TSTP Solution File: GRP125-4.003 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP125-4.003 : TPTP v8.1.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n029.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 11:45:36 EDT 2022
% Result : Unsatisfiable 0.22s 0.46s
% Output : Refutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 12
% Syntax : Number of clauses : 31 ( 16 unt; 8 nHn; 31 RR)
% Number of literals : 63 ( 0 equ; 22 neg)
% Maximal clause size : 5 ( 2 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 7 con; 0-0 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
( ~ group_element(u)
| ~ group_element(v)
| product(e_3,v,u)
| product(e_2,v,u)
| product(e_1,v,u) ),
file('GRP125-4.003.p',unknown),
[] ).
cnf(3,axiom,
group_element(e_1),
file('GRP125-4.003.p',unknown),
[] ).
cnf(4,axiom,
group_element(e_2),
file('GRP125-4.003.p',unknown),
[] ).
cnf(5,axiom,
group_element(e_3),
file('GRP125-4.003.p',unknown),
[] ).
cnf(6,axiom,
~ equalish(e_1,e_2),
file('GRP125-4.003.p',unknown),
[] ).
cnf(8,axiom,
~ equalish(e_2,e_1),
file('GRP125-4.003.p',unknown),
[] ).
cnf(10,axiom,
~ equalish(e_3,e_1),
file('GRP125-4.003.p',unknown),
[] ).
cnf(11,axiom,
~ equalish(e_3,e_2),
file('GRP125-4.003.p',unknown),
[] ).
cnf(13,axiom,
( ~ product(u,v,w)
| ~ product(u,v,x)
| equalish(x,w) ),
file('GRP125-4.003.p',unknown),
[] ).
cnf(14,axiom,
( ~ product(u,v,w)
| ~ product(u,x,w)
| equalish(x,v) ),
file('GRP125-4.003.p',unknown),
[] ).
cnf(16,axiom,
product(u,u,u),
file('GRP125-4.003.p',unknown),
[] ).
cnf(18,axiom,
( ~ product(u,v,w)
| ~ product(w,x,u)
| product(v,u,x) ),
file('GRP125-4.003.p',unknown),
[] ).
cnf(37,plain,
( ~ product(u,v,u)
| equalish(v,u) ),
inference(res,[status(thm),theory(equality)],[16,14]),
[iquote('0:Res:16.0,14.0')] ).
cnf(39,plain,
( ~ product(u,u,v)
| equalish(v,u) ),
inference(res,[status(thm),theory(equality)],[16,13]),
[iquote('0:Res:16.0,13.0')] ).
cnf(44,plain,
( ~ group_element(u)
| ~ group_element(e_1)
| product(e_3,e_1,u)
| product(e_2,e_1,u)
| equalish(u,e_1) ),
inference(res,[status(thm),theory(equality)],[1,39]),
[iquote('0:Res:1.4,39.0')] ).
cnf(59,plain,
( ~ group_element(u)
| product(e_3,e_1,u)
| product(e_2,e_1,u)
| equalish(u,e_1) ),
inference(ssi,[status(thm)],[44,3]),
[iquote('0:SSi:44.1,3.0')] ).
cnf(71,plain,
( ~ group_element(e_2)
| product(e_3,e_1,e_2)
| equalish(e_2,e_1)
| equalish(e_1,e_2) ),
inference(res,[status(thm),theory(equality)],[59,37]),
[iquote('0:Res:59.2,37.0')] ).
cnf(80,plain,
( product(e_3,e_1,e_2)
| equalish(e_2,e_1)
| equalish(e_1,e_2) ),
inference(ssi,[status(thm)],[71,4]),
[iquote('0:SSi:71.0,4.0')] ).
cnf(81,plain,
product(e_3,e_1,e_2),
inference(mrr,[status(thm)],[80,8,6]),
[iquote('0:MRR:80.1,80.2,8.0,6.0')] ).
cnf(83,plain,
( ~ product(e_2,u,e_3)
| product(e_1,e_3,u) ),
inference(res,[status(thm),theory(equality)],[81,18]),
[iquote('0:Res:81.0,18.0')] ).
cnf(85,plain,
( ~ product(e_3,e_1,u)
| equalish(u,e_2) ),
inference(res,[status(thm),theory(equality)],[81,13]),
[iquote('0:Res:81.0,13.0')] ).
cnf(151,plain,
( ~ group_element(e_3)
| product(e_3,e_1,e_3)
| equalish(e_3,e_1)
| product(e_1,e_3,e_1) ),
inference(res,[status(thm),theory(equality)],[59,83]),
[iquote('0:Res:59.2,83.0')] ).
cnf(153,plain,
( product(e_3,e_1,e_3)
| equalish(e_3,e_1)
| product(e_1,e_3,e_1) ),
inference(ssi,[status(thm)],[151,5]),
[iquote('0:SSi:151.0,5.0')] ).
cnf(154,plain,
( product(e_3,e_1,e_3)
| product(e_1,e_3,e_1) ),
inference(mrr,[status(thm)],[153,10]),
[iquote('0:MRR:153.1,10.0')] ).
cnf(156,plain,
product(e_3,e_1,e_3),
inference(spt,[spt(split,[position(s1)])],[154]),
[iquote('1:Spt:154.0')] ).
cnf(166,plain,
equalish(e_3,e_2),
inference(res,[status(thm),theory(equality)],[156,85]),
[iquote('1:Res:156.0,85.0')] ).
cnf(168,plain,
$false,
inference(mrr,[status(thm)],[166,11]),
[iquote('1:MRR:166.0,11.0')] ).
cnf(169,plain,
~ product(e_3,e_1,e_3),
inference(spt,[spt(split,[position(sa)])],[168,156]),
[iquote('1:Spt:168.0,154.0,156.0')] ).
cnf(170,plain,
product(e_1,e_3,e_1),
inference(spt,[spt(split,[position(s2)])],[154]),
[iquote('1:Spt:168.0,154.1')] ).
cnf(171,plain,
equalish(e_3,e_1),
inference(res,[status(thm),theory(equality)],[170,37]),
[iquote('1:Res:170.0,37.0')] ).
cnf(180,plain,
$false,
inference(mrr,[status(thm)],[171,10]),
[iquote('1:MRR:171.0,10.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : GRP125-4.003 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.08/0.14 % Command : run_spass %d %s
% 0.14/0.36 % Computer : n029.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 600
% 0.14/0.36 % DateTime : Mon Jun 13 11:04:40 EDT 2022
% 0.14/0.36 % CPUTime :
% 0.22/0.46
% 0.22/0.46 SPASS V 3.9
% 0.22/0.46 SPASS beiseite: Proof found.
% 0.22/0.46 % SZS status Theorem
% 0.22/0.46 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.22/0.46 SPASS derived 120 clauses, backtracked 2 clauses, performed 1 splits and kept 118 clauses.
% 0.22/0.46 SPASS allocated 75728 KBytes.
% 0.22/0.46 SPASS spent 0:00:00.08 on the problem.
% 0.22/0.46 0:00:00.04 for the input.
% 0.22/0.46 0:00:00.00 for the FLOTTER CNF translation.
% 0.22/0.46 0:00:00.00 for inferences.
% 0.22/0.46 0:00:00.00 for the backtracking.
% 0.22/0.46 0:00:00.02 for the reduction.
% 0.22/0.46
% 0.22/0.46
% 0.22/0.46 Here is a proof with depth 7, length 31 :
% 0.22/0.46 % SZS output start Refutation
% See solution above
% 0.22/0.46 Formulae used in the proof : row_surjectivity element_1 element_2 element_3 e_1_is_not_e_2 e_2_is_not_e_1 e_3_is_not_e_1 e_3_is_not_e_2 product_total_function2 product_right_cancellation product_idempotence qg3_2
% 0.22/0.46
%------------------------------------------------------------------------------