%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SET618+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 : n012.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 7.82s 1.38s
% Output : Proof 7.82s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 3
% Syntax : Number of formulae : 16 ( 16 unt; 0 def)
% Number of atoms : 16 ( 15 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 5 ( 5 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 3 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 16 ( 0 sgn 11 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [B] : difference(B,B) = empty_set,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',self_difference_is_empty_set) ).
fof(f2_nnf,plain,
! [B] : difference(B,B) = empty_set,
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
! [B] : difference(B,B) = empty_set,
inference(skolemisation,[status(esa)],[f2_nnf]) ).
cnf(c2,plain,
difference(X0,X0) = empty_set,
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
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]) ).
cnf(p23,plain,
symmetric_difference(X0,X0) = empty_set,
inference(superposition,[status(thm)],[c2,c0]) ).
fof(f11,conjecture,
! [B] : symmetric_difference(B,B) = empty_set,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_th93) ).
fof(f11_neg,negated_conjecture,
~ ! [B] : symmetric_difference(B,B) = empty_set,
inference(negated_conjecture,[status(cth)],[f11]) ).
fof(f11_nnf,plain,
? [B] : symmetric_difference(B,B) != empty_set,
inference(nnf_transformation,[status(thm)],[f11_neg]) ).
fof(f11_sk,plain,
symmetric_difference(sk3,sk3) != empty_set,
inference(skolemisation,[status(esa),new_symbols(skolem,[sk3])],[f11_nnf]) ).
cnf(c21,plain,
symmetric_difference(sk3,sk3) != empty_set,
inference(cnf_transformation,[status(esa)],[f11_sk]) ).
cnf(p24,plain,
empty_set != empty_set,
inference(demodulation,[status(thm)],[p23,c21]) ).
cnf(p38,plain,
$false,
inference(equality_resolution,[status(thm)],[p24]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SET618+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.02 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.03/0.29 % Computer : n012.cluster.edu
% 0.03/0.29 % Model : x86_64 x86_64
% 0.03/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.03/0.29 % Memory : 8046.5625MB
% 0.03/0.29 % OS : Linux 6.8.0-71-generic
% 0.03/0.30 % CPULimit : 300
% 0.03/0.30 % WCLimit : 300
% 0.03/0.30 % DateTime : Thu Sep 24 11:28:35 UTC 2026
% 0.03/0.30 % CPUTime :
% 0.03/0.30 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 7.82/1.38 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 7.82/1.38 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------