TSTP Solution File: SET902+1 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SET902+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n014.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 05:29:40 EDT 2022
% Result : Theorem 0.18s 0.43s
% Output : Refutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 9
% Syntax : Number of clauses : 31 ( 22 unt; 4 nHn; 31 RR)
% Number of literals : 41 ( 0 equ; 16 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 6 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(5,axiom,
equal(set_union2(u,u),u),
file('SET902+1.p',unknown),
[] ).
cnf(6,axiom,
~ equal(singleton(u),empty_set),
file('SET902+1.p',unknown),
[] ).
cnf(7,axiom,
subset(u,set_union2(u,v)),
file('SET902+1.p',unknown),
[] ).
cnf(8,axiom,
equal(set_union2(skc6,skc7),singleton(skc5)),
file('SET902+1.p',unknown),
[] ).
cnf(9,axiom,
equal(set_union2(u,v),set_union2(v,u)),
file('SET902+1.p',unknown),
[] ).
cnf(13,axiom,
( ~ equal(skc6,empty_set)
| ~ equal(singleton(skc5),skc7) ),
file('SET902+1.p',unknown),
[] ).
cnf(14,axiom,
( ~ equal(skc7,empty_set)
| ~ equal(singleton(skc5),skc6) ),
file('SET902+1.p',unknown),
[] ).
cnf(16,axiom,
( ~ equal(singleton(skc5),skc7)
| ~ equal(singleton(skc5),skc6) ),
file('SET902+1.p',unknown),
[] ).
cnf(17,axiom,
( ~ subset(u,singleton(v))
| equal(u,empty_set)
| equal(u,singleton(v)) ),
file('SET902+1.p',unknown),
[] ).
cnf(22,plain,
subset(skc6,singleton(skc5)),
inference(spr,[status(thm),theory(equality)],[8,7]),
[iquote('0:SpR:8.0,7.0')] ).
cnf(29,plain,
subset(u,set_union2(v,u)),
inference(spr,[status(thm),theory(equality)],[9,7]),
[iquote('0:SpR:9.0,7.0')] ).
cnf(42,plain,
subset(skc7,singleton(skc5)),
inference(spr,[status(thm),theory(equality)],[8,29]),
[iquote('0:SpR:8.0,29.0')] ).
cnf(44,plain,
~ equal(singleton(skc5),skc7),
inference(spt,[spt(split,[position(s1)])],[16]),
[iquote('1:Spt:16.0')] ).
cnf(48,plain,
( equal(skc6,empty_set)
| equal(singleton(skc5),skc6) ),
inference(res,[status(thm),theory(equality)],[22,17]),
[iquote('0:Res:22.0,17.0')] ).
cnf(49,plain,
( equal(skc7,empty_set)
| equal(singleton(skc5),skc7) ),
inference(res,[status(thm),theory(equality)],[42,17]),
[iquote('0:Res:42.0,17.0')] ).
cnf(50,plain,
equal(skc7,empty_set),
inference(mrr,[status(thm)],[49,44]),
[iquote('1:MRR:49.1,44.0')] ).
cnf(51,plain,
equal(set_union2(skc6,empty_set),singleton(skc5)),
inference(rew,[status(thm),theory(equality)],[50,8]),
[iquote('1:Rew:50.0,8.0')] ).
cnf(54,plain,
( ~ equal(empty_set,empty_set)
| ~ equal(singleton(skc5),skc6) ),
inference(rew,[status(thm),theory(equality)],[50,14]),
[iquote('1:Rew:50.0,14.0')] ).
cnf(56,plain,
equal(set_union2(empty_set,skc6),singleton(skc5)),
inference(rew,[status(thm),theory(equality)],[9,51]),
[iquote('1:Rew:9.0,51.0')] ).
cnf(57,plain,
~ equal(singleton(skc5),skc6),
inference(obv,[status(thm),theory(equality)],[54]),
[iquote('1:Obv:54.0')] ).
cnf(58,plain,
equal(skc6,empty_set),
inference(mrr,[status(thm)],[48,57]),
[iquote('1:MRR:48.1,57.0')] ).
cnf(61,plain,
equal(set_union2(empty_set,empty_set),singleton(skc5)),
inference(rew,[status(thm),theory(equality)],[58,56]),
[iquote('1:Rew:58.0,56.0')] ).
cnf(63,plain,
equal(singleton(skc5),empty_set),
inference(rew,[status(thm),theory(equality)],[5,61]),
[iquote('1:Rew:5.0,61.0')] ).
cnf(64,plain,
$false,
inference(mrr,[status(thm)],[63,6]),
[iquote('1:MRR:63.0,6.0')] ).
cnf(65,plain,
equal(singleton(skc5),skc7),
inference(spt,[spt(split,[position(sa)])],[64,44]),
[iquote('1:Spt:64.0,16.0,44.0')] ).
cnf(66,plain,
~ equal(singleton(skc5),skc6),
inference(spt,[spt(split,[position(s2)])],[16]),
[iquote('1:Spt:64.0,16.1')] ).
cnf(69,plain,
~ equal(skc7,skc6),
inference(rew,[status(thm),theory(equality)],[65,66]),
[iquote('1:Rew:65.0,66.0')] ).
cnf(73,plain,
( equal(skc6,empty_set)
| equal(skc7,skc6) ),
inference(rew,[status(thm),theory(equality)],[65,48]),
[iquote('1:Rew:65.0,48.1')] ).
cnf(74,plain,
equal(skc6,empty_set),
inference(mrr,[status(thm)],[73,69]),
[iquote('1:MRR:73.1,69.0')] ).
cnf(79,plain,
( ~ equal(empty_set,empty_set)
| ~ equal(skc7,skc7) ),
inference(rew,[status(thm),theory(equality)],[65,13,74]),
[iquote('1:Rew:65.0,13.1,74.0,13.0')] ).
cnf(80,plain,
$false,
inference(obv,[status(thm),theory(equality)],[79]),
[iquote('1:Obv:79.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : SET902+1 : TPTP v8.1.0. Released v3.2.0.
% 0.03/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n014.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Sun Jul 10 02:20:50 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.18/0.43
% 0.18/0.43 SPASS V 3.9
% 0.18/0.43 SPASS beiseite: Proof found.
% 0.18/0.43 % SZS status Theorem
% 0.18/0.43 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.18/0.43 SPASS derived 47 clauses, backtracked 11 clauses, performed 1 splits and kept 42 clauses.
% 0.18/0.43 SPASS allocated 85119 KBytes.
% 0.18/0.43 SPASS spent 0:00:00.08 on the problem.
% 0.18/0.43 0:00:00.03 for the input.
% 0.18/0.43 0:00:00.03 for the FLOTTER CNF translation.
% 0.18/0.43 0:00:00.00 for inferences.
% 0.18/0.43 0:00:00.00 for the backtracking.
% 0.18/0.43 0:00:00.00 for the reduction.
% 0.18/0.43
% 0.18/0.43
% 0.18/0.43 Here is a proof with depth 3, length 31 :
% 0.18/0.43 % SZS output start Refutation
% See solution above
% 0.18/0.43 Formulae used in the proof : idempotence_k2_xboole_0 l1_zfmisc_1 t7_xboole_1 t43_zfmisc_1 commutativity_k2_xboole_0 l4_zfmisc_1
% 0.18/0.43
%------------------------------------------------------------------------------