TSTP Solution File: NUN071+2 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : NUN071+2 : TPTP v8.1.0. Released v7.3.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n021.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 0.22s 0.50s
% Output : Refutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 22
% Syntax : Number of clauses : 56 ( 39 unt; 4 nHn; 56 RR)
% Number of literals : 82 ( 0 equ; 32 neg)
% Maximal clause size : 5 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 10 ( 9 usr; 1 prp; 0-4 aty)
% Number of functors : 17 ( 17 usr; 5 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
r1(skf22(u)),
file('NUN071+2.p',unknown),
[] ).
cnf(2,axiom,
r1(skf24(u)),
file('NUN071+2.p',unknown),
[] ).
cnf(3,axiom,
r1(skf23(u)),
file('NUN071+2.p',unknown),
[] ).
cnf(5,axiom,
r2(u,skf17(v,u)),
file('NUN071+2.p',unknown),
[] ).
cnf(6,axiom,
r2(u,skf20(v,u)),
file('NUN071+2.p',unknown),
[] ).
cnf(7,axiom,
r3(u,skf22(u),u),
file('NUN071+2.p',unknown),
[] ).
cnf(8,axiom,
( equal(u,skc1)
| skP0(skc1,u) ),
file('NUN071+2.p',unknown),
[] ).
cnf(9,axiom,
r3(u,v,skf18(v,u)),
file('NUN071+2.p',unknown),
[] ).
cnf(10,axiom,
r4(u,v,skf21(v,u)),
file('NUN071+2.p',unknown),
[] ).
cnf(11,axiom,
r4(u,skf24(u),skf23(u)),
file('NUN071+2.p',unknown),
[] ).
cnf(13,axiom,
( ~ r1(u)
| ~ skP0(v,u) ),
file('NUN071+2.p',unknown),
[] ).
cnf(14,axiom,
r2(skf18(u,v),skf16(v,u)),
file('NUN071+2.p',unknown),
[] ).
cnf(18,axiom,
r3(u,skf17(u,v),skf16(u,v)),
file('NUN071+2.p',unknown),
[] ).
cnf(19,axiom,
r3(skf21(u,v),v,skf19(v,u)),
file('NUN071+2.p',unknown),
[] ).
cnf(20,axiom,
r4(u,skf20(u,v),skf19(u,v)),
file('NUN071+2.p',unknown),
[] ).
cnf(21,axiom,
( equal(u,skf13(v))
| skP1(skf13(v),u,v) ),
file('NUN071+2.p',unknown),
[] ).
cnf(22,axiom,
( ~ r2(u,v)
| ~ skP1(w,v,u) ),
file('NUN071+2.p',unknown),
[] ).
cnf(27,axiom,
( ~ r3(u,v,w)
| ~ skP2(x,w,v,u) ),
file('NUN071+2.p',unknown),
[] ).
cnf(29,axiom,
( ~ r4(u,v,w)
| ~ skP3(x,w,v,u) ),
file('NUN071+2.p',unknown),
[] ).
cnf(31,axiom,
( equal(u,skf14(v,w))
| skP2(skf14(v,w),u,w,v) ),
file('NUN071+2.p',unknown),
[] ).
cnf(32,axiom,
( equal(u,skf15(v,w))
| skP3(skf15(v,w),u,w,v) ),
file('NUN071+2.p',unknown),
[] ).
cnf(33,axiom,
( ~ r1(u)
| ~ r1(v)
| ~ r2(u,w)
| ~ r2(v,x)
| ~ r4(x,x,w) ),
file('NUN071+2.p',unknown),
[] ).
cnf(47,plain,
( ~ r1(u)
| equal(u,skc1) ),
inference(res,[status(thm),theory(equality)],[8,13]),
[iquote('0:Res:8.1,13.1')] ).
cnf(49,plain,
equal(skf22(u),skc1),
inference(ems,[status(thm)],[47,1]),
[iquote('0:EmS:47.0,1.0')] ).
cnf(50,plain,
equal(skf24(u),skc1),
inference(ems,[status(thm)],[47,2]),
[iquote('0:EmS:47.0,2.0')] ).
cnf(51,plain,
equal(skf23(u),skc1),
inference(ems,[status(thm)],[47,3]),
[iquote('0:EmS:47.0,3.0')] ).
cnf(52,plain,
r1(skc1),
inference(rew,[status(thm),theory(equality)],[49,1]),
[iquote('0:Rew:49.0,1.0')] ).
cnf(53,plain,
r3(u,skc1,u),
inference(rew,[status(thm),theory(equality)],[49,7]),
[iquote('0:Rew:49.0,7.0')] ).
cnf(57,plain,
r4(u,skc1,skf23(u)),
inference(rew,[status(thm),theory(equality)],[50,11]),
[iquote('0:Rew:50.0,11.0')] ).
cnf(63,plain,
r4(u,skc1,skc1),
inference(rew,[status(thm),theory(equality)],[51,57]),
[iquote('0:Rew:51.0,57.0')] ).
cnf(84,plain,
( ~ r2(u,v)
| equal(v,skf13(u)) ),
inference(res,[status(thm),theory(equality)],[21,22]),
[iquote('0:Res:21.1,22.1')] ).
cnf(85,plain,
equal(skf20(u,v),skf13(v)),
inference(res,[status(thm),theory(equality)],[6,84]),
[iquote('0:Res:6.0,84.0')] ).
cnf(86,plain,
equal(skf17(u,v),skf13(v)),
inference(res,[status(thm),theory(equality)],[5,84]),
[iquote('0:Res:5.0,84.0')] ).
cnf(91,plain,
r4(u,skf13(v),skf19(u,v)),
inference(rew,[status(thm),theory(equality)],[85,20]),
[iquote('0:Rew:85.0,20.0')] ).
cnf(92,plain,
r2(u,skf13(u)),
inference(rew,[status(thm),theory(equality)],[85,6]),
[iquote('0:Rew:85.0,6.0')] ).
cnf(96,plain,
r3(u,skf13(v),skf16(u,v)),
inference(rew,[status(thm),theory(equality)],[86,18]),
[iquote('0:Rew:86.0,18.0')] ).
cnf(336,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(337,plain,
equal(skf21(u,v),skf15(v,u)),
inference(res,[status(thm),theory(equality)],[10,336]),
[iquote('0:Res:10.0,336.0')] ).
cnf(338,plain,
equal(skf15(u,skc1),skc1),
inference(res,[status(thm),theory(equality)],[63,336]),
[iquote('0:Res:63.0,336.0')] ).
cnf(343,plain,
r3(skf15(u,v),u,skf19(u,v)),
inference(rew,[status(thm),theory(equality)],[337,19]),
[iquote('0:Rew:337.0,19.0')] ).
cnf(355,plain,
r3(skc1,u,skf19(u,skc1)),
inference(spr,[status(thm),theory(equality)],[338,343]),
[iquote('0:SpR:338.0,343.0')] ).
cnf(375,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(409,plain,
equal(skf18(u,v),skf14(v,u)),
inference(res,[status(thm),theory(equality)],[9,375]),
[iquote('0:Res:9.0,375.0')] ).
cnf(410,plain,
equal(skf14(u,skc1),u),
inference(res,[status(thm),theory(equality)],[53,375]),
[iquote('0:Res:53.0,375.0')] ).
cnf(411,plain,
equal(skf14(u,skf13(v)),skf16(u,v)),
inference(res,[status(thm),theory(equality)],[96,375]),
[iquote('0:Res:96.0,375.0')] ).
cnf(416,plain,
equal(skf19(u,skc1),skf14(skc1,u)),
inference(res,[status(thm),theory(equality)],[355,375]),
[iquote('0:Res:355.0,375.0')] ).
cnf(419,plain,
r2(skf14(u,v),skf16(u,v)),
inference(rew,[status(thm),theory(equality)],[409,14]),
[iquote('0:Rew:409.0,14.0')] ).
cnf(442,plain,
r2(u,skf16(u,skc1)),
inference(spr,[status(thm),theory(equality)],[410,419]),
[iquote('0:SpR:410.0,419.0')] ).
cnf(449,plain,
equal(skf16(u,skc1),skf13(u)),
inference(res,[status(thm),theory(equality)],[442,84]),
[iquote('0:Res:442.0,84.0')] ).
cnf(467,plain,
r4(u,skf13(skc1),skf14(skc1,u)),
inference(spr,[status(thm),theory(equality)],[416,91]),
[iquote('0:SpR:416.0,91.0')] ).
cnf(480,plain,
( ~ r1(u)
| ~ r1(v)
| ~ r2(u,skf14(skc1,skf13(skc1)))
| ~ r2(v,skf13(skc1)) ),
inference(res,[status(thm),theory(equality)],[467,33]),
[iquote('0:Res:467.0,33.4')] ).
cnf(482,plain,
( ~ r1(u)
| ~ r1(v)
| ~ r2(u,skf16(skc1,skc1))
| ~ r2(v,skf13(skc1)) ),
inference(rew,[status(thm),theory(equality)],[411,480]),
[iquote('0:Rew:411.0,480.2')] ).
cnf(483,plain,
( ~ r1(u)
| ~ r1(v)
| ~ r2(u,skf13(skc1))
| ~ r2(v,skf13(skc1)) ),
inference(rew,[status(thm),theory(equality)],[449,482]),
[iquote('0:Rew:449.0,482.2')] ).
cnf(484,plain,
( ~ r1(u)
| ~ r2(u,skf13(skc1)) ),
inference(con,[status(thm)],[483]),
[iquote('0:Con:483.1')] ).
cnf(488,plain,
~ r1(skc1),
inference(res,[status(thm),theory(equality)],[92,484]),
[iquote('0:Res:92.0,484.1')] ).
cnf(493,plain,
$false,
inference(ssi,[status(thm)],[488,52]),
[iquote('0:SSi:488.0,52.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.13 % Problem : NUN071+2 : TPTP v8.1.0. Released v7.3.0.
% 0.09/0.14 % Command : run_spass %d %s
% 0.15/0.35 % Computer : n021.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 600
% 0.15/0.35 % DateTime : Thu Jun 2 04:16:46 EDT 2022
% 0.15/0.35 % CPUTime :
% 0.22/0.50
% 0.22/0.50 SPASS V 3.9
% 0.22/0.50 SPASS beiseite: Proof found.
% 0.22/0.50 % SZS status Theorem
% 0.22/0.50 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.22/0.50 SPASS derived 384 clauses, backtracked 0 clauses, performed 0 splits and kept 221 clauses.
% 0.22/0.50 SPASS allocated 97970 KBytes.
% 0.22/0.50 SPASS spent 0:00:00.13 on the problem.
% 0.22/0.50 0:00:00.04 for the input.
% 0.22/0.50 0:00:00.03 for the FLOTTER CNF translation.
% 0.22/0.50 0:00:00.01 for inferences.
% 0.22/0.50 0:00:00.00 for the backtracking.
% 0.22/0.50 0:00:00.04 for the reduction.
% 0.22/0.50
% 0.22/0.50
% 0.22/0.50 Here is a proof with depth 7, length 56 :
% 0.22/0.50 % SZS output start Refutation
% See solution above
% 0.22/0.50 Formulae used in the proof : axiom_4a axiom_5a axiom_1a axiom_2a axiom_1 axiom_2 axiom_3 axiom_4 onetimesoneeqone
% 0.22/0.50
%------------------------------------------------------------------------------