TSTP Solution File: NUN056+2 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : NUN056+2 : TPTP v8.1.0. Released v7.3.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n022.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 16:38:42 EDT 2022
% Result : Theorem 18.31s 18.48s
% Output : Refutation 18.31s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 14
% Syntax : Number of clauses : 43 ( 27 unt; 3 nHn; 43 RR)
% Number of literals : 93 ( 0 equ; 58 neg)
% Maximal clause size : 10 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 8 ( 7 usr; 1 prp; 0-4 aty)
% Number of functors : 17 ( 17 usr; 10 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
r1(skf22(u)),
file('NUN056+2.p',unknown),
[] ).
cnf(5,axiom,
r2(u,skf17(v,u)),
file('NUN056+2.p',unknown),
[] ).
cnf(6,axiom,
r2(u,skf20(v,u)),
file('NUN056+2.p',unknown),
[] ).
cnf(7,axiom,
r3(u,skf22(u),u),
file('NUN056+2.p',unknown),
[] ).
cnf(8,axiom,
( equal(u,skc1)
| skP0(skc1,u) ),
file('NUN056+2.p',unknown),
[] ).
cnf(9,axiom,
r3(u,v,skf18(v,u)),
file('NUN056+2.p',unknown),
[] ).
cnf(13,axiom,
( ~ r1(u)
| ~ skP0(v,u) ),
file('NUN056+2.p',unknown),
[] ).
cnf(14,axiom,
r2(skf18(u,v),skf16(v,u)),
file('NUN056+2.p',unknown),
[] ).
cnf(18,axiom,
r3(u,skf17(u,v),skf16(u,v)),
file('NUN056+2.p',unknown),
[] ).
cnf(21,axiom,
( equal(u,skf13(v))
| skP1(skf13(v),u,v) ),
file('NUN056+2.p',unknown),
[] ).
cnf(22,axiom,
( ~ r2(u,v)
| ~ skP1(w,v,u) ),
file('NUN056+2.p',unknown),
[] ).
cnf(27,axiom,
( ~ r3(u,v,w)
| ~ skP2(x,w,v,u) ),
file('NUN056+2.p',unknown),
[] ).
cnf(31,axiom,
( equal(u,skf14(v,w))
| skP2(skf14(v,w),u,w,v) ),
file('NUN056+2.p',unknown),
[] ).
cnf(33,axiom,
( ~ r1(u)
| ~ r1(v)
| ~ r1(w)
| ~ r2(u,x)
| ~ r2(y,z)
| ~ r2(x,x1)
| ~ r2(v,x2)
| ~ r2(x3,y)
| ~ r2(w,x3)
| ~ r3(x2,x1,z) ),
file('NUN056+2.p',unknown),
[] ).
cnf(50,plain,
( ~ r1(u)
| ~ r1(v)
| ~ r1(w)
| ~ r2(u,x)
| ~ r2(x,y)
| ~ r2(v,z)
| ~ r2(w,x1)
| ~ r2(skf20(x2,x1),x3)
| ~ r3(z,y,x3) ),
inference(res,[status(thm),theory(equality)],[6,33]),
[iquote('0:Res:6.0,33.5')] ).
cnf(65,plain,
( ~ r1(u)
| equal(u,skc1) ),
inference(res,[status(thm),theory(equality)],[8,13]),
[iquote('0:Res:8.1,13.1')] ).
cnf(67,plain,
equal(skf22(u),skc1),
inference(ems,[status(thm)],[65,1]),
[iquote('0:EmS:65.0,1.0')] ).
cnf(70,plain,
r1(skc1),
inference(rew,[status(thm),theory(equality)],[67,1]),
[iquote('0:Rew:67.0,1.0')] ).
cnf(71,plain,
r3(u,skc1,u),
inference(rew,[status(thm),theory(equality)],[67,7]),
[iquote('0:Rew:67.0,7.0')] ).
cnf(106,plain,
( ~ r2(u,v)
| equal(v,skf13(u)) ),
inference(res,[status(thm),theory(equality)],[21,22]),
[iquote('0:Res:21.1,22.1')] ).
cnf(107,plain,
equal(skf20(u,v),skf13(v)),
inference(res,[status(thm),theory(equality)],[6,106]),
[iquote('0:Res:6.0,106.0')] ).
cnf(108,plain,
equal(skf17(u,v),skf13(v)),
inference(res,[status(thm),theory(equality)],[5,106]),
[iquote('0:Res:5.0,106.0')] ).
cnf(111,plain,
equal(skf13(skf18(u,v)),skf16(v,u)),
inference(res,[status(thm),theory(equality)],[14,106]),
[iquote('0:Res:14.0,106.0')] ).
cnf(114,plain,
r2(u,skf13(u)),
inference(rew,[status(thm),theory(equality)],[107,6]),
[iquote('0:Rew:107.0,6.0')] ).
cnf(116,plain,
( ~ r1(u)
| ~ r1(v)
| ~ r1(w)
| ~ r2(u,x)
| ~ r2(x,y)
| ~ r2(v,z)
| ~ r2(w,x1)
| ~ r2(skf13(x1),x2)
| ~ r3(z,y,x2) ),
inference(rew,[status(thm),theory(equality)],[107,50]),
[iquote('0:Rew:107.0,50.7')] ).
cnf(122,plain,
r3(u,skf13(v),skf16(u,v)),
inference(rew,[status(thm),theory(equality)],[108,18]),
[iquote('0:Rew:108.0,18.0')] ).
cnf(406,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(441,plain,
equal(skf18(u,v),skf14(v,u)),
inference(res,[status(thm),theory(equality)],[9,406]),
[iquote('0:Res:9.0,406.0')] ).
cnf(442,plain,
equal(skf14(u,skc1),u),
inference(res,[status(thm),theory(equality)],[71,406]),
[iquote('0:Res:71.0,406.0')] ).
cnf(443,plain,
equal(skf14(u,skf13(v)),skf16(u,v)),
inference(res,[status(thm),theory(equality)],[122,406]),
[iquote('0:Res:122.0,406.0')] ).
cnf(451,plain,
r2(skf14(u,v),skf16(u,v)),
inference(rew,[status(thm),theory(equality)],[441,14]),
[iquote('0:Rew:441.0,14.0')] ).
cnf(452,plain,
equal(skf13(skf14(u,v)),skf16(u,v)),
inference(rew,[status(thm),theory(equality)],[441,111]),
[iquote('0:Rew:441.0,111.0')] ).
cnf(487,plain,
r2(u,skf16(u,skc1)),
inference(spr,[status(thm),theory(equality)],[442,451]),
[iquote('0:SpR:442.0,451.0')] ).
cnf(494,plain,
equal(skf16(u,skc1),skf13(u)),
inference(res,[status(thm),theory(equality)],[487,106]),
[iquote('0:Res:487.0,106.0')] ).
cnf(578,plain,
equal(skf16(u,skf13(v)),skf13(skf16(u,v))),
inference(spr,[status(thm),theory(equality)],[443,452]),
[iquote('0:SpR:443.0,452.0')] ).
cnf(721,plain,
r3(u,skf13(skf13(v)),skf13(skf16(u,v))),
inference(spr,[status(thm),theory(equality)],[578,122]),
[iquote('0:SpR:578.0,122.0')] ).
cnf(742,plain,
r3(u,skf13(skf13(skc1)),skf13(skf13(u))),
inference(spr,[status(thm),theory(equality)],[494,721]),
[iquote('0:SpR:494.0,721.0')] ).
cnf(805,plain,
( ~ r1(u)
| ~ r1(v)
| ~ r1(w)
| ~ r2(u,x)
| ~ r2(x,y)
| ~ r2(v,z)
| ~ r2(w,x1)
| ~ r3(z,y,skf13(skf13(x1))) ),
inference(res,[status(thm),theory(equality)],[114,116]),
[iquote('0:Res:114.0,116.7')] ).
cnf(3169,plain,
( ~ r1(u)
| ~ r1(v)
| ~ r1(w)
| ~ r2(u,x)
| ~ r2(x,skf13(skf13(skc1)))
| ~ r2(v,y)
| ~ r2(w,y) ),
inference(res,[status(thm),theory(equality)],[742,805]),
[iquote('0:Res:742.0,805.7')] ).
cnf(3176,plain,
( ~ r1(u)
| ~ r2(u,v)
| ~ r2(v,skf13(skf13(skc1))) ),
inference(con,[status(thm)],[3169]),
[iquote('0:Con:3169.1')] ).
cnf(16288,plain,
( ~ r1(u)
| ~ r2(u,skf13(skc1)) ),
inference(res,[status(thm),theory(equality)],[114,3176]),
[iquote('0:Res:114.0,3176.2')] ).
cnf(16322,plain,
~ r1(skc1),
inference(res,[status(thm),theory(equality)],[114,16288]),
[iquote('0:Res:114.0,16288.1')] ).
cnf(16331,plain,
$false,
inference(ssi,[status(thm)],[16322,70]),
[iquote('0:SSi:16322.0,70.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : NUN056+2 : TPTP v8.1.0. Released v7.3.0.
% 0.03/0.13 % Command : run_spass %d %s
% 0.12/0.34 % Computer : n022.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Thu Jun 2 03:07:21 EDT 2022
% 0.12/0.34 % CPUTime :
% 18.31/18.48
% 18.31/18.48 SPASS V 3.9
% 18.31/18.48 SPASS beiseite: Proof found.
% 18.31/18.48 % SZS status Theorem
% 18.31/18.48 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 18.31/18.48 SPASS derived 12404 clauses, backtracked 0 clauses, performed 0 splits and kept 5106 clauses.
% 18.31/18.48 SPASS allocated 114753 KBytes.
% 18.31/18.48 SPASS spent 0:0:17.90 on the problem.
% 18.31/18.48 0:00:00.03 for the input.
% 18.31/18.48 0:00:00.04 for the FLOTTER CNF translation.
% 18.31/18.48 0:00:00.19 for inferences.
% 18.31/18.48 0:00:00.00 for the backtracking.
% 18.31/18.48 0:0:17.51 for the reduction.
% 18.31/18.48
% 18.31/18.48
% 18.31/18.48 Here is a proof with depth 8, length 43 :
% 18.31/18.48 % SZS output start Refutation
% See solution above
% 18.31/18.48 Formulae used in the proof : axiom_4a axiom_1a axiom_2a axiom_1 axiom_2 axiom_3 oneplustwoeqthree
% 18.31/18.48
%------------------------------------------------------------------------------