%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET183+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 : n015.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 08:35:59 AM UTC 2026
% Result : Theorem 0.17s 0.45s
% Output : CNFRefutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 5
% Syntax : Number of formulae : 29 ( 9 unt; 0 def)
% Number of atoms : 69 ( 7 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 68 ( 28 ~; 24 |; 10 &)
% ( 3 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 50 ( 1 sgn 27 !; 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(intersection_is_subset,axiom,
! [B,C] : subset(intersection(B,C),B),
file('theBenchmark.p',intersection_is_subset) ).
fof(subset_defn,axiom,
! [B,C] :
( subset(B,C)
<=> ! [D] :
( member(D,B)
=> member(D,C) ) ),
file('theBenchmark.p',subset_defn) ).
fof(equal_defn,axiom,
! [B,C] :
( B = C
<=> ( subset(C,B)
& subset(B,C) ) ),
file('theBenchmark.p',equal_defn) ).
fof(prove_subset_intersection,conjecture,
! [B,C] :
( subset(B,C)
=> intersection(B,C) = B ),
file('theBenchmark.p',prove_subset_intersection) ).
fof(prove_subset_intersection_neg,negated_conjecture,
~ ! [B,C] :
( subset(B,C)
=> intersection(B,C) = B ),
inference(assume_negation,[status(cth)],[prove_subset_intersection]) ).
cnf(c_11,plain,
( ~ member(A,C)
| ~ member(A,B)
| member(A,intersection(B,C)) ),
inference(clausify,[status(thm)],[intersection_defn]) ).
cnf(c_12,plain,
subset(intersection(A,B),A),
inference(clausify,[status(thm)],[intersection_is_subset]) ).
fof(nnf_3,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_3]) ).
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_13,plain,
( member(C,B)
| ~ member(C,A)
| ~ subset(A,B) ),
inference(split_conjunct,[status(thm)],[sk_subset_defn]) ).
cnf(c_14,plain,
( member(sK0(A,B),A)
| subset(A,B) ),
inference(split_conjunct,[status(thm)],[sk_subset_defn]) ).
cnf(c_15,plain,
( ~ member(sK0(A,B),B)
| subset(A,B) ),
inference(split_conjunct,[status(thm)],[sk_subset_defn]) ).
cnf(c_18,plain,
( ~ subset(A,B)
| ~ subset(B,A)
| A = B ),
inference(clausify,[status(thm)],[equal_defn]) ).
fof(nnf_8,plain,
? [B,C] :
( intersection(B,C) != B
& subset(B,C) ),
inference(fof_nnf,[status(thm)],[prove_subset_intersection_neg]) ).
fof(sk_prove_subset_intersection_neg,plain,
( intersection(sK1,sK2) != sK1
& subset(sK1,sK2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2]),skolemize(B,sK1),skolemize(C,sK2)],[nnf_8]) ).
cnf(c_25,negated_conjecture,
subset(sK1,sK2),
inference(split_conjunct,[status(thm)],[sk_prove_subset_intersection_neg]) ).
cnf(c_26,negated_conjecture,
intersection(sK1,sK2) != sK1,
inference(split_conjunct,[status(thm)],[sk_prove_subset_intersection_neg]) ).
cnf(c_30,plain,
( ~ member(sK0(A,B),C)
| member(sK0(A,B),intersection(A,C))
| subset(A,B) ),
inference(resolve,[status(thm)],[c_14,c_11]) ).
cnf(c_65,plain,
( member(A,sK2)
| ~ member(A,sK1) ),
inference(resolve,[status(thm)],[c_25,c_13]) ).
cnf(c_114,negated_conjecture,
( ~ subset(intersection(sK1,sK2),sK1)
| ~ subset(sK1,intersection(sK1,sK2)) ),
inference(resolve,[status(thm)],[c_18,c_26]) ).
cnf(c_68,negated_conjecture,
~ subset(sK1,intersection(sK1,sK2)),
inference(resolve,[status(thm)],[c_114,c_12]) ).
cnf(c_81,plain,
~ member(sK0(sK1,intersection(sK1,sK2)),intersection(sK1,sK2)),
inference(resolve,[status(thm)],[c_15,c_68]) ).
cnf(c_115,plain,
( ~ member(sK0(sK1,intersection(sK1,sK2)),A)
| member(sK0(sK1,intersection(sK1,sK2)),intersection(sK1,A)) ),
inference(resolve,[status(thm)],[c_30,c_68]) ).
cnf(c_87,plain,
~ member(sK0(sK1,intersection(sK1,sK2)),sK2),
inference(resolve,[status(thm)],[c_115,c_81]) ).
cnf(c_95,plain,
( subset(sK1,A)
| member(sK0(sK1,A),sK2) ),
inference(resolve,[status(thm)],[c_65,c_14]) ).
cnf(c_116,plain,
member(sK0(sK1,intersection(sK1,sK2)),sK2),
inference(resolve,[status(thm)],[c_95,c_68]) ).
cnf(c_113,plain,
$false,
inference(resolve,[status(thm)],[c_87,c_116]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SET183+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.17/0.43 % Computer : n015.cluster.edu
% 0.17/0.43 % Model : x86_64 x86_64
% 0.17/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.43 % Memory : 8046.5625MB
% 0.17/0.43 % OS : Linux 6.8.0-71-generic
% 0.17/0.43 % CPULimit : 300
% 0.17/0.43 % WCLimit : 300
% 0.17/0.43 % DateTime : Sat Sep 26 07:20:30 UTC 2026
% 0.17/0.43 % CPUTime :
% 0.17/0.43 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.17/0.43 % Process 3424358 was started by sandbox2 on n015,
% 0.17/0.43 % Sat Sep 26 07:20:30 2026
% 0.17/0.43 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.17/0.44
% 0.17/0.44 % From the command line: assign(max_seconds, 300).
% 0.17/0.45
% 0.17/0.45 % SZS status Theorem for theBenchmark
% 0.17/0.45
% 0.17/0.45 % Proof 1 at 0.01 (+ 0.00) seconds.
% 0.17/0.45 % Length of proof is 20.
% 0.17/0.45 % Level of proof is 5.
% 0.17/0.45 % Maximum clause weight is 25.000.
% 0.17/0.45 % Given clauses 32.
% 0.17/0.45
% 0.17/0.45 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------