TSTP Solution File: NUN057+2 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : NUN057+2 : TPTP v8.1.0. Released v7.3.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n019.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 16:38:43 EDT 2022
% Result : Theorem 14.31s 14.50s
% Output : Refutation 14.31s
% 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 : 88 ( 0 equ; 53 neg)
% Maximal clause size : 9 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 8 ( 7 usr; 1 prp; 0-4 aty)
% Number of functors : 16 ( 16 usr; 9 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
r1(skf22(u)),
file('NUN057+2.p',unknown),
[] ).
cnf(5,axiom,
r2(u,skf17(v,u)),
file('NUN057+2.p',unknown),
[] ).
cnf(6,axiom,
r2(u,skf20(v,u)),
file('NUN057+2.p',unknown),
[] ).
cnf(7,axiom,
r3(u,skf22(u),u),
file('NUN057+2.p',unknown),
[] ).
cnf(8,axiom,
( equal(u,skc1)
| skP0(skc1,u) ),
file('NUN057+2.p',unknown),
[] ).
cnf(9,axiom,
r3(u,v,skf18(v,u)),
file('NUN057+2.p',unknown),
[] ).
cnf(13,axiom,
( ~ r1(u)
| ~ skP0(v,u) ),
file('NUN057+2.p',unknown),
[] ).
cnf(14,axiom,
r2(skf18(u,v),skf16(v,u)),
file('NUN057+2.p',unknown),
[] ).
cnf(18,axiom,
r3(u,skf17(u,v),skf16(u,v)),
file('NUN057+2.p',unknown),
[] ).
cnf(21,axiom,
( equal(u,skf13(v))
| skP1(skf13(v),u,v) ),
file('NUN057+2.p',unknown),
[] ).
cnf(22,axiom,
( ~ r2(u,v)
| ~ skP1(w,v,u) ),
file('NUN057+2.p',unknown),
[] ).
cnf(27,axiom,
( ~ r3(u,v,w)
| ~ skP2(x,w,v,u) ),
file('NUN057+2.p',unknown),
[] ).
cnf(31,axiom,
( equal(u,skf14(v,w))
| skP2(skf14(v,w),u,w,v) ),
file('NUN057+2.p',unknown),
[] ).
cnf(33,axiom,
( ~ r1(u)
| ~ r1(v)
| ~ r2(u,w)
| ~ r2(x,y)
| ~ r2(w,z)
| ~ r2(v,x1)
| ~ r2(y,x2)
| ~ r2(x1,x)
| ~ r3(z,z,x2) ),
file('NUN057+2.p',unknown),
[] ).
cnf(53,plain,
( ~ r1(u)
| ~ r1(v)
| ~ r2(u,w)
| ~ r2(w,x)
| ~ r2(v,y)
| ~ r2(y,z)
| ~ r2(skf20(x1,z),x2)
| ~ r3(x,x,x2) ),
inference(res,[status(thm),theory(equality)],[6,33]),
[iquote('0:Res:6.0,33.7')] ).
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(96,plain,
( ~ r2(u,v)
| equal(v,skf13(u)) ),
inference(res,[status(thm),theory(equality)],[21,22]),
[iquote('0:Res:21.1,22.1')] ).
cnf(97,plain,
equal(skf20(u,v),skf13(v)),
inference(res,[status(thm),theory(equality)],[6,96]),
[iquote('0:Res:6.0,96.0')] ).
cnf(98,plain,
equal(skf17(u,v),skf13(v)),
inference(res,[status(thm),theory(equality)],[5,96]),
[iquote('0:Res:5.0,96.0')] ).
cnf(101,plain,
equal(skf13(skf18(u,v)),skf16(v,u)),
inference(res,[status(thm),theory(equality)],[14,96]),
[iquote('0:Res:14.0,96.0')] ).
cnf(104,plain,
r2(u,skf13(u)),
inference(rew,[status(thm),theory(equality)],[97,6]),
[iquote('0:Rew:97.0,6.0')] ).
cnf(109,plain,
( ~ r1(u)
| ~ r1(v)
| ~ r2(u,w)
| ~ r2(w,x)
| ~ r2(v,y)
| ~ r2(y,z)
| ~ r2(skf13(z),x1)
| ~ r3(x,x,x1) ),
inference(rew,[status(thm),theory(equality)],[97,53]),
[iquote('0:Rew:97.0,53.6')] ).
cnf(112,plain,
r3(u,skf13(v),skf16(u,v)),
inference(rew,[status(thm),theory(equality)],[98,18]),
[iquote('0:Rew:98.0,18.0')] ).
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(427,plain,
equal(skf18(u,v),skf14(v,u)),
inference(res,[status(thm),theory(equality)],[9,394]),
[iquote('0:Res:9.0,394.0')] ).
cnf(428,plain,
equal(skf14(u,skc1),u),
inference(res,[status(thm),theory(equality)],[65,394]),
[iquote('0:Res:65.0,394.0')] ).
cnf(429,plain,
equal(skf14(u,skf13(v)),skf16(u,v)),
inference(res,[status(thm),theory(equality)],[112,394]),
[iquote('0:Res:112.0,394.0')] ).
cnf(437,plain,
r2(skf14(u,v),skf16(u,v)),
inference(rew,[status(thm),theory(equality)],[427,14]),
[iquote('0:Rew:427.0,14.0')] ).
cnf(438,plain,
equal(skf13(skf14(u,v)),skf16(u,v)),
inference(rew,[status(thm),theory(equality)],[427,101]),
[iquote('0:Rew:427.0,101.0')] ).
cnf(474,plain,
r2(u,skf16(u,skc1)),
inference(spr,[status(thm),theory(equality)],[428,437]),
[iquote('0:SpR:428.0,437.0')] ).
cnf(481,plain,
equal(skf16(u,skc1),skf13(u)),
inference(res,[status(thm),theory(equality)],[474,96]),
[iquote('0:Res:474.0,96.0')] ).
cnf(563,plain,
equal(skf16(u,skf13(v)),skf13(skf16(u,v))),
inference(spr,[status(thm),theory(equality)],[429,438]),
[iquote('0:SpR:429.0,438.0')] ).
cnf(687,plain,
r3(u,skf13(skf13(v)),skf13(skf16(u,v))),
inference(spr,[status(thm),theory(equality)],[563,112]),
[iquote('0:SpR:563.0,112.0')] ).
cnf(708,plain,
r3(u,skf13(skf13(skc1)),skf13(skf13(u))),
inference(spr,[status(thm),theory(equality)],[481,687]),
[iquote('0:SpR:481.0,687.0')] ).
cnf(810,plain,
( ~ r1(u)
| ~ r1(v)
| ~ r2(u,w)
| ~ r2(w,x)
| ~ r2(v,y)
| ~ r2(y,z)
| ~ r3(x,x,skf13(skf13(z))) ),
inference(res,[status(thm),theory(equality)],[104,109]),
[iquote('0:Res:104.0,109.6')] ).
cnf(2349,plain,
( ~ r1(u)
| ~ r1(v)
| ~ r2(u,w)
| ~ r2(w,skf13(skf13(skc1)))
| ~ r2(v,x)
| ~ r2(x,skf13(skf13(skc1))) ),
inference(res,[status(thm),theory(equality)],[708,810]),
[iquote('0:Res:708.0,810.6')] ).
cnf(2354,plain,
( ~ r1(u)
| ~ r2(u,v)
| ~ r2(v,skf13(skf13(skc1))) ),
inference(con,[status(thm)],[2349]),
[iquote('0:Con:2349.1')] ).
cnf(16201,plain,
( ~ r1(u)
| ~ r2(u,skf13(skc1)) ),
inference(res,[status(thm),theory(equality)],[104,2354]),
[iquote('0:Res:104.0,2354.2')] ).
cnf(16211,plain,
~ r1(skc1),
inference(res,[status(thm),theory(equality)],[104,16201]),
[iquote('0:Res:104.0,16201.1')] ).
cnf(16220,plain,
$false,
inference(ssi,[status(thm)],[16211,64]),
[iquote('0:SSi:16211.0,64.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : NUN057+2 : TPTP v8.1.0. Released v7.3.0.
% 0.07/0.13 % Command : run_spass %d %s
% 0.12/0.34 % Computer : n019.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 04:29:25 EDT 2022
% 0.12/0.34 % CPUTime :
% 14.31/14.50
% 14.31/14.50 SPASS V 3.9
% 14.31/14.50 SPASS beiseite: Proof found.
% 14.31/14.50 % SZS status Theorem
% 14.31/14.50 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 14.31/14.50 SPASS derived 12115 clauses, backtracked 0 clauses, performed 0 splits and kept 4910 clauses.
% 14.31/14.50 SPASS allocated 114502 KBytes.
% 14.31/14.50 SPASS spent 0:0:13.96 on the problem.
% 14.31/14.50 0:00:00.03 for the input.
% 14.31/14.50 0:00:00.03 for the FLOTTER CNF translation.
% 14.31/14.50 0:00:00.18 for inferences.
% 14.31/14.50 0:00:00.00 for the backtracking.
% 14.31/14.50 0:0:13.63 for the reduction.
% 14.31/14.50
% 14.31/14.50
% 14.31/14.50 Here is a proof with depth 8, length 43 :
% 14.31/14.50 % SZS output start Refutation
% See solution above
% 14.31/14.50 Formulae used in the proof : axiom_4a axiom_1a axiom_2a axiom_1 axiom_2 axiom_3 twoplustwoeqfour
% 14.31/14.50
%------------------------------------------------------------------------------