TSTP Solution File: ALG225+1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : ALG225+1 : TPTP v8.1.0. Released v3.4.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n019.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 : Thu Jul 14 18:03:05 EDT 2022
% Result : Theorem 9.64s 9.97s
% Output : Refutation 9.64s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 21
% Syntax : Number of clauses : 68 ( 21 unt; 19 nHn; 68 RR)
% Number of literals : 159 ( 0 equ; 85 neg)
% Maximal clause size : 6 ( 2 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 10 ( 9 usr; 1 prp; 0-2 aty)
% Number of functors : 15 ( 15 usr; 6 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
v2_relat_1(skc13),
file('ALG225+1.p',unknown),
[] ).
cnf(2,axiom,
v1_xboole_0(k1_xboole_0),
file('ALG225+1.p',unknown),
[] ).
cnf(28,axiom,
~ v1_xboole_0(skc12),
file('ALG225+1.p',unknown),
[] ).
cnf(29,axiom,
m1_pboole(skc13,skc12),
file('ALG225+1.p',unknown),
[] ).
cnf(46,axiom,
m1_pboole(k1_pboole(u),u),
file('ALG225+1.p',unknown),
[] ).
cnf(62,axiom,
~ r2_hidden(skf12(u,v),u),
file('ALG225+1.p',unknown),
[] ).
cnf(64,axiom,
( ~ m1_pboole(u,v)
| v1_relat_1(u) ),
file('ALG225+1.p',unknown),
[] ).
cnf(65,axiom,
( ~ m1_pboole(u,v)
| v1_funct_1(u) ),
file('ALG225+1.p',unknown),
[] ).
cnf(73,axiom,
( ~ r2_hidden(u,v)
| m1_subset_1(u,v) ),
file('ALG225+1.p',unknown),
[] ).
cnf(76,axiom,
( r1_tarski(u,v)
| r2_hidden(skf12(v,u),u) ),
file('ALG225+1.p',unknown),
[] ).
cnf(85,axiom,
~ equal(k1_funct_4(k1_pboole(skc12),k7_relat_1(skc13,k1_closure3(skc12,skc13))),skc13),
file('ALG225+1.p',unknown),
[] ).
cnf(87,axiom,
( ~ r1_tarski(u,v)
| ~ r1_tarski(v,u)
| equal(v,u) ),
file('ALG225+1.p',unknown),
[] ).
cnf(98,axiom,
( ~ v1_relat_1(u)
| ~ r1_tarski(k1_relat_1(u),v)
| equal(k7_relat_1(u,v),u) ),
file('ALG225+1.p',unknown),
[] ).
cnf(99,axiom,
( ~ v1_funct_1(u)
| ~ v1_relat_1(u)
| ~ m1_pboole(u,v)
| equal(k1_relat_1(u),v) ),
file('ALG225+1.p',unknown),
[] ).
cnf(101,axiom,
( ~ m1_pboole(u,v)
| ~ r2_hidden(w,a_2_0_closure3(v,u))
| v1_xboole_0(v)
| m1_subset_1(w,v) ),
file('ALG225+1.p',unknown),
[] ).
cnf(102,axiom,
( ~ m1_pboole(u,v)
| ~ m1_pboole(w,v)
| v1_xboole_0(v)
| equal(k1_funct_4(w,u),u) ),
file('ALG225+1.p',unknown),
[] ).
cnf(107,axiom,
( ~ m1_pboole(u,v)
| ~ equal(w,a_2_0_closure3(v,u))
| v1_xboole_0(v)
| equal(w,k1_closure3(v,u)) ),
file('ALG225+1.p',unknown),
[] ).
cnf(108,axiom,
( ~ v2_relat_1(u)
| ~ v1_xboole_0(k1_funct_1(u,v))
| ~ m1_pboole(u,w)
| ~ m1_subset_1(v,w)
| v1_xboole_0(w) ),
file('ALG225+1.p',unknown),
[] ).
cnf(110,axiom,
( ~ v2_relat_1(u)
| ~ m1_pboole(u,v)
| ~ r2_hidden(w,a_2_1_closure3(v,u))
| v1_xboole_0(v)
| m1_subset_1(w,v) ),
file('ALG225+1.p',unknown),
[] ).
cnf(111,axiom,
( ~ m1_pboole(u,v)
| ~ m1_subset_1(w,v)
| v1_xboole_0(v)
| r2_hidden(w,a_2_0_closure3(v,u))
| equal(k1_funct_1(u,w),k1_xboole_0) ),
file('ALG225+1.p',unknown),
[] ).
cnf(113,axiom,
( ~ v2_relat_1(u)
| ~ m1_subset_1(v,w)
| ~ m1_pboole(u,w)
| v1_xboole_0(w)
| r2_hidden(v,a_2_1_closure3(w,u))
| equal(k1_funct_1(u,v),k1_xboole_0) ),
file('ALG225+1.p',unknown),
[] ).
cnf(115,plain,
( ~ m1_pboole(u,v)
| equal(k1_relat_1(u),v) ),
inference(mrr,[status(thm)],[99,65,64]),
[iquote('0:MRR:99.0,99.1,65.1,64.1')] ).
cnf(122,plain,
( ~ v2_relat_1(skc13)
| ~ m1_subset_1(u,skc12)
| equal(k1_funct_1(skc13,u),k1_xboole_0)
| r2_hidden(u,a_2_1_closure3(skc12,skc13))
| v1_xboole_0(skc12) ),
inference(res,[status(thm),theory(equality)],[29,113]),
[iquote('0:Res:29.0,113.1')] ).
cnf(123,plain,
( ~ v2_relat_1(skc13)
| ~ r2_hidden(u,a_2_1_closure3(skc12,skc13))
| m1_subset_1(u,skc12)
| v1_xboole_0(skc12) ),
inference(res,[status(thm),theory(equality)],[29,110]),
[iquote('0:Res:29.0,110.1')] ).
cnf(125,plain,
equal(k1_relat_1(skc13),skc12),
inference(res,[status(thm),theory(equality)],[29,115]),
[iquote('0:Res:29.0,115.0')] ).
cnf(130,plain,
v1_relat_1(skc13),
inference(res,[status(thm),theory(equality)],[29,64]),
[iquote('0:Res:29.0,64.0')] ).
cnf(131,plain,
v1_funct_1(skc13),
inference(res,[status(thm),theory(equality)],[29,65]),
[iquote('0:Res:29.0,65.0')] ).
cnf(132,plain,
( ~ m1_subset_1(u,skc12)
| equal(k1_funct_1(skc13,u),k1_xboole_0)
| r2_hidden(u,a_2_0_closure3(skc12,skc13))
| v1_xboole_0(skc12) ),
inference(res,[status(thm),theory(equality)],[29,111]),
[iquote('0:Res:29.0,111.1')] ).
cnf(134,plain,
( ~ equal(u,a_2_0_closure3(skc12,skc13))
| equal(u,k1_closure3(skc12,skc13))
| v1_xboole_0(skc12) ),
inference(res,[status(thm),theory(equality)],[29,107]),
[iquote('0:Res:29.0,107.1')] ).
cnf(135,plain,
( ~ r2_hidden(u,a_2_0_closure3(skc12,skc13))
| m1_subset_1(u,skc12)
| v1_xboole_0(skc12) ),
inference(res,[status(thm),theory(equality)],[29,101]),
[iquote('0:Res:29.0,101.1')] ).
cnf(138,plain,
( ~ v2_relat_1(skc13)
| ~ m1_subset_1(u,skc12)
| ~ v1_xboole_0(k1_funct_1(skc13,u))
| v1_xboole_0(skc12) ),
inference(res,[status(thm),theory(equality)],[29,108]),
[iquote('0:Res:29.0,108.3')] ).
cnf(152,plain,
( ~ m1_pboole(u,skc12)
| ~ m1_pboole(v,skc12)
| equal(k1_funct_4(v,u),u) ),
inference(res,[status(thm),theory(equality)],[102,28]),
[iquote('0:Res:102.2,28.0')] ).
cnf(166,plain,
( ~ r2_hidden(u,a_2_0_closure3(skc12,skc13))
| m1_subset_1(u,skc12) ),
inference(mrr,[status(thm)],[135,28]),
[iquote('0:MRR:135.2,28.0')] ).
cnf(170,plain,
( ~ equal(u,a_2_0_closure3(skc12,skc13))
| equal(u,k1_closure3(skc12,skc13)) ),
inference(mrr,[status(thm)],[134,28]),
[iquote('0:MRR:134.2,28.0')] ).
cnf(171,plain,
( ~ r2_hidden(u,a_2_1_closure3(skc12,skc13))
| m1_subset_1(u,skc12) ),
inference(mrr,[status(thm)],[123,1,28]),
[iquote('0:MRR:123.0,123.3,1.0,28.0')] ).
cnf(172,plain,
( ~ v1_xboole_0(k1_funct_1(skc13,u))
| ~ m1_subset_1(u,skc12) ),
inference(mrr,[status(thm)],[138,1,28]),
[iquote('0:MRR:138.0,138.3,1.0,28.0')] ).
cnf(174,plain,
( ~ m1_subset_1(u,skc12)
| r2_hidden(u,a_2_0_closure3(skc12,skc13))
| equal(k1_funct_1(skc13,u),k1_xboole_0) ),
inference(mrr,[status(thm)],[132,28]),
[iquote('0:MRR:132.3,28.0')] ).
cnf(176,plain,
( ~ m1_subset_1(u,skc12)
| r2_hidden(u,a_2_1_closure3(skc12,skc13))
| equal(k1_funct_1(skc13,u),k1_xboole_0) ),
inference(mrr,[status(thm)],[122,1,28]),
[iquote('0:MRR:122.0,122.4,1.0,28.0')] ).
cnf(266,plain,
( r1_tarski(a_2_1_closure3(skc12,skc13),u)
| m1_subset_1(skf12(u,a_2_1_closure3(skc12,skc13)),skc12) ),
inference(res,[status(thm),theory(equality)],[76,171]),
[iquote('0:Res:76.1,171.0')] ).
cnf(267,plain,
( r1_tarski(a_2_0_closure3(skc12,skc13),u)
| m1_subset_1(skf12(u,a_2_0_closure3(skc12,skc13)),skc12) ),
inference(res,[status(thm),theory(equality)],[76,166]),
[iquote('0:Res:76.1,166.0')] ).
cnf(530,plain,
( ~ v1_relat_1(skc13)
| ~ r1_tarski(skc12,u)
| equal(k7_relat_1(skc13,u),skc13) ),
inference(spl,[status(thm),theory(equality)],[125,98]),
[iquote('0:SpL:125.0,98.1')] ).
cnf(538,plain,
( ~ r1_tarski(skc12,u)
| equal(k7_relat_1(skc13,u),skc13) ),
inference(ssi,[status(thm)],[530,1,131,130]),
[iquote('0:SSi:530.0,1.0,131.0,130.0')] ).
cnf(1233,plain,
equal(a_2_0_closure3(skc12,skc13),k1_closure3(skc12,skc13)),
inference(eqr,[status(thm),theory(equality)],[170]),
[iquote('0:EqR:170.0')] ).
cnf(1236,plain,
( ~ m1_subset_1(u,skc12)
| r2_hidden(u,k1_closure3(skc12,skc13))
| equal(k1_funct_1(skc13,u),k1_xboole_0) ),
inference(rew,[status(thm),theory(equality)],[1233,174]),
[iquote('0:Rew:1233.0,174.1')] ).
cnf(1240,plain,
( r1_tarski(k1_closure3(skc12,skc13),u)
| m1_subset_1(skf12(u,a_2_0_closure3(skc12,skc13)),skc12) ),
inference(rew,[status(thm),theory(equality)],[1233,267]),
[iquote('0:Rew:1233.0,267.0')] ).
cnf(1257,plain,
( r1_tarski(k1_closure3(skc12,skc13),u)
| m1_subset_1(skf12(u,k1_closure3(skc12,skc13)),skc12) ),
inference(rew,[status(thm),theory(equality)],[1233,1240]),
[iquote('0:Rew:1233.0,1240.1')] ).
cnf(2057,plain,
( ~ m1_pboole(k7_relat_1(skc13,k1_closure3(skc12,skc13)),skc12)
| ~ m1_pboole(k1_pboole(skc12),skc12)
| ~ equal(k7_relat_1(skc13,k1_closure3(skc12,skc13)),skc13) ),
inference(spl,[status(thm),theory(equality)],[152,85]),
[iquote('0:SpL:152.2,85.0')] ).
cnf(2058,plain,
( ~ m1_pboole(k7_relat_1(skc13,k1_closure3(skc12,skc13)),skc12)
| ~ equal(k7_relat_1(skc13,k1_closure3(skc12,skc13)),skc13) ),
inference(mrr,[status(thm)],[2057,46]),
[iquote('0:MRR:2057.1,46.0')] ).
cnf(2604,plain,
( ~ m1_subset_1(skf12(a_2_1_closure3(skc12,skc13),u),skc12)
| equal(k1_funct_1(skc13,skf12(a_2_1_closure3(skc12,skc13),u)),k1_xboole_0) ),
inference(res,[status(thm),theory(equality)],[176,62]),
[iquote('0:Res:176.1,62.0')] ).
cnf(2676,plain,
( ~ m1_subset_1(skf12(k1_closure3(skc12,skc13),u),skc12)
| equal(k1_funct_1(skc13,skf12(k1_closure3(skc12,skc13),u)),k1_xboole_0) ),
inference(res,[status(thm),theory(equality)],[1236,62]),
[iquote('0:Res:1236.1,62.0')] ).
cnf(11026,plain,
( ~ r1_tarski(skc12,k1_closure3(skc12,skc13))
| ~ m1_pboole(skc13,skc12)
| ~ equal(k7_relat_1(skc13,k1_closure3(skc12,skc13)),skc13) ),
inference(spl,[status(thm),theory(equality)],[538,2058]),
[iquote('0:SpL:538.1,2058.0')] ).
cnf(11028,plain,
( ~ r1_tarski(skc12,k1_closure3(skc12,skc13))
| ~ m1_pboole(skc13,skc12)
| ~ equal(skc13,skc13) ),
inference(rew,[status(thm),theory(equality)],[538,11026]),
[iquote('0:Rew:538.1,11026.2')] ).
cnf(11029,plain,
( ~ r1_tarski(skc12,k1_closure3(skc12,skc13))
| ~ m1_pboole(skc13,skc12) ),
inference(obv,[status(thm),theory(equality)],[11028]),
[iquote('0:Obv:11028.2')] ).
cnf(11030,plain,
~ r1_tarski(skc12,k1_closure3(skc12,skc13)),
inference(mrr,[status(thm)],[11029,29]),
[iquote('0:MRR:11029.1,29.0')] ).
cnf(13802,plain,
( ~ m1_subset_1(skf12(a_2_1_closure3(skc12,skc13),u),skc12)
| ~ v1_xboole_0(k1_xboole_0)
| ~ m1_subset_1(skf12(a_2_1_closure3(skc12,skc13),u),skc12) ),
inference(spl,[status(thm),theory(equality)],[2604,172]),
[iquote('0:SpL:2604.1,172.0')] ).
cnf(13815,plain,
( ~ v1_xboole_0(k1_xboole_0)
| ~ m1_subset_1(skf12(a_2_1_closure3(skc12,skc13),u),skc12) ),
inference(obv,[status(thm),theory(equality)],[13802]),
[iquote('0:Obv:13802.0')] ).
cnf(13816,plain,
~ m1_subset_1(skf12(a_2_1_closure3(skc12,skc13),u),skc12),
inference(mrr,[status(thm)],[13815,2]),
[iquote('0:MRR:13815.0,2.0')] ).
cnf(13825,plain,
~ r2_hidden(skf12(a_2_1_closure3(skc12,skc13),u),skc12),
inference(res,[status(thm),theory(equality)],[73,13816]),
[iquote('0:Res:73.1,13816.0')] ).
cnf(13836,plain,
r1_tarski(k1_closure3(skc12,skc13),a_2_1_closure3(skc12,skc13)),
inference(res,[status(thm),theory(equality)],[1257,13816]),
[iquote('0:Res:1257.1,13816.0')] ).
cnf(13880,plain,
( ~ m1_subset_1(skf12(k1_closure3(skc12,skc13),u),skc12)
| ~ v1_xboole_0(k1_xboole_0)
| ~ m1_subset_1(skf12(k1_closure3(skc12,skc13),u),skc12) ),
inference(spl,[status(thm),theory(equality)],[2676,172]),
[iquote('0:SpL:2676.1,172.0')] ).
cnf(13893,plain,
( ~ v1_xboole_0(k1_xboole_0)
| ~ m1_subset_1(skf12(k1_closure3(skc12,skc13),u),skc12) ),
inference(obv,[status(thm),theory(equality)],[13880]),
[iquote('0:Obv:13880.0')] ).
cnf(13894,plain,
~ m1_subset_1(skf12(k1_closure3(skc12,skc13),u),skc12),
inference(mrr,[status(thm)],[13893,2]),
[iquote('0:MRR:13893.0,2.0')] ).
cnf(13924,plain,
( ~ r1_tarski(a_2_1_closure3(skc12,skc13),k1_closure3(skc12,skc13))
| equal(a_2_1_closure3(skc12,skc13),k1_closure3(skc12,skc13)) ),
inference(res,[status(thm),theory(equality)],[13836,87]),
[iquote('0:Res:13836.0,87.0')] ).
cnf(13931,plain,
r1_tarski(skc12,a_2_1_closure3(skc12,skc13)),
inference(res,[status(thm),theory(equality)],[76,13825]),
[iquote('0:Res:76.1,13825.0')] ).
cnf(14207,plain,
r1_tarski(a_2_1_closure3(skc12,skc13),k1_closure3(skc12,skc13)),
inference(res,[status(thm),theory(equality)],[266,13894]),
[iquote('0:Res:266.1,13894.0')] ).
cnf(14210,plain,
equal(a_2_1_closure3(skc12,skc13),k1_closure3(skc12,skc13)),
inference(mrr,[status(thm)],[13924,14207]),
[iquote('0:MRR:13924.0,14207.0')] ).
cnf(14338,plain,
r1_tarski(skc12,k1_closure3(skc12,skc13)),
inference(rew,[status(thm),theory(equality)],[14210,13931]),
[iquote('0:Rew:14210.0,13931.0')] ).
cnf(14677,plain,
$false,
inference(mrr,[status(thm)],[14338,11030]),
[iquote('0:MRR:14338.0,11030.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.17 % Problem : ALG225+1 : TPTP v8.1.0. Released v3.4.0.
% 0.03/0.19 % Command : run_spass %d %s
% 0.12/0.41 % Computer : n019.cluster.edu
% 0.12/0.41 % Model : x86_64 x86_64
% 0.12/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.41 % Memory : 8042.1875MB
% 0.12/0.41 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.41 % CPULimit : 300
% 0.12/0.41 % WCLimit : 600
% 0.12/0.41 % DateTime : Wed Jun 8 06:41:55 EDT 2022
% 0.12/0.41 % CPUTime :
% 9.64/9.97
% 9.64/9.97 SPASS V 3.9
% 9.64/9.97 SPASS beiseite: Proof found.
% 9.64/9.97 % SZS status Theorem
% 9.64/9.97 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 9.64/9.97 SPASS derived 12697 clauses, backtracked 88 clauses, performed 2 splits and kept 6276 clauses.
% 9.64/9.97 SPASS allocated 109737 KBytes.
% 9.64/9.97 SPASS spent 0:00:09.40 on the problem.
% 9.64/9.97 0:00:00.04 for the input.
% 9.64/9.97 0:00:00.03 for the FLOTTER CNF translation.
% 9.64/9.97 0:00:00.25 for inferences.
% 9.64/9.97 0:00:00.05 for the backtracking.
% 9.64/9.97 0:00:08.83 for the reduction.
% 9.64/9.97
% 9.64/9.97
% 9.64/9.97 Here is a proof with depth 5, length 68 :
% 9.64/9.97 % SZS output start Refutation
% See solution above
% 9.64/9.97 Formulae used in the proof : t6_closure3 fc1_xboole_0 dt_k1_pboole d3_tarski antisymmetry_r2_hidden dt_m1_pboole t1_subset d10_xboole_0 t97_relat_1 d3_pboole fraenkel_a_2_0_closure3 t1_closure3 d3_closure3 fc2_pboole fraenkel_a_2_1_closure3
% 9.64/9.97
%------------------------------------------------------------------------------