TSTP Solution File: SET618+3 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SET618+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n020.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Tue Jul 19 05:27:31 EDT 2022
% Result : Theorem 0.20s 0.44s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 4
% Syntax : Number of clauses : 7 ( 7 unt; 0 nHn; 7 RR)
% Number of literals : 7 ( 0 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(3,axiom,
equal(union(u,u),u),
file('SET618+3.p',unknown),
[] ).
cnf(4,axiom,
equal(difference(u,u),empty_set),
file('SET618+3.p',unknown),
[] ).
cnf(5,axiom,
~ equal(symmetric_difference(skc1,skc1),empty_set),
file('SET618+3.p',unknown),
[] ).
cnf(14,axiom,
equal(union(difference(u,v),difference(v,u)),symmetric_difference(u,v)),
file('SET618+3.p',unknown),
[] ).
cnf(52,plain,
equal(difference(u,u),symmetric_difference(u,u)),
inference(spr,[status(thm),theory(equality)],[14,3]),
[iquote('0:SpR:14.0,3.0')] ).
cnf(58,plain,
equal(symmetric_difference(u,u),empty_set),
inference(rew,[status(thm),theory(equality)],[4,52]),
[iquote('0:Rew:4.0,52.0')] ).
cnf(59,plain,
$false,
inference(unc,[status(thm)],[58,5]),
[iquote('0:UnC:58.0,5.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11 % Problem : SET618+3 : TPTP v8.1.0. Released v2.2.0.
% 0.11/0.12 % Command : run_spass %d %s
% 0.13/0.33 % Computer : n020.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Sun Jul 10 06:46:13 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.20/0.44
% 0.20/0.44 SPASS V 3.9
% 0.20/0.44 SPASS beiseite: Proof found.
% 0.20/0.44 % SZS status Theorem
% 0.20/0.44 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.20/0.44 SPASS derived 32 clauses, backtracked 0 clauses, performed 0 splits and kept 27 clauses.
% 0.20/0.44 SPASS allocated 97823 KBytes.
% 0.20/0.44 SPASS spent 0:00:00.10 on the problem.
% 0.20/0.44 0:00:00.04 for the input.
% 0.20/0.44 0:00:00.03 for the FLOTTER CNF translation.
% 0.20/0.44 0:00:00.00 for inferences.
% 0.20/0.44 0:00:00.00 for the backtracking.
% 0.20/0.44 0:00:00.00 for the reduction.
% 0.20/0.44
% 0.20/0.44
% 0.20/0.44 Here is a proof with depth 1, length 7 :
% 0.20/0.44 % SZS output start Refutation
% See solution above
% 0.20/0.44 Formulae used in the proof : idempotency_of_union self_difference_is_empty_set prove_th93 symmetric_difference_defn
% 0.20/0.44
%------------------------------------------------------------------------------