%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET199+4 : 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 : n006.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 81.42s 10.78s
% Output : CNFRefutation 81.42s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 3
% Syntax : Number of formulae : 44 ( 5 unt; 0 def)
% Number of atoms : 124 ( 0 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 117 ( 37 ~; 60 |; 15 &)
% ( 4 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 2 ( 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 : 58 ( 2 sgn 25 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(subset,axiom,
! [A,B] :
( subset(A,B)
<=> ! [X] :
( member(X,A)
=> member(X,B) ) ),
file('theBenchmark.p',subset) ).
fof(intersection,axiom,
! [X,A,B] :
( member(X,intersection(A,B))
<=> ( member(X,B)
& member(X,A) ) ),
file('theBenchmark.p',intersection) ).
fof(thI46,conjecture,
! [A,X,Y] :
( ( subset(A,Y)
& subset(A,X) )
<=> subset(A,intersection(X,Y)) ),
file('theBenchmark.p',thI46) ).
fof(thI46_neg,negated_conjecture,
~ ! [A,X,Y] :
( ( subset(A,Y)
& subset(A,X) )
<=> subset(A,intersection(X,Y)) ),
inference(assume_negation,[status(cth)],[thI46]) ).
fof(nnf_12,plain,
? [A,X,Y] :
( ( ~ subset(A,intersection(X,Y))
| ~ subset(A,Y)
| ~ subset(A,X) )
& ( subset(A,intersection(X,Y))
| ( subset(A,Y)
& subset(A,X) ) ) ),
inference(fof_nnf,[status(thm)],[thI46_neg]) ).
fof(sk_thI46_neg_sk,plain,
( ( ~ subset(sK0,intersection(sK1,sK2))
| ~ subset(sK0,sK2)
| ~ subset(sK0,sK1) )
& ( subset(sK0,intersection(sK1,sK2))
| ( subset(sK0,sK2)
& subset(sK0,sK1) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(A,sK0),skolemize(X,sK1),skolemize(Y,sK2)],[nnf_12]) ).
fof(sk_thI46_neg,plain,
( ( ~ subset(sK0,intersection(sK1,sK2))
| ~ subset(sK0,sK2)
| ~ subset(sK0,sK1) )
& ( subset(sK0,intersection(sK1,sK2))
| subset(sK0,sK2) )
& ( subset(sK0,intersection(sK1,sK2))
| subset(sK0,sK1) ) ),
inference(cnf_transformation,[status(thm)],[sk_thI46_neg_sk]) ).
cnf(c_16,negated_conjecture,
( ~ subset(sK0,intersection(sK1,sK2))
| ~ subset(sK0,sK2)
| ~ subset(sK0,sK1) ),
inference(split_conjunct,[status(thm)],[sk_thI46_neg]) ).
cnf(c_17,negated_conjecture,
( subset(sK0,intersection(sK1,sK2))
| subset(sK0,sK2) ),
inference(split_conjunct,[status(thm)],[sk_thI46_neg]) ).
cnf(c_18,negated_conjecture,
( subset(sK0,intersection(sK1,sK2))
| subset(sK0,sK1) ),
inference(split_conjunct,[status(thm)],[sk_thI46_neg]) ).
cnf(c_37,plain,
( ~ member(A,C)
| ~ member(A,B)
| member(A,intersection(B,C)) ),
inference(clausify,[status(thm)],[intersection]) ).
cnf(c_38,plain,
( member(A,C)
| ~ member(A,intersection(B,C)) ),
inference(clausify,[status(thm)],[intersection]) ).
cnf(c_39,plain,
( member(A,B)
| ~ member(A,intersection(B,C)) ),
inference(clausify,[status(thm)],[intersection]) ).
fof(nnf_1,plain,
! [A,B] :
( ( ? [X] :
( ~ member(X,B)
& member(X,A) )
| subset(A,B) )
& ( ! [X0] :
( member(X0,B)
| ~ member(X0,A) )
| ~ subset(A,B) ) ),
inference(fof_nnf,[status(thm)],[subset]) ).
fof(sk_subset_sk,plain,
! [A,B] :
( ( ( ~ member(sK3(A,B),B)
& member(sK3(A,B),A) )
| subset(A,B) )
& ( ! [X0] :
( member(X0,B)
| ~ member(X0,A) )
| ~ subset(A,B) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(X,sK3(A,B))],[nnf_1]) ).
fof(sk_subset,plain,
( ! [VAR_0,VAR_1] :
( ~ member(sK3(VAR_0,VAR_1),VAR_1)
| subset(VAR_0,VAR_1) )
& ! [VAR_0,VAR_1] :
( member(sK3(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_sk]) ).
cnf(c_42,plain,
( ~ member(sK3(A,B),B)
| subset(A,B) ),
inference(split_conjunct,[status(thm)],[sk_subset]) ).
cnf(c_43,plain,
( member(sK3(A,B),A)
| subset(A,B) ),
inference(split_conjunct,[status(thm)],[sk_subset]) ).
cnf(c_44,plain,
( member(C,B)
| ~ member(C,A)
| ~ subset(A,B) ),
inference(split_conjunct,[status(thm)],[sk_subset]) ).
cnf(c_10919,negated_conjecture,
( subset(sK0,sK1)
| member(A,intersection(sK1,sK2))
| ~ member(A,sK0) ),
inference(resolve,[status(thm)],[c_44,c_18]) ).
cnf(c_157,negated_conjecture,
( subset(sK0,A)
| subset(sK0,sK1)
| member(sK3(sK0,A),intersection(sK1,sK2)) ),
inference(resolve,[status(thm)],[c_10919,c_43]) ).
cnf(c_10920,negated_conjecture,
( subset(sK0,sK2)
| member(A,intersection(sK1,sK2))
| ~ member(A,sK0) ),
inference(resolve,[status(thm)],[c_44,c_17]) ).
cnf(c_161,negated_conjecture,
( subset(sK0,A)
| subset(sK0,sK2)
| member(sK3(sK0,A),intersection(sK1,sK2)) ),
inference(resolve,[status(thm)],[c_10920,c_43]) ).
cnf(c_10921,negated_conjecture,
( subset(sK0,intersection(sK1,sK2))
| member(A,sK2)
| ~ member(A,sK0) ),
inference(resolve,[status(thm)],[c_44,c_17]) ).
cnf(c_163,negated_conjecture,
( subset(sK0,A)
| subset(sK0,intersection(sK1,sK2))
| member(sK3(sK0,A),sK2) ),
inference(resolve,[status(thm)],[c_10921,c_43]) ).
cnf(c_165,plain,
( subset(sK0,sK1)
| member(sK3(sK0,sK1),intersection(sK1,sK2)) ),
inference(factor,[status(thm)],[c_157]) ).
cnf(c_167,plain,
( subset(sK0,sK2)
| member(sK3(sK0,sK2),intersection(sK1,sK2)) ),
inference(factor,[status(thm)],[c_161]) ).
cnf(c_4088,plain,
( member(sK3(sK0,sK1),sK1)
| subset(sK0,sK1) ),
inference(resolve,[status(thm)],[c_165,c_39]) ).
cnf(c_10922,plain,
( subset(sK0,sK1)
| subset(sK0,sK1) ),
inference(resolve,[status(thm)],[c_4088,c_42]) ).
cnf(c_4207,plain,
subset(sK0,sK1),
inference(copy,[status(thm)],[c_10922]) ).
cnf(c_4237,negated_conjecture,
( ~ subset(sK0,intersection(sK1,sK2))
| ~ subset(sK0,sK2) ),
inference(resolve,[status(thm)],[c_4207,c_16]) ).
cnf(c_10923,plain,
( member(A,sK1)
| ~ member(A,sK0) ),
inference(resolve,[status(thm)],[c_44,c_4207]) ).
cnf(c_4250,plain,
( subset(sK0,A)
| member(sK3(sK0,A),sK1) ),
inference(resolve,[status(thm)],[c_10923,c_43]) ).
cnf(c_5082,plain,
( member(sK3(sK0,sK2),sK2)
| subset(sK0,sK2) ),
inference(resolve,[status(thm)],[c_167,c_38]) ).
cnf(c_10924,plain,
( subset(sK0,sK2)
| subset(sK0,sK2) ),
inference(resolve,[status(thm)],[c_5082,c_42]) ).
cnf(c_5194,plain,
subset(sK0,sK2),
inference(copy,[status(thm)],[c_10924]) ).
cnf(c_5210,negated_conjecture,
~ subset(sK0,intersection(sK1,sK2)),
inference(resolve,[status(thm)],[c_5194,c_4237]) ).
cnf(c_5298,negated_conjecture,
( subset(sK0,A)
| member(sK3(sK0,A),sK2) ),
inference(resolve,[status(thm)],[c_5210,c_163]) ).
cnf(c_10925,plain,
( subset(sK0,A)
| ~ member(sK3(sK0,A),B)
| member(sK3(sK0,A),intersection(sK1,B)) ),
inference(resolve,[status(thm)],[c_37,c_4250]) ).
cnf(c_10926,plain,
( subset(sK0,A)
| subset(sK0,A)
| member(sK3(sK0,A),intersection(sK1,sK2)) ),
inference(resolve,[status(thm)],[c_10925,c_5298]) ).
cnf(c_5672,plain,
( subset(sK0,A)
| member(sK3(sK0,A),intersection(sK1,sK2)) ),
inference(copy,[status(thm)],[c_10926]) ).
cnf(c_10927,plain,
( subset(sK0,intersection(sK1,sK2))
| subset(sK0,intersection(sK1,sK2)) ),
inference(resolve,[status(thm)],[c_5672,c_42]) ).
cnf(c_10928,plain,
subset(sK0,intersection(sK1,sK2)),
inference(copy,[status(thm)],[c_10927]) ).
cnf(c_10918,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_5210,c_10928]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SET199+4 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.15/0.42 % Computer : n006.cluster.edu
% 0.15/0.42 % Model : x86_64 x86_64
% 0.15/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.42 % Memory : 8046.5625MB
% 0.15/0.42 % OS : Linux 6.8.0-71-generic
% 0.15/0.42 % CPULimit : 300
% 0.15/0.42 % WCLimit : 300
% 0.15/0.42 % DateTime : Sat Sep 26 07:18:40 UTC 2026
% 0.15/0.42 % CPUTime :
% 0.15/0.42 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.15/0.42 % Process 667074 was started by sandbox on n006,
% 0.15/0.42 % Sat Sep 26 07:18:40 2026
% 0.15/0.42 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.15/0.43
% 0.15/0.43 % From the command line: assign(max_seconds, 300).
% 81.42/10.78
% 81.42/10.78 % SZS status Theorem for theBenchmark
% 81.42/10.78
% 81.42/10.78 % Proof 1 at 1.96 (+ 0.31) seconds.
% 81.42/10.78 % Length of proof is 27.
% 81.42/10.78 % Level of proof is 10.
% 81.42/10.78 % Maximum clause weight is 23.000.
% 81.42/10.78 % Given clauses 208.
% 81.42/10.78
% 81.42/10.78 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------