%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SET931+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n016.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 05:29:54 EDT 2022
% Result : Theorem 0.19s 0.44s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 12
% Syntax : Number of clauses : 55 ( 31 unt; 6 nHn; 55 RR)
% Number of literals : 90 ( 0 equ; 50 neg)
% Maximal clause size : 5 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 7 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(4,axiom,
subset(u,u),
file('SET931+1.p',unknown),
[] ).
cnf(6,axiom,
( ~ equal(u,empty_set)
| subset(u,unordered_pair(v,w)) ),
file('SET931+1.p',unknown),
[] ).
cnf(7,axiom,
( ~ equal(set_difference(u,v),empty_set)
| subset(u,v) ),
file('SET931+1.p',unknown),
[] ).
cnf(8,axiom,
( ~ subset(u,v)
| equal(set_difference(u,v),empty_set) ),
file('SET931+1.p',unknown),
[] ).
cnf(9,axiom,
( ~ equal(u,singleton(v))
| subset(u,unordered_pair(v,w)) ),
file('SET931+1.p',unknown),
[] ).
cnf(10,axiom,
( ~ equal(u,singleton(v))
| subset(u,unordered_pair(w,v)) ),
file('SET931+1.p',unknown),
[] ).
cnf(12,axiom,
( ~ equal(skc5,empty_set)
| ~ equal(set_difference(skc5,unordered_pair(skc6,skc7)),empty_set) ),
file('SET931+1.p',unknown),
[] ).
cnf(13,axiom,
( ~ equal(singleton(skc6),skc5)
| ~ equal(set_difference(skc5,unordered_pair(skc6,skc7)),empty_set) ),
file('SET931+1.p',unknown),
[] ).
cnf(14,axiom,
( ~ equal(singleton(skc7),skc5)
| ~ equal(set_difference(skc5,unordered_pair(skc6,skc7)),empty_set) ),
file('SET931+1.p',unknown),
[] ).
cnf(15,axiom,
( ~ equal(unordered_pair(skc6,skc7),skc5)
| ~ equal(set_difference(skc5,unordered_pair(skc6,skc7)),empty_set) ),
file('SET931+1.p',unknown),
[] ).
cnf(16,axiom,
( ~ subset(u,unordered_pair(v,w))
| equal(u,empty_set)
| equal(u,singleton(v))
| equal(u,singleton(w))
| equal(u,unordered_pair(v,w)) ),
file('SET931+1.p',unknown),
[] ).
cnf(17,axiom,
( equal(skc5,empty_set)
| equal(singleton(skc7),skc5)
| equal(singleton(skc6),skc5)
| equal(unordered_pair(skc6,skc7),skc5)
| equal(set_difference(skc5,unordered_pair(skc6,skc7)),empty_set) ),
file('SET931+1.p',unknown),
[] ).
cnf(18,plain,
equal(skc5,empty_set),
inference(spt,[spt(split,[position(s1)])],[17]),
[iquote('1:Spt:17.0')] ).
cnf(19,plain,
( ~ equal(empty_set,empty_set)
| ~ equal(set_difference(skc5,unordered_pair(skc6,skc7)),empty_set) ),
inference(rew,[status(thm),theory(equality)],[18,12]),
[iquote('1:Rew:18.0,12.0')] ).
cnf(23,plain,
~ equal(set_difference(skc5,unordered_pair(skc6,skc7)),empty_set),
inference(obv,[status(thm),theory(equality)],[19]),
[iquote('1:Obv:19.0')] ).
cnf(24,plain,
~ equal(set_difference(empty_set,unordered_pair(skc6,skc7)),empty_set),
inference(rew,[status(thm),theory(equality)],[18,23]),
[iquote('1:Rew:18.0,23.0')] ).
cnf(31,plain,
( ~ subset(empty_set,unordered_pair(skc6,skc7))
| ~ equal(empty_set,empty_set) ),
inference(spl,[status(thm),theory(equality)],[8,24]),
[iquote('1:SpL:8.1,24.0')] ).
cnf(32,plain,
~ subset(empty_set,unordered_pair(skc6,skc7)),
inference(obv,[status(thm),theory(equality)],[31]),
[iquote('1:Obv:31.1')] ).
cnf(36,plain,
~ equal(empty_set,empty_set),
inference(res,[status(thm),theory(equality)],[6,32]),
[iquote('1:Res:6.1,32.0')] ).
cnf(37,plain,
$false,
inference(obv,[status(thm),theory(equality)],[36]),
[iquote('1:Obv:36.0')] ).
cnf(38,plain,
~ equal(skc5,empty_set),
inference(spt,[spt(split,[position(sa)])],[37,18]),
[iquote('1:Spt:37.0,17.0,18.0')] ).
cnf(39,plain,
( equal(singleton(skc7),skc5)
| equal(singleton(skc6),skc5)
| equal(unordered_pair(skc6,skc7),skc5)
| equal(set_difference(skc5,unordered_pair(skc6,skc7)),empty_set) ),
inference(spt,[spt(split,[position(s2)])],[17]),
[iquote('1:Spt:37.0,17.1,17.2,17.3,17.4')] ).
cnf(40,plain,
equal(singleton(skc7),skc5),
inference(spt,[spt(split,[position(s2s1)])],[39]),
[iquote('2:Spt:39.0')] ).
cnf(41,plain,
( ~ equal(skc5,skc5)
| ~ equal(set_difference(skc5,unordered_pair(skc6,skc7)),empty_set) ),
inference(rew,[status(thm),theory(equality)],[40,14]),
[iquote('2:Rew:40.0,14.0')] ).
cnf(42,plain,
~ equal(set_difference(skc5,unordered_pair(skc6,skc7)),empty_set),
inference(obv,[status(thm),theory(equality)],[41]),
[iquote('2:Obv:41.0')] ).
cnf(44,plain,
( ~ subset(skc5,unordered_pair(skc6,skc7))
| ~ equal(empty_set,empty_set) ),
inference(spl,[status(thm),theory(equality)],[8,42]),
[iquote('2:SpL:8.1,42.0')] ).
cnf(45,plain,
~ subset(skc5,unordered_pair(skc6,skc7)),
inference(obv,[status(thm),theory(equality)],[44]),
[iquote('2:Obv:44.1')] ).
cnf(49,plain,
~ equal(singleton(skc7),skc5),
inference(res,[status(thm),theory(equality)],[10,45]),
[iquote('2:Res:10.1,45.0')] ).
cnf(50,plain,
~ equal(skc5,skc5),
inference(rew,[status(thm),theory(equality)],[40,49]),
[iquote('2:Rew:40.0,49.0')] ).
cnf(51,plain,
$false,
inference(obv,[status(thm),theory(equality)],[50]),
[iquote('2:Obv:50.0')] ).
cnf(52,plain,
~ equal(singleton(skc7),skc5),
inference(spt,[spt(split,[position(s2sa)])],[51,40]),
[iquote('2:Spt:51.0,39.0,40.0')] ).
cnf(53,plain,
( equal(singleton(skc6),skc5)
| equal(unordered_pair(skc6,skc7),skc5)
| equal(set_difference(skc5,unordered_pair(skc6,skc7)),empty_set) ),
inference(spt,[spt(split,[position(s2s2)])],[39]),
[iquote('2:Spt:51.0,39.1,39.2,39.3')] ).
cnf(54,plain,
equal(singleton(skc6),skc5),
inference(spt,[spt(split,[position(s2s2s1)])],[53]),
[iquote('3:Spt:53.0')] ).
cnf(55,plain,
( ~ equal(skc5,skc5)
| ~ equal(set_difference(skc5,unordered_pair(skc6,skc7)),empty_set) ),
inference(rew,[status(thm),theory(equality)],[54,13]),
[iquote('3:Rew:54.0,13.0')] ).
cnf(56,plain,
~ equal(set_difference(skc5,unordered_pair(skc6,skc7)),empty_set),
inference(obv,[status(thm),theory(equality)],[55]),
[iquote('3:Obv:55.0')] ).
cnf(58,plain,
( ~ subset(skc5,unordered_pair(skc6,skc7))
| ~ equal(empty_set,empty_set) ),
inference(spl,[status(thm),theory(equality)],[8,56]),
[iquote('3:SpL:8.1,56.0')] ).
cnf(59,plain,
~ subset(skc5,unordered_pair(skc6,skc7)),
inference(obv,[status(thm),theory(equality)],[58]),
[iquote('3:Obv:58.1')] ).
cnf(64,plain,
~ equal(singleton(skc6),skc5),
inference(res,[status(thm),theory(equality)],[9,59]),
[iquote('3:Res:9.1,59.0')] ).
cnf(65,plain,
~ equal(skc5,skc5),
inference(rew,[status(thm),theory(equality)],[54,64]),
[iquote('3:Rew:54.0,64.0')] ).
cnf(66,plain,
$false,
inference(obv,[status(thm),theory(equality)],[65]),
[iquote('3:Obv:65.0')] ).
cnf(67,plain,
~ equal(singleton(skc6),skc5),
inference(spt,[spt(split,[position(s2s2sa)])],[66,54]),
[iquote('3:Spt:66.0,53.0,54.0')] ).
cnf(68,plain,
( equal(unordered_pair(skc6,skc7),skc5)
| equal(set_difference(skc5,unordered_pair(skc6,skc7)),empty_set) ),
inference(spt,[spt(split,[position(s2s2s2)])],[53]),
[iquote('3:Spt:66.0,53.1,53.2')] ).
cnf(69,plain,
equal(unordered_pair(skc6,skc7),skc5),
inference(spt,[spt(split,[position(s2s2s2s1)])],[68]),
[iquote('4:Spt:68.0')] ).
cnf(70,plain,
( ~ equal(skc5,skc5)
| ~ equal(set_difference(skc5,unordered_pair(skc6,skc7)),empty_set) ),
inference(rew,[status(thm),theory(equality)],[69,15]),
[iquote('4:Rew:69.0,15.0')] ).
cnf(71,plain,
~ equal(set_difference(skc5,unordered_pair(skc6,skc7)),empty_set),
inference(obv,[status(thm),theory(equality)],[70]),
[iquote('4:Obv:70.0')] ).
cnf(72,plain,
~ equal(set_difference(skc5,skc5),empty_set),
inference(rew,[status(thm),theory(equality)],[69,71]),
[iquote('4:Rew:69.0,71.0')] ).
cnf(77,plain,
( ~ subset(skc5,skc5)
| ~ equal(empty_set,empty_set) ),
inference(spl,[status(thm),theory(equality)],[8,72]),
[iquote('4:SpL:8.1,72.0')] ).
cnf(78,plain,
~ subset(skc5,skc5),
inference(obv,[status(thm),theory(equality)],[77]),
[iquote('4:Obv:77.1')] ).
cnf(79,plain,
$false,
inference(mrr,[status(thm)],[78,4]),
[iquote('4:MRR:78.0,4.0')] ).
cnf(80,plain,
~ equal(unordered_pair(skc6,skc7),skc5),
inference(spt,[spt(split,[position(s2s2s2sa)])],[79,69]),
[iquote('4:Spt:79.0,68.0,69.0')] ).
cnf(81,plain,
equal(set_difference(skc5,unordered_pair(skc6,skc7)),empty_set),
inference(spt,[spt(split,[position(s2s2s2s2)])],[68]),
[iquote('4:Spt:79.0,68.1')] ).
cnf(84,plain,
( ~ equal(empty_set,empty_set)
| subset(skc5,unordered_pair(skc6,skc7)) ),
inference(spl,[status(thm),theory(equality)],[81,7]),
[iquote('4:SpL:81.0,7.0')] ).
cnf(85,plain,
subset(skc5,unordered_pair(skc6,skc7)),
inference(obv,[status(thm),theory(equality)],[84]),
[iquote('4:Obv:84.0')] ).
cnf(98,plain,
( equal(skc5,empty_set)
| equal(singleton(skc6),skc5)
| equal(singleton(skc7),skc5)
| equal(unordered_pair(skc6,skc7),skc5) ),
inference(res,[status(thm),theory(equality)],[85,16]),
[iquote('4:Res:85.0,16.0')] ).
cnf(99,plain,
$false,
inference(mrr,[status(thm)],[98,38,67,52,80]),
[iquote('4:MRR:98.0,98.1,98.2,98.3,38.0,67.0,52.0,80.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : SET931+1 : TPTP v8.1.0. Released v3.2.0.
% 0.04/0.13 % Command : run_spass %d %s
% 0.13/0.34 % Computer : n016.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 : Sun Jul 10 22:08:12 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.19/0.44
% 0.19/0.44 SPASS V 3.9
% 0.19/0.44 SPASS beiseite: Proof found.
% 0.19/0.44 % SZS status Theorem
% 0.19/0.44 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.44 SPASS derived 56 clauses, backtracked 18 clauses, performed 4 splits and kept 54 clauses.
% 0.19/0.44 SPASS allocated 85130 KBytes.
% 0.19/0.44 SPASS spent 0:00:00.09 on the problem.
% 0.19/0.44 0:00:00.03 for the input.
% 0.19/0.44 0:00:00.03 for the FLOTTER CNF translation.
% 0.19/0.44 0:00:00.00 for inferences.
% 0.19/0.44 0:00:00.00 for the backtracking.
% 0.19/0.44 0:00:00.00 for the reduction.
% 0.19/0.44
% 0.19/0.44
% 0.19/0.44 Here is a proof with depth 6, length 55 :
% 0.19/0.44 % SZS output start Refutation
% See solution above
% 0.19/0.44 Formulae used in the proof : reflexivity_r1_tarski l46_zfmisc_1 t37_xboole_1 t75_zfmisc_1
% 0.19/0.44
%------------------------------------------------------------------------------