TSTP Solution File: GRP123-1.003 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP123-1.003 : TPTP v8.1.0. Released v1.2.0.
% 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 11:45:26 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(1,axiom,
group_element(e_1),
file('GRP123-1.003.p',unknown),
[] ).
cnf(2,axiom,
group_element(e_2),
file('GRP123-1.003.p',unknown),
[] ).
cnf(3,axiom,
group_element(e_3),
file('GRP123-1.003.p',unknown),
[] ).
cnf(4,axiom,
~ equalish(e_1,e_2),
file('GRP123-1.003.p',unknown),
[] ).
cnf(5,axiom,
~ equalish(e_1,e_3),
file('GRP123-1.003.p',unknown),
[] ).
cnf(6,axiom,
~ equalish(e_2,e_1),
file('GRP123-1.003.p',unknown),
[] ).
cnf(8,axiom,
~ equalish(e_3,e_1),
file('GRP123-1.003.p',unknown),
[] ).
cnf(9,axiom,
~ equalish(e_3,e_2),
file('GRP123-1.003.p',unknown),
[] ).
cnf(10,axiom,
( ~ group_element(u)
| ~ group_element(v)
| product(v,u,e_3)
| product(v,u,e_2)
| product(v,u,e_1) ),
file('GRP123-1.003.p',unknown),
[] ).
cnf(12,axiom,
( ~ product(u,v,w)
| ~ product(u,x,w)
| equalish(x,v) ),
file('GRP123-1.003.p',unknown),
[] ).
cnf(13,axiom,
( ~ product(u,v,w)
| ~ product(x,v,w)
| equalish(x,u) ),
file('GRP123-1.003.p',unknown),
[] ).
cnf(14,axiom,
product(u,u,u),
file('GRP123-1.003.p',unknown),
[] ).
cnf(15,axiom,
( ~ product(u,v,w)
| ~ product(u,x,y)
| ~ product(w,v,z)
| ~ product(y,x,z)
| equalish(y,w) ),
file('GRP123-1.003.p',unknown),
[] ).
cnf(28,plain,
( ~ product(u,v,v)
| ~ product(u,w,x)
| ~ product(x,w,v)
| equalish(x,v) ),
inference(res,[status(thm),theory(equality)],[14,15]),
[iquote('0:Res:14.0,15.1')] ).
cnf(40,plain,
( ~ product(u,v,v)
| equalish(u,v) ),
inference(res,[status(thm),theory(equality)],[14,13]),
[iquote('0:Res:14.0,13.0')] ).
cnf(42,plain,
( ~ product(u,v,u)
| equalish(v,u) ),
inference(res,[status(thm),theory(equality)],[14,12]),
[iquote('0:Res:14.0,12.0')] ).
cnf(50,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)],[10,40]),
[iquote('0:Res:10.4,40.0')] ).
cnf(53,plain,
( ~ group_element(u)
| product(u,e_1,e_3)
| product(u,e_1,e_2)
| equalish(u,e_1) ),
inference(ssi,[status(thm)],[50,1]),
[iquote('0:SSi:50.0,1.0')] ).
cnf(59,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)],[53,42]),
[iquote('0:Res:53.2,42.0')] ).
cnf(60,plain,
( product(e_2,e_1,e_3)
| equalish(e_2,e_1)
| equalish(e_1,e_2) ),
inference(ssi,[status(thm)],[59,2]),
[iquote('0:SSi:59.0,2.0')] ).
cnf(61,plain,
product(e_2,e_1,e_3),
inference(mrr,[status(thm)],[60,6,4]),
[iquote('0:MRR:60.1,60.2,6.0,4.0')] ).
cnf(96,plain,
( ~ product(u,v,w)
| ~ product(w,v,u)
| equalish(w,u) ),
inference(res,[status(thm),theory(equality)],[14,28]),
[iquote('0:Res:14.0,28.0')] ).
cnf(105,plain,
( ~ product(e_3,e_1,e_2)
| equalish(e_3,e_2) ),
inference(res,[status(thm),theory(equality)],[61,96]),
[iquote('0:Res:61.0,96.0')] ).
cnf(107,plain,
~ product(e_3,e_1,e_2),
inference(mrr,[status(thm)],[105,9]),
[iquote('0:MRR:105.1,9.0')] ).
cnf(110,plain,
( ~ group_element(e_3)
| product(e_3,e_1,e_3)
| equalish(e_3,e_1) ),
inference(res,[status(thm),theory(equality)],[53,107]),
[iquote('0:Res:53.2,107.0')] ).
cnf(111,plain,
( product(e_3,e_1,e_3)
| equalish(e_3,e_1) ),
inference(ssi,[status(thm)],[110,3]),
[iquote('0:SSi:110.0,3.0')] ).
cnf(112,plain,
product(e_3,e_1,e_3),
inference(mrr,[status(thm)],[111,8]),
[iquote('0:MRR:111.1,8.0')] ).
cnf(119,plain,
equalish(e_1,e_3),
inference(res,[status(thm),theory(equality)],[112,42]),
[iquote('0:Res:112.0,42.0')] ).
cnf(121,plain,
$false,
inference(mrr,[status(thm)],[119,5]),
[iquote('0:MRR:119.0,5.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GRP123-1.003 : TPTP v8.1.0. Released v1.2.0.
% 0.03/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n017.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 04:15:37 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 88 clauses, backtracked 0 clauses, performed 0 splits and kept 79 clauses.
% 0.18/0.42 SPASS allocated 75699 KBytes.
% 0.18/0.42 SPASS spent 0:00:00.08 on the problem.
% 0.18/0.42 0:00:00.04 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
%------------------------------------------------------------------------------