%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET196+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 : n018.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 08:36:01 AM UTC 2026
% Result : Theorem 0.19s 0.47s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 3
% Syntax : Number of formulae : 17 ( 9 unt; 0 def)
% Number of atoms : 40 ( 0 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 40 ( 17 ~; 13 |; 7 &)
% ( 2 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 34 ( 2 sgn 23 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(intersection_defn,axiom,
! [B,C,D] :
( member(D,intersection(B,C))
<=> ( member(D,C)
& member(D,B) ) ),
file('theBenchmark.p',intersection_defn) ).
fof(subset_defn,axiom,
! [B,C] :
( subset(B,C)
<=> ! [D] :
( member(D,B)
=> member(D,C) ) ),
file('theBenchmark.p',subset_defn) ).
fof(prove_intersection_is_subset,conjecture,
! [B,C] : subset(intersection(B,C),B),
file('theBenchmark.p',prove_intersection_is_subset) ).
fof(prove_intersection_is_subset_neg,negated_conjecture,
~ ! [B,C] : subset(intersection(B,C),B),
inference(assume_negation,[status(cth)],[prove_intersection_is_subset]) ).
cnf(c_7,plain,
( member(A,B)
| ~ member(A,intersection(B,C)) ),
inference(clausify,[status(thm)],[intersection_defn]) ).
fof(nnf_2,plain,
! [B,C] :
( ( ? [D] :
( ~ member(D,C)
& member(D,B) )
| subset(B,C) )
& ( ! [X0] :
( member(X0,C)
| ~ member(X0,B) )
| ~ subset(B,C) ) ),
inference(fof_nnf,[status(thm)],[subset_defn]) ).
fof(sk_subset_defn_sk,plain,
! [B,C] :
( ( ( ~ member(sK0(B,C),C)
& member(sK0(B,C),B) )
| subset(B,C) )
& ( ! [X0] :
( member(X0,C)
| ~ member(X0,B) )
| ~ subset(B,C) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(D,sK0(B,C))],[nnf_2]) ).
fof(sk_subset_defn,plain,
( ! [VAR_0,VAR_1] :
( ~ member(sK0(VAR_0,VAR_1),VAR_1)
| subset(VAR_0,VAR_1) )
& ! [VAR_0,VAR_1] :
( member(sK0(VAR_0,VAR_1),VAR_0)
| subset(VAR_0,VAR_1) )
& ! [VAR_0,VAR_1,VAR_2] :
( member(VAR_2,VAR_1)
| ~ member(VAR_2,VAR_0)
| ~ subset(VAR_0,VAR_1) ) ),
inference(cnf_transformation,[status(thm)],[sk_subset_defn_sk]) ).
cnf(c_11,plain,
( member(sK0(A,B),A)
| subset(A,B) ),
inference(split_conjunct,[status(thm)],[sk_subset_defn]) ).
cnf(c_12,plain,
( ~ member(sK0(A,B),B)
| subset(A,B) ),
inference(split_conjunct,[status(thm)],[sk_subset_defn]) ).
fof(nnf_6,plain,
? [B,C] : ~ subset(intersection(B,C),B),
inference(fof_nnf,[status(thm)],[prove_intersection_is_subset_neg]) ).
fof(sk_prove_intersection_is_subset_neg,plain,
~ subset(intersection(sK1,sK2),sK1),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2]),skolemize(B,sK1),skolemize(C,sK2)],[nnf_6]) ).
cnf(c_19,negated_conjecture,
~ subset(intersection(sK1,sK2),sK1),
inference(split_conjunct,[status(thm)],[sk_prove_intersection_is_subset_neg]) ).
cnf(c_44,plain,
member(sK0(intersection(sK1,sK2),sK1),intersection(sK1,sK2)),
inference(resolve,[status(thm)],[c_19,c_11]) ).
cnf(c_45,negated_conjecture,
~ member(sK0(intersection(sK1,sK2),sK1),sK1),
inference(resolve,[status(thm)],[c_12,c_19]) ).
cnf(c_55,plain,
~ member(sK0(intersection(sK1,sK2),sK1),intersection(sK1,A)),
inference(resolve,[status(thm)],[c_7,c_45]) ).
cnf(c_56,plain,
$false,
inference(resolve,[status(thm)],[c_55,c_44]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SET196+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.44 % Computer : n018.cluster.edu
% 0.19/0.44 % Model : x86_64 x86_64
% 0.19/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.44 % Memory : 8046.5625MB
% 0.19/0.44 % OS : Linux 6.8.0-71-generic
% 0.19/0.44 % CPULimit : 300
% 0.19/0.44 % WCLimit : 300
% 0.19/0.44 % DateTime : Sat Sep 26 07:21:06 UTC 2026
% 0.19/0.45 % CPUTime :
% 0.19/0.45 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.19/0.45 % Process 4037518 was started by sandbox2 on n018,
% 0.19/0.45 % Sat Sep 26 07:21:06 2026
% 0.19/0.45 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.19/0.46
% 0.19/0.46 % From the command line: assign(max_seconds, 300).
% 0.19/0.47
% 0.19/0.47 % SZS status Theorem for theBenchmark
% 0.19/0.47
% 0.19/0.47 % Proof 1 at 0.01 (+ 0.00) seconds.
% 0.19/0.47 % Length of proof is 11.
% 0.19/0.47 % Level of proof is 4.
% 0.19/0.47 % Maximum clause weight is 9.000.
% 0.19/0.47 % Given clauses 16.
% 0.19/0.47
% 0.19/0.47 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------