%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SET587+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 : n014.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 15.46s 2.54s
% Output : Proof 15.46s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 7
% Syntax : Number of formulae : 57 ( 11 unt; 0 def)
% Number of atoms : 152 ( 22 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 151 ( 56 ~; 62 |; 24 &)
% ( 7 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 87 ( 6 sgn 44 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
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(c6,plain,
( member(X2,X1)
| ~ member(X2,X0)
| member(X2,difference(X0,X1)) ),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
fof(f3,axiom,
! [B,C] :
( subset(B,C)
<=> ! [D] :
( member(D,B)
=> member(D,C) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subset_defn) ).
fof(f3_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)],[f3]) ).
fof(f3_sk,plain,
! [B,C,D] :
( ( ( ~ member(sk1(B,C),C)
& member(sk1(B,C),B) )
| subset(B,C) )
& ( member(D,C)
| ~ member(D,B)
| ~ subset(B,C) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk1])],[f3_nnf]) ).
cnf(c9,plain,
( member(sk1(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(p48,plain,
( subset(X0,X1)
| member(sk1(X0,X1),X2)
| member(sk1(X0,X1),difference(X0,X2)) ),
inference(resolution,[status(thm)],[c6,c9]) ).
cnf(c8,plain,
( member(X2,X1)
| ~ member(X2,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
fof(f4,axiom,
! [B,C] :
( B = C
<=> ( subset(C,B)
& subset(B,C) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equal_defn) ).
fof(f4_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)],[f4]) ).
fof(f4_sk,plain,
! [B,C] :
( ( ~ subset(C,B)
| ~ subset(B,C)
| B = C )
& ( ( subset(C,B)
& subset(B,C) )
| B != C ) ),
inference(skolemisation,[status(esa)],[f4_nnf]) ).
cnf(c11,plain,
( subset(X0,X1)
| X0 != X1 ),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
fof(f8,conjecture,
! [B,C] :
( difference(B,C) = empty_set
<=> subset(B,C) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_difference_empty_set) ).
fof(f8_neg,negated_conjecture,
~ ! [B,C] :
( difference(B,C) = empty_set
<=> subset(B,C) ),
inference(negated_conjecture,[status(cth)],[f8]) ).
fof(f8_nnf,plain,
? [B,C] :
( ( subset(B,C)
& difference(B,C) != empty_set )
| ( ~ subset(B,C)
& difference(B,C) = empty_set ) ),
inference(nnf_transformation,[status(thm)],[f8_neg]) ).
fof(f8_sk,plain,
( ( subset(sk4,sk5)
& difference(sk4,sk5) != empty_set )
| ( ~ subset(sk4,sk5)
& difference(sk4,sk5) = empty_set ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk4,sk5])],[f8_nnf]) ).
cnf(c24,plain,
( subset(sk4,sk5)
| difference(sk4,sk5) = empty_set ),
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
cnf(p27,plain,
( subset(sk4,sk5)
| subset(difference(sk4,sk5),empty_set) ),
inference(resolution,[status(thm)],[c11,c24]) ).
cnf(p51,plain,
( subset(sk4,sk5)
| member(X0,empty_set)
| ~ member(X0,difference(sk4,sk5)) ),
inference(resolution,[status(thm)],[c8,p27]) ).
fof(f7,axiom,
! [B] :
( empty(B)
<=> ! [C] : ~ member(C,B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',empty_defn) ).
fof(f7_nnf,plain,
! [B] :
( ( ? [C] : member(C,B)
| empty(B) )
& ( ! [C] : ~ member(C,B)
| ~ empty(B) ) ),
inference(nnf_transformation,[status(thm)],[f7]) ).
fof(f7_sk,plain,
! [B,C] :
( ( member(sk3(B),B)
| empty(B) )
& ( ~ member(C,B)
| ~ empty(B) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk3])],[f7_nnf]) ).
cnf(c22,plain,
( member(sk3(X0),X0)
| empty(X0) ),
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
cnf(p54,plain,
( empty(difference(sk4,sk5))
| subset(sk4,sk5)
| member(sk3(difference(sk4,sk5)),empty_set) ),
inference(resolution,[status(thm)],[p51,c22]) ).
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(c7,plain,
~ member(X0,empty_set),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(p58,plain,
( empty(difference(sk4,sk5))
| subset(sk4,sk5) ),
inference(resolution,[status(thm)],[p54,c7]) ).
cnf(c21,plain,
( ~ member(X1,X0)
| ~ empty(X0) ),
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
cnf(p59,plain,
( ~ member(X0,difference(sk4,sk5))
| subset(sk4,sk5) ),
inference(resolution,[status(thm)],[p58,c21]) ).
cnf(p442,plain,
( subset(sk4,sk5)
| subset(sk4,X0)
| member(sk1(sk4,X0),sk5) ),
inference(resolution,[status(thm)],[p48,p59]) ).
cnf(p443,plain,
( subset(sk4,sk5)
| member(sk1(sk4,sk5),sk5) ),
inference(factoring,[status(thm)],[p442]) ).
cnf(c10,plain,
( ~ member(sk1(X0,X1),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(p446,plain,
( subset(sk4,sk5)
| subset(sk4,sk5) ),
inference(resolution,[status(thm)],[p443,c10]) ).
cnf(p448,plain,
subset(sk4,sk5),
inference(factoring,[status(thm)],[p446]) ).
cnf(p450,plain,
( member(X0,sk5)
| ~ member(X0,sk4) ),
inference(resolution,[status(thm)],[p448,c8]) ).
cnf(c4,plain,
( member(X2,X0)
| ~ member(X2,difference(X0,X1)) ),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(p34,plain,
( empty(difference(X0,X1))
| member(sk3(difference(X0,X1)),X0) ),
inference(resolution,[status(thm)],[c4,c22]) ).
cnf(p465,plain,
( empty(difference(sk4,X0))
| member(sk3(difference(sk4,X0)),sk5) ),
inference(resolution,[status(thm)],[p450,p34]) ).
cnf(c5,plain,
( ~ member(X2,X1)
| ~ member(X2,difference(X0,X1)) ),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(p37,plain,
( empty(difference(X0,X1))
| ~ member(sk3(difference(X0,X1)),X1) ),
inference(resolution,[status(thm)],[c5,c22]) ).
cnf(p477,plain,
( empty(difference(sk4,sk5))
| empty(difference(sk4,sk5)) ),
inference(resolution,[status(thm)],[p465,p37]) ).
cnf(p478,plain,
empty(difference(sk4,sk5)),
inference(factoring,[status(thm)],[p477]) ).
cnf(p479,plain,
~ member(X0,difference(sk4,sk5)),
inference(resolution,[status(thm)],[p478,c21]) ).
fof(f0,axiom,
! [B,C] :
( ! [D] :
( member(D,B)
<=> member(D,C) )
=> B = C ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',member_equal) ).
fof(f0_nnf,plain,
! [B,C] :
( B = C
| ? [D] :
( ( member(D,C)
& ~ member(D,B) )
| ( ~ member(D,C)
& member(D,B) ) ) ),
inference(nnf_transformation,[status(thm)],[f0]) ).
fof(f0_sk,plain,
! [B,C] :
( B = C
| ( member(sk0(B,C),C)
& ~ member(sk0(B,C),B) )
| ( ~ member(sk0(B,C),C)
& member(sk0(B,C),B) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0])],[f0_nnf]) ).
cnf(c1,plain,
( X0 = X1
| member(sk0(X0,X1),X1)
| member(sk0(X0,X1),X0) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p29,plain,
( X0 = empty_set
| member(sk0(X0,empty_set),X0) ),
inference(resolution,[status(thm)],[c1,c7]) ).
cnf(p484,plain,
difference(sk4,sk5) = empty_set,
inference(resolution,[status(thm)],[p479,p29]) ).
cnf(c25,plain,
( difference(sk4,sk5) != empty_set
| ~ subset(sk4,sk5) ),
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
cnf(p449,plain,
difference(sk4,sk5) != empty_set,
inference(resolution,[status(thm)],[p448,c25]) ).
cnf(p485,plain,
empty_set != empty_set,
inference(demodulation,[status(thm)],[p484,p449]) ).
cnf(p486,plain,
$false,
inference(equality_resolution,[status(thm)],[p485]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET587+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.09/0.37 % Computer : n014.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Thu Sep 24 11:21:34 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 15.46/2.54 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 15.46/2.54 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------