%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SET622+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 : n006.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 13.26s 2.40s
% Output : Proof 13.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 4
% Syntax : Number of formulae : 21 ( 21 unt; 0 def)
% Number of atoms : 21 ( 20 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 7 ( 7 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 41 ( 0 sgn 30 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [B,C] : symmetric_difference(B,C) = difference(union(B,C),intersection(B,C)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',symmetric_difference_and_difference) ).
fof(f2_nnf,plain,
! [B,C] : symmetric_difference(B,C) = difference(union(B,C),intersection(B,C)),
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
! [B,C] : symmetric_difference(B,C) = difference(union(B,C),intersection(B,C)),
inference(skolemisation,[status(esa)],[f2_nnf]) ).
cnf(c2,plain,
symmetric_difference(X0,X1) = difference(union(X0,X1),intersection(X0,X1)),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
fof(f1,axiom,
! [B,C,D] : difference(B,difference(C,D)) = union(difference(B,C),intersection(B,D)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',difference_difference_union2) ).
fof(f1_nnf,plain,
! [B,C,D] : difference(B,difference(C,D)) = union(difference(B,C),intersection(B,D)),
inference(nnf_transformation,[status(thm)],[f1]) ).
fof(f1_sk,plain,
! [B,C,D] : difference(B,difference(C,D)) = union(difference(B,C),intersection(B,D)),
inference(skolemisation,[status(esa)],[f1_nnf]) ).
cnf(c1,plain,
difference(X0,difference(X1,X2)) = union(difference(X0,X1),intersection(X0,X2)),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
fof(f0,axiom,
! [B,C,D] : intersection(intersection(B,C),D) = intersection(B,intersection(C,D)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associativity_of_intersection) ).
fof(f0_nnf,plain,
! [B,C,D] : intersection(intersection(B,C),D) = intersection(B,intersection(C,D)),
inference(nnf_transformation,[status(thm)],[f0]) ).
fof(f0_sk,plain,
! [B,C,D] : intersection(intersection(B,C),D) = intersection(B,intersection(C,D)),
inference(skolemisation,[status(esa)],[f0_nnf]) ).
cnf(c0,plain,
intersection(intersection(X0,X1),X2) = intersection(X0,intersection(X1,X2)),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
fof(f14,conjecture,
! [B,C,D] : difference(B,symmetric_difference(C,D)) = union(difference(B,union(C,D)),intersection(intersection(B,C),D)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_th98) ).
fof(f14_neg,negated_conjecture,
~ ! [B,C,D] : difference(B,symmetric_difference(C,D)) = union(difference(B,union(C,D)),intersection(intersection(B,C),D)),
inference(negated_conjecture,[status(cth)],[f14]) ).
fof(f14_nnf,plain,
? [B,C,D] : difference(B,symmetric_difference(C,D)) != union(difference(B,union(C,D)),intersection(intersection(B,C),D)),
inference(nnf_transformation,[status(thm)],[f14_neg]) ).
fof(f14_sk,plain,
difference(sk2,symmetric_difference(sk3,sk4)) != union(difference(sk2,union(sk3,sk4)),intersection(intersection(sk2,sk3),sk4)),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk2,sk3,sk4])],[f14_nnf]) ).
cnf(c29,plain,
difference(sk2,symmetric_difference(sk3,sk4)) != union(difference(sk2,union(sk3,sk4)),intersection(intersection(sk2,sk3),sk4)),
inference(cnf_transformation,[status(esa)],[f14_sk]) ).
cnf(p30,plain,
difference(sk2,symmetric_difference(sk3,sk4)) != union(difference(sk2,union(sk3,sk4)),intersection(sk2,intersection(sk3,sk4))),
inference(superposition,[status(thm)],[c0,c29]) ).
cnf(p45,plain,
difference(sk2,symmetric_difference(sk3,sk4)) != difference(sk2,difference(union(sk3,sk4),intersection(sk3,sk4))),
inference(superposition,[status(thm)],[c1,p30]) ).
cnf(p60,plain,
difference(sk2,symmetric_difference(sk3,sk4)) != difference(sk2,symmetric_difference(sk3,sk4)),
inference(superposition,[status(thm)],[c2,p45]) ).
cnf(p62,plain,
$false,
inference(equality_resolution,[status(thm)],[p60]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET622+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.09/0.35 % Computer : n006.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 11:28:56 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 13.26/2.40 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 13.26/2.40 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------