TSTP Solution File: NUN084+2 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : NUN084+2 : TPTP v8.1.0. Released v7.3.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n032.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 0.14s 0.42s
% Output : Refutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 24
% Syntax : Number of clauses : 57 ( 37 unt; 5 nHn; 57 RR)
% Number of literals : 81 ( 0 equ; 31 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 10 ( 9 usr; 1 prp; 0-4 aty)
% Number of functors : 18 ( 18 usr; 6 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
r1(skf22(u)),
file('NUN084+2.p',unknown),
[] ).
cnf(2,axiom,
r1(skf24(u)),
file('NUN084+2.p',unknown),
[] ).
cnf(3,axiom,
r1(skf23(u)),
file('NUN084+2.p',unknown),
[] ).
cnf(4,axiom,
( r1(u)
| skP0(skc1,u) ),
file('NUN084+2.p',unknown),
[] ).
cnf(5,axiom,
r2(u,skf17(v,u)),
file('NUN084+2.p',unknown),
[] ).
cnf(6,axiom,
r2(u,skf20(v,u)),
file('NUN084+2.p',unknown),
[] ).
cnf(7,axiom,
r3(u,skf22(u),u),
file('NUN084+2.p',unknown),
[] ).
cnf(8,axiom,
( equal(u,skc1)
| skP0(skc1,u) ),
file('NUN084+2.p',unknown),
[] ).
cnf(9,axiom,
r3(u,v,skf18(v,u)),
file('NUN084+2.p',unknown),
[] ).
cnf(10,axiom,
r4(u,v,skf21(v,u)),
file('NUN084+2.p',unknown),
[] ).
cnf(11,axiom,
r4(u,skf24(u),skf23(u)),
file('NUN084+2.p',unknown),
[] ).
cnf(13,axiom,
( ~ r1(u)
| ~ skP0(v,u) ),
file('NUN084+2.p',unknown),
[] ).
cnf(14,axiom,
r2(skf18(u,v),skf16(v,u)),
file('NUN084+2.p',unknown),
[] ).
cnf(16,axiom,
( ~ skP0(u,v)
| ~ equal(v,u) ),
file('NUN084+2.p',unknown),
[] ).
cnf(18,axiom,
r3(u,skf17(u,v),skf16(u,v)),
file('NUN084+2.p',unknown),
[] ).
cnf(19,axiom,
r3(skf21(u,v),v,skf19(v,u)),
file('NUN084+2.p',unknown),
[] ).
cnf(20,axiom,
r4(u,skf20(u,v),skf19(u,v)),
file('NUN084+2.p',unknown),
[] ).
cnf(21,axiom,
( equal(u,skf13(v))
| skP1(skf13(v),u,v) ),
file('NUN084+2.p',unknown),
[] ).
cnf(22,axiom,
( ~ r2(u,v)
| ~ skP1(w,v,u) ),
file('NUN084+2.p',unknown),
[] ).
cnf(27,axiom,
( ~ r3(u,v,w)
| ~ skP2(x,w,v,u) ),
file('NUN084+2.p',unknown),
[] ).
cnf(29,axiom,
( ~ r4(u,v,w)
| ~ skP3(x,w,v,u) ),
file('NUN084+2.p',unknown),
[] ).
cnf(31,axiom,
( equal(u,skf14(v,w))
| skP2(skf14(v,w),u,w,v) ),
file('NUN084+2.p',unknown),
[] ).
cnf(32,axiom,
( equal(u,skf15(v,w))
| skP3(skf15(v,w),u,w,v) ),
file('NUN084+2.p',unknown),
[] ).
cnf(33,axiom,
( ~ r1(u)
| ~ r2(u,v)
| ~ r2(v,w)
| ~ r4(x,y,w) ),
file('NUN084+2.p',unknown),
[] ).
cnf(39,plain,
( ~ r1(u)
| ~ r2(u,skf18(v,w))
| ~ r4(x,y,skf16(w,v)) ),
inference(res,[status(thm),theory(equality)],[14,33]),
[iquote('0:Res:14.0,33.1')] ).
cnf(46,plain,
( ~ r1(u)
| equal(u,skc1) ),
inference(res,[status(thm),theory(equality)],[8,13]),
[iquote('0:Res:8.1,13.1')] ).
cnf(48,plain,
equal(skf22(u),skc1),
inference(ems,[status(thm)],[46,1]),
[iquote('0:EmS:46.0,1.0')] ).
cnf(49,plain,
equal(skf24(u),skc1),
inference(ems,[status(thm)],[46,2]),
[iquote('0:EmS:46.0,2.0')] ).
cnf(50,plain,
equal(skf23(u),skc1),
inference(ems,[status(thm)],[46,3]),
[iquote('0:EmS:46.0,3.0')] ).
cnf(52,plain,
r3(u,skc1,u),
inference(rew,[status(thm),theory(equality)],[48,7]),
[iquote('0:Rew:48.0,7.0')] ).
cnf(55,plain,
r4(u,skc1,skf23(u)),
inference(rew,[status(thm),theory(equality)],[49,11]),
[iquote('0:Rew:49.0,11.0')] ).
cnf(60,plain,
r4(u,skc1,skc1),
inference(rew,[status(thm),theory(equality)],[50,55]),
[iquote('0:Rew:50.0,55.0')] ).
cnf(70,plain,
( ~ equal(u,skc1)
| r1(u) ),
inference(res,[status(thm),theory(equality)],[4,16]),
[iquote('0:Res:4.1,16.0')] ).
cnf(81,plain,
( ~ r2(u,v)
| equal(v,skf13(u)) ),
inference(res,[status(thm),theory(equality)],[21,22]),
[iquote('0:Res:21.1,22.1')] ).
cnf(82,plain,
equal(skf20(u,v),skf13(v)),
inference(res,[status(thm),theory(equality)],[6,81]),
[iquote('0:Res:6.0,81.0')] ).
cnf(83,plain,
equal(skf17(u,v),skf13(v)),
inference(res,[status(thm),theory(equality)],[5,81]),
[iquote('0:Res:5.0,81.0')] ).
cnf(88,plain,
r4(u,skf13(v),skf19(u,v)),
inference(rew,[status(thm),theory(equality)],[82,20]),
[iquote('0:Rew:82.0,20.0')] ).
cnf(93,plain,
r3(u,skf13(v),skf16(u,v)),
inference(rew,[status(thm),theory(equality)],[83,18]),
[iquote('0:Rew:83.0,18.0')] ).
cnf(258,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(259,plain,
equal(skf21(u,v),skf15(v,u)),
inference(res,[status(thm),theory(equality)],[10,258]),
[iquote('0:Res:10.0,258.0')] ).
cnf(260,plain,
equal(skf15(u,skc1),skc1),
inference(res,[status(thm),theory(equality)],[60,258]),
[iquote('0:Res:60.0,258.0')] ).
cnf(265,plain,
r3(skf15(u,v),u,skf19(u,v)),
inference(rew,[status(thm),theory(equality)],[259,19]),
[iquote('0:Rew:259.0,19.0')] ).
cnf(276,plain,
r3(skc1,u,skf19(u,skc1)),
inference(spr,[status(thm),theory(equality)],[260,265]),
[iquote('0:SpR:260.0,265.0')] ).
cnf(285,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(321,plain,
equal(skf18(u,v),skf14(v,u)),
inference(res,[status(thm),theory(equality)],[9,285]),
[iquote('0:Res:9.0,285.0')] ).
cnf(322,plain,
equal(skf14(u,skc1),u),
inference(res,[status(thm),theory(equality)],[52,285]),
[iquote('0:Res:52.0,285.0')] ).
cnf(323,plain,
equal(skf14(u,skf13(v)),skf16(u,v)),
inference(res,[status(thm),theory(equality)],[93,285]),
[iquote('0:Res:93.0,285.0')] ).
cnf(328,plain,
equal(skf19(u,skc1),skf14(skc1,u)),
inference(res,[status(thm),theory(equality)],[276,285]),
[iquote('0:Res:276.0,285.0')] ).
cnf(331,plain,
r2(skf14(u,v),skf16(u,v)),
inference(rew,[status(thm),theory(equality)],[321,14]),
[iquote('0:Rew:321.0,14.0')] ).
cnf(339,plain,
( ~ r1(u)
| ~ r2(u,skf14(v,w))
| ~ r4(x,y,skf16(v,w)) ),
inference(rew,[status(thm),theory(equality)],[321,39]),
[iquote('0:Rew:321.0,39.1')] ).
cnf(385,plain,
r4(u,skf13(skc1),skf14(skc1,u)),
inference(spr,[status(thm),theory(equality)],[328,88]),
[iquote('0:SpR:328.0,88.0')] ).
cnf(422,plain,
r4(skf13(u),skf13(skc1),skf16(skc1,u)),
inference(spr,[status(thm),theory(equality)],[323,385]),
[iquote('0:SpR:323.0,385.0')] ).
cnf(637,plain,
( ~ r1(u)
| ~ r2(u,skf14(skc1,v)) ),
inference(res,[status(thm),theory(equality)],[422,339]),
[iquote('0:Res:422.0,339.2')] ).
cnf(641,plain,
( ~ r1(u)
| ~ r2(u,skf16(skc1,v)) ),
inference(spl,[status(thm),theory(equality)],[323,637]),
[iquote('0:SpL:323.0,637.1')] ).
cnf(650,plain,
~ r1(skf14(skc1,u)),
inference(res,[status(thm),theory(equality)],[331,641]),
[iquote('0:Res:331.0,641.1')] ).
cnf(656,plain,
~ equal(skf14(skc1,u),skc1),
inference(sor,[status(thm)],[650,70]),
[iquote('0:SoR:650.0,70.1')] ).
cnf(658,plain,
$false,
inference(unc,[status(thm)],[656,322]),
[iquote('0:UnC:656.0,322.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : NUN084+2 : TPTP v8.1.0. Released v7.3.0.
% 0.09/0.11 % Command : run_spass %d %s
% 0.11/0.29 % Computer : n032.cluster.edu
% 0.11/0.29 % Model : x86_64 x86_64
% 0.11/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.29 % Memory : 8042.1875MB
% 0.11/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.29 % CPULimit : 300
% 0.11/0.29 % WCLimit : 600
% 0.11/0.29 % DateTime : Thu Jun 2 05:24:45 EDT 2022
% 0.11/0.30 % CPUTime :
% 0.14/0.42
% 0.14/0.42 SPASS V 3.9
% 0.14/0.42 SPASS beiseite: Proof found.
% 0.14/0.42 % SZS status Theorem
% 0.14/0.42 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.14/0.42 SPASS derived 515 clauses, backtracked 0 clauses, performed 0 splits and kept 269 clauses.
% 0.14/0.42 SPASS allocated 98114 KBytes.
% 0.14/0.42 SPASS spent 0:00:00.11 on the problem.
% 0.14/0.42 0:00:00.03 for the input.
% 0.14/0.42 0:00:00.02 for the FLOTTER CNF translation.
% 0.14/0.42 0:00:00.01 for inferences.
% 0.14/0.42 0:00:00.00 for the backtracking.
% 0.14/0.42 0:00:00.03 for the reduction.
% 0.14/0.42
% 0.14/0.42
% 0.14/0.42 Here is a proof with depth 10, length 57 :
% 0.14/0.42 % SZS output start Refutation
% See solution above
% 0.14/0.42 Formulae used in the proof : axiom_4a axiom_5a axiom_1 axiom_1a axiom_2a axiom_2 axiom_3 axiom_4 xtimesyeqtwo
% 0.14/0.42
%------------------------------------------------------------------------------