%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SET621+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 : n011.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 02:43:37 PM UTC 2026
% Result : Theorem 21.30s 3.13s
% Output : Proof 21.30s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 4
% Syntax : Number of formulae : 22 ( 22 unt; 0 def)
% Number of atoms : 22 ( 21 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 5 ( 5 ~; 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 : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 45 ( 0 sgn 27 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f0,axiom,
! [B,C] : symmetric_difference(B,C) = union(difference(B,C),difference(C,B)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',symmetric_difference_defn) ).
fof(f0_nnf,plain,
! [B,C] : symmetric_difference(B,C) = union(difference(B,C),difference(C,B)),
inference(nnf_transformation,[status(thm)],[f0]) ).
fof(f0_sk,plain,
! [B,C] : symmetric_difference(B,C) = union(difference(B,C),difference(C,B)),
inference(skolemisation,[status(esa)],[f0_nnf]) ).
cnf(c0,plain,
symmetric_difference(X0,X1) = union(difference(X0,X1),difference(X1,X0)),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
fof(f6,axiom,
! [B,C] : union(B,C) = union(C,B),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_union) ).
fof(f6_nnf,plain,
! [B,C] : union(B,C) = union(C,B),
inference(nnf_transformation,[status(thm)],[f6]) ).
fof(f6_sk,plain,
! [B,C] : union(B,C) = union(C,B),
inference(skolemisation,[status(esa)],[f6_nnf]) ).
cnf(c12,plain,
union(X0,X1) = union(X1,X0),
inference(cnf_transformation,[status(esa)],[f6_sk]) ).
cnf(p29,plain,
union(difference(X0,X1),difference(X1,X0)) = symmetric_difference(X1,X0),
inference(superposition,[status(thm)],[c0,c12]) ).
fof(f2,axiom,
! [B,C,D] : difference(union(B,C),D) = union(difference(B,D),difference(C,D)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',difference_distributes_over_union) ).
fof(f2_nnf,plain,
! [B,C,D] : difference(union(B,C),D) = union(difference(B,D),difference(C,D)),
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
! [B,C,D] : difference(union(B,C),D) = union(difference(B,D),difference(C,D)),
inference(skolemisation,[status(esa)],[f2_nnf]) ).
cnf(c2,plain,
difference(union(X0,X1),X2) = union(difference(X0,X2),difference(X1,X2)),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(p41,plain,
union(difference(X0,X1),difference(X2,X1)) = difference(union(X2,X0),X1),
inference(superposition,[status(thm)],[c2,c12]) ).
cnf(p286,plain,
union(difference(X0,union(X1,X2)),difference(X1,union(X0,X2))) = difference(symmetric_difference(X0,X1),X2),
inference(superposition,[status(thm)],[p29,p41]) ).
fof(f11,conjecture,
! [B,C,D] : difference(symmetric_difference(B,C),D) = union(difference(B,union(C,D)),difference(C,union(B,D))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_th97) ).
fof(f11_neg,negated_conjecture,
~ ! [B,C,D] : difference(symmetric_difference(B,C),D) = union(difference(B,union(C,D)),difference(C,union(B,D))),
inference(negated_conjecture,[status(cth)],[f11]) ).
fof(f11_nnf,plain,
? [B,C,D] : difference(symmetric_difference(B,C),D) != union(difference(B,union(C,D)),difference(C,union(B,D))),
inference(nnf_transformation,[status(thm)],[f11_neg]) ).
fof(f11_sk,plain,
difference(symmetric_difference(sk2,sk3),sk4) != union(difference(sk2,union(sk3,sk4)),difference(sk3,union(sk2,sk4))),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk2,sk3,sk4])],[f11_nnf]) ).
cnf(c24,plain,
difference(symmetric_difference(sk2,sk3),sk4) != union(difference(sk2,union(sk3,sk4)),difference(sk3,union(sk2,sk4))),
inference(cnf_transformation,[status(esa)],[f11_sk]) ).
cnf(p287,plain,
difference(symmetric_difference(sk2,sk3),sk4) != difference(symmetric_difference(sk2,sk3),sk4),
inference(demodulation,[status(thm)],[p286,c24]) ).
cnf(p844,plain,
$false,
inference(equality_resolution,[status(thm)],[p287]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET621+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.08/0.35 % Computer : n011.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
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Thu Sep 24 11:28:57 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.36 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 21.30/3.13 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 21.30/3.13 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------