TSTP Solution File: GRP123-2.003 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP123-2.003 : TPTP v8.1.0. Released v1.2.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n022.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 11:45:26 EDT 2022
% Result : Unsatisfiable 0.18s 0.42s
% Output : Refutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 13
% Syntax : Number of clauses : 29 ( 14 unt; 7 nHn; 29 RR)
% Number of literals : 64 ( 0 equ; 29 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 : 9 ( 9 usr; 9 con; 0-0 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(7,axiom,
group_element(e_1),
file('GRP123-2.003.p',unknown),
[] ).
cnf(8,axiom,
group_element(e_2),
file('GRP123-2.003.p',unknown),
[] ).
cnf(9,axiom,
group_element(e_3),
file('GRP123-2.003.p',unknown),
[] ).
cnf(10,axiom,
~ equalish(e_1,e_2),
file('GRP123-2.003.p',unknown),
[] ).
cnf(11,axiom,
~ equalish(e_1,e_3),
file('GRP123-2.003.p',unknown),
[] ).
cnf(12,axiom,
~ equalish(e_2,e_1),
file('GRP123-2.003.p',unknown),
[] ).
cnf(14,axiom,
~ equalish(e_3,e_1),
file('GRP123-2.003.p',unknown),
[] ).
cnf(15,axiom,
~ equalish(e_3,e_2),
file('GRP123-2.003.p',unknown),
[] ).
cnf(16,axiom,
( ~ group_element(u)
| ~ group_element(v)
| product(v,u,e_3)
| product(v,u,e_2)
| product(v,u,e_1) ),
file('GRP123-2.003.p',unknown),
[] ).
cnf(18,axiom,
( ~ product(u,v,w)
| ~ product(u,x,w)
| equalish(x,v) ),
file('GRP123-2.003.p',unknown),
[] ).
cnf(19,axiom,
( ~ product(u,v,w)
| ~ product(x,v,w)
| equalish(x,u) ),
file('GRP123-2.003.p',unknown),
[] ).
cnf(20,axiom,
product(u,u,u),
file('GRP123-2.003.p',unknown),
[] ).
cnf(21,axiom,
( ~ product(u,v,w)
| ~ product(u,x,y)
| ~ product(w,v,z)
| ~ product(y,x,z)
| equalish(y,w) ),
file('GRP123-2.003.p',unknown),
[] ).
cnf(34,plain,
( ~ product(u,v,v)
| ~ product(u,w,x)
| ~ product(x,w,v)
| equalish(x,v) ),
inference(res,[status(thm),theory(equality)],[20,21]),
[iquote('0:Res:20.0,21.1')] ).
cnf(47,plain,
( ~ product(u,v,v)
| equalish(u,v) ),
inference(res,[status(thm),theory(equality)],[20,19]),
[iquote('0:Res:20.0,19.0')] ).
cnf(49,plain,
( ~ product(u,v,u)
| equalish(v,u) ),
inference(res,[status(thm),theory(equality)],[20,18]),
[iquote('0:Res:20.0,18.0')] ).
cnf(57,plain,
( ~ group_element(e_1)
| ~ group_element(u)
| product(u,e_1,e_3)
| product(u,e_1,e_2)
| equalish(u,e_1) ),
inference(res,[status(thm),theory(equality)],[16,47]),
[iquote('0:Res:16.4,47.0')] ).
cnf(60,plain,
( ~ group_element(u)
| product(u,e_1,e_3)
| product(u,e_1,e_2)
| equalish(u,e_1) ),
inference(ssi,[status(thm)],[57,7]),
[iquote('0:SSi:57.0,7.0')] ).
cnf(68,plain,
( ~ group_element(e_2)
| product(e_2,e_1,e_3)
| equalish(e_2,e_1)
| equalish(e_1,e_2) ),
inference(res,[status(thm),theory(equality)],[60,49]),
[iquote('0:Res:60.2,49.0')] ).
cnf(70,plain,
( product(e_2,e_1,e_3)
| equalish(e_2,e_1)
| equalish(e_1,e_2) ),
inference(ssi,[status(thm)],[68,8]),
[iquote('0:SSi:68.0,8.0')] ).
cnf(71,plain,
product(e_2,e_1,e_3),
inference(mrr,[status(thm)],[70,12,10]),
[iquote('0:MRR:70.1,70.2,12.0,10.0')] ).
cnf(110,plain,
( ~ product(u,v,w)
| ~ product(w,v,u)
| equalish(w,u) ),
inference(res,[status(thm),theory(equality)],[20,34]),
[iquote('0:Res:20.0,34.0')] ).
cnf(119,plain,
( ~ product(e_3,e_1,e_2)
| equalish(e_3,e_2) ),
inference(res,[status(thm),theory(equality)],[71,110]),
[iquote('0:Res:71.0,110.0')] ).
cnf(121,plain,
~ product(e_3,e_1,e_2),
inference(mrr,[status(thm)],[119,15]),
[iquote('0:MRR:119.1,15.0')] ).
cnf(124,plain,
( ~ group_element(e_3)
| product(e_3,e_1,e_3)
| equalish(e_3,e_1) ),
inference(res,[status(thm),theory(equality)],[60,121]),
[iquote('0:Res:60.2,121.0')] ).
cnf(125,plain,
( product(e_3,e_1,e_3)
| equalish(e_3,e_1) ),
inference(ssi,[status(thm)],[124,9]),
[iquote('0:SSi:124.0,9.0')] ).
cnf(126,plain,
product(e_3,e_1,e_3),
inference(mrr,[status(thm)],[125,14]),
[iquote('0:MRR:125.1,14.0')] ).
cnf(134,plain,
equalish(e_1,e_3),
inference(res,[status(thm),theory(equality)],[126,49]),
[iquote('0:Res:126.0,49.0')] ).
cnf(136,plain,
$false,
inference(mrr,[status(thm)],[134,11]),
[iquote('0:MRR:134.0,11.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GRP123-2.003 : TPTP v8.1.0. Released v1.2.0.
% 0.00/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n022.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Mon Jun 13 06:43:03 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.18/0.42
% 0.18/0.42 SPASS V 3.9
% 0.18/0.42 SPASS beiseite: Proof found.
% 0.18/0.42 % SZS status Theorem
% 0.18/0.42 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.18/0.42 SPASS derived 96 clauses, backtracked 0 clauses, performed 0 splits and kept 92 clauses.
% 0.18/0.42 SPASS allocated 75714 KBytes.
% 0.18/0.42 SPASS spent 0:00:00.07 on the problem.
% 0.18/0.42 0:00:00.03 for the input.
% 0.18/0.42 0:00:00.00 for the FLOTTER CNF translation.
% 0.18/0.42 0:00:00.00 for inferences.
% 0.18/0.42 0:00:00.00 for the backtracking.
% 0.18/0.42 0:00:00.01 for the reduction.
% 0.18/0.42
% 0.18/0.42
% 0.18/0.42 Here is a proof with depth 6, length 29 :
% 0.18/0.42 % SZS output start Refutation
% See solution above
% 0.18/0.42 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 e_3_is_not_e_2 product_total_function1 product_right_cancellation product_left_cancellation product_idempotence qg1_1
% 0.18/0.42
%------------------------------------------------------------------------------