TSTP Solution File: NUN072+2 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : NUN072+2 : TPTP v8.1.0. Released v7.3.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n025.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 : Mon Jul 18 16:38:45 EDT 2022
% Result : Theorem 11.61s 11.85s
% Output : Refutation 11.61s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 22
% Syntax : Number of clauses : 66 ( 47 unt; 4 nHn; 66 RR)
% Number of literals : 112 ( 0 equ; 54 neg)
% Maximal clause size : 9 ( 1 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 10 ( 9 usr; 1 prp; 0-4 aty)
% Number of functors : 21 ( 21 usr; 9 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
r1(skf22(u)),
file('NUN072+2.p',unknown),
[] ).
cnf(2,axiom,
r1(skf24(u)),
file('NUN072+2.p',unknown),
[] ).
cnf(3,axiom,
r1(skf23(u)),
file('NUN072+2.p',unknown),
[] ).
cnf(5,axiom,
r2(u,skf17(v,u)),
file('NUN072+2.p',unknown),
[] ).
cnf(6,axiom,
r2(u,skf20(v,u)),
file('NUN072+2.p',unknown),
[] ).
cnf(7,axiom,
r3(u,skf22(u),u),
file('NUN072+2.p',unknown),
[] ).
cnf(8,axiom,
( equal(u,skc1)
| skP0(skc1,u) ),
file('NUN072+2.p',unknown),
[] ).
cnf(9,axiom,
r3(u,v,skf18(v,u)),
file('NUN072+2.p',unknown),
[] ).
cnf(10,axiom,
r4(u,v,skf21(v,u)),
file('NUN072+2.p',unknown),
[] ).
cnf(11,axiom,
r4(u,skf24(u),skf23(u)),
file('NUN072+2.p',unknown),
[] ).
cnf(13,axiom,
( ~ r1(u)
| ~ skP0(v,u) ),
file('NUN072+2.p',unknown),
[] ).
cnf(14,axiom,
r2(skf18(u,v),skf16(v,u)),
file('NUN072+2.p',unknown),
[] ).
cnf(18,axiom,
r3(u,skf17(u,v),skf16(u,v)),
file('NUN072+2.p',unknown),
[] ).
cnf(19,axiom,
r3(skf21(u,v),v,skf19(v,u)),
file('NUN072+2.p',unknown),
[] ).
cnf(20,axiom,
r4(u,skf20(u,v),skf19(u,v)),
file('NUN072+2.p',unknown),
[] ).
cnf(21,axiom,
( equal(u,skf13(v))
| skP1(skf13(v),u,v) ),
file('NUN072+2.p',unknown),
[] ).
cnf(22,axiom,
( ~ r2(u,v)
| ~ skP1(w,v,u) ),
file('NUN072+2.p',unknown),
[] ).
cnf(27,axiom,
( ~ r3(u,v,w)
| ~ skP2(x,w,v,u) ),
file('NUN072+2.p',unknown),
[] ).
cnf(29,axiom,
( ~ r4(u,v,w)
| ~ skP3(x,w,v,u) ),
file('NUN072+2.p',unknown),
[] ).
cnf(31,axiom,
( equal(u,skf14(v,w))
| skP2(skf14(v,w),u,w,v) ),
file('NUN072+2.p',unknown),
[] ).
cnf(32,axiom,
( equal(u,skf15(v,w))
| skP3(skf15(v,w),u,w,v) ),
file('NUN072+2.p',unknown),
[] ).
cnf(33,axiom,
( ~ r1(u)
| ~ r1(v)
| ~ r1(w)
| ~ r2(u,x)
| ~ r2(w,y)
| ~ r2(x,z)
| ~ r2(v,x1)
| ~ r2(y,x2)
| ~ r4(x1,x2,z) ),
file('NUN072+2.p',unknown),
[] ).
cnf(49,plain,
( ~ r1(u)
| ~ r1(v)
| ~ r1(w)
| ~ r2(u,x)
| ~ r2(w,y)
| ~ r2(x,z)
| ~ r2(y,x1)
| ~ r4(skf20(x2,v),x1,z) ),
inference(res,[status(thm),theory(equality)],[6,33]),
[iquote('0:Res:6.0,33.5')] ).
cnf(61,plain,
( ~ r1(u)
| equal(u,skc1) ),
inference(res,[status(thm),theory(equality)],[8,13]),
[iquote('0:Res:8.1,13.1')] ).
cnf(63,plain,
equal(skf22(u),skc1),
inference(ems,[status(thm)],[61,1]),
[iquote('0:EmS:61.0,1.0')] ).
cnf(64,plain,
equal(skf24(u),skc1),
inference(ems,[status(thm)],[61,2]),
[iquote('0:EmS:61.0,2.0')] ).
cnf(65,plain,
equal(skf23(u),skc1),
inference(ems,[status(thm)],[61,3]),
[iquote('0:EmS:61.0,3.0')] ).
cnf(66,plain,
r1(skc1),
inference(rew,[status(thm),theory(equality)],[63,1]),
[iquote('0:Rew:63.0,1.0')] ).
cnf(67,plain,
r3(u,skc1,u),
inference(rew,[status(thm),theory(equality)],[63,7]),
[iquote('0:Rew:63.0,7.0')] ).
cnf(72,plain,
r4(u,skc1,skf23(u)),
inference(rew,[status(thm),theory(equality)],[64,11]),
[iquote('0:Rew:64.0,11.0')] ).
cnf(81,plain,
r4(u,skc1,skc1),
inference(rew,[status(thm),theory(equality)],[65,72]),
[iquote('0:Rew:65.0,72.0')] ).
cnf(104,plain,
( ~ r2(u,v)
| equal(v,skf13(u)) ),
inference(res,[status(thm),theory(equality)],[21,22]),
[iquote('0:Res:21.1,22.1')] ).
cnf(105,plain,
equal(skf20(u,v),skf13(v)),
inference(res,[status(thm),theory(equality)],[6,104]),
[iquote('0:Res:6.0,104.0')] ).
cnf(106,plain,
equal(skf17(u,v),skf13(v)),
inference(res,[status(thm),theory(equality)],[5,104]),
[iquote('0:Res:5.0,104.0')] ).
cnf(111,plain,
r4(u,skf13(v),skf19(u,v)),
inference(rew,[status(thm),theory(equality)],[105,20]),
[iquote('0:Rew:105.0,20.0')] ).
cnf(112,plain,
r2(u,skf13(u)),
inference(rew,[status(thm),theory(equality)],[105,6]),
[iquote('0:Rew:105.0,6.0')] ).
cnf(117,plain,
( ~ r1(u)
| ~ r1(v)
| ~ r1(w)
| ~ r2(u,x)
| ~ r2(w,y)
| ~ r2(x,z)
| ~ r2(y,x1)
| ~ r4(skf13(v),x1,z) ),
inference(rew,[status(thm),theory(equality)],[105,49]),
[iquote('0:Rew:105.0,49.7')] ).
cnf(120,plain,
r3(u,skf13(v),skf16(u,v)),
inference(rew,[status(thm),theory(equality)],[106,18]),
[iquote('0:Rew:106.0,18.0')] ).
cnf(288,plain,
( ~ r4(u,v,w)
| equal(w,skf15(u,v)) ),
inference(res,[status(thm),theory(equality)],[32,29]),
[iquote('0:Res:32.1,29.1')] ).
cnf(289,plain,
equal(skf21(u,v),skf15(v,u)),
inference(res,[status(thm),theory(equality)],[10,288]),
[iquote('0:Res:10.0,288.0')] ).
cnf(290,plain,
equal(skf15(u,skc1),skc1),
inference(res,[status(thm),theory(equality)],[81,288]),
[iquote('0:Res:81.0,288.0')] ).
cnf(291,plain,
equal(skf15(u,skf13(v)),skf19(u,v)),
inference(res,[status(thm),theory(equality)],[111,288]),
[iquote('0:Res:111.0,288.0')] ).
cnf(295,plain,
r3(skf15(u,v),u,skf19(u,v)),
inference(rew,[status(thm),theory(equality)],[289,19]),
[iquote('0:Rew:289.0,19.0')] ).
cnf(306,plain,
r3(skc1,u,skf19(u,skc1)),
inference(spr,[status(thm),theory(equality)],[290,295]),
[iquote('0:SpR:290.0,295.0')] ).
cnf(315,plain,
( ~ r3(u,v,w)
| equal(w,skf14(u,v)) ),
inference(res,[status(thm),theory(equality)],[31,27]),
[iquote('0:Res:31.1,27.1')] ).
cnf(318,plain,
r3(skf19(u,v),u,skf19(u,skf13(v))),
inference(spr,[status(thm),theory(equality)],[291,295]),
[iquote('0:SpR:291.0,295.0')] ).
cnf(353,plain,
equal(skf18(u,v),skf14(v,u)),
inference(res,[status(thm),theory(equality)],[9,315]),
[iquote('0:Res:9.0,315.0')] ).
cnf(354,plain,
equal(skf14(u,skc1),u),
inference(res,[status(thm),theory(equality)],[67,315]),
[iquote('0:Res:67.0,315.0')] ).
cnf(355,plain,
equal(skf14(u,skf13(v)),skf16(u,v)),
inference(res,[status(thm),theory(equality)],[120,315]),
[iquote('0:Res:120.0,315.0')] ).
cnf(360,plain,
equal(skf19(u,skc1),skf14(skc1,u)),
inference(res,[status(thm),theory(equality)],[306,315]),
[iquote('0:Res:306.0,315.0')] ).
cnf(363,plain,
r2(skf14(u,v),skf16(u,v)),
inference(rew,[status(thm),theory(equality)],[353,14]),
[iquote('0:Rew:353.0,14.0')] ).
cnf(392,plain,
r2(u,skf16(u,skc1)),
inference(spr,[status(thm),theory(equality)],[354,363]),
[iquote('0:SpR:354.0,363.0')] ).
cnf(401,plain,
equal(skf16(u,skc1),skf13(u)),
inference(res,[status(thm),theory(equality)],[392,104]),
[iquote('0:Res:392.0,104.0')] ).
cnf(420,plain,
r3(skf14(skc1,u),u,skf19(u,skf13(skc1))),
inference(spr,[status(thm),theory(equality)],[360,318]),
[iquote('0:SpR:360.0,318.0')] ).
cnf(613,plain,
equal(skf14(skf14(skc1,u),u),skf19(u,skf13(skc1))),
inference(res,[status(thm),theory(equality)],[420,315]),
[iquote('0:Res:420.0,315.0')] ).
cnf(788,plain,
equal(skf16(skf14(skc1,skf13(u)),u),skf19(skf13(u),skf13(skc1))),
inference(spr,[status(thm),theory(equality)],[613,355]),
[iquote('0:SpR:613.0,355.0')] ).
cnf(797,plain,
equal(skf16(skf16(skc1,u),u),skf19(skf13(u),skf13(skc1))),
inference(rew,[status(thm),theory(equality)],[355,788]),
[iquote('0:Rew:355.0,788.0')] ).
cnf(1089,plain,
r4(skf13(u),skf13(skf13(skc1)),skf16(skf16(skc1,u),u)),
inference(spr,[status(thm),theory(equality)],[797,111]),
[iquote('0:SpR:797.0,111.0')] ).
cnf(1190,plain,
r4(skf13(skc1),skf13(skf13(skc1)),skf16(skf13(skc1),skc1)),
inference(spr,[status(thm),theory(equality)],[401,1089]),
[iquote('0:SpR:401.0,1089.0')] ).
cnf(1205,plain,
r4(skf13(skc1),skf13(skf13(skc1)),skf13(skf13(skc1))),
inference(rew,[status(thm),theory(equality)],[401,1190]),
[iquote('0:Rew:401.0,1190.0')] ).
cnf(1223,plain,
( ~ r1(u)
| ~ r1(skc1)
| ~ r1(v)
| ~ r2(u,w)
| ~ r2(v,x)
| ~ r2(w,skf13(skf13(skc1)))
| ~ r2(x,skf13(skf13(skc1))) ),
inference(res,[status(thm),theory(equality)],[1205,117]),
[iquote('0:Res:1205.0,117.7')] ).
cnf(1225,plain,
( ~ r1(u)
| ~ r1(skc1)
| ~ r2(u,v)
| ~ r2(v,skf13(skf13(skc1))) ),
inference(con,[status(thm)],[1223]),
[iquote('0:Con:1223.2')] ).
cnf(1226,plain,
( ~ r1(u)
| ~ r2(u,v)
| ~ r2(v,skf13(skf13(skc1))) ),
inference(ssi,[status(thm)],[1225,66]),
[iquote('0:SSi:1225.1,66.0')] ).
cnf(13543,plain,
( ~ r1(u)
| ~ r2(u,skf13(skc1)) ),
inference(res,[status(thm),theory(equality)],[112,1226]),
[iquote('0:Res:112.0,1226.2')] ).
cnf(13552,plain,
~ r1(skc1),
inference(res,[status(thm),theory(equality)],[112,13543]),
[iquote('0:Res:112.0,13543.1')] ).
cnf(13560,plain,
$false,
inference(ssi,[status(thm)],[13552,66]),
[iquote('0:SSi:13552.0,66.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.15 % Problem : NUN072+2 : TPTP v8.1.0. Released v7.3.0.
% 0.07/0.15 % Command : run_spass %d %s
% 0.14/0.37 % Computer : n025.cluster.edu
% 0.14/0.37 % Model : x86_64 x86_64
% 0.14/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.37 % Memory : 8042.1875MB
% 0.14/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.37 % CPULimit : 300
% 0.14/0.37 % WCLimit : 600
% 0.14/0.37 % DateTime : Thu Jun 2 10:12:14 EDT 2022
% 0.14/0.37 % CPUTime :
% 11.61/11.85
% 11.61/11.85 SPASS V 3.9
% 11.61/11.85 SPASS beiseite: Proof found.
% 11.61/11.85 % SZS status Theorem
% 11.61/11.85 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 11.61/11.85 SPASS derived 10249 clauses, backtracked 0 clauses, performed 0 splits and kept 3892 clauses.
% 11.61/11.85 SPASS allocated 111847 KBytes.
% 11.61/11.85 SPASS spent 0:0:11.28 on the problem.
% 11.61/11.85 0:00:00.03 for the input.
% 11.61/11.85 0:00:00.03 for the FLOTTER CNF translation.
% 11.61/11.85 0:00:00.17 for inferences.
% 11.61/11.85 0:00:00.00 for the backtracking.
% 11.61/11.85 0:0:10.93 for the reduction.
% 11.61/11.85
% 11.61/11.85
% 11.61/11.85 Here is a proof with depth 12, length 66 :
% 11.61/11.85 % SZS output start Refutation
% See solution above
% 11.61/11.85 Formulae used in the proof : axiom_4a axiom_5a axiom_1a axiom_2a axiom_1 axiom_2 axiom_3 axiom_4 onetimestwoeqtwo
% 11.61/11.85
%------------------------------------------------------------------------------