%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SET593+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 : n010.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 02:43:32 PM UTC 2026
% Result : Theorem 22.01s 3.63s
% Output : Proof 22.01s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 4
% Syntax : Number of formulae : 36 ( 5 unt; 0 def)
% Number of atoms : 103 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 103 ( 36 ~; 44 |; 17 &)
% ( 3 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 68 ( 2 sgn 33 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [B,C] :
( subset(B,C)
<=> ! [D] :
( member(D,B)
=> member(D,C) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subset_defn) ).
fof(f2_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)],[f2]) ).
fof(f2_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])],[f2_nnf]) ).
cnf(c7,plain,
( member(sk0(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
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(c3,plain,
( member(X2,X0)
| ~ member(X2,difference(X0,X1)) ),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(p23,plain,
( member(sk0(difference(X0,X1),X2),X0)
| subset(difference(X0,X1),X2) ),
inference(resolution,[status(thm)],[c7,c3]) ).
cnf(c6,plain,
( member(X2,X1)
| ~ member(X2,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
fof(f6,conjecture,
! [B,C,D] :
( subset(B,union(C,D))
=> ( subset(difference(B,D),C)
& subset(difference(B,C),D) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_th52) ).
fof(f6_neg,negated_conjecture,
~ ! [B,C,D] :
( subset(B,union(C,D))
=> ( subset(difference(B,D),C)
& subset(difference(B,C),D) ) ),
inference(negated_conjecture,[status(cth)],[f6]) ).
fof(f6_nnf,plain,
? [B,C,D] :
( ( ~ subset(difference(B,D),C)
| ~ subset(difference(B,C),D) )
& subset(B,union(C,D)) ),
inference(nnf_transformation,[status(thm)],[f6_neg]) ).
fof(f6_sk,plain,
( ( ~ subset(difference(sk2,sk4),sk3)
| ~ subset(difference(sk2,sk3),sk4) )
& subset(sk2,union(sk3,sk4)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk2,sk3,sk4])],[f6_nnf]) ).
cnf(c17,plain,
subset(sk2,union(sk3,sk4)),
inference(cnf_transformation,[status(esa)],[f6_sk]) ).
cnf(p27,plain,
( member(X0,union(sk3,sk4))
| ~ member(X0,sk2) ),
inference(resolution,[status(thm)],[c6,c17]) ).
cnf(p208,plain,
( member(sk0(difference(sk2,X0),X1),union(sk3,sk4))
| subset(difference(sk2,X0),X1) ),
inference(resolution,[status(thm)],[p23,p27]) ).
fof(f0,axiom,
! [B,C,D] :
( member(D,union(B,C))
<=> ( member(D,C)
| member(D,B) ) ),
file('/export/starexec/sandbox2/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(p215,plain,
( member(sk0(difference(sk2,X0),X1),sk4)
| member(sk0(difference(sk2,X0),X1),sk3)
| subset(difference(sk2,X0),X1) ),
inference(resolution,[status(thm)],[p208,c0]) ).
cnf(c4,plain,
( ~ member(X2,X1)
| ~ member(X2,difference(X0,X1)) ),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(p24,plain,
( ~ member(sk0(difference(X0,X1),X2),X1)
| subset(difference(X0,X1),X2) ),
inference(resolution,[status(thm)],[c7,c4]) ).
cnf(p4120,plain,
( subset(difference(sk2,sk4),X0)
| member(sk0(difference(sk2,sk4),X0),sk3)
| subset(difference(sk2,sk4),X0) ),
inference(resolution,[status(thm)],[p215,p24]) ).
cnf(p8265,plain,
( member(sk0(difference(sk2,sk4),X0),sk3)
| subset(difference(sk2,sk4),X0) ),
inference(factoring,[status(thm)],[p4120]) ).
cnf(c8,plain,
( ~ member(sk0(X0,X1),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(p8269,plain,
( subset(difference(sk2,sk4),sk3)
| subset(difference(sk2,sk4),sk3) ),
inference(resolution,[status(thm)],[p8265,c8]) ).
cnf(p8274,plain,
subset(difference(sk2,sk4),sk3),
inference(factoring,[status(thm)],[p8269]) ).
cnf(p4119,plain,
( subset(difference(sk2,X0),sk4)
| member(sk0(difference(sk2,X0),sk4),sk3)
| subset(difference(sk2,X0),sk4) ),
inference(resolution,[status(thm)],[p215,c8]) ).
cnf(p7485,plain,
( member(sk0(difference(sk2,X0),sk4),sk3)
| subset(difference(sk2,X0),sk4) ),
inference(factoring,[status(thm)],[p4119]) ).
cnf(p7489,plain,
( subset(difference(sk2,sk3),sk4)
| subset(difference(sk2,sk3),sk4) ),
inference(resolution,[status(thm)],[p7485,p24]) ).
cnf(p7493,plain,
subset(difference(sk2,sk3),sk4),
inference(factoring,[status(thm)],[p7489]) ).
cnf(c18,plain,
( ~ subset(difference(sk2,sk4),sk3)
| ~ subset(difference(sk2,sk3),sk4) ),
inference(cnf_transformation,[status(esa)],[f6_sk]) ).
cnf(p7494,plain,
~ subset(difference(sk2,sk4),sk3),
inference(resolution,[status(thm)],[p7493,c18]) ).
cnf(p8276,plain,
$false,
inference(resolution,[status(thm)],[p8274,p7494]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET593+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 : n010.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 11:23:13 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 22.01/3.63 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 22.01/3.63 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------