%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SET577+3 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 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 : Fri Sep 25 02:43:29 PM UTC 2026
% Result : Theorem 101.42s 25.19s
% Output : Proof 101.42s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 4
% Syntax : Number of formulae : 40 ( 5 unt; 0 def)
% Number of atoms : 125 ( 13 equ)
% Maximal formula atoms : 7 ( 3 avg)
% Number of connectives : 123 ( 38 ~; 58 |; 19 &)
% ( 5 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 70 ( 4 sgn 34 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [B,C] :
( subset(B,C)
<=> ! [D] :
( member(D,B)
=> member(D,C) ) ),
file('/export/starexec/sandbox/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(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])],[f3_nnf]) ).
cnf(c8,plain,
( member(sk0(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
fof(f0,axiom,
! [B,C,D] :
( member(D,union(B,C))
<=> ( member(D,C)
| member(D,B) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',union_defn) ).
fof(f0_nnf,plain,
! [B,C,D] :
( ( ( ~ member(D,C)
& ~ member(D,B) )
| member(D,union(B,C)) )
& ( member(D,C)
| member(D,B)
| ~ member(D,union(B,C)) ) ),
inference(nnf_transformation,[status(thm)],[f0]) ).
fof(f0_sk,plain,
! [D,B,C] :
( ( ( ~ member(D,C)
& ~ member(D,B) )
| member(D,union(B,C)) )
& ( member(D,C)
| member(D,B)
| ~ member(D,union(B,C)) ) ),
inference(skolemisation,[status(esa)],[f0_nnf]) ).
cnf(c0,plain,
( member(X2,X1)
| member(X2,X0)
| ~ member(X2,union(X0,X1)) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p25,plain,
( member(sk0(union(X0,X1),X2),X1)
| member(sk0(union(X0,X1),X2),X0)
| subset(union(X0,X1),X2) ),
inference(resolution,[status(thm)],[c8,c0]) ).
fof(f6,conjecture,
! [B,C,D] :
( ! [E] :
( member(E,B)
<=> ( member(E,D)
| member(E,C) ) )
=> B = union(C,D) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_th18) ).
fof(f6_neg,negated_conjecture,
~ ! [B,C,D] :
( ! [E] :
( member(E,B)
<=> ( member(E,D)
| member(E,C) ) )
=> B = union(C,D) ),
inference(negated_conjecture,[status(cth)],[f6]) ).
fof(f6_nnf,plain,
? [B,C,D] :
( B != union(C,D)
& ! [E] :
( ( ( ~ member(E,D)
& ~ member(E,C) )
| member(E,B) )
& ( member(E,D)
| member(E,C)
| ~ member(E,B) ) ) ),
inference(nnf_transformation,[status(thm)],[f6_neg]) ).
fof(f6_sk,plain,
! [E] :
( sk2 != union(sk3,sk4)
& ( ( ~ member(E,sk4)
& ~ member(E,sk3) )
| member(E,sk2) )
& ( member(E,sk4)
| member(E,sk3)
| ~ member(E,sk2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk2,sk3,sk4])],[f6_nnf]) ).
cnf(c19,plain,
( ~ member(X3,sk4)
| member(X3,sk2) ),
inference(cnf_transformation,[status(esa)],[f6_sk]) ).
cnf(p123,plain,
( member(sk0(union(sk4,X0),X1),sk2)
| member(sk0(union(sk4,X0),X1),X0)
| subset(union(sk4,X0),X1) ),
inference(resolution,[status(thm)],[p25,c19]) ).
cnf(c9,plain,
( ~ member(sk0(X0,X1),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(p903,plain,
( subset(union(sk4,X0),sk2)
| member(sk0(union(sk4,X0),sk2),X0)
| subset(union(sk4,X0),sk2) ),
inference(resolution,[status(thm)],[p123,c9]) ).
cnf(p14941,plain,
( member(sk0(union(sk4,X0),sk2),X0)
| subset(union(sk4,X0),sk2) ),
inference(factoring,[status(thm)],[p903]) ).
cnf(c18,plain,
( ~ member(X3,sk3)
| member(X3,sk2) ),
inference(cnf_transformation,[status(esa)],[f6_sk]) ).
cnf(p14943,plain,
( member(sk0(union(sk3,sk4),sk2),sk2)
| subset(union(sk3,sk4),sk2) ),
inference(resolution,[status(thm)],[p14941,c18]) ).
cnf(p14974,plain,
( subset(union(sk3,sk4),sk2)
| subset(union(sk3,sk4),sk2) ),
inference(resolution,[status(thm)],[p14943,c9]) ).
cnf(p14977,plain,
subset(union(sk3,sk4),sk2),
inference(factoring,[status(thm)],[p14974]) ).
cnf(c17,plain,
( member(X3,sk4)
| member(X3,sk3)
| ~ member(X3,sk2) ),
inference(cnf_transformation,[status(esa)],[f6_sk]) ).
cnf(p23,plain,
( member(sk0(sk2,X0),sk4)
| member(sk0(sk2,X0),sk3)
| subset(sk2,X0) ),
inference(resolution,[status(thm)],[c8,c17]) ).
cnf(c1,plain,
( ~ member(X2,X0)
| member(X2,union(X0,X1)) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p115,plain,
( member(sk0(sk2,X0),union(sk4,X1))
| member(sk0(sk2,X0),sk3)
| subset(sk2,X0) ),
inference(resolution,[status(thm)],[p23,c1]) ).
cnf(p834,plain,
( subset(sk2,union(sk4,X0))
| member(sk0(sk2,union(sk4,X0)),sk3)
| subset(sk2,union(sk4,X0)) ),
inference(resolution,[status(thm)],[p115,c9]) ).
cnf(p10181,plain,
( member(sk0(sk2,union(sk4,X0)),sk3)
| subset(sk2,union(sk4,X0)) ),
inference(factoring,[status(thm)],[p834]) ).
cnf(c2,plain,
( ~ member(X2,X1)
| member(X2,union(X0,X1)) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p10184,plain,
( member(sk0(sk2,union(sk4,X0)),union(X1,sk3))
| subset(sk2,union(sk4,X0)) ),
inference(resolution,[status(thm)],[p10181,c2]) ).
cnf(p10250,plain,
( subset(sk2,union(sk3,sk4))
| subset(sk2,union(sk3,sk4)) ),
inference(resolution,[status(thm)],[p10184,c9]) ).
cnf(p10295,plain,
subset(sk2,union(sk3,sk4)),
inference(factoring,[status(thm)],[p10250]) ).
fof(f1,axiom,
! [B,C] :
( B = C
<=> ( subset(C,B)
& subset(B,C) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',equal_defn) ).
fof(f1_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)],[f1]) ).
fof(f1_sk,plain,
! [B,C] :
( ( ~ subset(C,B)
| ~ subset(B,C)
| B = C )
& ( ( subset(C,B)
& subset(B,C) )
| B != C ) ),
inference(skolemisation,[status(esa)],[f1_nnf]) ).
cnf(c5,plain,
( ~ subset(X1,X0)
| ~ subset(X0,X1)
| X0 = X1 ),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(p10296,plain,
( ~ subset(union(sk3,sk4),sk2)
| sk2 = union(sk3,sk4) ),
inference(resolution,[status(thm)],[p10295,c5]) ).
cnf(p14999,plain,
sk2 = union(sk3,sk4),
inference(resolution,[status(thm)],[p14977,p10296]) ).
cnf(c20,plain,
sk2 != union(sk3,sk4),
inference(cnf_transformation,[status(esa)],[f6_sk]) ).
cnf(p15000,plain,
$false,
inference(resolution,[status(thm)],[p14999,c20]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET577+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.03 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.11/10.38 % Computer : n004.cluster.edu
% 0.11/10.38 % Model : x86_64 x86_64
% 0.11/10.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/10.38 % Memory : 8046.5625MB
% 0.11/10.38 % OS : Linux 6.8.0-71-generic
% 0.11/10.38 % CPULimit : 300
% 0.11/10.38 % WCLimit : 300
% 0.11/10.38 % DateTime : Thu Sep 24 11:20:01 UTC 2026
% 0.11/10.38 % CPUTime :
% 0.11/10.38 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 101.42/25.19 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 101.42/25.19 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------