TSTP Solution File: SEU180+2 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SEU180+2 : TPTP v8.1.0. Released v3.3.0.
% 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 14:34:46 EDT 2022
% Result : Theorem 35.53s 35.74s
% Output : Refutation 35.53s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 17
% Syntax : Number of clauses : 45 ( 31 unt; 0 nHn; 45 RR)
% Number of literals : 63 ( 0 equ; 22 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 16 ( 16 usr; 9 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
relation(skc6),
file('SEU180+2.p',unknown),
[] ).
cnf(3,axiom,
empty(skc84),
file('SEU180+2.p',unknown),
[] ).
cnf(17,axiom,
in(ordered_pair(skc8,skc7),skc6),
file('SEU180+2.p',unknown),
[] ).
cnf(28,axiom,
equal(set_union2(u,empty_set),u),
file('SEU180+2.p',unknown),
[] ).
cnf(32,axiom,
equal(set_difference(u,empty_set),u),
file('SEU180+2.p',unknown),
[] ).
cnf(33,axiom,
equal(set_difference(empty_set,u),empty_set),
file('SEU180+2.p',unknown),
[] ).
cnf(40,axiom,
( ~ empty(u)
| equal(u,empty_set) ),
file('SEU180+2.p',unknown),
[] ).
cnf(42,axiom,
equal(set_union2(u,v),set_union2(v,u)),
file('SEU180+2.p',unknown),
[] ).
cnf(97,axiom,
equal(set_union2(u,set_difference(v,u)),set_union2(u,v)),
file('SEU180+2.p',unknown),
[] ).
cnf(99,axiom,
equal(set_difference(set_union2(u,v),v),set_difference(u,v)),
file('SEU180+2.p',unknown),
[] ).
cnf(100,axiom,
equal(set_difference(u,set_difference(u,v)),set_intersection2(u,v)),
file('SEU180+2.p',unknown),
[] ).
cnf(106,axiom,
( ~ in(skc7,relation_field(skc6))
| ~ in(skc8,relation_field(skc6)) ),
file('SEU180+2.p',unknown),
[] ).
cnf(123,axiom,
( ~ relation(u)
| equal(set_union2(relation_dom(u),relation_rng(u)),relation_field(u)) ),
file('SEU180+2.p',unknown),
[] ).
cnf(160,axiom,
( ~ in(u,v)
| ~ equal(w,set_union2(v,x))
| in(u,w) ),
file('SEU180+2.p',unknown),
[] ).
cnf(163,axiom,
( ~ in(u,v)
| ~ equal(v,set_intersection2(w,x))
| in(u,x) ),
file('SEU180+2.p',unknown),
[] ).
cnf(171,axiom,
( ~ relation(u)
| ~ in(ordered_pair(v,w),u)
| in(v,relation_dom(u)) ),
file('SEU180+2.p',unknown),
[] ).
cnf(172,axiom,
( ~ relation(u)
| ~ in(ordered_pair(v,w),u)
| in(w,relation_rng(u)) ),
file('SEU180+2.p',unknown),
[] ).
cnf(269,plain,
equal(set_union2(relation_dom(skc6),relation_rng(skc6)),relation_field(skc6)),
inference(res,[status(thm),theory(equality)],[1,123]),
[iquote('0:Res:1.0,123.0')] ).
cnf(315,plain,
( ~ relation(skc6)
| in(skc8,relation_dom(skc6)) ),
inference(res,[status(thm),theory(equality)],[17,171]),
[iquote('0:Res:17.0,171.1')] ).
cnf(316,plain,
( ~ relation(skc6)
| in(skc7,relation_rng(skc6)) ),
inference(res,[status(thm),theory(equality)],[17,172]),
[iquote('0:Res:17.0,172.1')] ).
cnf(327,plain,
in(skc8,relation_dom(skc6)),
inference(mrr,[status(thm)],[315,1]),
[iquote('0:MRR:315.0,1.0')] ).
cnf(328,plain,
in(skc7,relation_rng(skc6)),
inference(mrr,[status(thm)],[316,1]),
[iquote('0:MRR:316.0,1.0')] ).
cnf(373,plain,
equal(empty_set,skc84),
inference(ems,[status(thm)],[40,3]),
[iquote('0:EmS:40.0,3.0')] ).
cnf(378,plain,
equal(set_difference(skc84,u),skc84),
inference(rew,[status(thm),theory(equality)],[373,33]),
[iquote('0:Rew:373.0,33.0')] ).
cnf(382,plain,
equal(set_difference(u,skc84),u),
inference(rew,[status(thm),theory(equality)],[373,32]),
[iquote('0:Rew:373.0,32.0')] ).
cnf(383,plain,
equal(set_union2(u,skc84),u),
inference(rew,[status(thm),theory(equality)],[373,28]),
[iquote('0:Rew:373.0,28.0')] ).
cnf(460,plain,
equal(set_union2(skc84,u),u),
inference(spr,[status(thm),theory(equality)],[42,383]),
[iquote('0:SpR:42.0,383.0')] ).
cnf(672,plain,
equal(set_difference(u,u),set_difference(skc84,u)),
inference(spr,[status(thm),theory(equality)],[460,99]),
[iquote('0:SpR:460.0,99.0')] ).
cnf(676,plain,
equal(set_difference(u,u),skc84),
inference(rew,[status(thm),theory(equality)],[378,672]),
[iquote('0:Rew:378.0,672.0')] ).
cnf(734,plain,
equal(set_union2(u,set_difference(v,u)),set_union2(u,set_union2(v,u))),
inference(spr,[status(thm),theory(equality)],[99,97]),
[iquote('0:SpR:99.0,97.0')] ).
cnf(739,plain,
equal(set_union2(u,set_union2(v,u)),set_union2(u,v)),
inference(rew,[status(thm),theory(equality)],[97,734]),
[iquote('0:Rew:97.0,734.0')] ).
cnf(3017,plain,
( ~ in(u,set_intersection2(v,w))
| in(u,w) ),
inference(eqr,[status(thm),theory(equality)],[163]),
[iquote('0:EqR:163.1')] ).
cnf(3250,plain,
( ~ in(u,v)
| in(u,set_union2(v,w)) ),
inference(eqr,[status(thm),theory(equality)],[160]),
[iquote('0:EqR:160.1')] ).
cnf(8752,plain,
equal(set_union2(relation_rng(skc6),relation_field(skc6)),set_union2(relation_rng(skc6),relation_dom(skc6))),
inference(spr,[status(thm),theory(equality)],[269,739]),
[iquote('0:SpR:269.0,739.0')] ).
cnf(8791,plain,
equal(set_union2(relation_rng(skc6),relation_field(skc6)),relation_field(skc6)),
inference(rew,[status(thm),theory(equality)],[269,8752,42]),
[iquote('0:Rew:269.0,8752.0,42.0,8752.0')] ).
cnf(8799,plain,
equal(set_difference(relation_field(skc6),relation_field(skc6)),set_difference(relation_rng(skc6),relation_field(skc6))),
inference(spr,[status(thm),theory(equality)],[8791,99]),
[iquote('0:SpR:8791.0,99.0')] ).
cnf(8815,plain,
equal(set_difference(relation_rng(skc6),relation_field(skc6)),skc84),
inference(rew,[status(thm),theory(equality)],[676,8799]),
[iquote('0:Rew:676.0,8799.0')] ).
cnf(8832,plain,
equal(set_intersection2(relation_rng(skc6),relation_field(skc6)),set_difference(relation_rng(skc6),skc84)),
inference(spr,[status(thm),theory(equality)],[8815,100]),
[iquote('0:SpR:8815.0,100.0')] ).
cnf(8848,plain,
equal(set_intersection2(relation_rng(skc6),relation_field(skc6)),relation_rng(skc6)),
inference(rew,[status(thm),theory(equality)],[382,8832]),
[iquote('0:Rew:382.0,8832.0')] ).
cnf(10393,plain,
( ~ in(u,relation_rng(skc6))
| in(u,relation_field(skc6)) ),
inference(spl,[status(thm),theory(equality)],[8848,3017]),
[iquote('0:SpL:8848.0,3017.0')] ).
cnf(10985,plain,
( ~ in(u,relation_dom(skc6))
| in(u,relation_field(skc6)) ),
inference(spr,[status(thm),theory(equality)],[269,3250]),
[iquote('0:SpR:269.0,3250.1')] ).
cnf(34328,plain,
( ~ in(skc8,relation_dom(skc6))
| ~ in(skc7,relation_field(skc6)) ),
inference(res,[status(thm),theory(equality)],[10985,106]),
[iquote('0:Res:10985.1,106.1')] ).
cnf(34414,plain,
~ in(skc7,relation_field(skc6)),
inference(mrr,[status(thm)],[34328,327]),
[iquote('0:MRR:34328.0,327.0')] ).
cnf(34422,plain,
~ in(skc7,relation_rng(skc6)),
inference(res,[status(thm),theory(equality)],[10393,34414]),
[iquote('0:Res:10393.1,34414.0')] ).
cnf(34427,plain,
$false,
inference(mrr,[status(thm)],[34422,328]),
[iquote('0:MRR:34422.0,328.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SEU180+2 : TPTP v8.1.0. Released v3.3.0.
% 0.07/0.13 % Command : run_spass %d %s
% 0.12/0.34 % Computer : n020.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Sun Jun 19 14:07:33 EDT 2022
% 0.12/0.34 % CPUTime :
% 35.53/35.74
% 35.53/35.74 SPASS V 3.9
% 35.53/35.74 SPASS beiseite: Proof found.
% 35.53/35.74 % SZS status Theorem
% 35.53/35.74 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 35.53/35.74 SPASS derived 30239 clauses, backtracked 1 clauses, performed 1 splits and kept 13517 clauses.
% 35.53/35.74 SPASS allocated 123815 KBytes.
% 35.53/35.74 SPASS spent 0:0:34.95 on the problem.
% 35.53/35.74 0:00:00.04 for the input.
% 35.53/35.74 0:00:00.60 for the FLOTTER CNF translation.
% 35.53/35.74 0:00:00.54 for inferences.
% 35.53/35.74 0:00:00.49 for the backtracking.
% 35.53/35.74 0:0:32.73 for the reduction.
% 35.53/35.74
% 35.53/35.74
% 35.53/35.74 Here is a proof with depth 6, length 45 :
% 35.53/35.74 % SZS output start Refutation
% See solution above
% 35.53/35.74 Formulae used in the proof : t30_relat_1 rc1_relat_1 t1_boole t3_boole t4_boole t6_boole commutativity_k2_xboole_0 t39_xboole_1 t40_xboole_1 t48_xboole_1 d6_relat_1 d2_xboole_0 d3_xboole_0 t20_relat_1
% 35.53/35.74
%------------------------------------------------------------------------------