%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SET591+3 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n002.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 : Fri Sep 25 02:43:31 PM UTC 2026
% Result : Theorem 15.09s 2.47s
% Output : Proof 15.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 6
% Syntax : Number of formulae : 40 ( 13 unt; 0 def)
% Number of atoms : 100 ( 14 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 105 ( 45 ~; 35 |; 18 &)
% ( 4 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 60 ( 6 sgn 37 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [B,C] :
( B = C
<=> ( subset(C,B)
& subset(B,C) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equal_defn) ).
fof(f3_nnf,plain,
! [B,C] :
( ( ~ subset(C,B)
| ~ subset(B,C)
| B = C )
& ( ( subset(C,B)
& subset(B,C) )
| B != C ) ),
inference(nnf_transformation,[status(thm)],[f3]) ).
fof(f3_sk,plain,
! [B,C] :
( ( ~ subset(C,B)
| ~ subset(B,C)
| B = C )
& ( ( subset(C,B)
& subset(B,C) )
| B != C ) ),
inference(skolemisation,[status(esa)],[f3_nnf]) ).
cnf(c9,plain,
( ~ subset(X1,X0)
| ~ subset(X0,X1)
| X0 = X1 ),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
fof(f0,axiom,
! [B,C] :
( subset(B,C)
<=> ! [D] :
( member(D,B)
=> member(D,C) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subset_defn) ).
fof(f0_nnf,plain,
! [B,C] :
( ( ? [D] :
( ~ member(D,C)
& member(D,B) )
| subset(B,C) )
& ( ! [D] :
( member(D,C)
| ~ member(D,B) )
| ~ subset(B,C) ) ),
inference(nnf_transformation,[status(thm)],[f0]) ).
fof(f0_sk,plain,
! [B,C,D] :
( ( ( ~ member(sk0(B,C),C)
& member(sk0(B,C),B) )
| subset(B,C) )
& ( member(D,C)
| ~ member(D,B)
| ~ subset(B,C) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0])],[f0_nnf]) ).
cnf(c1,plain,
( member(sk0(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
fof(f2,axiom,
! [B] : ~ member(B,empty_set),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',empty_set_defn) ).
fof(f2_nnf,plain,
! [B] : ~ member(B,empty_set),
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
! [B] : ~ member(B,empty_set),
inference(skolemisation,[status(esa)],[f2_nnf]) ).
cnf(c6,plain,
~ member(X0,empty_set),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(p17,plain,
subset(empty_set,X0),
inference(resolution,[status(thm)],[c1,c6]) ).
cnf(p34,plain,
( ~ subset(X0,empty_set)
| empty_set = X0 ),
inference(resolution,[status(thm)],[c9,p17]) ).
cnf(c0,plain,
( member(X2,X1)
| ~ member(X2,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
fof(f6,conjecture,
! [B,C] :
( subset(B,difference(C,B))
=> B = empty_set ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_th50) ).
fof(f6_neg,negated_conjecture,
~ ! [B,C] :
( subset(B,difference(C,B))
=> B = empty_set ),
inference(negated_conjecture,[status(cth)],[f6]) ).
fof(f6_nnf,plain,
? [B,C] :
( B != empty_set
& subset(B,difference(C,B)) ),
inference(nnf_transformation,[status(thm)],[f6_neg]) ).
fof(f6_sk,plain,
( sk2 != empty_set
& subset(sk2,difference(sk3,sk2)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk2,sk3])],[f6_nnf]) ).
cnf(c13,plain,
subset(sk2,difference(sk3,sk2)),
inference(cnf_transformation,[status(esa)],[f6_sk]) ).
cnf(p15,plain,
( member(X0,difference(sk3,sk2))
| ~ member(X0,sk2) ),
inference(resolution,[status(thm)],[c0,c13]) ).
fof(f5,axiom,
! [B] :
( empty(B)
<=> ! [C] : ~ member(C,B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',empty_defn) ).
fof(f5_nnf,plain,
! [B] :
( ( ? [C] : member(C,B)
| empty(B) )
& ( ! [C] : ~ member(C,B)
| ~ empty(B) ) ),
inference(nnf_transformation,[status(thm)],[f5]) ).
fof(f5_sk,plain,
! [B,C] :
( ( member(sk1(B),B)
| empty(B) )
& ( ~ member(C,B)
| ~ empty(B) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk1])],[f5_nnf]) ).
cnf(c12,plain,
( member(sk1(X0),X0)
| empty(X0) ),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
cnf(p22,plain,
( empty(sk2)
| member(sk1(sk2),difference(sk3,sk2)) ),
inference(resolution,[status(thm)],[p15,c12]) ).
fof(f1,axiom,
! [B,C,D] :
( member(D,difference(B,C))
<=> ( ~ member(D,C)
& member(D,B) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',difference_defn) ).
fof(f1_nnf,plain,
! [B,C,D] :
( ( member(D,C)
| ~ member(D,B)
| member(D,difference(B,C)) )
& ( ( ~ member(D,C)
& member(D,B) )
| ~ member(D,difference(B,C)) ) ),
inference(nnf_transformation,[status(thm)],[f1]) ).
fof(f1_sk,plain,
! [D,B,C] :
( ( member(D,C)
| ~ member(D,B)
| member(D,difference(B,C)) )
& ( ( ~ member(D,C)
& member(D,B) )
| ~ member(D,difference(B,C)) ) ),
inference(skolemisation,[status(esa)],[f1_nnf]) ).
cnf(c4,plain,
( ~ member(X2,X1)
| ~ member(X2,difference(X0,X1)) ),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(p25,plain,
( ~ member(sk1(sk2),sk2)
| empty(sk2) ),
inference(resolution,[status(thm)],[p22,c4]) ).
cnf(p26,plain,
( empty(sk2)
| empty(sk2) ),
inference(resolution,[status(thm)],[p25,c12]) ).
cnf(p31,plain,
empty(sk2),
inference(factoring,[status(thm)],[p26]) ).
cnf(c11,plain,
( ~ member(X1,X0)
| ~ empty(X0) ),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
cnf(p32,plain,
~ member(X0,sk2),
inference(resolution,[status(thm)],[p31,c11]) ).
cnf(p33,plain,
subset(sk2,X0),
inference(resolution,[status(thm)],[p32,c1]) ).
cnf(p36,plain,
empty_set = sk2,
inference(resolution,[status(thm)],[p34,p33]) ).
cnf(c14,plain,
sk2 != empty_set,
inference(cnf_transformation,[status(esa)],[f6_sk]) ).
cnf(p37,plain,
empty_set != empty_set,
inference(superposition,[status(thm)],[p36,c14]) ).
cnf(p38,plain,
$false,
inference(equality_resolution,[status(thm)],[p37]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET591+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.10/0.37 % Computer : n002.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Thu Sep 24 11:25:19 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.38 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 15.09/2.47 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 15.09/2.47 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------