%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP123-8.003 : TPTP v8.1.0. Released v1.2.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n019.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 0.19s 0.43s
% 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(17,axiom,
group_element(e_1),
file('GRP123-8.003.p',unknown),
[] ).
cnf(18,axiom,
group_element(e_2),
file('GRP123-8.003.p',unknown),
[] ).
cnf(19,axiom,
group_element(e_3),
file('GRP123-8.003.p',unknown),
[] ).
cnf(20,axiom,
~ equalish(e_1,e_2),
file('GRP123-8.003.p',unknown),
[] ).
cnf(21,axiom,
~ equalish(e_1,e_3),
file('GRP123-8.003.p',unknown),
[] ).
cnf(22,axiom,
~ equalish(e_2,e_1),
file('GRP123-8.003.p',unknown),
[] ).
cnf(24,axiom,
~ equalish(e_3,e_1),
file('GRP123-8.003.p',unknown),
[] ).
cnf(26,axiom,
( ~ group_element(u)
| ~ group_element(v)
| product1(v,u,e_3)
| product1(v,u,e_2)
| product1(v,u,e_1) ),
file('GRP123-8.003.p',unknown),
[] ).
cnf(28,axiom,
( ~ product1(u,v,w)
| ~ product1(u,x,w)
| equalish(x,v) ),
file('GRP123-8.003.p',unknown),
[] ).
cnf(29,axiom,
( ~ product1(u,v,w)
| ~ product1(x,v,w)
| equalish(x,u) ),
file('GRP123-8.003.p',unknown),
[] ).
cnf(30,axiom,
product1(u,u,u),
file('GRP123-8.003.p',unknown),
[] ).
cnf(32,axiom,
( ~ product2(u,v,w)
| ~ product2(u,v,x)
| equalish(x,w) ),
file('GRP123-8.003.p',unknown),
[] ).
cnf(35,axiom,
product2(u,u,u),
file('GRP123-8.003.p',unknown),
[] ).
cnf(36,axiom,
( ~ product1(u,v,w)
| ~ product1(x,v,u)
| product2(w,x,v) ),
file('GRP123-8.003.p',unknown),
[] ).
cnf(52,plain,
( ~ product2(u,u,v)
| equalish(v,u) ),
inference(res,[status(thm),theory(equality)],[35,32]),
[iquote('0:Res:35.0,32.0')] ).
cnf(53,plain,
( ~ product1(u,v,v)
| equalish(u,v) ),
inference(res,[status(thm),theory(equality)],[30,29]),
[iquote('0:Res:30.0,29.0')] ).
cnf(56,plain,
( ~ product1(u,v,u)
| equalish(v,u) ),
inference(res,[status(thm),theory(equality)],[30,28]),
[iquote('0:Res:30.0,28.0')] ).
cnf(74,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)],[26,53]),
[iquote('0:Res:26.4,53.0')] ).
cnf(83,plain,
( ~ group_element(u)
| product1(u,e_1,e_3)
| product1(u,e_1,e_2)
| equalish(u,e_1) ),
inference(ssi,[status(thm)],[74,17]),
[iquote('0:SSi:74.0,17.0')] ).
cnf(150,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)],[83,56]),
[iquote('0:Res:83.2,56.0')] ).
cnf(157,plain,
( product1(e_2,e_1,e_3)
| equalish(e_2,e_1)
| equalish(e_1,e_2) ),
inference(ssi,[status(thm)],[150,18]),
[iquote('0:SSi:150.0,18.0')] ).
cnf(158,plain,
product1(e_2,e_1,e_3),
inference(mrr,[status(thm)],[157,22,20]),
[iquote('0:MRR:157.1,157.2,22.0,20.0')] ).
cnf(159,plain,
( ~ product1(u,e_1,e_2)
| product2(e_3,u,e_1) ),
inference(res,[status(thm),theory(equality)],[158,36]),
[iquote('0:Res:158.0,36.0')] ).
cnf(171,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)],[83,159]),
[iquote('0:Res:83.2,159.0')] ).
cnf(173,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)],[171,52]),
[iquote('0:Res:171.3,52.0')] ).
cnf(178,plain,
( product1(e_3,e_1,e_3)
| equalish(e_3,e_1)
| equalish(e_1,e_3) ),
inference(ssi,[status(thm)],[173,19]),
[iquote('0:SSi:173.0,19.0')] ).
cnf(179,plain,
$false,
inference(mrr,[status(thm)],[178,56,24,21]),
[iquote('0:MRR:178.0,178.1,178.2,56.0,24.0,21.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GRP123-8.003 : TPTP v8.1.0. Released v1.2.0.
% 0.13/0.13 % Command : run_spass %d %s
% 0.13/0.34 % Computer : n019.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Mon Jun 13 05:16:09 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.19/0.43
% 0.19/0.43 SPASS V 3.9
% 0.19/0.43 SPASS beiseite: Proof found.
% 0.19/0.43 % SZS status Theorem
% 0.19/0.43 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.43 SPASS derived 120 clauses, backtracked 0 clauses, performed 0 splits and kept 116 clauses.
% 0.19/0.43 SPASS allocated 75742 KBytes.
% 0.19/0.43 SPASS spent 0:00:00.08 on the problem.
% 0.19/0.43 0:00:00.04 for the input.
% 0.19/0.43 0:00:00.00 for the FLOTTER CNF translation.
% 0.19/0.43 0:00:00.00 for inferences.
% 0.19/0.43 0:00:00.00 for the backtracking.
% 0.19/0.43 0:00:00.01 for the reduction.
% 0.19/0.43
% 0.19/0.43
% 0.19/0.43 Here is a proof with depth 6, length 27 :
% 0.19/0.43 % SZS output start Refutation
% See solution above
% 0.19/0.43 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
% 0.19/0.43
%------------------------------------------------------------------------------