%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SET588+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 : n012.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 2.93s 11.21s
% Output : Proof 2.93s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 3
% Syntax : Number of formulae : 28 ( 4 unt; 0 def)
% Number of atoms : 74 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 72 ( 26 ~; 30 |; 11 &)
% ( 2 <=>; 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 : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 62 ( 2 sgn 24 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [B,C] :
( subset(B,C)
<=> ! [D] :
( member(D,B)
=> member(D,C) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subset_defn) ).
fof(f1_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)],[f1]) ).
fof(f1_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])],[f1_nnf]) ).
cnf(c4,plain,
( member(sk0(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
fof(f0,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(f0_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)],[f0]) ).
fof(f0_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)],[f0_nnf]) ).
cnf(c0,plain,
( member(X2,X0)
| ~ member(X2,difference(X0,X1)) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p9,plain,
( member(sk0(difference(X0,X1),X2),X0)
| subset(difference(X0,X1),X2) ),
inference(resolution,[status(thm)],[c4,c0]) ).
cnf(c3,plain,
( member(X2,X1)
| ~ member(X2,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
fof(f3,conjecture,
! [B,C,D] :
( subset(B,C)
=> subset(difference(B,D),difference(C,D)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_difference_subset1) ).
fof(f3_neg,negated_conjecture,
~ ! [B,C,D] :
( subset(B,C)
=> subset(difference(B,D),difference(C,D)) ),
inference(negated_conjecture,[status(cth)],[f3]) ).
fof(f3_nnf,plain,
? [B,C,D] :
( ~ subset(difference(B,D),difference(C,D))
& subset(B,C) ),
inference(nnf_transformation,[status(thm)],[f3_neg]) ).
fof(f3_sk,plain,
( ~ subset(difference(sk1,sk3),difference(sk2,sk3))
& subset(sk1,sk2) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk1,sk2,sk3])],[f3_nnf]) ).
cnf(c7,plain,
subset(sk1,sk2),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(p11,plain,
( member(X0,sk2)
| ~ member(X0,sk1) ),
inference(resolution,[status(thm)],[c3,c7]) ).
cnf(p24,plain,
( member(sk0(difference(sk1,X0),X1),sk2)
| subset(difference(sk1,X0),X1) ),
inference(resolution,[status(thm)],[p9,p11]) ).
cnf(c2,plain,
( member(X2,X1)
| ~ member(X2,X0)
| member(X2,difference(X0,X1)) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p27,plain,
( member(sk0(difference(sk1,X0),X1),X2)
| member(sk0(difference(sk1,X0),X1),difference(sk2,X2))
| subset(difference(sk1,X0),X1) ),
inference(resolution,[status(thm)],[p24,c2]) ).
cnf(c5,plain,
( ~ member(sk0(X0,X1),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(p112,plain,
( subset(difference(sk1,X0),difference(sk2,X1))
| member(sk0(difference(sk1,X0),difference(sk2,X1)),X1)
| subset(difference(sk1,X0),difference(sk2,X1)) ),
inference(resolution,[status(thm)],[p27,c5]) ).
cnf(p513,plain,
( member(sk0(difference(sk1,X0),difference(sk2,X1)),X1)
| subset(difference(sk1,X0),difference(sk2,X1)) ),
inference(factoring,[status(thm)],[p112]) ).
cnf(c1,plain,
( ~ member(X2,X1)
| ~ member(X2,difference(X0,X1)) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p10,plain,
( ~ member(sk0(difference(X0,X1),X2),X1)
| subset(difference(X0,X1),X2) ),
inference(resolution,[status(thm)],[c4,c1]) ).
cnf(p517,plain,
( subset(difference(sk1,X0),difference(sk2,X0))
| subset(difference(sk1,X0),difference(sk2,X0)) ),
inference(resolution,[status(thm)],[p513,p10]) ).
cnf(p525,plain,
subset(difference(sk1,X0),difference(sk2,X0)),
inference(factoring,[status(thm)],[p517]) ).
cnf(c8,plain,
~ subset(difference(sk1,sk3),difference(sk2,sk3)),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(p526,plain,
$false,
inference(resolution,[status(thm)],[p525,c8]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SET588+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.02 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.04/10.70 % Computer : n012.cluster.edu
% 0.04/10.70 % Model : x86_64 x86_64
% 0.04/10.70 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.04/10.70 % Memory : 8046.5625MB
% 0.04/10.70 % OS : Linux 6.8.0-71-generic
% 0.04/10.70 % CPULimit : 300
% 0.04/10.70 % WCLimit : 300
% 0.04/10.70 % DateTime : Thu Sep 24 11:22:12 UTC 2026
% 0.04/10.70 % CPUTime :
% 0.04/10.70 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 2.93/11.21 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 2.93/11.21 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------