%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SET625+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 : n009.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 02:43:38 PM UTC 2026
% Result : Theorem 3.14s 0.84s
% Output : Proof 3.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 3
% Syntax : Number of formulae : 24 ( 8 unt; 0 def)
% Number of atoms : 64 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 64 ( 24 ~; 20 |; 15 &)
% ( 2 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 41 ( 0 sgn 23 !; 6 ?)
% 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(sk1(B,C),C)
& member(sk1(B,C),B) )
| subset(B,C) )
& ( member(D,C)
| ~ member(D,B)
| ~ subset(B,C) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk1])],[f1_nnf]) ).
cnf(c3,plain,
( member(X2,X1)
| ~ member(X2,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
fof(f4,conjecture,
! [B,C,D] :
( ( subset(C,D)
& intersect(B,C) )
=> intersect(B,D) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_th101) ).
fof(f4_neg,negated_conjecture,
~ ! [B,C,D] :
( ( subset(C,D)
& intersect(B,C) )
=> intersect(B,D) ),
inference(negated_conjecture,[status(cth)],[f4]) ).
fof(f4_nnf,plain,
? [B,C,D] :
( ~ intersect(B,D)
& subset(C,D)
& intersect(B,C) ),
inference(nnf_transformation,[status(thm)],[f4_neg]) ).
fof(f4_sk,plain,
( ~ intersect(sk2,sk4)
& subset(sk3,sk4)
& intersect(sk2,sk3) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk2,sk3,sk4])],[f4_nnf]) ).
cnf(c9,plain,
subset(sk3,sk4),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(p26,plain,
( member(X0,sk4)
| ~ member(X0,sk3) ),
inference(resolution,[status(thm)],[c3,c9]) ).
fof(f0,axiom,
! [B,C] :
( intersect(B,C)
<=> ? [D] :
( member(D,C)
& member(D,B) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',intersect_defn) ).
fof(f0_nnf,plain,
! [B,C] :
( ( ! [D] :
( ~ member(D,C)
| ~ member(D,B) )
| intersect(B,C) )
& ( ? [D] :
( member(D,C)
& member(D,B) )
| ~ intersect(B,C) ) ),
inference(nnf_transformation,[status(thm)],[f0]) ).
fof(f0_sk,plain,
! [B,C,D] :
( ( ~ member(D,C)
| ~ member(D,B)
| intersect(B,C) )
& ( ( member(sk0(B,C),C)
& member(sk0(B,C),B) )
| ~ intersect(B,C) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0])],[f0_nnf]) ).
cnf(c1,plain,
( member(sk0(X0,X1),X1)
| ~ intersect(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(c8,plain,
intersect(sk2,sk3),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(p14,plain,
member(sk0(sk2,sk3),sk3),
inference(resolution,[status(thm)],[c1,c8]) ).
cnf(p30,plain,
member(sk0(sk2,sk3),sk4),
inference(resolution,[status(thm)],[p26,p14]) ).
cnf(c2,plain,
( ~ member(X2,X1)
| ~ member(X2,X0)
| intersect(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(c0,plain,
( member(sk0(X0,X1),X0)
| ~ intersect(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p11,plain,
member(sk0(sk2,sk3),sk2),
inference(resolution,[status(thm)],[c0,c8]) ).
cnf(p17,plain,
( ~ member(sk0(sk2,sk3),X0)
| intersect(sk2,X0) ),
inference(resolution,[status(thm)],[c2,p11]) ).
cnf(p44,plain,
intersect(sk2,sk4),
inference(resolution,[status(thm)],[p30,p17]) ).
cnf(c10,plain,
~ intersect(sk2,sk4),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(p45,plain,
$false,
inference(resolution,[status(thm)],[p44,c10]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET625+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.03 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.09/0.35 % Computer : n009.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Thu Sep 24 11:29:44 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.09/0.35 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 3.14/0.84 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.14/0.84 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------