%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET629+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 : n008.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 0.15s 5.42s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 5
% Syntax : Number of formulae : 23 ( 11 unt; 0 def)
% Number of atoms : 51 ( 0 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 51 ( 23 ~; 15 |; 9 &)
% ( 4 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 44 ( 3 sgn 27 !; 4 ?)
% 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(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(disjoint_defn,axiom,
! [B,C] :
( disjoint(B,C)
<=> ~ intersect(B,C) ),
file('theBenchmark.p',disjoint_defn) ).
fof(prove_intersection_and_difference_disjoint,conjecture,
! [B,C] : disjoint(intersection(B,C),difference(B,C)),
file('theBenchmark.p',prove_intersection_and_difference_disjoint) ).
fof(prove_intersection_and_difference_disjoint_neg,negated_conjecture,
~ ! [B,C] : disjoint(intersection(B,C),difference(B,C)),
inference(assume_negation,[status(cth)],[prove_intersection_and_difference_disjoint]) ).
cnf(c_10,plain,
( member(A,C)
| ~ member(A,intersection(B,C)) ),
inference(clausify,[status(thm)],[intersection_defn]) ).
cnf(c_13,plain,
( ~ member(A,C)
| ~ member(A,difference(B,C)) ),
inference(clausify,[status(thm)],[difference_defn]) ).
fof(nnf_3,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_3]) ).
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_15,plain,
( member(sK0(A,B),A)
| ~ intersect(A,B) ),
inference(split_conjunct,[status(thm)],[sk_intersect_defn]) ).
cnf(c_16,plain,
( member(sK0(A,B),B)
| ~ intersect(A,B) ),
inference(split_conjunct,[status(thm)],[sk_intersect_defn]) ).
cnf(c_19,plain,
( intersect(A,B)
| disjoint(A,B) ),
inference(clausify,[status(thm)],[disjoint_defn]) ).
fof(nnf_8,plain,
? [B,C] : ~ disjoint(intersection(B,C),difference(B,C)),
inference(fof_nnf,[status(thm)],[prove_intersection_and_difference_disjoint_neg]) ).
fof(sk_prove_intersection_and_difference_disjoint_neg,plain,
~ disjoint(intersection(sK1,sK2),difference(sK1,sK2)),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2]),skolemize(B,sK1),skolemize(C,sK2)],[nnf_8]) ).
cnf(c_26,negated_conjecture,
~ disjoint(intersection(sK1,sK2),difference(sK1,sK2)),
inference(split_conjunct,[status(thm)],[sk_prove_intersection_and_difference_disjoint_neg]) ).
cnf(c_67,plain,
intersect(intersection(sK1,sK2),difference(sK1,sK2)),
inference(resolve,[status(thm)],[c_26,c_19]) ).
cnf(c_76,plain,
member(sK0(intersection(sK1,sK2),difference(sK1,sK2)),difference(sK1,sK2)),
inference(resolve,[status(thm)],[c_67,c_16]) ).
cnf(c_77,plain,
member(sK0(intersection(sK1,sK2),difference(sK1,sK2)),intersection(sK1,sK2)),
inference(resolve,[status(thm)],[c_67,c_15]) ).
cnf(c_89,plain,
~ member(sK0(intersection(sK1,sK2),difference(sK1,sK2)),sK2),
inference(resolve,[status(thm)],[c_76,c_13]) ).
cnf(c_98,plain,
~ member(sK0(intersection(sK1,sK2),difference(sK1,sK2)),intersection(A,sK2)),
inference(resolve,[status(thm)],[c_10,c_89]) ).
cnf(c_99,plain,
$false,
inference(resolve,[status(thm)],[c_98,c_77]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET629+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/5.38 % Computer : n008.cluster.edu
% 0.10/5.38 % Model : x86_64 x86_64
% 0.10/5.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/5.38 % Memory : 8046.5625MB
% 0.10/5.38 % OS : Linux 6.8.0-71-generic
% 0.10/5.38 % CPULimit : 300
% 0.10/5.38 % WCLimit : 300
% 0.10/5.38 % DateTime : Sat Sep 26 08:02:30 UTC 2026
% 0.10/5.38 % CPUTime :
% 0.10/5.39 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/5.39 % Process 3155366 was started by sandbox2 on n008,
% 0.10/5.39 % Sat Sep 26 08:02:30 2026
% 0.10/5.39 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.10/5.39
% 0.10/5.39 % From the command line: assign(max_seconds, 300).
% 0.15/5.42
% 0.15/5.42 % SZS status Theorem for theBenchmark
% 0.15/5.42
% 0.15/5.42 % Proof 1 at 0.01 (+ 0.00) seconds.
% 0.15/5.42 % Length of proof is 17.
% 0.15/5.42 % Level of proof is 6.
% 0.15/5.42 % Maximum clause weight is 11.000.
% 0.15/5.42 % Given clauses 34.
% 0.15/5.42
% 0.15/5.42 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------