TSTP Solution File: GRP123-9.003 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP123-9.003 : TPTP v8.1.0. Bugfixed v1.2.1.
% 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 11:45:29 EDT 2022
% Result : Unsatisfiable 0.22s 0.45s
% Output : Refutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 14
% Syntax : Number of clauses : 27 ( 11 unt; 8 nHn; 27 RR)
% Number of literals : 63 ( 0 equ; 24 neg)
% Maximal clause size : 5 ( 2 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 5 ( 4 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(3,axiom,
group_element(e_1),
file('GRP123-9.003.p',unknown),
[] ).
cnf(4,axiom,
group_element(e_2),
file('GRP123-9.003.p',unknown),
[] ).
cnf(5,axiom,
group_element(e_3),
file('GRP123-9.003.p',unknown),
[] ).
cnf(6,axiom,
~ equalish(e_1,e_2),
file('GRP123-9.003.p',unknown),
[] ).
cnf(7,axiom,
~ equalish(e_1,e_3),
file('GRP123-9.003.p',unknown),
[] ).
cnf(8,axiom,
~ equalish(e_2,e_1),
file('GRP123-9.003.p',unknown),
[] ).
cnf(10,axiom,
~ equalish(e_3,e_1),
file('GRP123-9.003.p',unknown),
[] ).
cnf(12,axiom,
( ~ group_element(u)
| ~ group_element(v)
| product1(v,u,e_3)
| product1(v,u,e_2)
| product1(v,u,e_1) ),
file('GRP123-9.003.p',unknown),
[] ).
cnf(14,axiom,
( ~ product1(u,v,w)
| ~ product1(u,x,w)
| equalish(x,v) ),
file('GRP123-9.003.p',unknown),
[] ).
cnf(15,axiom,
( ~ product1(u,v,w)
| ~ product1(x,v,w)
| equalish(x,u) ),
file('GRP123-9.003.p',unknown),
[] ).
cnf(16,axiom,
product1(u,u,u),
file('GRP123-9.003.p',unknown),
[] ).
cnf(18,axiom,
( ~ product2(u,v,w)
| ~ product2(u,v,x)
| equalish(x,w) ),
file('GRP123-9.003.p',unknown),
[] ).
cnf(21,axiom,
product2(u,u,u),
file('GRP123-9.003.p',unknown),
[] ).
cnf(22,axiom,
( ~ product1(u,v,w)
| ~ product1(x,v,u)
| product2(w,x,v) ),
file('GRP123-9.003.p',unknown),
[] ).
cnf(34,plain,
( ~ product2(u,u,v)
| equalish(v,u) ),
inference(res,[status(thm),theory(equality)],[21,18]),
[iquote('0:Res:21.0,18.0')] ).
cnf(35,plain,
( ~ product1(u,v,v)
| equalish(u,v) ),
inference(res,[status(thm),theory(equality)],[16,15]),
[iquote('0:Res:16.0,15.0')] ).
cnf(38,plain,
( ~ product1(u,v,u)
| equalish(v,u) ),
inference(res,[status(thm),theory(equality)],[16,14]),
[iquote('0:Res:16.0,14.0')] ).
cnf(67,plain,
( ~ group_element(e_1)
| ~ group_element(u)
| product1(u,e_1,e_3)
| product1(u,e_1,e_2)
| equalish(u,e_1) ),
inference(res,[status(thm),theory(equality)],[12,35]),
[iquote('0:Res:12.4,35.0')] ).
cnf(76,plain,
( ~ group_element(u)
| product1(u,e_1,e_3)
| product1(u,e_1,e_2)
| equalish(u,e_1) ),
inference(ssi,[status(thm)],[67,3]),
[iquote('0:SSi:67.0,3.0')] ).
cnf(135,plain,
( ~ group_element(e_2)
| product1(e_2,e_1,e_3)
| equalish(e_2,e_1)
| equalish(e_1,e_2) ),
inference(res,[status(thm),theory(equality)],[76,38]),
[iquote('0:Res:76.2,38.0')] ).
cnf(142,plain,
( product1(e_2,e_1,e_3)
| equalish(e_2,e_1)
| equalish(e_1,e_2) ),
inference(ssi,[status(thm)],[135,4]),
[iquote('0:SSi:135.0,4.0')] ).
cnf(143,plain,
product1(e_2,e_1,e_3),
inference(mrr,[status(thm)],[142,8,6]),
[iquote('0:MRR:142.1,142.2,8.0,6.0')] ).
cnf(144,plain,
( ~ product1(u,e_1,e_2)
| product2(e_3,u,e_1) ),
inference(res,[status(thm),theory(equality)],[143,22]),
[iquote('0:Res:143.0,22.0')] ).
cnf(157,plain,
( ~ group_element(u)
| product1(u,e_1,e_3)
| equalish(u,e_1)
| product2(e_3,u,e_1) ),
inference(res,[status(thm),theory(equality)],[76,144]),
[iquote('0:Res:76.2,144.0')] ).
cnf(191,plain,
( ~ group_element(e_3)
| product1(e_3,e_1,e_3)
| equalish(e_3,e_1)
| equalish(e_1,e_3) ),
inference(res,[status(thm),theory(equality)],[157,34]),
[iquote('0:Res:157.3,34.0')] ).
cnf(199,plain,
( product1(e_3,e_1,e_3)
| equalish(e_3,e_1)
| equalish(e_1,e_3) ),
inference(ssi,[status(thm)],[191,5]),
[iquote('0:SSi:191.0,5.0')] ).
cnf(200,plain,
$false,
inference(mrr,[status(thm)],[199,38,10,7]),
[iquote('0:MRR:199.0,199.1,199.2,38.0,10.0,7.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13 % Problem : GRP123-9.003 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.13/0.14 % Command : run_spass %d %s
% 0.14/0.36 % Computer : n028.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 06:02:37 EDT 2022
% 0.14/0.36 % CPUTime :
% 0.22/0.45
% 0.22/0.45 SPASS V 3.9
% 0.22/0.45 SPASS beiseite: Proof found.
% 0.22/0.45 % SZS status Theorem
% 0.22/0.45 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.22/0.45 SPASS derived 139 clauses, backtracked 0 clauses, performed 0 splits and kept 106 clauses.
% 0.22/0.45 SPASS allocated 75756 KBytes.
% 0.22/0.45 SPASS spent 0:00:00.08 on the problem.
% 0.22/0.45 0:00:00.03 for the input.
% 0.22/0.45 0:00:00.00 for the FLOTTER CNF translation.
% 0.22/0.45 0:00:00.00 for inferences.
% 0.22/0.45 0:00:00.00 for the backtracking.
% 0.22/0.45 0:00:00.02 for the reduction.
% 0.22/0.45
% 0.22/0.45
% 0.22/0.45 Here is a proof with depth 6, length 27 :
% 0.22/0.45 % SZS output start Refutation
% See solution above
% 0.22/0.45 Formulae used in the proof : element_1 element_2 element_3 e_1_is_not_e_2 e_1_is_not_e_3 e_2_is_not_e_1 e_3_is_not_e_1 product1_total_function1 product1_right_cancellation product1_left_cancellation product1_idempotence product2_total_function2 product2_idempotence qg1a
% 0.22/0.45
%------------------------------------------------------------------------------