TSTP Solution File: NUN076+2 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : NUN076+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 16:38:46 EDT 2022
% Result : Theorem 0.19s 0.51s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 11
% Syntax : Number of clauses : 27 ( 15 unt; 2 nHn; 27 RR)
% Number of literals : 49 ( 0 equ; 29 neg)
% Maximal clause size : 5 ( 1 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 8 ( 7 usr; 1 prp; 0-3 aty)
% Number of functors : 12 ( 12 usr; 7 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
r1(skf22(u)),
file('NUN076+2.p',unknown),
[] ).
cnf(2,axiom,
r1(skf24(u)),
file('NUN076+2.p',unknown),
[] ).
cnf(3,axiom,
r1(skf23(u)),
file('NUN076+2.p',unknown),
[] ).
cnf(6,axiom,
r2(u,skf20(v,u)),
file('NUN076+2.p',unknown),
[] ).
cnf(7,axiom,
r3(u,skf22(u),u),
file('NUN076+2.p',unknown),
[] ).
cnf(8,axiom,
( equal(u,skc1)
| skP0(skc1,u) ),
file('NUN076+2.p',unknown),
[] ).
cnf(11,axiom,
r4(u,skf24(u),skf23(u)),
file('NUN076+2.p',unknown),
[] ).
cnf(13,axiom,
( ~ r1(u)
| ~ skP0(v,u) ),
file('NUN076+2.p',unknown),
[] ).
cnf(21,axiom,
( equal(u,skf13(v))
| skP1(skf13(v),u,v) ),
file('NUN076+2.p',unknown),
[] ).
cnf(22,axiom,
( ~ r2(u,v)
| ~ skP1(w,v,u) ),
file('NUN076+2.p',unknown),
[] ).
cnf(33,axiom,
( ~ r1(u)
| ~ r2(u,v)
| ~ r2(v,w)
| ~ r3(x,y,z)
| ~ r4(w,x,z) ),
file('NUN076+2.p',unknown),
[] ).
cnf(37,plain,
( ~ r1(u)
| ~ r2(u,v)
| ~ r2(v,w)
| ~ r3(skf24(w),x,skf23(w)) ),
inference(res,[status(thm),theory(equality)],[11,33]),
[iquote('0:Res:11.0,33.1')] ).
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(60,plain,
( ~ r1(u)
| ~ r2(u,v)
| ~ r2(v,w)
| ~ r3(skc1,x,skf23(w)) ),
inference(rew,[status(thm),theory(equality)],[53,37]),
[iquote('0:Rew:53.0,37.3')] ).
cnf(65,plain,
( ~ r1(u)
| ~ r2(u,v)
| ~ r2(v,w)
| ~ r3(skc1,x,skc1) ),
inference(rew,[status(thm),theory(equality)],[54,60]),
[iquote('0:Rew:54.0,60.3')] ).
cnf(86,plain,
( ~ r2(u,v)
| equal(v,skf13(u)) ),
inference(res,[status(thm),theory(equality)],[21,22]),
[iquote('0:Res:21.1,22.1')] ).
cnf(87,plain,
equal(skf20(u,v),skf13(v)),
inference(res,[status(thm),theory(equality)],[6,86]),
[iquote('0:Res:6.0,86.0')] ).
cnf(94,plain,
r2(u,skf13(u)),
inference(rew,[status(thm),theory(equality)],[87,6]),
[iquote('0:Rew:87.0,6.0')] ).
cnf(514,plain,
( ~ r1(u)
| ~ r2(u,v)
| ~ r2(v,w) ),
inference(res,[status(thm),theory(equality)],[56,65]),
[iquote('0:Res:56.0,65.3')] ).
cnf(794,plain,
( ~ r1(u)
| ~ r2(skf13(u),v) ),
inference(res,[status(thm),theory(equality)],[94,514]),
[iquote('0:Res:94.0,514.1')] ).
cnf(805,plain,
~ r1(u),
inference(res,[status(thm),theory(equality)],[94,794]),
[iquote('0:Res:94.0,794.1')] ).
cnf(808,plain,
$false,
inference(unc,[status(thm)],[805,55]),
[iquote('0:UnC:805.0,55.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUN076+2 : TPTP v8.1.0. Released v7.3.0.
% 0.12/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n021.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 10:42:31 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.19/0.51
% 0.19/0.51 SPASS V 3.9
% 0.19/0.51 SPASS beiseite: Proof found.
% 0.19/0.51 % SZS status Theorem
% 0.19/0.51 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.51 SPASS derived 624 clauses, backtracked 0 clauses, performed 0 splits and kept 347 clauses.
% 0.19/0.51 SPASS allocated 98273 KBytes.
% 0.19/0.51 SPASS spent 0:00:00.16 on the problem.
% 0.19/0.51 0:00:00.03 for the input.
% 0.19/0.51 0:00:00.03 for the FLOTTER CNF translation.
% 0.19/0.51 0:00:00.01 for inferences.
% 0.19/0.51 0:00:00.00 for the backtracking.
% 0.19/0.51 0:00:00.07 for the reduction.
% 0.19/0.51
% 0.19/0.51
% 0.19/0.51 Here is a proof with depth 4, length 27 :
% 0.19/0.51 % SZS output start Refutation
% See solution above
% 0.19/0.51 Formulae used in the proof : axiom_4a axiom_5a axiom_2a axiom_1 axiom_2 thereexistsanevennumber
% 0.19/0.51
%------------------------------------------------------------------------------