TSTP Solution File: SET633+3 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SET633+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n008.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 05:27:42 EDT 2022
% Result : Theorem 0.19s 0.46s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 6
% Syntax : Number of clauses : 10 ( 6 unt; 0 nHn; 10 RR)
% Number of literals : 16 ( 0 equ; 7 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 6 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(2,axiom,
subset(difference(skc3,skc4),skc5),
file('SET633+3.p',unknown),
[] ).
cnf(3,axiom,
subset(difference(skc4,skc3),skc5),
file('SET633+3.p',unknown),
[] ).
cnf(4,axiom,
~ subset(symmetric_difference(skc3,skc4),skc5),
file('SET633+3.p',unknown),
[] ).
cnf(6,axiom,
equal(symmetric_difference(u,v),symmetric_difference(v,u)),
file('SET633+3.p',unknown),
[] ).
cnf(11,axiom,
equal(union(difference(u,v),difference(v,u)),symmetric_difference(u,v)),
file('SET633+3.p',unknown),
[] ).
cnf(16,axiom,
( ~ subset(u,v)
| ~ subset(w,v)
| subset(union(w,u),v) ),
file('SET633+3.p',unknown),
[] ).
cnf(65,plain,
( ~ subset(difference(u,v),w)
| ~ subset(difference(v,u),w)
| subset(symmetric_difference(v,u),w) ),
inference(spr,[status(thm),theory(equality)],[11,16]),
[iquote('0:SpR:11.0,16.2')] ).
cnf(153,plain,
( ~ subset(difference(skc4,skc3),skc5)
| subset(symmetric_difference(skc4,skc3),skc5) ),
inference(res,[status(thm),theory(equality)],[2,65]),
[iquote('0:Res:2.0,65.0')] ).
cnf(159,plain,
( ~ subset(difference(skc4,skc3),skc5)
| subset(symmetric_difference(skc3,skc4),skc5) ),
inference(rew,[status(thm),theory(equality)],[6,153]),
[iquote('0:Rew:6.0,153.1')] ).
cnf(160,plain,
$false,
inference(mrr,[status(thm)],[159,3,4]),
[iquote('0:MRR:159.0,159.1,3.0,4.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : SET633+3 : TPTP v8.1.0. Released v2.2.0.
% 0.10/0.13 % Command : run_spass %d %s
% 0.13/0.34 % Computer : n008.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Sat Jul 9 22:04:53 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.19/0.46
% 0.19/0.46 SPASS V 3.9
% 0.19/0.46 SPASS beiseite: Proof found.
% 0.19/0.46 % SZS status Theorem
% 0.19/0.46 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.46 SPASS derived 117 clauses, backtracked 0 clauses, performed 1 splits and kept 92 clauses.
% 0.19/0.46 SPASS allocated 85325 KBytes.
% 0.19/0.46 SPASS spent 0:00:00.10 on the problem.
% 0.19/0.46 0:00:00.03 for the input.
% 0.19/0.46 0:00:00.03 for the FLOTTER CNF translation.
% 0.19/0.46 0:00:00.00 for inferences.
% 0.19/0.46 0:00:00.00 for the backtracking.
% 0.19/0.46 0:00:00.01 for the reduction.
% 0.19/0.46
% 0.19/0.46
% 0.19/0.46 Here is a proof with depth 2, length 10 :
% 0.19/0.46 % SZS output start Refutation
% See solution above
% 0.19/0.46 Formulae used in the proof : prove_th115 commutativity_of_symmetric_difference symmetric_difference_defn union_subset
% 0.19/0.46
%------------------------------------------------------------------------------