%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET696+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 : n004.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 63.72s 8.70s
% Output : CNFRefutation 63.72s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 6
% Syntax : Number of formulae : 28 ( 7 unt; 0 def)
% Number of atoms : 67 ( 0 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 65 ( 26 ~; 21 |; 11 &)
% ( 4 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 63 ( 7 sgn 29 !; 3 ?)
% 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(thI28,conjecture,
! [A,E] :
( subset(A,E)
=> equal_set(intersection(difference(E,A),A),empty_set) ),
file('theBenchmark.p',thI28) ).
fof(thI28_neg,negated_conjecture,
~ ! [A,E] :
( subset(A,E)
=> equal_set(intersection(difference(E,A),A),empty_set) ),
inference(assume_negation,[status(cth)],[thI28]) ).
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_14,plain,
( member(sK0(A,B),A)
| subset(A,B) ),
inference(split_conjunct,[status(thm)],[sk_subset]) ).
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_27,plain,
~ member(A,empty_set),
inference(clausify,[status(thm)],[empty_set]) ).
cnf(c_29,plain,
( ~ member(A,C)
| ~ member(A,difference(B,C)) ),
inference(clausify,[status(thm)],[difference]) ).
fof(nnf_12,plain,
? [A,E] :
( ~ equal_set(intersection(difference(E,A),A),empty_set)
& subset(A,E) ),
inference(fof_nnf,[status(thm)],[thI28_neg]) ).
fof(sk_thI28_neg,plain,
( ~ equal_set(intersection(difference(sK1,sK2),sK2),empty_set)
& subset(sK2,sK1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK1]),skolemize(A,sK2),skolemize(E,sK1)],[nnf_12]) ).
cnf(c_43,negated_conjecture,
~ equal_set(intersection(difference(sK1,sK2),sK2),empty_set),
inference(split_conjunct,[status(thm)],[sk_thI28_neg]) ).
cnf(c_58,plain,
( subset(intersection(A,B),C)
| member(sK0(intersection(A,B),C),A) ),
inference(resolve,[status(thm)],[c_21,c_14]) ).
cnf(c_59,plain,
( subset(intersection(A,B),C)
| member(sK0(intersection(A,B),C),B) ),
inference(resolve,[status(thm)],[c_22,c_14]) ).
cnf(c_67,plain,
subset(empty_set,A),
inference(resolve,[status(thm)],[c_27,c_14]) ).
cnf(c_1719,negated_conjecture,
( ~ subset(empty_set,intersection(difference(sK1,sK2),sK2))
| ~ subset(intersection(difference(sK1,sK2),sK2),empty_set) ),
inference(resolve,[status(thm)],[c_18,c_43]) ).
cnf(c_215,negated_conjecture,
~ subset(intersection(difference(sK1,sK2),sK2),empty_set),
inference(resolve,[status(thm)],[c_1719,c_67]) ).
cnf(c_1720,plain,
( subset(intersection(difference(A,B),C),D)
| ~ member(sK0(intersection(difference(A,B),C),D),B) ),
inference(resolve,[status(thm)],[c_29,c_58]) ).
cnf(c_1721,plain,
( subset(intersection(difference(A,B),B),C)
| subset(intersection(difference(A,B),B),C) ),
inference(resolve,[status(thm)],[c_1720,c_59]) ).
cnf(c_1717,plain,
subset(intersection(difference(A,B),B),C),
inference(copy,[status(thm)],[c_1721]) ).
cnf(c_1718,plain,
$false,
inference(resolve,[status(thm)],[c_1717,c_215]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SET696+4 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.07 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.18/0.44 % Computer : n004.cluster.edu
% 0.18/0.44 % Model : x86_64 x86_64
% 0.18/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.44 % Memory : 8046.5625MB
% 0.18/0.44 % OS : Linux 6.8.0-71-generic
% 0.18/0.44 % CPULimit : 300
% 0.18/0.44 % WCLimit : 300
% 0.18/0.44 % DateTime : Sat Sep 26 08:05:52 UTC 2026
% 0.18/0.45 % CPUTime :
% 0.18/0.45 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.18/0.45 % Process 1191783 was started by sandbox on n004,
% 0.18/0.45 % Sat Sep 26 08:05:52 2026
% 0.18/0.45 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.18/0.46
% 0.18/0.46 % From the command line: assign(max_seconds, 300).
% 63.72/8.70
% 63.72/8.70 % SZS status Theorem for theBenchmark
% 63.72/8.70
% 63.72/8.70 % Proof 1 at 0.12 (+ 0.07) seconds.
% 63.72/8.70 % Length of proof is 19.
% 63.72/8.70 % Level of proof is 4.
% 63.72/8.70 % Maximum clause weight is 27.000.
% 63.72/8.70 % Given clauses 124.
% 63.72/8.70
% 63.72/8.70 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------