%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SET009+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 : n018.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 02:41:26 PM UTC 2026
% Result : Theorem 8.96s 1.68s
% Output : Proof 8.96s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% 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 : 65 ( 2 sgn 24 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [B,C] :
( subset(B,C)
<=> ! [D] :
( member(D,B)
=> member(D,C) ) ),
file('/export/starexec/sandbox/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/sandbox/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(c2,plain,
( member(X2,X1)
| ~ member(X2,X0)
| member(X2,difference(X0,X1)) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p19,plain,
( member(sk0(difference(X0,X1),X2),X3)
| member(sk0(difference(X0,X1),X2),difference(X0,X3))
| subset(difference(X0,X1),X2) ),
inference(resolution,[status(thm)],[p9,c2]) ).
cnf(c5,plain,
( ~ member(sk0(X0,X1),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(p52,plain,
( subset(difference(X0,X1),difference(X0,X2))
| member(sk0(difference(X0,X1),difference(X0,X2)),X2)
| subset(difference(X0,X1),difference(X0,X2)) ),
inference(resolution,[status(thm)],[p19,c5]) ).
cnf(p320,plain,
( member(sk0(difference(X0,X1),difference(X0,X2)),X2)
| subset(difference(X0,X1),difference(X0,X2)) ),
inference(factoring,[status(thm)],[p52]) ).
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(D,C),difference(D,B)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_subset_difference) ).
fof(f3_neg,negated_conjecture,
~ ! [B,C,D] :
( subset(B,C)
=> subset(difference(D,C),difference(D,B)) ),
inference(negated_conjecture,[status(cth)],[f3]) ).
fof(f3_nnf,plain,
? [B,C,D] :
( ~ subset(difference(D,C),difference(D,B))
& subset(B,C) ),
inference(nnf_transformation,[status(thm)],[f3_neg]) ).
fof(f3_sk,plain,
( ~ subset(difference(sk3,sk2),difference(sk3,sk1))
& 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(p593,plain,
( member(sk0(difference(X0,X1),difference(X0,sk1)),sk2)
| subset(difference(X0,X1),difference(X0,sk1)) ),
inference(resolution,[status(thm)],[p320,p11]) ).
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(p771,plain,
( subset(difference(X0,sk2),difference(X0,sk1))
| subset(difference(X0,sk2),difference(X0,sk1)) ),
inference(resolution,[status(thm)],[p593,p10]) ).
cnf(p803,plain,
subset(difference(X0,sk2),difference(X0,sk1)),
inference(factoring,[status(thm)],[p771]) ).
cnf(c8,plain,
~ subset(difference(sk3,sk2),difference(sk3,sk1)),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(p804,plain,
$false,
inference(resolution,[status(thm)],[p803,c8]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SET009+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.06 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.17/0.43 % Computer : n018.cluster.edu
% 0.17/0.43 % Model : x86_64 x86_64
% 0.17/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.43 % Memory : 8046.5625MB
% 0.17/0.43 % OS : Linux 6.8.0-71-generic
% 0.17/0.43 % CPULimit : 300
% 0.17/0.43 % WCLimit : 300
% 0.17/0.43 % DateTime : Thu Sep 24 09:06:18 UTC 2026
% 0.17/0.43 % CPUTime :
% 0.17/0.43 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 8.96/1.68 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 8.96/1.68 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------