%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SET148+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 : n004.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 02:42:36 PM UTC 2026
% Result : Theorem 6.16s 1.24s
% Output : Proof 6.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 3
% Syntax : Number of formulae : 21 ( 17 unt; 0 def)
% Number of atoms : 25 ( 16 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 13 ( 9 ~; 3 |; 0 &)
% ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-4 aty)
% Number of variables : 18 ( 0 sgn 11 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f5,axiom,
! [B] : subset(B,B),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_of_subset) ).
fof(f5_nnf,plain,
! [B] : subset(B,B),
inference(nnf_transformation,[status(thm)],[f5]) ).
fof(f5_sk,plain,
! [B] : subset(B,B),
inference(skolemisation,[status(esa)],[f5_nnf]) ).
cnf(c11,plain,
subset(X0,X0),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
cnf(hi11,axiom,
subset(X0,X0) = true,
inference(equality_encoding,[status(esa)],[c11]) ).
cnf(h0,plain,
subset(sk2,sk2) = true,
inference(hyper_resolution,[status(thm)],[hi11]) ).
fof(f0,axiom,
! [B,C] :
( subset(B,C)
=> intersection(B,C) = B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subset_intersection) ).
fof(f0_nnf,plain,
! [B,C] :
( intersection(B,C) = B
| ~ subset(B,C) ),
inference(nnf_transformation,[status(thm)],[f0]) ).
fof(f0_sk,plain,
! [B,C] :
( intersection(B,C) = B
| ~ subset(B,C) ),
inference(skolemisation,[status(esa)],[f0_nnf]) ).
cnf(c0,plain,
( intersection(X0,X1) = X0
| ~ subset(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(hi0,axiom,
ifeq(subset(X0,X1),true,intersection(X0,X1),X0) = X0,
inference(equality_encoding,[status(esa)],[c0]) ).
cnf(t1,plain,
intersection(sk2,sk2) = sk2,
inference(hyper_resolution,[status(thm)],[hi0,h0]) ).
cnf(t63,plain,
intersection(sk2,sk2) = sk2,
inference(orient,[status(thm)],[t1]) ).
fof(f7,conjecture,
! [B] : intersection(B,B) = B,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_idempotency_of_intersection) ).
fof(f7_neg,negated_conjecture,
~ ! [B] : intersection(B,B) = B,
inference(negated_conjecture,[status(cth)],[f7]) ).
fof(f7_nnf,plain,
? [B] : intersection(B,B) != B,
inference(nnf_transformation,[status(thm)],[f7_neg]) ).
fof(f7_sk,plain,
intersection(sk2,sk2) != sk2,
inference(skolemisation,[status(esa),new_symbols(skolem,[sk2])],[f7_nnf]) ).
cnf(c18,plain,
intersection(sk2,sk2) != sk2,
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
cnf(goal_0,negated_conjecture,
intersection(sk2,sk2) != sk2,
inference(equality_encoding,[status(esa)],[c18]) ).
cnf(g0_0,plain,
sk2 != sk2,
inference(rw,[status(thm)],[goal_0,t63]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET148+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.10/0.37 % Computer : n004.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Thu Sep 24 10:02:05 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 6.16/1.24 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 6.16/1.24 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------