TSTP Solution File: COM013+1 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : COM013+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n026.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 : Fri Jul 15 01:44:17 EDT 2022
% Result : Theorem 0.40s 0.61s
% Output : Refutation 0.40s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 16
% Syntax : Number of clauses : 69 ( 8 unt; 8 nHn; 69 RR)
% Number of literals : 263 ( 0 equ; 202 neg)
% Maximal clause size : 7 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 10 ( 9 usr; 1 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 6 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
aElement0(skc1),
file('COM013+1.p',unknown),
[] ).
cnf(2,axiom,
aRewritingSystem0(xR),
file('COM013+1.p',unknown),
[] ).
cnf(3,axiom,
isTerminating0(xR),
file('COM013+1.p',unknown),
[] ).
cnf(12,axiom,
~ aNormalFormOfIn0(u,skc1,xR),
file('COM013+1.p',unknown),
[] ).
cnf(22,axiom,
( ~ aElement0(u)
| ~ iLess0(u,skc1)
| aNormalFormOfIn0(skf13(u),u,xR) ),
file('COM013+1.p',unknown),
[] ).
cnf(23,axiom,
( ~ aRewritingSystem0(u)
| ~ aElement0(v)
| ~ aReductOfIn0(w,v,u)
| aElement0(w) ),
file('COM013+1.p',unknown),
[] ).
cnf(24,axiom,
( ~ aRewritingSystem0(u)
| ~ aElement0(v)
| ~ aNormalFormOfIn0(w,v,u)
| aElement0(w) ),
file('COM013+1.p',unknown),
[] ).
cnf(25,axiom,
( ~ aRewritingSystem0(u)
| ~ aElement0(v)
| ~ aNormalFormOfIn0(w,v,u)
| sdtmndtasgtdt0(v,u,w) ),
file('COM013+1.p',unknown),
[] ).
cnf(26,axiom,
( ~ aRewritingSystem0(u)
| ~ aElement0(v)
| ~ aNormalFormOfIn0(w,v,u)
| ~ aReductOfIn0(x,w,u) ),
file('COM013+1.p',unknown),
[] ).
cnf(27,axiom,
( ~ aElement0(u)
| ~ aRewritingSystem0(v)
| ~ aElement0(w)
| ~ equal(w,u)
| sdtmndtasgtdt0(w,v,u) ),
file('COM013+1.p',unknown),
[] ).
cnf(28,axiom,
( ~ aElement0(u)
| ~ aRewritingSystem0(v)
| ~ aElement0(w)
| ~ aReductOfIn0(w,u,v)
| sdtmndtplgtdt0(u,v,w) ),
file('COM013+1.p',unknown),
[] ).
cnf(29,axiom,
( ~ aElement0(u)
| ~ aRewritingSystem0(v)
| ~ aElement0(w)
| ~ sdtmndtplgtdt0(w,v,u)
| sdtmndtasgtdt0(w,v,u) ),
file('COM013+1.p',unknown),
[] ).
cnf(30,axiom,
( ~ aRewritingSystem0(u)
| ~ aElement0(v)
| ~ aElement0(w)
| ~ isTerminating0(u)
| ~ sdtmndtplgtdt0(w,u,v)
| iLess0(v,w) ),
file('COM013+1.p',unknown),
[] ).
cnf(33,axiom,
( ~ aElement0(u)
| ~ aRewritingSystem0(v)
| ~ aElement0(w)
| ~ sdtmndtasgtdt0(w,v,u)
| equal(w,u)
| sdtmndtplgtdt0(w,v,u) ),
file('COM013+1.p',unknown),
[] ).
cnf(34,axiom,
( ~ aRewritingSystem0(u)
| ~ aElement0(v)
| ~ aElement0(w)
| ~ sdtmndtasgtdt0(v,u,w)
| aNormalFormOfIn0(w,v,u)
| aReductOfIn0(skf29(u,w),w,u) ),
file('COM013+1.p',unknown),
[] ).
cnf(39,axiom,
( ~ aElement0(u)
| ~ aElement0(v)
| ~ aRewritingSystem0(w)
| ~ aElement0(x)
| ~ sdtmndtplgtdt0(u,w,x)
| ~ aReductOfIn0(u,v,w)
| sdtmndtplgtdt0(v,w,x) ),
file('COM013+1.p',unknown),
[] ).
cnf(44,plain,
( ~ aRewritingSystem0(u)
| ~ aElement0(v)
| ~ aReductOfIn0(w,v,u)
| sdtmndtplgtdt0(v,u,w) ),
inference(mrr,[status(thm)],[28,23]),
[iquote('0:MRR:28.2,23.3')] ).
cnf(45,plain,
( ~ aElement0(u)
| ~ aRewritingSystem0(v)
| ~ aElement0(w)
| ~ aReductOfIn0(x,w,v)
| ~ sdtmndtplgtdt0(x,v,u)
| sdtmndtplgtdt0(w,v,u) ),
inference(mrr,[status(thm)],[39,23]),
[iquote('0:MRR:39.0,23.3')] ).
cnf(48,plain,
( ~ aElement0(u)
| ~ aRewritingSystem0(v)
| ~ sdtmndtplgtdt0(w,v,u)
| ~ aReductOfIn0(w,skc1,v)
| sdtmndtplgtdt0(skc1,v,u) ),
inference(res,[status(thm),theory(equality)],[1,45]),
[iquote('0:Res:1.0,45.0')] ).
cnf(57,plain,
( ~ aRewritingSystem0(u)
| ~ aReductOfIn0(v,skc1,u)
| sdtmndtplgtdt0(skc1,u,v) ),
inference(res,[status(thm),theory(equality)],[1,44]),
[iquote('0:Res:1.0,44.0')] ).
cnf(58,plain,
( ~ aElement0(u)
| ~ aRewritingSystem0(v)
| ~ sdtmndtplgtdt0(skc1,v,u)
| sdtmndtasgtdt0(skc1,v,u) ),
inference(res,[status(thm),theory(equality)],[1,29]),
[iquote('0:Res:1.0,29.0')] ).
cnf(62,plain,
( ~ aRewritingSystem0(u)
| ~ aReductOfIn0(v,skc1,u)
| aElement0(v) ),
inference(res,[status(thm),theory(equality)],[1,23]),
[iquote('0:Res:1.0,23.0')] ).
cnf(75,plain,
( ~ aRewritingSystem0(u)
| ~ aElement0(v)
| ~ equal(v,skc1)
| sdtmndtasgtdt0(v,u,skc1) ),
inference(res,[status(thm),theory(equality)],[1,27]),
[iquote('0:Res:1.0,27.2')] ).
cnf(87,plain,
( ~ aElement0(u)
| ~ aElement0(skc1)
| ~ aRewritingSystem0(xR)
| ~ sdtmndtasgtdt0(skc1,xR,u)
| aReductOfIn0(skf29(xR,u),u,xR) ),
inference(res,[status(thm),theory(equality)],[34,12]),
[iquote('0:Res:34.5,12.0')] ).
cnf(102,plain,
( ~ aElement0(u)
| ~ sdtmndtasgtdt0(skc1,xR,u)
| aReductOfIn0(skf29(xR,u),u,xR) ),
inference(mrr,[status(thm)],[87,1,2]),
[iquote('0:MRR:87.1,87.2,1.0,2.0')] ).
cnf(112,plain,
( ~ sdtmndtasgtdt0(skc1,xR,skc1)
| aReductOfIn0(skf29(xR,skc1),skc1,xR) ),
inference(res,[status(thm),theory(equality)],[1,102]),
[iquote('0:Res:1.0,102.0')] ).
cnf(115,plain,
( ~ aRewritingSystem0(u)
| ~ equal(skc1,skc1)
| sdtmndtasgtdt0(skc1,u,skc1) ),
inference(res,[status(thm),theory(equality)],[1,75]),
[iquote('0:Res:1.0,75.0')] ).
cnf(145,plain,
( ~ aRewritingSystem0(u)
| sdtmndtasgtdt0(skc1,u,skc1) ),
inference(obv,[status(thm),theory(equality)],[115]),
[iquote('0:Obv:115.1')] ).
cnf(185,plain,
( ~ aRewritingSystem0(xR)
| ~ sdtmndtasgtdt0(skc1,xR,skc1)
| aElement0(skf29(xR,skc1)) ),
inference(res,[status(thm),theory(equality)],[112,62]),
[iquote('0:Res:112.1,62.1')] ).
cnf(186,plain,
( ~ sdtmndtasgtdt0(skc1,xR,skc1)
| aElement0(skf29(xR,skc1)) ),
inference(ssi,[status(thm)],[185,3,2]),
[iquote('0:SSi:185.0,3.0,2.0')] ).
cnf(187,plain,
( ~ aRewritingSystem0(xR)
| aElement0(skf29(xR,skc1)) ),
inference(res,[status(thm),theory(equality)],[145,186]),
[iquote('0:Res:145.1,186.0')] ).
cnf(188,plain,
aElement0(skf29(xR,skc1)),
inference(ssi,[status(thm)],[187,3,2]),
[iquote('0:SSi:187.0,3.0,2.0')] ).
cnf(196,plain,
( ~ aElement0(u)
| ~ aRewritingSystem0(xR)
| ~ aElement0(u)
| ~ iLess0(u,skc1)
| aElement0(skf13(u)) ),
inference(res,[status(thm),theory(equality)],[22,24]),
[iquote('0:Res:22.2,24.2')] ).
cnf(197,plain,
( ~ aRewritingSystem0(xR)
| ~ aElement0(u)
| ~ iLess0(u,skc1)
| aElement0(skf13(u)) ),
inference(obv,[status(thm),theory(equality)],[196]),
[iquote('0:Obv:196.0')] ).
cnf(198,plain,
( ~ aElement0(u)
| ~ iLess0(u,skc1)
| aElement0(skf13(u)) ),
inference(ssi,[status(thm)],[197,3,2]),
[iquote('0:SSi:197.0,3.0,2.0')] ).
cnf(230,plain,
( ~ aElement0(u)
| ~ aRewritingSystem0(xR)
| ~ aElement0(u)
| ~ iLess0(u,skc1)
| sdtmndtasgtdt0(u,xR,skf13(u)) ),
inference(res,[status(thm),theory(equality)],[22,25]),
[iquote('0:Res:22.2,25.2')] ).
cnf(232,plain,
( ~ aRewritingSystem0(xR)
| ~ aElement0(u)
| ~ iLess0(u,skc1)
| sdtmndtasgtdt0(u,xR,skf13(u)) ),
inference(obv,[status(thm),theory(equality)],[230]),
[iquote('0:Obv:230.0')] ).
cnf(233,plain,
( ~ aElement0(u)
| ~ iLess0(u,skc1)
| sdtmndtasgtdt0(u,xR,skf13(u)) ),
inference(ssi,[status(thm)],[232,3,2]),
[iquote('0:SSi:232.0,3.0,2.0')] ).
cnf(241,plain,
( ~ aElement0(u)
| ~ aRewritingSystem0(xR)
| ~ aElement0(u)
| ~ iLess0(u,skc1)
| ~ aReductOfIn0(v,skf13(u),xR) ),
inference(res,[status(thm),theory(equality)],[22,26]),
[iquote('0:Res:22.2,26.2')] ).
cnf(244,plain,
( ~ aRewritingSystem0(xR)
| ~ aElement0(u)
| ~ iLess0(u,skc1)
| ~ aReductOfIn0(v,skf13(u),xR) ),
inference(obv,[status(thm),theory(equality)],[241]),
[iquote('0:Obv:241.0')] ).
cnf(245,plain,
( ~ aElement0(u)
| ~ iLess0(u,skc1)
| ~ aReductOfIn0(v,skf13(u),xR) ),
inference(ssi,[status(thm)],[244,3,2]),
[iquote('0:SSi:244.0,3.0,2.0')] ).
cnf(261,plain,
( ~ aElement0(skf13(u))
| ~ aElement0(u)
| ~ sdtmndtasgtdt0(skc1,xR,skf13(u))
| ~ iLess0(u,skc1) ),
inference(res,[status(thm),theory(equality)],[102,245]),
[iquote('0:Res:102.2,245.2')] ).
cnf(262,plain,
( ~ aElement0(u)
| ~ sdtmndtasgtdt0(skc1,xR,skf13(u))
| ~ iLess0(u,skc1) ),
inference(mrr,[status(thm)],[261,198]),
[iquote('0:MRR:261.0,198.2')] ).
cnf(263,plain,
( ~ aElement0(skf13(u))
| ~ aRewritingSystem0(xR)
| ~ aElement0(u)
| ~ sdtmndtplgtdt0(skc1,xR,skf13(u))
| ~ iLess0(u,skc1) ),
inference(res,[status(thm),theory(equality)],[58,262]),
[iquote('0:Res:58.3,262.1')] ).
cnf(270,plain,
( ~ aElement0(skf13(u))
| ~ aElement0(u)
| ~ sdtmndtplgtdt0(skc1,xR,skf13(u))
| ~ iLess0(u,skc1) ),
inference(ssi,[status(thm)],[263,3,2]),
[iquote('0:SSi:263.1,3.0,2.0')] ).
cnf(271,plain,
( ~ aElement0(u)
| ~ sdtmndtplgtdt0(skc1,xR,skf13(u))
| ~ iLess0(u,skc1) ),
inference(mrr,[status(thm)],[270,198]),
[iquote('0:MRR:270.0,198.2')] ).
cnf(272,plain,
( ~ aRewritingSystem0(xR)
| ~ aElement0(u)
| ~ aReductOfIn0(skf13(u),skc1,xR)
| ~ iLess0(u,skc1) ),
inference(res,[status(thm),theory(equality)],[57,271]),
[iquote('0:Res:57.2,271.1')] ).
cnf(274,plain,
( ~ aElement0(u)
| ~ aReductOfIn0(skf13(u),skc1,xR)
| ~ iLess0(u,skc1) ),
inference(ssi,[status(thm)],[272,3,2]),
[iquote('0:SSi:272.0,3.0,2.0')] ).
cnf(350,plain,
( ~ aRewritingSystem0(u)
| ~ aRewritingSystem0(u)
| ~ aElement0(v)
| ~ aElement0(skc1)
| ~ isTerminating0(u)
| ~ aReductOfIn0(v,skc1,u)
| iLess0(v,skc1) ),
inference(res,[status(thm),theory(equality)],[57,30]),
[iquote('0:Res:57.2,30.4')] ).
cnf(353,plain,
( ~ aRewritingSystem0(u)
| ~ aElement0(v)
| ~ aElement0(skc1)
| ~ isTerminating0(u)
| ~ aReductOfIn0(v,skc1,u)
| iLess0(v,skc1) ),
inference(obv,[status(thm),theory(equality)],[350]),
[iquote('0:Obv:350.0')] ).
cnf(354,plain,
( ~ aRewritingSystem0(u)
| ~ aElement0(v)
| ~ isTerminating0(u)
| ~ aReductOfIn0(v,skc1,u)
| iLess0(v,skc1) ),
inference(ssi,[status(thm)],[353,1]),
[iquote('0:SSi:353.2,1.0')] ).
cnf(355,plain,
( ~ aRewritingSystem0(u)
| ~ isTerminating0(u)
| ~ aReductOfIn0(v,skc1,u)
| iLess0(v,skc1) ),
inference(mrr,[status(thm)],[354,62]),
[iquote('0:MRR:354.1,62.2')] ).
cnf(359,plain,
( ~ aRewritingSystem0(xR)
| ~ isTerminating0(xR)
| ~ sdtmndtasgtdt0(skc1,xR,skc1)
| iLess0(skf29(xR,skc1),skc1) ),
inference(res,[status(thm),theory(equality)],[112,355]),
[iquote('0:Res:112.1,355.2')] ).
cnf(361,plain,
( ~ sdtmndtasgtdt0(skc1,xR,skc1)
| iLess0(skf29(xR,skc1),skc1) ),
inference(ssi,[status(thm)],[359,3,2]),
[iquote('0:SSi:359.1,359.0,3.0,2.0,3.0,2.0')] ).
cnf(374,plain,
( ~ aElement0(u)
| ~ aElement0(skf13(u))
| ~ aRewritingSystem0(xR)
| ~ aElement0(u)
| ~ iLess0(u,skc1)
| equal(skf13(u),u)
| sdtmndtplgtdt0(u,xR,skf13(u)) ),
inference(res,[status(thm),theory(equality)],[233,33]),
[iquote('0:Res:233.2,33.3')] ).
cnf(377,plain,
( ~ aElement0(skf13(u))
| ~ aRewritingSystem0(xR)
| ~ aElement0(u)
| ~ iLess0(u,skc1)
| equal(skf13(u),u)
| sdtmndtplgtdt0(u,xR,skf13(u)) ),
inference(obv,[status(thm),theory(equality)],[374]),
[iquote('0:Obv:374.0')] ).
cnf(378,plain,
( ~ aElement0(skf13(u))
| ~ aElement0(u)
| ~ iLess0(u,skc1)
| equal(skf13(u),u)
| sdtmndtplgtdt0(u,xR,skf13(u)) ),
inference(ssi,[status(thm)],[377,3,2]),
[iquote('0:SSi:377.1,3.0,2.0')] ).
cnf(379,plain,
( ~ aElement0(u)
| ~ iLess0(u,skc1)
| equal(skf13(u),u)
| sdtmndtplgtdt0(u,xR,skf13(u)) ),
inference(mrr,[status(thm)],[378,198]),
[iquote('0:MRR:378.0,198.2')] ).
cnf(988,plain,
( ~ aElement0(u)
| ~ aElement0(skf13(u))
| ~ aRewritingSystem0(xR)
| ~ iLess0(u,skc1)
| ~ aReductOfIn0(u,skc1,xR)
| equal(skf13(u),u)
| sdtmndtplgtdt0(skc1,xR,skf13(u)) ),
inference(res,[status(thm),theory(equality)],[379,48]),
[iquote('0:Res:379.3,48.2')] ).
cnf(994,plain,
( ~ aElement0(u)
| ~ aElement0(skf13(u))
| ~ iLess0(u,skc1)
| ~ aReductOfIn0(u,skc1,xR)
| equal(skf13(u),u)
| sdtmndtplgtdt0(skc1,xR,skf13(u)) ),
inference(ssi,[status(thm)],[988,3,2]),
[iquote('0:SSi:988.2,3.0,2.0')] ).
cnf(995,plain,
( ~ aElement0(u)
| ~ iLess0(u,skc1)
| ~ aReductOfIn0(u,skc1,xR)
| equal(skf13(u),u) ),
inference(mrr,[status(thm)],[994,198,271]),
[iquote('0:MRR:994.1,994.5,198.2,271.1')] ).
cnf(1005,plain,
( ~ aElement0(skf29(xR,skc1))
| ~ sdtmndtasgtdt0(skc1,xR,skc1)
| ~ iLess0(skf29(xR,skc1),skc1)
| equal(skf13(skf29(xR,skc1)),skf29(xR,skc1)) ),
inference(res,[status(thm),theory(equality)],[112,995]),
[iquote('0:Res:112.1,995.2')] ).
cnf(1009,plain,
( ~ sdtmndtasgtdt0(skc1,xR,skc1)
| ~ iLess0(skf29(xR,skc1),skc1)
| equal(skf13(skf29(xR,skc1)),skf29(xR,skc1)) ),
inference(ssi,[status(thm)],[1005,188]),
[iquote('0:SSi:1005.0,188.0')] ).
cnf(1010,plain,
( ~ sdtmndtasgtdt0(skc1,xR,skc1)
| equal(skf13(skf29(xR,skc1)),skf29(xR,skc1)) ),
inference(mrr,[status(thm)],[1009,361]),
[iquote('0:MRR:1009.1,361.1')] ).
cnf(1038,plain,
( ~ aElement0(skf29(xR,skc1))
| ~ sdtmndtasgtdt0(skc1,xR,skc1)
| ~ aReductOfIn0(skf29(xR,skc1),skc1,xR)
| ~ iLess0(skf29(xR,skc1),skc1) ),
inference(spl,[status(thm),theory(equality)],[1010,274]),
[iquote('0:SpL:1010.1,274.1')] ).
cnf(1041,plain,
( ~ sdtmndtasgtdt0(skc1,xR,skc1)
| ~ aReductOfIn0(skf29(xR,skc1),skc1,xR)
| ~ iLess0(skf29(xR,skc1),skc1) ),
inference(ssi,[status(thm)],[1038,188]),
[iquote('0:SSi:1038.0,188.0')] ).
cnf(1042,plain,
~ sdtmndtasgtdt0(skc1,xR,skc1),
inference(mrr,[status(thm)],[1041,112,361]),
[iquote('0:MRR:1041.1,1041.2,112.1,361.1')] ).
cnf(1063,plain,
~ aRewritingSystem0(xR),
inference(res,[status(thm),theory(equality)],[145,1042]),
[iquote('0:Res:145.1,1042.0')] ).
cnf(1070,plain,
$false,
inference(ssi,[status(thm)],[1063,3,2]),
[iquote('0:SSi:1063.0,3.0,2.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : COM013+1 : TPTP v8.1.0. Released v4.0.0.
% 0.03/0.12 % Command : run_spass %d %s
% 0.11/0.32 % Computer : n026.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 600
% 0.11/0.32 % DateTime : Thu Jun 16 17:19:08 EDT 2022
% 0.11/0.32 % CPUTime :
% 0.40/0.61
% 0.40/0.61 SPASS V 3.9
% 0.40/0.61 SPASS beiseite: Proof found.
% 0.40/0.61 % SZS status Theorem
% 0.40/0.61 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.40/0.61 SPASS derived 492 clauses, backtracked 0 clauses, performed 0 splits and kept 319 clauses.
% 0.40/0.61 SPASS allocated 104992 KBytes.
% 0.40/0.61 SPASS spent 0:00:00.27 on the problem.
% 0.40/0.61 0:00:00.04 for the input.
% 0.40/0.61 0:00:00.07 for the FLOTTER CNF translation.
% 0.40/0.61 0:00:00.01 for inferences.
% 0.40/0.61 0:00:00.00 for the backtracking.
% 0.40/0.61 0:00:00.11 for the reduction.
% 0.40/0.61
% 0.40/0.61
% 0.40/0.61 Here is a proof with depth 6, length 69 :
% 0.40/0.61 % SZS output start Refutation
% See solution above
% 0.40/0.61 Formulae used in the proof : m__ m__587 mReduct mNFRDef mTCRDef mTCDef mTermin
% 0.40/0.61
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