TSTP Solution File: NUN086+2 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : NUN086+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 16:38:48 EDT 2022
% Result : Theorem 0.20s 0.50s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 18
% Syntax : Number of clauses : 45 ( 29 unt; 4 nHn; 45 RR)
% Number of literals : 67 ( 0 equ; 27 neg)
% Maximal clause size : 5 ( 1 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 10 ( 9 usr; 1 prp; 0-4 aty)
% Number of functors : 14 ( 14 usr; 5 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
r1(skf22(u)),
file('NUN086+2.p',unknown),
[] ).
cnf(2,axiom,
r1(skf24(u)),
file('NUN086+2.p',unknown),
[] ).
cnf(3,axiom,
r1(skf23(u)),
file('NUN086+2.p',unknown),
[] ).
cnf(6,axiom,
r2(u,skf20(v,u)),
file('NUN086+2.p',unknown),
[] ).
cnf(7,axiom,
r3(u,skf22(u),u),
file('NUN086+2.p',unknown),
[] ).
cnf(8,axiom,
( equal(u,skc1)
| skP0(skc1,u) ),
file('NUN086+2.p',unknown),
[] ).
cnf(10,axiom,
r4(u,v,skf21(v,u)),
file('NUN086+2.p',unknown),
[] ).
cnf(11,axiom,
r4(u,skf24(u),skf23(u)),
file('NUN086+2.p',unknown),
[] ).
cnf(13,axiom,
( ~ r1(u)
| ~ skP0(v,u) ),
file('NUN086+2.p',unknown),
[] ).
cnf(19,axiom,
r3(skf21(u,v),v,skf19(v,u)),
file('NUN086+2.p',unknown),
[] ).
cnf(20,axiom,
r4(u,skf20(u,v),skf19(u,v)),
file('NUN086+2.p',unknown),
[] ).
cnf(21,axiom,
( equal(u,skf13(v))
| skP1(skf13(v),u,v) ),
file('NUN086+2.p',unknown),
[] ).
cnf(22,axiom,
( ~ r2(u,v)
| ~ skP1(w,v,u) ),
file('NUN086+2.p',unknown),
[] ).
cnf(27,axiom,
( ~ r3(u,v,w)
| ~ skP2(x,w,v,u) ),
file('NUN086+2.p',unknown),
[] ).
cnf(29,axiom,
( ~ r4(u,v,w)
| ~ skP3(x,w,v,u) ),
file('NUN086+2.p',unknown),
[] ).
cnf(31,axiom,
( equal(u,skf14(v,w))
| skP2(skf14(v,w),u,w,v) ),
file('NUN086+2.p',unknown),
[] ).
cnf(32,axiom,
( equal(u,skf15(v,w))
| skP3(skf15(v,w),u,w,v) ),
file('NUN086+2.p',unknown),
[] ).
cnf(33,axiom,
( ~ r1(u)
| ~ r1(v)
| ~ r1(w)
| ~ r2(w,x)
| ~ r4(v,x,u) ),
file('NUN086+2.p',unknown),
[] ).
cnf(50,plain,
( ~ r1(u)
| equal(u,skc1) ),
inference(res,[status(thm),theory(equality)],[8,13]),
[iquote('0:Res:8.1,13.1')] ).
cnf(52,plain,
equal(skf22(u),skc1),
inference(ems,[status(thm)],[50,1]),
[iquote('0:EmS:50.0,1.0')] ).
cnf(53,plain,
equal(skf24(u),skc1),
inference(ems,[status(thm)],[50,2]),
[iquote('0:EmS:50.0,2.0')] ).
cnf(54,plain,
equal(skf23(u),skc1),
inference(ems,[status(thm)],[50,3]),
[iquote('0:EmS:50.0,3.0')] ).
cnf(55,plain,
r1(skc1),
inference(rew,[status(thm),theory(equality)],[52,1]),
[iquote('0:Rew:52.0,1.0')] ).
cnf(56,plain,
r3(u,skc1,u),
inference(rew,[status(thm),theory(equality)],[52,7]),
[iquote('0:Rew:52.0,7.0')] ).
cnf(61,plain,
r4(u,skc1,skf23(u)),
inference(rew,[status(thm),theory(equality)],[53,11]),
[iquote('0:Rew:53.0,11.0')] ).
cnf(70,plain,
r4(u,skc1,skc1),
inference(rew,[status(thm),theory(equality)],[54,61]),
[iquote('0:Rew:54.0,61.0')] ).
cnf(92,plain,
( ~ r2(u,v)
| equal(v,skf13(u)) ),
inference(res,[status(thm),theory(equality)],[21,22]),
[iquote('0:Res:21.1,22.1')] ).
cnf(95,plain,
equal(skf20(u,v),skf13(v)),
inference(res,[status(thm),theory(equality)],[6,92]),
[iquote('0:Res:6.0,92.0')] ).
cnf(101,plain,
r4(u,skf13(v),skf19(u,v)),
inference(rew,[status(thm),theory(equality)],[95,20]),
[iquote('0:Rew:95.0,20.0')] ).
cnf(102,plain,
r2(u,skf13(u)),
inference(rew,[status(thm),theory(equality)],[95,6]),
[iquote('0:Rew:95.0,6.0')] ).
cnf(309,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(347,plain,
equal(skf21(u,v),skf15(v,u)),
inference(res,[status(thm),theory(equality)],[10,309]),
[iquote('0:Res:10.0,309.0')] ).
cnf(348,plain,
equal(skf15(u,skc1),skc1),
inference(res,[status(thm),theory(equality)],[70,309]),
[iquote('0:Res:70.0,309.0')] ).
cnf(353,plain,
r3(skf15(u,v),u,skf19(u,v)),
inference(rew,[status(thm),theory(equality)],[347,19]),
[iquote('0:Rew:347.0,19.0')] ).
cnf(381,plain,
r3(skc1,u,skf19(u,skc1)),
inference(spr,[status(thm),theory(equality)],[348,353]),
[iquote('0:SpR:348.0,353.0')] ).
cnf(395,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(410,plain,
equal(skf14(u,skc1),u),
inference(res,[status(thm),theory(equality)],[56,395]),
[iquote('0:Res:56.0,395.0')] ).
cnf(416,plain,
equal(skf19(u,skc1),skf14(skc1,u)),
inference(res,[status(thm),theory(equality)],[381,395]),
[iquote('0:Res:381.0,395.0')] ).
cnf(467,plain,
r4(u,skf13(skc1),skf14(skc1,u)),
inference(spr,[status(thm),theory(equality)],[416,101]),
[iquote('0:SpR:416.0,101.0')] ).
cnf(479,plain,
r4(skc1,skf13(skc1),skc1),
inference(spr,[status(thm),theory(equality)],[410,467]),
[iquote('0:SpR:410.0,467.0')] ).
cnf(484,plain,
( ~ r1(skc1)
| ~ r1(skc1)
| ~ r1(u)
| ~ r2(u,skf13(skc1)) ),
inference(res,[status(thm),theory(equality)],[479,33]),
[iquote('0:Res:479.0,33.4')] ).
cnf(486,plain,
( ~ r1(skc1)
| ~ r1(u)
| ~ r2(u,skf13(skc1)) ),
inference(obv,[status(thm),theory(equality)],[484]),
[iquote('0:Obv:484.0')] ).
cnf(487,plain,
( ~ r1(u)
| ~ r2(u,skf13(skc1)) ),
inference(ssi,[status(thm)],[486,55]),
[iquote('0:SSi:486.0,55.0')] ).
cnf(489,plain,
~ r1(skc1),
inference(res,[status(thm),theory(equality)],[102,487]),
[iquote('0:Res:102.0,487.1')] ).
cnf(494,plain,
$false,
inference(ssi,[status(thm)],[489,55]),
[iquote('0:SSi:489.0,55.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : NUN086+2 : TPTP v8.1.0. Released v7.3.0.
% 0.07/0.14 % Command : run_spass %d %s
% 0.13/0.35 % Computer : n021.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 600
% 0.13/0.35 % DateTime : Thu Jun 2 06:20:46 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.20/0.50
% 0.20/0.50 SPASS V 3.9
% 0.20/0.50 SPASS beiseite: Proof found.
% 0.20/0.50 % SZS status Theorem
% 0.20/0.50 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.20/0.50 SPASS derived 384 clauses, backtracked 0 clauses, performed 0 splits and kept 225 clauses.
% 0.20/0.50 SPASS allocated 97970 KBytes.
% 0.20/0.50 SPASS spent 0:00:00.13 on the problem.
% 0.20/0.50 0:00:00.04 for the input.
% 0.20/0.50 0:00:00.03 for the FLOTTER CNF translation.
% 0.20/0.50 0:00:00.01 for inferences.
% 0.20/0.50 0:00:00.00 for the backtracking.
% 0.20/0.50 0:00:00.04 for the reduction.
% 0.20/0.50
% 0.20/0.50
% 0.20/0.50 Here is a proof with depth 8, length 45 :
% 0.20/0.50 % SZS output start Refutation
% See solution above
% 0.20/0.50 Formulae used in the proof : axiom_4a axiom_5a axiom_2a axiom_1 axiom_2 axiom_3 axiom_4 zerotimesoneeqzero
% 0.20/0.50
%------------------------------------------------------------------------------