%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET692+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 : n016.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 08:36:50 AM UTC 2026
% Result : Theorem 24.12s 6.97s
% Output : CNFRefutation 24.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 7
% Syntax : Number of formulae : 62 ( 12 unt; 0 def)
% Number of atoms : 160 ( 0 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 153 ( 55 ~; 72 |; 18 &)
% ( 7 <=>; 1 =>; 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 : 8 ( 8 usr; 3 con; 0-2 aty)
% Number of variables : 120 ( 10 sgn 44 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(subset,axiom,
! [A,B] :
( subset(A,B)
<=> ! [X] :
( member(X,A)
=> member(X,B) ) ),
file('theBenchmark.p',subset) ).
fof(equal_set,axiom,
! [A,B] :
( equal_set(A,B)
<=> ( subset(B,A)
& subset(A,B) ) ),
file('theBenchmark.p',equal_set) ).
fof(intersection,axiom,
! [X,A,B] :
( member(X,intersection(A,B))
<=> ( member(X,B)
& member(X,A) ) ),
file('theBenchmark.p',intersection) ).
fof(empty_set,axiom,
! [X] : ~ member(X,empty_set),
file('theBenchmark.p',empty_set) ).
fof(difference,axiom,
! [B,A,E] :
( member(B,difference(E,A))
<=> ( ~ member(B,A)
& member(B,E) ) ),
file('theBenchmark.p',difference) ).
fof(sum,axiom,
! [X,A] :
( member(X,sum(A))
<=> ? [Y] :
( member(X,Y)
& member(Y,A) ) ),
file('theBenchmark.p',sum) ).
fof(thI19,conjecture,
! [A,B] :
( equal_set(A,intersection(A,B))
<=> subset(A,B) ),
file('theBenchmark.p',thI19) ).
fof(thI19_neg,negated_conjecture,
~ ! [A,B] :
( equal_set(A,intersection(A,B))
<=> subset(A,B) ),
inference(assume_negation,[status(cth)],[thI19]) ).
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(sK0(A,B),B)
& member(sK0(A,B),A) )
| subset(A,B) )
& ( ! [X0] :
( member(X0,B)
| ~ member(X0,A) )
| ~ subset(A,B) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X,sK0(A,B))],[nnf_1]) ).
fof(sk_subset,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_sk]) ).
cnf(c_13,plain,
( member(C,B)
| ~ member(C,A)
| ~ subset(A,B) ),
inference(split_conjunct,[status(thm)],[sk_subset]) ).
cnf(c_14,plain,
( member(sK0(A,B),A)
| subset(A,B) ),
inference(split_conjunct,[status(thm)],[sk_subset]) ).
cnf(c_15,plain,
( ~ member(sK0(A,B),B)
| subset(A,B) ),
inference(split_conjunct,[status(thm)],[sk_subset]) ).
cnf(c_16,plain,
( subset(A,B)
| ~ equal_set(A,B) ),
inference(clausify,[status(thm)],[equal_set]) ).
cnf(c_18,plain,
( ~ subset(B,A)
| ~ subset(A,B)
| equal_set(A,B) ),
inference(clausify,[status(thm)],[equal_set]) ).
cnf(c_21,plain,
( member(A,B)
| ~ member(A,intersection(B,C)) ),
inference(clausify,[status(thm)],[intersection]) ).
cnf(c_22,plain,
( member(A,C)
| ~ member(A,intersection(B,C)) ),
inference(clausify,[status(thm)],[intersection]) ).
cnf(c_23,plain,
( ~ member(A,C)
| ~ member(A,B)
| member(A,intersection(B,C)) ),
inference(clausify,[status(thm)],[intersection]) ).
cnf(c_27,plain,
~ member(A,empty_set),
inference(clausify,[status(thm)],[empty_set]) ).
cnf(c_28,plain,
( member(A,B)
| ~ member(A,difference(B,C)) ),
inference(clausify,[status(thm)],[difference]) ).
cnf(c_29,plain,
( ~ member(A,C)
| ~ member(A,difference(B,C)) ),
inference(clausify,[status(thm)],[difference]) ).
cnf(c_30,plain,
( member(A,C)
| ~ member(A,B)
| member(A,difference(B,C)) ),
inference(clausify,[status(thm)],[difference]) ).
fof(nnf_10,plain,
! [X,A] :
( ( ! [Y] :
( ~ member(X,Y)
| ~ member(Y,A) )
| member(X,sum(A)) )
& ( ? [X0] :
( member(X,X0)
& member(X0,A) )
| ~ member(X,sum(A)) ) ),
inference(fof_nnf,[status(thm)],[sum]) ).
fof(sk_sum_sk,plain,
! [X,A] :
( ( ! [Y] :
( ~ member(X,Y)
| ~ member(Y,A) )
| member(X,sum(A)) )
& ( ( member(X,sK1(X,A))
& member(sK1(X,A),A) )
| ~ member(X,sum(A)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(X0,sK1(X,A))],[nnf_10]) ).
fof(sk_sum,plain,
( ! [VAR_0,VAR_1,VAR_2] :
( ~ member(VAR_0,VAR_2)
| ~ member(VAR_2,VAR_1)
| member(VAR_0,sum(VAR_1)) )
& ! [VAR_0,VAR_1] :
( member(VAR_0,sK1(VAR_0,VAR_1))
| ~ member(VAR_0,sum(VAR_1)) )
& ! [VAR_0,VAR_1] :
( member(sK1(VAR_0,VAR_1),VAR_1)
| ~ member(VAR_0,sum(VAR_1)) ) ),
inference(cnf_transformation,[status(thm)],[sk_sum_sk]) ).
cnf(c_36,plain,
( member(sK1(A,B),B)
| ~ member(A,sum(B)) ),
inference(split_conjunct,[status(thm)],[sk_sum]) ).
fof(nnf_12,plain,
? [A,B] :
( ( ~ subset(A,B)
| ~ equal_set(A,intersection(A,B)) )
& ( subset(A,B)
| equal_set(A,intersection(A,B)) ) ),
inference(fof_nnf,[status(thm)],[thI19_neg]) ).
fof(sk_thI19_neg,plain,
( ( ~ subset(sK2,sK3)
| ~ equal_set(sK2,intersection(sK2,sK3)) )
& ( subset(sK2,sK3)
| equal_set(sK2,intersection(sK2,sK3)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3]),skolemize(A,sK2),skolemize(B,sK3)],[nnf_12]) ).
cnf(c_42,negated_conjecture,
( subset(sK2,sK3)
| equal_set(sK2,intersection(sK2,sK3)) ),
inference(split_conjunct,[status(thm)],[sk_thI19_neg]) ).
cnf(c_43,negated_conjecture,
( ~ subset(sK2,sK3)
| ~ equal_set(sK2,intersection(sK2,sK3)) ),
inference(split_conjunct,[status(thm)],[sk_thI19_neg]) ).
cnf(c_56,plain,
( subset(intersection(A,B),C)
| member(sK0(intersection(A,B),C),A) ),
inference(resolve,[status(thm)],[c_21,c_14]) ).
cnf(c_58,plain,
( subset(A,B)
| ~ member(sK0(A,B),C)
| member(sK0(A,B),intersection(A,C)) ),
inference(resolve,[status(thm)],[c_23,c_14]) ).
cnf(c_68,plain,
( subset(difference(A,B),C)
| member(sK0(difference(A,B),C),A) ),
inference(resolve,[status(thm)],[c_28,c_14]) ).
cnf(c_70,plain,
( subset(difference(A,B),C)
| ~ member(sK0(difference(A,B),C),B) ),
inference(resolve,[status(thm)],[c_29,c_14]) ).
cnf(c_71,plain,
( subset(A,B)
| member(sK0(A,B),C)
| member(sK0(A,B),difference(A,C)) ),
inference(resolve,[status(thm)],[c_30,c_14]) ).
cnf(c_79,plain,
~ member(A,sum(empty_set)),
inference(resolve,[status(thm)],[c_36,c_27]) ).
cnf(c_119,plain,
( subset(sK2,intersection(sK2,sK3))
| subset(sK2,sK3) ),
inference(resolve,[status(thm)],[c_42,c_16]) ).
cnf(c_123,plain,
( member(A,sK3)
| ~ member(A,sK2)
| equal_set(sK2,intersection(sK2,sK3)) ),
inference(resolve,[status(thm)],[c_42,c_13]) ).
cnf(c_24059,plain,
( subset(intersection(A,B),A)
| subset(intersection(A,B),A) ),
inference(resolve,[status(thm)],[c_56,c_15]) ).
cnf(c_438,plain,
subset(intersection(A,B),A),
inference(copy,[status(thm)],[c_24059]) ).
cnf(c_610,plain,
( ~ subset(A,intersection(A,B))
| equal_set(A,intersection(A,B)) ),
inference(resolve,[status(thm)],[c_438,c_18]) ).
cnf(c_24060,plain,
( subset(difference(A,A),B)
| subset(difference(A,A),B) ),
inference(resolve,[status(thm)],[c_70,c_68]) ).
cnf(c_891,plain,
subset(difference(A,A),B),
inference(copy,[status(thm)],[c_24060]) ).
cnf(c_24061,plain,
( member(A,C)
| ~ member(A,difference(B,B)) ),
inference(resolve,[status(thm)],[c_13,c_891]) ).
cnf(c_930,plain,
~ member(A,difference(B,B)),
inference(resolve,[status(thm)],[c_24061,c_79]) ).
cnf(c_1298,plain,
( member(A,intersection(sK2,sK3))
| ~ member(A,sK2)
| subset(sK2,sK3) ),
inference(resolve,[status(thm)],[c_119,c_13]) ).
cnf(c_6538,plain,
( subset(sK2,A)
| member(sK0(sK2,A),sK3)
| equal_set(sK2,intersection(sK2,sK3)) ),
inference(resolve,[status(thm)],[c_123,c_14]) ).
cnf(c_18394,plain,
( subset(A,B)
| member(sK0(A,B),difference(A,sK2))
| member(sK0(A,B),intersection(sK2,sK3))
| subset(sK2,sK3) ),
inference(resolve,[status(thm)],[c_1298,c_71]) ).
cnf(c_24062,plain,
( member(sK0(sK2,sK3),difference(sK2,sK2))
| member(sK0(sK2,sK3),intersection(sK2,sK3))
| subset(sK2,sK3) ),
inference(factor,[status(thm)],[c_18394]) ).
cnf(c_18404,plain,
( member(sK0(sK2,sK3),intersection(sK2,sK3))
| subset(sK2,sK3) ),
inference(resolve,[status(thm)],[c_930,c_24062]) ).
cnf(c_20645,plain,
( member(sK0(sK2,sK3),sK3)
| subset(sK2,sK3) ),
inference(resolve,[status(thm)],[c_18404,c_22]) ).
cnf(c_24063,plain,
( subset(sK2,sK3)
| subset(sK2,sK3) ),
inference(resolve,[status(thm)],[c_20645,c_15]) ).
cnf(c_20671,plain,
subset(sK2,sK3),
inference(copy,[status(thm)],[c_24063]) ).
cnf(c_20673,negated_conjecture,
~ equal_set(sK2,intersection(sK2,sK3)),
inference(resolve,[status(thm)],[c_20671,c_43]) ).
cnf(c_20701,negated_conjecture,
( subset(sK2,A)
| member(sK0(sK2,A),sK3) ),
inference(resolve,[status(thm)],[c_20673,c_6538]) ).
cnf(c_24064,plain,
( subset(sK2,A)
| member(sK0(sK2,A),intersection(sK2,sK3))
| subset(sK2,A) ),
inference(resolve,[status(thm)],[c_20701,c_58]) ).
cnf(c_21071,plain,
( member(sK0(sK2,A),intersection(sK2,sK3))
| subset(sK2,A) ),
inference(copy,[status(thm)],[c_24064]) ).
cnf(c_21591,negated_conjecture,
~ subset(sK2,intersection(sK2,sK3)),
inference(resolve,[status(thm)],[c_610,c_20673]) ).
cnf(c_21799,plain,
~ member(sK0(sK2,intersection(sK2,sK3)),intersection(sK2,sK3)),
inference(resolve,[status(thm)],[c_15,c_21591]) ).
cnf(c_24065,plain,
member(sK0(sK2,intersection(sK2,sK3)),intersection(sK2,sK3)),
inference(resolve,[status(thm)],[c_21071,c_21591]) ).
cnf(c_24058,plain,
$false,
inference(resolve,[status(thm)],[c_21799,c_24065]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.06 % Problem : SET692+4 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.08 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.12/0.44 % Computer : n016.cluster.edu
% 0.12/0.44 % Model : x86_64 x86_64
% 0.12/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.44 % Memory : 8046.5625MB
% 0.12/0.44 % OS : Linux 6.8.0-71-generic
% 0.12/0.44 % CPULimit : 300
% 0.12/0.44 % WCLimit : 300
% 0.12/0.44 % DateTime : Sat Sep 26 08:10:59 UTC 2026
% 0.12/0.45 % CPUTime :
% 0.12/0.45 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.12/0.45 % Process 381479 was started by sandbox on n016,
% 0.12/0.45 % Sat Sep 26 08:10:59 2026
% 0.12/0.45 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.12/0.45
% 0.12/0.45 % From the command line: assign(max_seconds, 300).
% 24.12/6.97
% 24.12/6.97 % given #500 (T,wt=20): 7813 member(f1(A,empty_set),A) | equal_set(A,intersection(empty_set,B)). [resolve(7685,b,540,b)].
% 24.12/6.97
% 24.12/6.97 % SZS status Theorem for theBenchmark
% 24.12/6.97
% 24.12/6.97 % Proof 1 at 2.20 (+ 0.90) seconds.
% 24.12/6.97 % Length of proof is 46.
% 24.12/6.97 % Level of proof is 11.
% 24.12/6.97 % Maximum clause weight is 30.000.
% 24.12/6.97 % Given clauses 883.
% 24.12/6.97
% 24.12/6.97 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------