TSTP Solution File: GRP123-6.003 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP123-6.003 : TPTP v8.1.0. Released v1.2.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n014.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 11:45:28 EDT 2022
% Result : Unsatisfiable 0.19s 0.42s
% Output : Refutation 0.19s
% 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(1,axiom,
group_element(e_1),
file('GRP123-6.003.p',unknown),
[] ).
cnf(2,axiom,
group_element(e_2),
file('GRP123-6.003.p',unknown),
[] ).
cnf(3,axiom,
group_element(e_3),
file('GRP123-6.003.p',unknown),
[] ).
cnf(4,axiom,
~ equalish(e_1,e_2),
file('GRP123-6.003.p',unknown),
[] ).
cnf(5,axiom,
~ equalish(e_1,e_3),
file('GRP123-6.003.p',unknown),
[] ).
cnf(6,axiom,
~ equalish(e_2,e_1),
file('GRP123-6.003.p',unknown),
[] ).
cnf(8,axiom,
~ equalish(e_3,e_1),
file('GRP123-6.003.p',unknown),
[] ).
cnf(10,axiom,
( ~ group_element(u)
| ~ group_element(v)
| product1(v,u,e_3)
| product1(v,u,e_2)
| product1(v,u,e_1) ),
file('GRP123-6.003.p',unknown),
[] ).
cnf(12,axiom,
( ~ product1(u,v,w)
| ~ product1(u,x,w)
| equalish(x,v) ),
file('GRP123-6.003.p',unknown),
[] ).
cnf(13,axiom,
( ~ product1(u,v,w)
| ~ product1(x,v,w)
| equalish(x,u) ),
file('GRP123-6.003.p',unknown),
[] ).
cnf(14,axiom,
product1(u,u,u),
file('GRP123-6.003.p',unknown),
[] ).
cnf(16,axiom,
( ~ product2(u,v,w)
| ~ product2(u,v,x)
| equalish(x,w) ),
file('GRP123-6.003.p',unknown),
[] ).
cnf(19,axiom,
product2(u,u,u),
file('GRP123-6.003.p',unknown),
[] ).
cnf(20,axiom,
( ~ product1(u,v,w)
| ~ product1(x,v,u)
| product2(w,x,v) ),
file('GRP123-6.003.p',unknown),
[] ).
cnf(32,plain,
( ~ product2(u,u,v)
| equalish(v,u) ),
inference(res,[status(thm),theory(equality)],[19,16]),
[iquote('0:Res:19.0,16.0')] ).
cnf(33,plain,
( ~ product1(u,v,v)
| equalish(u,v) ),
inference(res,[status(thm),theory(equality)],[14,13]),
[iquote('0:Res:14.0,13.0')] ).
cnf(36,plain,
( ~ product1(u,v,u)
| equalish(v,u) ),
inference(res,[status(thm),theory(equality)],[14,12]),
[iquote('0:Res:14.0,12.0')] ).
cnf(58,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)],[10,33]),
[iquote('0:Res:10.4,33.0')] ).
cnf(67,plain,
( ~ group_element(u)
| product1(u,e_1,e_3)
| product1(u,e_1,e_2)
| equalish(u,e_1) ),
inference(ssi,[status(thm)],[58,1]),
[iquote('0:SSi:58.0,1.0')] ).
cnf(133,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)],[67,36]),
[iquote('0:Res:67.2,36.0')] ).
cnf(140,plain,
( product1(e_2,e_1,e_3)
| equalish(e_2,e_1)
| equalish(e_1,e_2) ),
inference(ssi,[status(thm)],[133,2]),
[iquote('0:SSi:133.0,2.0')] ).
cnf(141,plain,
product1(e_2,e_1,e_3),
inference(mrr,[status(thm)],[140,6,4]),
[iquote('0:MRR:140.1,140.2,6.0,4.0')] ).
cnf(146,plain,
( ~ product1(u,e_1,e_2)
| product2(e_3,u,e_1) ),
inference(res,[status(thm),theory(equality)],[141,20]),
[iquote('0:Res:141.0,20.0')] ).
cnf(159,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)],[67,146]),
[iquote('0:Res:67.2,146.0')] ).
cnf(214,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)],[159,32]),
[iquote('0:Res:159.3,32.0')] ).
cnf(222,plain,
( product1(e_3,e_1,e_3)
| equalish(e_3,e_1)
| equalish(e_1,e_3) ),
inference(ssi,[status(thm)],[214,3]),
[iquote('0:SSi:214.0,3.0')] ).
cnf(223,plain,
$false,
inference(mrr,[status(thm)],[222,36,8,5]),
[iquote('0:MRR:222.0,222.1,222.2,36.0,8.0,5.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11 % Problem : GRP123-6.003 : TPTP v8.1.0. Released v1.2.0.
% 0.11/0.12 % Command : run_spass %d %s
% 0.11/0.33 % Computer : n014.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 600
% 0.11/0.33 % DateTime : Mon Jun 13 15:33:22 EDT 2022
% 0.11/0.33 % CPUTime :
% 0.19/0.42
% 0.19/0.42 SPASS V 3.9
% 0.19/0.42 SPASS beiseite: Proof found.
% 0.19/0.42 % SZS status Theorem
% 0.19/0.42 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.42 SPASS derived 157 clauses, backtracked 0 clauses, performed 0 splits and kept 109 clauses.
% 0.19/0.42 SPASS allocated 75767 KBytes.
% 0.19/0.42 SPASS spent 0:00:00.08 on the problem.
% 0.19/0.42 0:00:00.04 for the input.
% 0.19/0.42 0:00:00.00 for the FLOTTER CNF translation.
% 0.19/0.42 0:00:00.00 for inferences.
% 0.19/0.42 0:00:00.00 for the backtracking.
% 0.19/0.42 0:00:00.02 for the reduction.
% 0.19/0.42
% 0.19/0.42
% 0.19/0.42 Here is a proof with depth 6, length 27 :
% 0.19/0.42 % SZS output start Refutation
% See solution above
% 0.19/0.42 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
% 0.19/0.42
%------------------------------------------------------------------------------