TSTP Solution File: GRP123-4.003 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP123-4.003 : TPTP v8.1.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n017.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 11:45:27 EDT 2022
% Result : Unsatisfiable 0.18s 0.46s
% Output : Refutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 9
% Syntax : Number of clauses : 25 ( 8 unt; 9 nHn; 25 RR)
% Number of literals : 69 ( 0 equ; 28 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(2,axiom,
( ~ group_element(u)
| ~ group_element(v)
| product(v,e_3,u)
| product(v,e_2,u)
| product(v,e_1,u) ),
file('GRP123-4.003.p',unknown),
[] ).
cnf(3,axiom,
group_element(e_1),
file('GRP123-4.003.p',unknown),
[] ).
cnf(4,axiom,
group_element(e_2),
file('GRP123-4.003.p',unknown),
[] ).
cnf(6,axiom,
~ equalish(e_1,e_2),
file('GRP123-4.003.p',unknown),
[] ).
cnf(8,axiom,
~ equalish(e_2,e_1),
file('GRP123-4.003.p',unknown),
[] ).
cnf(13,axiom,
( ~ product(u,v,w)
| ~ product(u,v,x)
| equalish(x,w) ),
file('GRP123-4.003.p',unknown),
[] ).
cnf(15,axiom,
( ~ product(u,v,w)
| ~ product(x,v,w)
| equalish(x,u) ),
file('GRP123-4.003.p',unknown),
[] ).
cnf(16,axiom,
product(u,u,u),
file('GRP123-4.003.p',unknown),
[] ).
cnf(17,axiom,
( ~ product(u,v,w)
| ~ product(u,x,y)
| ~ product(w,v,z)
| ~ product(y,x,z)
| equalish(y,w) ),
file('GRP123-4.003.p',unknown),
[] ).
cnf(30,plain,
( ~ product(u,v,v)
| ~ product(u,w,x)
| ~ product(x,w,v)
| equalish(x,v) ),
inference(res,[status(thm),theory(equality)],[16,17]),
[iquote('0:Res:16.0,17.1')] ).
cnf(42,plain,
( ~ product(u,v,v)
| equalish(u,v) ),
inference(res,[status(thm),theory(equality)],[16,15]),
[iquote('0:Res:16.0,15.0')] ).
cnf(45,plain,
( ~ product(u,u,v)
| equalish(v,u) ),
inference(res,[status(thm),theory(equality)],[16,13]),
[iquote('0:Res:16.0,13.0')] ).
cnf(64,plain,
( ~ group_element(u)
| ~ group_element(e_1)
| product(e_1,e_3,u)
| product(e_1,e_2,u)
| equalish(u,e_1) ),
inference(res,[status(thm),theory(equality)],[2,45]),
[iquote('0:Res:2.4,45.0')] ).
cnf(68,plain,
( ~ group_element(e_1)
| ~ group_element(u)
| product(u,e_3,e_1)
| product(u,e_2,e_1)
| equalish(u,e_1) ),
inference(res,[status(thm),theory(equality)],[2,42]),
[iquote('0:Res:2.4,42.0')] ).
cnf(70,plain,
( ~ group_element(u)
| product(e_1,e_3,u)
| product(e_1,e_2,u)
| equalish(u,e_1) ),
inference(ssi,[status(thm)],[64,3]),
[iquote('0:SSi:64.1,3.0')] ).
cnf(71,plain,
( ~ group_element(u)
| product(u,e_3,e_1)
| product(u,e_2,e_1)
| equalish(u,e_1) ),
inference(ssi,[status(thm)],[68,3]),
[iquote('0:SSi:68.0,3.0')] ).
cnf(129,plain,
( ~ group_element(e_2)
| product(e_1,e_3,e_2)
| equalish(e_2,e_1)
| equalish(e_1,e_2) ),
inference(res,[status(thm),theory(equality)],[70,42]),
[iquote('0:Res:70.2,42.0')] ).
cnf(132,plain,
( product(e_1,e_3,e_2)
| equalish(e_2,e_1)
| equalish(e_1,e_2) ),
inference(ssi,[status(thm)],[129,4]),
[iquote('0:SSi:129.0,4.0')] ).
cnf(133,plain,
product(e_1,e_3,e_2),
inference(mrr,[status(thm)],[132,8,6]),
[iquote('0:MRR:132.1,132.2,8.0,6.0')] ).
cnf(159,plain,
( ~ group_element(e_2)
| product(e_2,e_3,e_1)
| equalish(e_2,e_1)
| equalish(e_1,e_2) ),
inference(res,[status(thm),theory(equality)],[71,45]),
[iquote('0:Res:71.2,45.0')] ).
cnf(169,plain,
( product(e_2,e_3,e_1)
| equalish(e_2,e_1)
| equalish(e_1,e_2) ),
inference(ssi,[status(thm)],[159,4]),
[iquote('0:SSi:159.0,4.0')] ).
cnf(170,plain,
product(e_2,e_3,e_1),
inference(mrr,[status(thm)],[169,8,6]),
[iquote('0:MRR:169.1,169.2,8.0,6.0')] ).
cnf(176,plain,
( ~ product(u,v,w)
| ~ product(w,v,u)
| equalish(w,u) ),
inference(res,[status(thm),theory(equality)],[16,30]),
[iquote('0:Res:16.0,30.0')] ).
cnf(251,plain,
( ~ product(e_2,e_3,e_1)
| equalish(e_2,e_1) ),
inference(res,[status(thm),theory(equality)],[133,176]),
[iquote('0:Res:133.0,176.0')] ).
cnf(255,plain,
$false,
inference(mrr,[status(thm)],[251,170,8]),
[iquote('0:MRR:251.0,251.1,170.0,8.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP123-4.003 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.07/0.12 % Command : run_spass %d %s
% 0.12/0.34 % Computer : n017.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 18:00:08 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.18/0.46
% 0.18/0.46 SPASS V 3.9
% 0.18/0.46 SPASS beiseite: Proof found.
% 0.18/0.46 % SZS status Theorem
% 0.18/0.46 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/0.46 SPASS derived 200 clauses, backtracked 0 clauses, performed 0 splits and kept 146 clauses.
% 0.18/0.46 SPASS allocated 75815 KBytes.
% 0.18/0.46 SPASS spent 0:00:00.11 on the problem.
% 0.18/0.46 0:00:00.04 for the input.
% 0.18/0.46 0:00:00.00 for the FLOTTER CNF translation.
% 0.18/0.46 0:00:00.00 for inferences.
% 0.18/0.46 0:00:00.00 for the backtracking.
% 0.18/0.46 0:00:00.04 for the reduction.
% 0.18/0.46
% 0.18/0.46
% 0.18/0.46 Here is a proof with depth 4, length 25 :
% 0.18/0.46 % SZS output start Refutation
% See solution above
% 0.18/0.46 Formulae used in the proof : column_surjectivity element_1 element_2 e_1_is_not_e_2 e_2_is_not_e_1 product_total_function2 product_left_cancellation product_idempotence qg1_1
% 0.18/0.46
%------------------------------------------------------------------------------