44,c_17]) ).
cnf(c_45,plain,
member(sK0(sK1,difference(sK2,sK3)),sK2),
inference(resolve,[status(thm)],[c_16,c_5]) ).
cnf(c_43,plain,
$false,
inference(resolve,[status(thm)],[c_25,c_45]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SET631+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.16/0.42 % Computer : n016.cluster.edu
% 0.16/0.42 % Model : x86_64 x86_64
% 0.16/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.42 % Memory : 8046.5625MB
% 0.16/0.42 % OS : Linux 6.8.0-71-generic
% 0.16/0.42 % CPULimit : 300
% 0.16/0.42 % WCLimit : 300
% 0.16/0.42 % DateTime : Sat Sep 26 08:06:45 UTC 2026
% 0.16/0.42 % CPUTime :
% 0.16/0.42 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.16/0.42 % Process 373038 was started by sandbox on n016,
% 0.16/0.42 % Sat Sep 26 08:06:45 2026
% 0.16/0.42 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.16/0.43
% 0.16/0.43 % From the command line: assign(max_seconds, 300).
% 0.16/0.44
% 0.16/0.44 % SZS status Theorem for theBenchmark
% 0.16/0.44
% 0.16/0.44 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.16/0.44 % Length of proof is 16.
% 0.16/0.44 % Level of proof is 4.
% 0.16/0.44 % Maximum clause weight is 9.000.
% 0.16/0.44 % Given clauses 17.
% 0.16/0.44
% 0.16/0.44 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------