TSTP Solution File: NUN055+2 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : NUN055+2 : TPTP v8.1.0. Released v7.3.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n027.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 10.76s 10.98s
% Output : Refutation 10.76s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 14
% Syntax : Number of clauses : 42 ( 27 unt; 3 nHn; 42 RR)
% Number of literals : 78 ( 0 equ; 43 neg)
% Maximal clause size : 8 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 8 ( 7 usr; 1 prp; 0-4 aty)
% Number of functors : 15 ( 15 usr; 8 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
r1(skf22(u)),
file('NUN055+2.p',unknown),
[] ).
cnf(5,axiom,
r2(u,skf17(v,u)),
file('NUN055+2.p',unknown),
[] ).
cnf(6,axiom,
r2(u,skf20(v,u)),
file('NUN055+2.p',unknown),
[] ).
cnf(7,axiom,
r3(u,skf22(u),u),
file('NUN055+2.p',unknown),
[] ).
cnf(8,axiom,
( equal(u,skc1)
| skP0(skc1,u) ),
file('NUN055+2.p',unknown),
[] ).
cnf(9,axiom,
r3(u,v,skf18(v,u)),
file('NUN055+2.p',unknown),
[] ).
cnf(13,axiom,
( ~ r1(u)
| ~ skP0(v,u) ),
file('NUN055+2.p',unknown),
[] ).
cnf(14,axiom,
r2(skf18(u,v),skf16(v,u)),
file('NUN055+2.p',unknown),
[] ).
cnf(18,axiom,
r3(u,skf17(u,v),skf16(u,v)),
file('NUN055+2.p',unknown),
[] ).
cnf(21,axiom,
( equal(u,skf13(v))
| skP1(skf13(v),u,v) ),
file('NUN055+2.p',unknown),
[] ).
cnf(22,axiom,
( ~ r2(u,v)
| ~ skP1(w,v,u) ),
file('NUN055+2.p',unknown),
[] ).
cnf(27,axiom,
( ~ r3(u,v,w)
| ~ skP2(x,w,v,u) ),
file('NUN055+2.p',unknown),
[] ).
cnf(31,axiom,
( equal(u,skf14(v,w))
| skP2(skf14(v,w),u,w,v) ),
file('NUN055+2.p',unknown),
[] ).
cnf(33,axiom,
( ~ r1(u)
| ~ r1(v)
| ~ r1(w)
| ~ r2(u,x)
| ~ r2(w,y)
| ~ r2(x,z)
| ~ r2(y,x1)
| ~ r3(v,x1,z) ),
file('NUN055+2.p',unknown),
[] ).
cnf(39,plain,
( ~ r1(u)
| ~ r1(v)
| ~ r2(u,w)
| ~ r2(v,x)
| ~ r2(w,y)
| ~ r2(x,z)
| ~ r3(skf22(x1),z,y) ),
inference(res,[status(thm),theory(equality)],[1,33]),
[iquote('0:Res:1.0,33.1')] ).
cnf(59,plain,
( ~ r1(u)
| equal(u,skc1) ),
inference(res,[status(thm),theory(equality)],[8,13]),
[iquote('0:Res:8.1,13.1')] ).
cnf(61,plain,
equal(skf22(u),skc1),
inference(ems,[status(thm)],[59,1]),
[iquote('0:EmS:59.0,1.0')] ).
cnf(64,plain,
r1(skc1),
inference(rew,[status(thm),theory(equality)],[61,1]),
[iquote('0:Rew:61.0,1.0')] ).
cnf(65,plain,
r3(u,skc1,u),
inference(rew,[status(thm),theory(equality)],[61,7]),
[iquote('0:Rew:61.0,7.0')] ).
cnf(67,plain,
( ~ r1(u)
| ~ r1(v)
| ~ r2(u,w)
| ~ r2(v,x)
| ~ r2(w,y)
| ~ r2(x,z)
| ~ r3(skc1,z,y) ),
inference(rew,[status(thm),theory(equality)],[61,39]),
[iquote('0:Rew:61.0,39.6')] ).
cnf(99,plain,
( ~ r2(u,v)
| equal(v,skf13(u)) ),
inference(res,[status(thm),theory(equality)],[21,22]),
[iquote('0:Res:21.1,22.1')] ).
cnf(100,plain,
equal(skf20(u,v),skf13(v)),
inference(res,[status(thm),theory(equality)],[6,99]),
[iquote('0:Res:6.0,99.0')] ).
cnf(101,plain,
equal(skf17(u,v),skf13(v)),
inference(res,[status(thm),theory(equality)],[5,99]),
[iquote('0:Res:5.0,99.0')] ).
cnf(104,plain,
equal(skf13(skf18(u,v)),skf16(v,u)),
inference(res,[status(thm),theory(equality)],[14,99]),
[iquote('0:Res:14.0,99.0')] ).
cnf(107,plain,
r2(u,skf13(u)),
inference(rew,[status(thm),theory(equality)],[100,6]),
[iquote('0:Rew:100.0,6.0')] ).
cnf(113,plain,
r3(u,skf13(v),skf16(u,v)),
inference(rew,[status(thm),theory(equality)],[101,18]),
[iquote('0:Rew:101.0,18.0')] ).
cnf(394,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(430,plain,
equal(skf18(u,v),skf14(v,u)),
inference(res,[status(thm),theory(equality)],[9,394]),
[iquote('0:Res:9.0,394.0')] ).
cnf(431,plain,
equal(skf14(u,skc1),u),
inference(res,[status(thm),theory(equality)],[65,394]),
[iquote('0:Res:65.0,394.0')] ).
cnf(432,plain,
equal(skf14(u,skf13(v)),skf16(u,v)),
inference(res,[status(thm),theory(equality)],[113,394]),
[iquote('0:Res:113.0,394.0')] ).
cnf(440,plain,
r2(skf14(u,v),skf16(u,v)),
inference(rew,[status(thm),theory(equality)],[430,14]),
[iquote('0:Rew:430.0,14.0')] ).
cnf(441,plain,
equal(skf13(skf14(u,v)),skf16(u,v)),
inference(rew,[status(thm),theory(equality)],[430,104]),
[iquote('0:Rew:430.0,104.0')] ).
cnf(475,plain,
r2(u,skf16(u,skc1)),
inference(spr,[status(thm),theory(equality)],[431,440]),
[iquote('0:SpR:431.0,440.0')] ).
cnf(482,plain,
equal(skf16(u,skc1),skf13(u)),
inference(res,[status(thm),theory(equality)],[475,99]),
[iquote('0:Res:475.0,99.0')] ).
cnf(568,plain,
equal(skf16(u,skf13(v)),skf13(skf16(u,v))),
inference(spr,[status(thm),theory(equality)],[432,441]),
[iquote('0:SpR:432.0,441.0')] ).
cnf(703,plain,
r3(u,skf13(skf13(v)),skf13(skf16(u,v))),
inference(spr,[status(thm),theory(equality)],[568,113]),
[iquote('0:SpR:568.0,113.0')] ).
cnf(724,plain,
r3(u,skf13(skf13(skc1)),skf13(skf13(u))),
inference(spr,[status(thm),theory(equality)],[482,703]),
[iquote('0:SpR:482.0,703.0')] ).
cnf(758,plain,
( ~ r1(u)
| ~ r1(v)
| ~ r2(u,w)
| ~ r2(v,x)
| ~ r2(w,skf13(skf13(skc1)))
| ~ r2(x,skf13(skf13(skc1))) ),
inference(res,[status(thm),theory(equality)],[724,67]),
[iquote('0:Res:724.0,67.6')] ).
cnf(760,plain,
( ~ r1(u)
| ~ r2(u,v)
| ~ r2(v,skf13(skf13(skc1))) ),
inference(con,[status(thm)],[758]),
[iquote('0:Con:758.1')] ).
cnf(15101,plain,
( ~ r1(u)
| ~ r2(u,skf13(skc1)) ),
inference(res,[status(thm),theory(equality)],[107,760]),
[iquote('0:Res:107.0,760.2')] ).
cnf(15110,plain,
~ r1(skc1),
inference(res,[status(thm),theory(equality)],[107,15101]),
[iquote('0:Res:107.0,15101.1')] ).
cnf(15118,plain,
$false,
inference(ssi,[status(thm)],[15110,64]),
[iquote('0:SSi:15110.0,64.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : NUN055+2 : TPTP v8.1.0. Released v7.3.0.
% 0.06/0.13 % Command : run_spass %d %s
% 0.13/0.34 % Computer : n027.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Thu Jun 2 04:53:49 EDT 2022
% 0.13/0.34 % CPUTime :
% 10.76/10.98
% 10.76/10.98 SPASS V 3.9
% 10.76/10.98 SPASS beiseite: Proof found.
% 10.76/10.98 % SZS status Theorem
% 10.76/10.98 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 10.76/10.98 SPASS derived 11428 clauses, backtracked 0 clauses, performed 0 splits and kept 4420 clauses.
% 10.76/10.98 SPASS allocated 112593 KBytes.
% 10.76/10.98 SPASS spent 0:0:10.46 on the problem.
% 10.76/10.98 0:00:00.04 for the input.
% 10.76/10.98 0:00:00.03 for the FLOTTER CNF translation.
% 10.76/10.98 0:00:00.16 for inferences.
% 10.76/10.98 0:00:00.00 for the backtracking.
% 10.76/10.98 0:0:10.16 for the reduction.
% 10.76/10.98
% 10.76/10.98
% 10.76/10.98 Here is a proof with depth 8, length 42 :
% 10.76/10.98 % SZS output start Refutation
% See solution above
% 10.76/10.98 Formulae used in the proof : axiom_4a axiom_1a axiom_2a axiom_1 axiom_2 axiom_3 zeroplustwoeqtwo
% 10.76/10.98
%------------------------------------------------------------------------------