TSTP Solution File: NUN085+2 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : NUN085+2 : TPTP v8.1.0. Released v7.3.0.
% 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 : Mon Jul 18 16:38:48 EDT 2022
% Result : Theorem 0.19s 0.45s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 17
% Syntax : Number of clauses : 49 ( 31 unt; 10 nHn; 49 RR)
% Number of literals : 67 ( 0 equ; 23 neg)
% Maximal clause size : 2 ( 1 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 8 ( 7 usr; 1 prp; 0-4 aty)
% Number of functors : 14 ( 14 usr; 9 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
r1(skc8),
file('NUN085+2.p',unknown),
[] ).
cnf(2,axiom,
r1(skc7),
file('NUN085+2.p',unknown),
[] ).
cnf(3,axiom,
r1(skc5),
file('NUN085+2.p',unknown),
[] ).
cnf(4,axiom,
r2(skc8,skc6),
file('NUN085+2.p',unknown),
[] ).
cnf(8,axiom,
r3(skc7,skc6,skc5),
file('NUN085+2.p',unknown),
[] ).
cnf(9,axiom,
( r1(u)
| skP0(skc9,u) ),
file('NUN085+2.p',unknown),
[] ).
cnf(10,axiom,
r2(u,skf17(v,u)),
file('NUN085+2.p',unknown),
[] ).
cnf(13,axiom,
( equal(u,skc9)
| skP0(skc9,u) ),
file('NUN085+2.p',unknown),
[] ).
cnf(18,axiom,
( ~ r1(u)
| ~ skP0(v,u) ),
file('NUN085+2.p',unknown),
[] ).
cnf(19,axiom,
r2(skf18(u,v),skf16(v,u)),
file('NUN085+2.p',unknown),
[] ).
cnf(20,axiom,
( ~ r1(u)
| ~ r2(v,u) ),
file('NUN085+2.p',unknown),
[] ).
cnf(21,axiom,
( ~ skP0(u,v)
| ~ equal(v,u) ),
file('NUN085+2.p',unknown),
[] ).
cnf(23,axiom,
r3(u,skf17(u,v),skf16(u,v)),
file('NUN085+2.p',unknown),
[] ).
cnf(26,axiom,
( equal(u,skf13(v))
| skP1(skf13(v),u,v) ),
file('NUN085+2.p',unknown),
[] ).
cnf(27,axiom,
( ~ r2(u,v)
| ~ skP1(w,v,u) ),
file('NUN085+2.p',unknown),
[] ).
cnf(32,axiom,
( ~ r3(u,v,w)
| ~ skP2(x,w,v,u) ),
file('NUN085+2.p',unknown),
[] ).
cnf(36,axiom,
( equal(u,skf14(v,w))
| skP2(skf14(v,w),u,w,v) ),
file('NUN085+2.p',unknown),
[] ).
cnf(38,plain,
~ skP0(u,skc5),
inference(res,[status(thm),theory(equality)],[3,18]),
[iquote('0:Res:3.0,18.0')] ).
cnf(40,plain,
~ skP0(u,skc7),
inference(res,[status(thm),theory(equality)],[2,18]),
[iquote('0:Res:2.0,18.0')] ).
cnf(42,plain,
~ skP0(u,skc8),
inference(res,[status(thm),theory(equality)],[1,18]),
[iquote('0:Res:1.0,18.0')] ).
cnf(45,plain,
~ skP1(u,skc6,skc8),
inference(res,[status(thm),theory(equality)],[4,27]),
[iquote('0:Res:4.0,27.0')] ).
cnf(48,plain,
~ skP2(u,skc5,skc6,skc7),
inference(res,[status(thm),theory(equality)],[8,32]),
[iquote('0:Res:8.0,32.0')] ).
cnf(53,plain,
equal(skc9,skc8),
inference(res,[status(thm),theory(equality)],[13,42]),
[iquote('0:Res:13.1,42.0')] ).
cnf(54,plain,
equal(skc9,skc7),
inference(res,[status(thm),theory(equality)],[13,40]),
[iquote('0:Res:13.1,40.0')] ).
cnf(55,plain,
equal(skc9,skc5),
inference(res,[status(thm),theory(equality)],[13,38]),
[iquote('0:Res:13.1,38.0')] ).
cnf(57,plain,
( r1(u)
| skP0(skc8,u) ),
inference(rew,[status(thm),theory(equality)],[53,9]),
[iquote('0:Rew:53.0,9.1')] ).
cnf(58,plain,
equal(skc8,skc7),
inference(rew,[status(thm),theory(equality)],[53,54]),
[iquote('0:Rew:53.0,54.0')] ).
cnf(63,plain,
~ skP1(u,skc6,skc7),
inference(rew,[status(thm),theory(equality)],[58,45]),
[iquote('0:Rew:58.0,45.0')] ).
cnf(65,plain,
equal(skc9,skc7),
inference(rew,[status(thm),theory(equality)],[58,53]),
[iquote('0:Rew:58.0,53.0')] ).
cnf(66,plain,
equal(skc7,skc5),
inference(rew,[status(thm),theory(equality)],[55,65]),
[iquote('0:Rew:55.0,65.0')] ).
cnf(71,plain,
~ skP2(u,skc5,skc6,skc5),
inference(rew,[status(thm),theory(equality)],[66,48]),
[iquote('0:Rew:66.0,48.0')] ).
cnf(72,plain,
equal(skc8,skc5),
inference(rew,[status(thm),theory(equality)],[66,58]),
[iquote('0:Rew:66.0,58.0')] ).
cnf(76,plain,
( r1(u)
| skP0(skc5,u) ),
inference(rew,[status(thm),theory(equality)],[72,57]),
[iquote('0:Rew:72.0,57.1')] ).
cnf(77,plain,
~ skP1(u,skc6,skc5),
inference(rew,[status(thm),theory(equality)],[66,63]),
[iquote('0:Rew:66.0,63.0')] ).
cnf(110,plain,
~ r1(skf16(u,v)),
inference(res,[status(thm),theory(equality)],[19,20]),
[iquote('0:Res:19.0,20.1')] ).
cnf(112,plain,
( ~ equal(u,skc5)
| r1(u) ),
inference(res,[status(thm),theory(equality)],[76,21]),
[iquote('0:Res:76.1,21.0')] ).
cnf(117,plain,
~ equal(skf16(u,v),skc5),
inference(sor,[status(thm)],[110,112]),
[iquote('0:SoR:110.0,112.1')] ).
cnf(119,plain,
equal(skf13(skc5),skc6),
inference(res,[status(thm),theory(equality)],[26,77]),
[iquote('0:Res:26.1,77.0')] ).
cnf(121,plain,
( equal(u,skf13(skc5))
| skP1(skc6,u,skc5) ),
inference(spr,[status(thm),theory(equality)],[119,26]),
[iquote('0:SpR:119.0,26.1')] ).
cnf(123,plain,
( equal(u,skc6)
| skP1(skc6,u,skc5) ),
inference(rew,[status(thm),theory(equality)],[119,121]),
[iquote('0:Rew:119.0,121.0')] ).
cnf(130,plain,
( ~ r2(skc5,u)
| equal(u,skc6) ),
inference(res,[status(thm),theory(equality)],[123,27]),
[iquote('0:Res:123.1,27.1')] ).
cnf(138,plain,
equal(skf17(u,skc5),skc6),
inference(res,[status(thm),theory(equality)],[10,130]),
[iquote('0:Res:10.0,130.0')] ).
cnf(146,plain,
r3(u,skc6,skf16(u,skc5)),
inference(spr,[status(thm),theory(equality)],[138,23]),
[iquote('0:SpR:138.0,23.0')] ).
cnf(310,plain,
equal(skf14(skc5,skc6),skc5),
inference(res,[status(thm),theory(equality)],[36,71]),
[iquote('0:Res:36.1,71.0')] ).
cnf(314,plain,
( equal(u,skf14(skc5,skc6))
| skP2(skc5,u,skc6,skc5) ),
inference(spr,[status(thm),theory(equality)],[310,36]),
[iquote('0:SpR:310.0,36.1')] ).
cnf(316,plain,
( equal(u,skc5)
| skP2(skc5,u,skc6,skc5) ),
inference(rew,[status(thm),theory(equality)],[310,314]),
[iquote('0:Rew:310.0,314.0')] ).
cnf(319,plain,
( ~ r3(skc5,skc6,u)
| equal(u,skc5) ),
inference(res,[status(thm),theory(equality)],[316,32]),
[iquote('0:Res:316.1,32.1')] ).
cnf(321,plain,
equal(skf16(skc5,skc5),skc5),
inference(res,[status(thm),theory(equality)],[146,319]),
[iquote('0:Res:146.0,319.0')] ).
cnf(325,plain,
$false,
inference(mrr,[status(thm)],[321,117]),
[iquote('0:MRR:321.0,117.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.11 % Problem : NUN085+2 : TPTP v8.1.0. Released v7.3.0.
% 0.07/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n020.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Thu Jun 2 07:21:38 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.19/0.45
% 0.19/0.45 SPASS V 3.9
% 0.19/0.45 SPASS beiseite: Proof found.
% 0.19/0.45 % SZS status Theorem
% 0.19/0.45 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.45 SPASS derived 259 clauses, backtracked 0 clauses, performed 0 splits and kept 149 clauses.
% 0.19/0.45 SPASS allocated 97788 KBytes.
% 0.19/0.45 SPASS spent 0:00:00.10 on the problem.
% 0.19/0.45 0:00:00.03 for the input.
% 0.19/0.45 0:00:00.03 for the FLOTTER CNF translation.
% 0.19/0.45 0:00:00.00 for inferences.
% 0.19/0.45 0:00:00.00 for the backtracking.
% 0.19/0.45 0:00:00.01 for the reduction.
% 0.19/0.45
% 0.19/0.45
% 0.19/0.45 Here is a proof with depth 7, length 49 :
% 0.19/0.45 % SZS output start Refutation
% See solution above
% 0.19/0.45 Formulae used in the proof : zeroplusoneidzero axiom_1 axiom_1a axiom_7a axiom_2 axiom_3
% 0.19/0.45
%------------------------------------------------------------------------------