%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SET014+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 02:41:28 PM UTC 2026
% Result : Theorem 50.27s 6.73s
% Output : Proof 50.27s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 3
% Syntax : Number of formulae : 27 ( 5 unt; 0 def)
% Number of atoms : 76 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 71 ( 22 ~; 30 |; 14 &)
% ( 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 : 47 ( 0 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,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(p18,plain,
( member(sk0(union(X0,X1),X2),X1)
| member(sk0(union(X0,X1),X2),X0)
| subset(union(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(f5,conjecture,
! [B,C,D] :
( ( subset(D,C)
& subset(B,C) )
=> subset(union(B,D),C) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_union_subset) ).
fof(f5_neg,negated_conjecture,
~ ! [B,C,D] :
( ( subset(D,C)
& subset(B,C) )
=> subset(union(B,D),C) ),
inference(negated_conjecture,[status(cth)],[f5]) ).
fof(f5_nnf,plain,
? [B,C,D] :
( ~ subset(union(B,D),C)
& subset(D,C)
& subset(B,C) ),
inference(nnf_transformation,[status(thm)],[f5_neg]) ).
fof(f5_sk,plain,
( ~ subset(union(sk2,sk4),sk3)
& subset(sk4,sk3)
& subset(sk2,sk3) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk2,sk3,sk4])],[f5_nnf]) ).
cnf(c14,plain,
subset(sk2,sk3),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
cnf(p21,plain,
( member(X0,sk3)
| ~ member(X0,sk2) ),
inference(resolution,[status(thm)],[c3,c14]) ).
cnf(p123,plain,
( member(sk0(union(sk2,X0),X1),sk3)
| member(sk0(union(sk2,X0),X1),X0)
| subset(union(sk2,X0),X1) ),
inference(resolution,[status(thm)],[p18,p21]) ).
cnf(c5,plain,
( ~ member(sk0(X0,X1),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(p1509,plain,
( subset(union(sk2,X0),sk3)
| member(sk0(union(sk2,X0),sk3),X0)
| subset(union(sk2,X0),sk3) ),
inference(resolution,[status(thm)],[p123,c5]) ).
cnf(p10490,plain,
( member(sk0(union(sk2,X0),sk3),X0)
| subset(union(sk2,X0),sk3) ),
inference(factoring,[status(thm)],[p1509]) ).
cnf(c15,plain,
subset(sk4,sk3),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
cnf(p22,plain,
( member(X0,sk3)
| ~ member(X0,sk4) ),
inference(resolution,[status(thm)],[c3,c15]) ).
cnf(p10495,plain,
( member(sk0(union(sk2,sk4),sk3),sk3)
| subset(union(sk2,sk4),sk3) ),
inference(resolution,[status(thm)],[p10490,p22]) ).
cnf(p10526,plain,
( subset(union(sk2,sk4),sk3)
| subset(union(sk2,sk4),sk3) ),
inference(resolution,[status(thm)],[p10495,c5]) ).
cnf(p10560,plain,
subset(union(sk2,sk4),sk3),
inference(factoring,[status(thm)],[p10526]) ).
cnf(c16,plain,
~ subset(union(sk2,sk4),sk3),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
cnf(p10561,plain,
$false,
inference(resolution,[status(thm)],[p10560,c16]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SET014+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.02 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.03/0.30 % Computer : n012.cluster.edu
% 0.03/0.30 % Model : x86_64 x86_64
% 0.03/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.03/0.30 % Memory : 8046.5625MB
% 0.03/0.30 % OS : Linux 6.8.0-71-generic
% 0.03/0.30 % CPULimit : 300
% 0.03/0.30 % WCLimit : 300
% 0.03/0.30 % DateTime : Thu Sep 24 09:06:05 UTC 2026
% 0.03/0.30 % CPUTime :
% 0.03/0.30 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 50.27/6.73 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 50.27/6.73 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------