TSTP Solution File: GRP126-2.004 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP126-2.004 : TPTP v8.1.0. Released v1.2.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n028.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 : Sat Jul 16 11:45:37 EDT 2022
% Result : Unsatisfiable 0.19s 0.43s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 33
% Number of leaves : 19
% Syntax : Number of clauses : 64 ( 27 unt; 24 nHn; 64 RR)
% Number of literals : 152 ( 0 equ; 46 neg)
% Maximal clause size : 6 ( 2 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 8 con; 0-0 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(2,axiom,
next(e_2,e_3),
file('GRP126-2.004.p',unknown),
[] ).
cnf(9,axiom,
greater(e_4,e_3),
file('GRP126-2.004.p',unknown),
[] ).
cnf(10,axiom,
( ~ greater(u,v)
| ~ next(w,v)
| ~ product(w,e_1,u) ),
file('GRP126-2.004.p',unknown),
[] ).
cnf(11,axiom,
group_element(e_1),
file('GRP126-2.004.p',unknown),
[] ).
cnf(12,axiom,
group_element(e_2),
file('GRP126-2.004.p',unknown),
[] ).
cnf(14,axiom,
group_element(e_4),
file('GRP126-2.004.p',unknown),
[] ).
cnf(15,axiom,
~ equalish(e_1,e_2),
file('GRP126-2.004.p',unknown),
[] ).
cnf(16,axiom,
~ equalish(e_1,e_3),
file('GRP126-2.004.p',unknown),
[] ).
cnf(17,axiom,
~ equalish(e_1,e_4),
file('GRP126-2.004.p',unknown),
[] ).
cnf(18,axiom,
~ equalish(e_2,e_1),
file('GRP126-2.004.p',unknown),
[] ).
cnf(19,axiom,
~ equalish(e_2,e_3),
file('GRP126-2.004.p',unknown),
[] ).
cnf(24,axiom,
~ equalish(e_4,e_1),
file('GRP126-2.004.p',unknown),
[] ).
cnf(25,axiom,
~ equalish(e_4,e_2),
file('GRP126-2.004.p',unknown),
[] ).
cnf(27,axiom,
( ~ group_element(u)
| ~ group_element(v)
| product(v,u,e_4)
| product(v,u,e_3)
| product(v,u,e_2)
| product(v,u,e_1) ),
file('GRP126-2.004.p',unknown),
[] ).
cnf(28,axiom,
( ~ product(u,v,w)
| ~ product(u,v,x)
| equalish(x,w) ),
file('GRP126-2.004.p',unknown),
[] ).
cnf(29,axiom,
( ~ product(u,v,w)
| ~ product(u,x,w)
| equalish(x,v) ),
file('GRP126-2.004.p',unknown),
[] ).
cnf(30,axiom,
( ~ product(u,v,w)
| ~ product(x,v,w)
| equalish(x,u) ),
file('GRP126-2.004.p',unknown),
[] ).
cnf(31,axiom,
product(u,u,u),
file('GRP126-2.004.p',unknown),
[] ).
cnf(32,axiom,
( ~ product(u,v,w)
| ~ product(v,u,x)
| product(x,w,u) ),
file('GRP126-2.004.p',unknown),
[] ).
cnf(42,plain,
( ~ product(u,v,v)
| equalish(u,v) ),
inference(res,[status(thm),theory(equality)],[31,30]),
[iquote('0:Res:31.0,30.0')] ).
cnf(44,plain,
( ~ product(u,v,u)
| equalish(v,u) ),
inference(res,[status(thm),theory(equality)],[31,29]),
[iquote('0:Res:31.0,29.0')] ).
cnf(45,plain,
( ~ product(u,u,v)
| equalish(v,u) ),
inference(res,[status(thm),theory(equality)],[31,28]),
[iquote('0:Res:31.0,28.0')] ).
cnf(52,plain,
( ~ group_element(u)
| ~ group_element(e_1)
| product(e_1,u,e_4)
| product(e_1,u,e_3)
| product(e_1,u,e_2)
| equalish(u,e_1) ),
inference(res,[status(thm),theory(equality)],[27,44]),
[iquote('0:Res:27.5,44.0')] ).
cnf(58,plain,
( ~ group_element(e_1)
| ~ group_element(u)
| product(u,e_1,e_4)
| product(u,e_1,e_3)
| product(u,e_1,e_2)
| equalish(u,e_1) ),
inference(res,[status(thm),theory(equality)],[27,42]),
[iquote('0:Res:27.5,42.0')] ).
cnf(59,plain,
( ~ group_element(u)
| product(u,e_1,e_4)
| product(u,e_1,e_3)
| product(u,e_1,e_2)
| equalish(u,e_1) ),
inference(ssi,[status(thm)],[58,11]),
[iquote('0:SSi:58.0,11.0')] ).
cnf(60,plain,
( ~ group_element(u)
| product(e_1,u,e_4)
| product(e_1,u,e_3)
| product(e_1,u,e_2)
| equalish(u,e_1) ),
inference(ssi,[status(thm)],[52,11]),
[iquote('0:SSi:52.1,11.0')] ).
cnf(68,plain,
( ~ group_element(e_2)
| product(e_2,e_1,e_4)
| product(e_2,e_1,e_3)
| equalish(e_2,e_1)
| equalish(e_1,e_2) ),
inference(res,[status(thm),theory(equality)],[59,44]),
[iquote('0:Res:59.3,44.0')] ).
cnf(74,plain,
( product(e_2,e_1,e_4)
| product(e_2,e_1,e_3)
| equalish(e_2,e_1)
| equalish(e_1,e_2) ),
inference(ssi,[status(thm)],[68,12]),
[iquote('0:SSi:68.0,12.0')] ).
cnf(75,plain,
( product(e_2,e_1,e_4)
| product(e_2,e_1,e_3) ),
inference(mrr,[status(thm)],[74,18,15]),
[iquote('0:MRR:74.2,74.3,18.0,15.0')] ).
cnf(77,plain,
( ~ product(e_1,e_2,u)
| product(e_2,e_1,e_4)
| product(u,e_3,e_2) ),
inference(res,[status(thm),theory(equality)],[75,32]),
[iquote('0:Res:75.1,32.0')] ).
cnf(78,plain,
( ~ product(e_2,e_1,u)
| product(e_2,e_1,e_4)
| equalish(u,e_3) ),
inference(res,[status(thm),theory(equality)],[75,28]),
[iquote('0:Res:75.1,28.0')] ).
cnf(80,plain,
( ~ product(u,e_1,e_3)
| product(e_2,e_1,e_4)
| equalish(u,e_2) ),
inference(res,[status(thm),theory(equality)],[75,30]),
[iquote('0:Res:75.1,30.0')] ).
cnf(87,plain,
product(e_2,e_1,e_4),
inference(spt,[spt(split,[position(s1)])],[78]),
[iquote('1:Spt:78.1')] ).
cnf(88,plain,
( ~ greater(e_4,u)
| ~ next(e_2,u) ),
inference(res,[status(thm),theory(equality)],[87,10]),
[iquote('1:Res:87.0,10.2')] ).
cnf(93,plain,
~ next(e_2,e_3),
inference(res,[status(thm),theory(equality)],[9,88]),
[iquote('1:Res:9.0,88.0')] ).
cnf(96,plain,
$false,
inference(mrr,[status(thm)],[93,2]),
[iquote('1:MRR:93.0,2.0')] ).
cnf(97,plain,
~ product(e_2,e_1,e_4),
inference(spt,[spt(split,[position(sa)])],[96,87]),
[iquote('1:Spt:96.0,78.1,87.0')] ).
cnf(98,plain,
( ~ product(e_2,e_1,u)
| equalish(u,e_3) ),
inference(spt,[spt(split,[position(s2)])],[78]),
[iquote('1:Spt:96.0,78.0,78.2')] ).
cnf(104,plain,
( ~ product(u,e_1,e_3)
| equalish(u,e_2) ),
inference(mrr,[status(thm)],[80,97]),
[iquote('1:MRR:80.1,97.0')] ).
cnf(105,plain,
( ~ product(e_1,e_2,u)
| product(u,e_3,e_2) ),
inference(mrr,[status(thm)],[77,97]),
[iquote('1:MRR:77.1,97.0')] ).
cnf(122,plain,
( ~ group_element(e_2)
| ~ group_element(e_1)
| product(e_1,e_2,e_4)
| product(e_1,e_2,e_3)
| product(e_1,e_2,e_2)
| product(e_1,e_3,e_2) ),
inference(res,[status(thm),theory(equality)],[27,105]),
[iquote('1:Res:27.5,105.0')] ).
cnf(123,plain,
( product(e_1,e_2,e_4)
| product(e_1,e_2,e_3)
| product(e_1,e_2,e_2)
| product(e_1,e_3,e_2) ),
inference(ssi,[status(thm)],[122,11,12]),
[iquote('1:SSi:122.1,122.0,11.0,12.0')] ).
cnf(129,plain,
( product(e_1,e_2,e_4)
| product(e_1,e_2,e_3)
| product(e_1,e_3,e_2)
| equalish(e_1,e_2) ),
inference(res,[status(thm),theory(equality)],[123,42]),
[iquote('1:Res:123.2,42.0')] ).
cnf(130,plain,
( product(e_1,e_2,e_4)
| product(e_1,e_2,e_3)
| product(e_1,e_3,e_2) ),
inference(mrr,[status(thm)],[129,15]),
[iquote('1:MRR:129.3,15.0')] ).
cnf(131,plain,
( product(e_1,e_2,e_4)
| product(e_1,e_3,e_2)
| product(e_3,e_3,e_2) ),
inference(res,[status(thm),theory(equality)],[130,105]),
[iquote('1:Res:130.1,105.0')] ).
cnf(145,plain,
product(e_1,e_2,e_4),
inference(spt,[spt(split,[position(s2s1)])],[131]),
[iquote('2:Spt:131.0')] ).
cnf(147,plain,
product(e_4,e_3,e_2),
inference(res,[status(thm),theory(equality)],[145,105]),
[iquote('2:Res:145.0,105.0')] ).
cnf(155,plain,
( ~ product(e_4,u,e_2)
| equalish(u,e_3) ),
inference(res,[status(thm),theory(equality)],[147,29]),
[iquote('2:Res:147.0,29.0')] ).
cnf(172,plain,
( ~ group_element(e_4)
| product(e_4,e_1,e_4)
| product(e_4,e_1,e_3)
| equalish(e_4,e_1)
| equalish(e_1,e_3) ),
inference(res,[status(thm),theory(equality)],[59,155]),
[iquote('2:Res:59.3,155.0')] ).
cnf(174,plain,
( product(e_4,e_1,e_4)
| product(e_4,e_1,e_3)
| equalish(e_4,e_1)
| equalish(e_1,e_3) ),
inference(ssi,[status(thm)],[172,14]),
[iquote('2:SSi:172.0,14.0')] ).
cnf(175,plain,
( product(e_4,e_1,e_4)
| product(e_4,e_1,e_3) ),
inference(mrr,[status(thm)],[174,24,16]),
[iquote('2:MRR:174.2,174.3,24.0,16.0')] ).
cnf(183,plain,
( product(e_4,e_1,e_4)
| equalish(e_4,e_2) ),
inference(res,[status(thm),theory(equality)],[175,104]),
[iquote('2:Res:175.1,104.0')] ).
cnf(184,plain,
product(e_4,e_1,e_4),
inference(mrr,[status(thm)],[183,25]),
[iquote('2:MRR:183.1,25.0')] ).
cnf(198,plain,
( ~ group_element(e_2)
| product(e_1,e_2,e_4)
| product(e_1,e_2,e_3)
| equalish(e_2,e_1)
| equalish(e_1,e_2) ),
inference(res,[status(thm),theory(equality)],[60,42]),
[iquote('0:Res:60.3,42.0')] ).
cnf(202,plain,
equalish(e_1,e_4),
inference(res,[status(thm),theory(equality)],[184,44]),
[iquote('2:Res:184.0,44.0')] ).
cnf(209,plain,
$false,
inference(mrr,[status(thm)],[202,17]),
[iquote('2:MRR:202.0,17.0')] ).
cnf(211,plain,
~ product(e_1,e_2,e_4),
inference(spt,[spt(split,[position(s2sa)])],[209,145]),
[iquote('2:Spt:209.0,131.0,145.0')] ).
cnf(212,plain,
( product(e_1,e_3,e_2)
| product(e_3,e_3,e_2) ),
inference(spt,[spt(split,[position(s2s2)])],[131]),
[iquote('2:Spt:209.0,131.1,131.2')] ).
cnf(218,plain,
( product(e_1,e_2,e_4)
| product(e_1,e_2,e_3)
| equalish(e_2,e_1)
| equalish(e_1,e_2) ),
inference(ssi,[status(thm)],[198,12]),
[iquote('0:SSi:198.0,12.0')] ).
cnf(219,plain,
( product(e_1,e_2,e_4)
| product(e_1,e_2,e_3) ),
inference(mrr,[status(thm)],[218,18,15]),
[iquote('0:MRR:218.2,218.3,18.0,15.0')] ).
cnf(220,plain,
product(e_1,e_2,e_3),
inference(mrr,[status(thm)],[219,211]),
[iquote('2:MRR:219.0,211.0')] ).
cnf(229,plain,
product(e_3,e_3,e_2),
inference(res,[status(thm),theory(equality)],[220,105]),
[iquote('2:Res:220.0,105.0')] ).
cnf(235,plain,
equalish(e_2,e_3),
inference(res,[status(thm),theory(equality)],[229,45]),
[iquote('2:Res:229.0,45.0')] ).
cnf(244,plain,
$false,
inference(mrr,[status(thm)],[235,19]),
[iquote('2:MRR:235.0,19.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : GRP126-2.004 : TPTP v8.1.0. Released v1.2.0.
% 0.06/0.13 % Command : run_spass %d %s
% 0.12/0.34 % Computer : n028.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 : Mon Jun 13 23:29:23 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.19/0.43
% 0.19/0.43 SPASS V 3.9
% 0.19/0.43 SPASS beiseite: Proof found.
% 0.19/0.43 % SZS status Theorem
% 0.19/0.43 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.43 SPASS derived 158 clauses, backtracked 19 clauses, performed 3 splits and kept 141 clauses.
% 0.19/0.43 SPASS allocated 75792 KBytes.
% 0.19/0.43 SPASS spent 0:00:00.08 on the problem.
% 0.19/0.43 0:00:00.04 for the input.
% 0.19/0.43 0:00:00.00 for the FLOTTER CNF translation.
% 0.19/0.43 0:00:00.00 for inferences.
% 0.19/0.43 0:00:00.00 for the backtracking.
% 0.19/0.43 0:00:00.02 for the reduction.
% 0.19/0.43
% 0.19/0.43
% 0.19/0.43 Here is a proof with depth 13, length 64 :
% 0.19/0.43 % SZS output start Refutation
% See solution above
% 0.19/0.43 Formulae used in the proof : e_2_then_e_3 e_4_greater_e_3 no_redundancy element_1 element_2 element_4 e_1_is_not_e_2 e_1_is_not_e_3 e_1_is_not_e_4 e_2_is_not_e_1 e_2_is_not_e_3 e_4_is_not_e_1 e_4_is_not_e_2 product_total_function1 product_total_function2 product_right_cancellation product_left_cancellation product_idempotence qg4
% 0.19/0.43
%------------------------------------------------------------------------------