%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SET626+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 : n014.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 6.29s 1.24s
% Output : Proof 6.29s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 3
% Syntax : Number of formulae : 30 ( 16 unt; 0 def)
% Number of atoms : 63 ( 13 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 56 ( 23 ~; 17 |; 12 &)
% ( 2 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-4 aty)
% Number of variables : 48 ( 2 sgn 23 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [B,C] :
( intersect(B,C)
<=> ? [D] :
( member(D,C)
& member(D,B) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',intersect_defn) ).
fof(f1_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)],[f1]) ).
fof(f1_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])],[f1_nnf]) ).
cnf(c4,plain,
( member(sk0(X0,X1),X1)
| ~ intersect(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(hi4,axiom,
ifeq(intersect(X0,X1),true,member(sk0(X0,X1),X1),true) = true,
inference(equality_encoding,[status(esa)],[c4]) ).
fof(f5,conjecture,
! [B,C,D] :
( intersect(B,intersection(C,D))
=> intersect(B,C) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_th102) ).
fof(f5_neg,negated_conjecture,
~ ! [B,C,D] :
( intersect(B,intersection(C,D))
=> intersect(B,C) ),
inference(negated_conjecture,[status(cth)],[f5]) ).
fof(f5_nnf,plain,
? [B,C,D] :
( ~ intersect(B,C)
& intersect(B,intersection(C,D)) ),
inference(nnf_transformation,[status(thm)],[f5_neg]) ).
fof(f5_sk,plain,
( ~ intersect(sk2,sk3)
& intersect(sk2,intersection(sk3,sk4)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk2,sk3,sk4])],[f5_nnf]) ).
cnf(c14,plain,
intersect(sk2,intersection(sk3,sk4)),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
cnf(hi12,negated_conjecture,
intersect(sk2,intersection(sk3,sk4)) = true,
inference(equality_encoding,[status(esa)],[c14]) ).
cnf(h2,plain,
member(sk0(sk2,intersection(sk3,sk4)),intersection(sk3,sk4)) = true,
inference(hyper_resolution,[status(thm)],[hi4,hi12]) ).
fof(f0,axiom,
! [B,C,D] :
( member(D,intersection(B,C))
<=> ( member(D,C)
& member(D,B) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',intersection_defn) ).
fof(f0_nnf,plain,
! [B,C,D] :
( ( ~ member(D,C)
| ~ member(D,B)
| member(D,intersection(B,C)) )
& ( ( member(D,C)
& member(D,B) )
| ~ member(D,intersection(B,C)) ) ),
inference(nnf_transformation,[status(thm)],[f0]) ).
fof(f0_sk,plain,
! [D,B,C] :
( ( ~ member(D,C)
| ~ member(D,B)
| member(D,intersection(B,C)) )
& ( ( member(D,C)
& member(D,B) )
| ~ member(D,intersection(B,C)) ) ),
inference(skolemisation,[status(esa)],[f0_nnf]) ).
cnf(c0,plain,
( member(X2,X0)
| ~ member(X2,intersection(X0,X1)) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(hi0,axiom,
ifeq(member(X0,intersection(X1,X2)),true,member(X0,X1),true) = true,
inference(equality_encoding,[status(esa)],[c0]) ).
cnf(h3,plain,
member(sk0(sk2,intersection(sk3,sk4)),sk3) = true,
inference(hyper_resolution,[status(thm)],[hi0,h2]) ).
cnf(h0,plain,
intersect(sk2,intersection(sk3,sk4)) = true,
inference(hyper_resolution,[status(thm)],[hi12]) ).
cnf(c3,plain,
( member(sk0(X0,X1),X0)
| ~ intersect(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(hi3,axiom,
ifeq(intersect(X0,X1),true,member(sk0(X0,X1),X0),true) = true,
inference(equality_encoding,[status(esa)],[c3]) ).
cnf(h1,plain,
member(sk0(sk2,intersection(sk3,sk4)),sk2) = true,
inference(hyper_resolution,[status(thm)],[hi3,h0]) ).
cnf(c5,plain,
( ~ member(X2,X1)
| ~ member(X2,X0)
| intersect(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(hi5,axiom,
ifeq(member(X0,X1),true,ifeq(member(X0,X2),true,intersect(X1,X2),true),true) = true,
inference(equality_encoding,[status(esa)],[c5]) ).
cnf(t2,plain,
intersect(sk2,sk3) = true,
inference(hyper_resolution,[status(thm)],[hi5,h1,h3]) ).
cnf(t48,plain,
intersect(sk2,sk3) = true,
inference(orient,[status(thm)],[t2]) ).
cnf(c15,plain,
~ intersect(sk2,sk3),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
cnf(goal_0,negated_conjecture,
intersect(sk2,sk3) != true,
inference(equality_encoding,[status(esa)],[c15]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t48]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET626+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.08/0.35 % Computer : n014.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Thu Sep 24 11:29:47 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.36 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 6.29/1.24 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 6.29/1.24 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
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