%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET014+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 : n005.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 08:35:18 AM UTC 2026
% Result : Theorem 42.48s 13.05s
% Output : CNFRefutation 42.48s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 4
% Syntax : Number of formulae : 60 ( 12 unt; 0 def)
% Number of atoms : 147 ( 0 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 134 ( 47 ~; 67 |; 14 &)
% ( 5 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 67 ( 4 sgn 27 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(subset,axiom,
! [A,B] :
( subset(A,B)
<=> ! [X] :
( member(X,A)
=> member(X,B) ) ),
file('theBenchmark.p',subset) ).
fof(power_set,axiom,
! [X,A] :
( member(X,power_set(A))
<=> subset(X,A) ),
file('theBenchmark.p',power_set) ).
fof(union,axiom,
! [X,A,B] :
( member(X,union(A,B))
<=> ( member(X,B)
| member(X,A) ) ),
file('theBenchmark.p',union) ).
fof(thI45,conjecture,
! [A,X,Y] :
( ( subset(Y,A)
& subset(X,A) )
<=> subset(union(X,Y),A) ),
file('theBenchmark.p',thI45) ).
fof(thI45_neg,negated_conjecture,
~ ! [A,X,Y] :
( ( subset(Y,A)
& subset(X,A) )
<=> subset(union(X,Y),A) ),
inference(assume_negation,[status(cth)],[thI45]) ).
fof(nnf_12,plain,
? [A,X,Y] :
( ( ~ subset(union(X,Y),A)
| ~ subset(Y,A)
| ~ subset(X,A) )
& ( subset(union(X,Y),A)
| ( subset(Y,A)
& subset(X,A) ) ) ),
inference(fof_nnf,[status(thm)],[thI45_neg]) ).
fof(sk_thI45_neg_sk,plain,
( ( ~ subset(union(sK0,sK2),sK1)
| ~ subset(sK2,sK1)
| ~ subset(sK0,sK1) )
& ( subset(union(sK0,sK2),sK1)
| ( subset(sK2,sK1)
& subset(sK0,sK1) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(A,sK1),skolemize(X,sK0),skolemize(Y,sK2)],[nnf_12]) ).
fof(sk_thI45_neg,plain,
( ( ~ subset(union(sK0,sK2),sK1)
| ~ subset(sK2,sK1)
| ~ subset(sK0,sK1) )
& ( subset(union(sK0,sK2),sK1)
| subset(sK2,sK1) )
& ( subset(union(sK0,sK2),sK1)
| subset(sK0,sK1) ) ),
inference(cnf_transformation,[status(thm)],[sk_thI45_neg_sk]) ).
cnf(c_16,negated_conjecture,
( ~ subset(union(sK0,sK2),sK1)
| ~ subset(sK2,sK1)
| ~ subset(sK0,sK1) ),
inference(split_conjunct,[status(thm)],[sk_thI45_neg]) ).
cnf(c_17,negated_conjecture,
( subset(union(sK0,sK2),sK1)
| subset(sK2,sK1) ),
inference(split_conjunct,[status(thm)],[sk_thI45_neg]) ).
cnf(c_18,negated_conjecture,
( subset(union(sK0,sK2),sK1)
| subset(sK0,sK1) ),
inference(split_conjunct,[status(thm)],[sk_thI45_neg]) ).
cnf(c_34,plain,
( ~ member(A,C)
| member(A,union(B,C)) ),
inference(clausify,[status(thm)],[union]) ).
cnf(c_35,plain,
( ~ member(A,B)
| member(A,union(B,C)) ),
inference(clausify,[status(thm)],[union]) ).
cnf(c_36,plain,
( member(A,C)
| member(A,B)
| ~ member(A,union(B,C)) ),
inference(clausify,[status(thm)],[union]) ).
cnf(c_40,plain,
( ~ subset(A,B)
| member(A,power_set(B)) ),
inference(clausify,[status(thm)],[power_set]) ).
cnf(c_41,plain,
( subset(A,B)
| ~ member(A,power_set(B)) ),
inference(clausify,[status(thm)],[power_set]) ).
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_79,plain,
( subset(sK0,sK1)
| member(union(sK0,sK2),power_set(sK1)) ),
inference(resolve,[status(thm)],[c_40,c_18]) ).
cnf(c_80,plain,
( subset(sK2,sK1)
| member(union(sK0,sK2),power_set(sK1)) ),
inference(resolve,[status(thm)],[c_40,c_17]) ).
cnf(c_82,plain,
( member(A,power_set(B))
| member(sK3(A,B),A) ),
inference(resolve,[status(thm)],[c_43,c_40]) ).
cnf(c_83,plain,
( ~ subset(sK2,sK1)
| ~ subset(sK0,sK1)
| member(sK3(union(sK0,sK2),sK1),union(sK0,sK2)) ),
inference(resolve,[status(thm)],[c_43,c_16]) ).
cnf(c_310,plain,
( member(sK0,power_set(sK1))
| member(union(sK0,sK2),power_set(sK1)) ),
inference(resolve,[status(thm)],[c_79,c_40]) ).
cnf(c_319,plain,
( member(A,sK1)
| ~ member(A,sK2)
| member(union(sK0,sK2),power_set(sK1)) ),
inference(resolve,[status(thm)],[c_80,c_44]) ).
cnf(c_320,plain,
( member(sK2,power_set(sK1))
| member(union(sK0,sK2),power_set(sK1)) ),
inference(resolve,[status(thm)],[c_80,c_40]) ).
cnf(c_337,plain,
( member(sK3(A,B),union(A,C))
| member(A,power_set(B)) ),
inference(resolve,[status(thm)],[c_82,c_35]) ).
cnf(c_338,plain,
( member(sK3(A,B),union(C,A))
| member(A,power_set(B)) ),
inference(resolve,[status(thm)],[c_82,c_34]) ).
cnf(c_987,plain,
( subset(union(sK0,sK2),sK1)
| member(sK0,power_set(sK1)) ),
inference(resolve,[status(thm)],[c_310,c_41]) ).
cnf(c_996,plain,
( member(A,sK1)
| ~ member(A,union(sK0,sK2))
| member(sK0,power_set(sK1)) ),
inference(resolve,[status(thm)],[c_987,c_44]) ).
cnf(c_999,plain,
( subset(union(sK0,sK2),sK1)
| member(sK2,power_set(sK1)) ),
inference(resolve,[status(thm)],[c_320,c_41]) ).
cnf(c_1127,plain,
( member(A,sK1)
| ~ member(A,union(sK0,sK2))
| member(sK2,power_set(sK1)) ),
inference(resolve,[status(thm)],[c_999,c_44]) ).
cnf(c_7893,plain,
( member(sK0,power_set(A))
| member(sK3(sK0,A),sK1)
| member(sK0,power_set(sK1)) ),
inference(resolve,[status(thm)],[c_996,c_337]) ).
cnf(c_7896,plain,
( member(sK3(sK0,sK1),sK1)
| member(sK0,power_set(sK1)) ),
inference(factor,[status(thm)],[c_7893]) ).
cnf(c_7900,plain,
( subset(sK0,sK1)
| member(sK0,power_set(sK1)) ),
inference(resolve,[status(thm)],[c_7896,c_42]) ).
cnf(c_15531,plain,
( member(sK0,power_set(sK1))
| member(sK0,power_set(sK1)) ),
inference(resolve,[status(thm)],[c_7900,c_40]) ).
cnf(c_7911,plain,
member(sK0,power_set(sK1)),
inference(copy,[status(thm)],[c_15531]) ).
cnf(c_7915,plain,
subset(sK0,sK1),
inference(resolve,[status(thm)],[c_7911,c_41]) ).
cnf(c_7931,plain,
( ~ subset(sK2,sK1)
| member(sK3(union(sK0,sK2),sK1),union(sK0,sK2)) ),
inference(resolve,[status(thm)],[c_7915,c_83]) ).
cnf(c_7932,negated_conjecture,
( ~ subset(union(sK0,sK2),sK1)
| ~ subset(sK2,sK1) ),
inference(resolve,[status(thm)],[c_7915,c_16]) ).
cnf(c_8215,plain,
( member(A,sK1)
| ~ member(A,sK0) ),
inference(resolve,[status(thm)],[c_7915,c_44]) ).
cnf(c_9044,plain,
( member(sK2,power_set(A))
| member(sK3(sK2,A),sK1)
| member(sK2,power_set(sK1)) ),
inference(resolve,[status(thm)],[c_1127,c_338]) ).
cnf(c_9046,plain,
( member(sK3(sK2,sK1),sK1)
| member(sK2,power_set(sK1)) ),
inference(factor,[status(thm)],[c_9044]) ).
cnf(c_9050,plain,
( subset(sK2,sK1)
| member(sK2,power_set(sK1)) ),
inference(resolve,[status(thm)],[c_9046,c_42]) ).
cnf(c_15532,plain,
( member(sK2,power_set(sK1))
| member(sK2,power_set(sK1)) ),
inference(resolve,[status(thm)],[c_9050,c_40]) ).
cnf(c_9062,plain,
member(sK2,power_set(sK1)),
inference(copy,[status(thm)],[c_15532]) ).
cnf(c_9066,plain,
subset(sK2,sK1),
inference(resolve,[status(thm)],[c_9062,c_41]) ).
cnf(c_9081,negated_conjecture,
~ subset(union(sK0,sK2),sK1),
inference(resolve,[status(thm)],[c_9066,c_7932]) ).
cnf(c_9082,plain,
member(sK3(union(sK0,sK2),sK1),union(sK0,sK2)),
inference(resolve,[status(thm)],[c_9066,c_7931]) ).
cnf(c_9083,negated_conjecture,
~ member(sK3(union(sK0,sK2),sK1),sK1),
inference(resolve,[status(thm)],[c_42,c_9081]) ).
cnf(c_9084,negated_conjecture,
~ member(union(sK0,sK2),power_set(sK1)),
inference(resolve,[status(thm)],[c_41,c_9081]) ).
cnf(c_9087,plain,
( member(A,sK1)
| ~ member(A,sK2) ),
inference(resolve,[status(thm)],[c_9084,c_319]) ).
cnf(c_11387,plain,
~ member(sK3(union(sK0,sK2),sK1),sK2),
inference(resolve,[status(thm)],[c_9087,c_9083]) ).
cnf(c_11388,plain,
~ member(sK3(union(sK0,sK2),sK1),sK0),
inference(resolve,[status(thm)],[c_8215,c_9083]) ).
cnf(c_15533,plain,
( member(sK3(union(sK0,sK2),sK1),A)
| ~ member(sK3(union(sK0,sK2),sK1),union(sK0,A)) ),
inference(resolve,[status(thm)],[c_36,c_11388]) ).
cnf(c_15534,plain,
~ member(sK3(union(sK0,sK2),sK1),union(sK0,sK2)),
inference(resolve,[status(thm)],[c_15533,c_11387]) ).
cnf(c_15530,plain,
$false,
inference(resolve,[status(thm)],[c_9082,c_15534]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET014+4 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n005.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sat Sep 26 06:50:02 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.37 % Process 1471894 was started by sandbox on n005,
% 0.09/0.37 % Sat Sep 26 06:50:02 2026
% 0.09/0.37 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.09/0.37
% 0.09/0.37 % From the command line: assign(max_seconds, 300).
% 42.48/13.05
% 42.48/13.05 % given #500 (T,wt=22): 10719 subset(intersection(A,difference(empty_set,B)),C). [resolve(3756,a,41,a)].
% 42.48/13.05
% 42.48/13.05 % SZS status Theorem for theBenchmark
% 42.48/13.05
% 42.48/13.05 % Proof 1 at 1.36 (+ 0.74) seconds.
% 42.48/13.05 % Length of proof is 49.
% 42.48/13.05 % Level of proof is 16.
% 42.48/13.05 % Maximum clause weight is 30.000.
% 42.48/13.05 % Given clauses 714.
% 42.48/13.05
% 42.48/13.05 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------