TSTP Solution File: GRP123-3.003 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP123-3.003 : TPTP v8.1.0. Released v1.2.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n024.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 0.20s 0.44s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 15
% Syntax : Number of clauses : 38 ( 14 unt; 14 nHn; 38 RR)
% Number of literals : 96 ( 0 equ; 41 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(17,axiom,
group_element(e_1),
file('GRP123-3.003.p',unknown),
[] ).
cnf(18,axiom,
group_element(e_2),
file('GRP123-3.003.p',unknown),
[] ).
cnf(19,axiom,
group_element(e_3),
file('GRP123-3.003.p',unknown),
[] ).
cnf(20,axiom,
~ equalish(e_1,e_2),
file('GRP123-3.003.p',unknown),
[] ).
cnf(21,axiom,
~ equalish(e_1,e_3),
file('GRP123-3.003.p',unknown),
[] ).
cnf(22,axiom,
~ equalish(e_2,e_1),
file('GRP123-3.003.p',unknown),
[] ).
cnf(23,axiom,
~ equalish(e_2,e_3),
file('GRP123-3.003.p',unknown),
[] ).
cnf(24,axiom,
~ equalish(e_3,e_1),
file('GRP123-3.003.p',unknown),
[] ).
cnf(25,axiom,
~ equalish(e_3,e_2),
file('GRP123-3.003.p',unknown),
[] ).
cnf(26,axiom,
( ~ group_element(u)
| ~ group_element(v)
| product(v,u,e_3)
| product(v,u,e_2)
| product(v,u,e_1) ),
file('GRP123-3.003.p',unknown),
[] ).
cnf(27,axiom,
( ~ product(u,v,w)
| ~ product(u,v,x)
| equalish(x,w) ),
file('GRP123-3.003.p',unknown),
[] ).
cnf(28,axiom,
( ~ product(u,v,w)
| ~ product(u,x,w)
| equalish(x,v) ),
file('GRP123-3.003.p',unknown),
[] ).
cnf(29,axiom,
( ~ product(u,v,w)
| ~ product(x,v,w)
| equalish(x,u) ),
file('GRP123-3.003.p',unknown),
[] ).
cnf(30,axiom,
product(u,u,u),
file('GRP123-3.003.p',unknown),
[] ).
cnf(31,axiom,
( ~ product(u,v,w)
| ~ product(u,x,y)
| ~ product(w,v,z)
| ~ product(y,x,z)
| equalish(y,w) ),
file('GRP123-3.003.p',unknown),
[] ).
cnf(44,plain,
( ~ product(u,v,v)
| ~ product(u,w,x)
| ~ product(x,w,v)
| equalish(x,v) ),
inference(res,[status(thm),theory(equality)],[30,31]),
[iquote('0:Res:30.0,31.1')] ).
cnf(61,plain,
( ~ product(u,v,v)
| equalish(u,v) ),
inference(res,[status(thm),theory(equality)],[30,29]),
[iquote('0:Res:30.0,29.0')] ).
cnf(63,plain,
( ~ product(u,v,u)
| equalish(v,u) ),
inference(res,[status(thm),theory(equality)],[30,28]),
[iquote('0:Res:30.0,28.0')] ).
cnf(65,plain,
( ~ product(u,u,v)
| equalish(v,u) ),
inference(res,[status(thm),theory(equality)],[30,27]),
[iquote('0:Res:30.0,27.0')] ).
cnf(74,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)],[26,61]),
[iquote('0:Res:26.4,61.0')] ).
cnf(76,plain,
( ~ group_element(u)
| ~ group_element(u)
| product(u,u,e_3)
| product(u,u,e_2)
| equalish(e_1,u) ),
inference(res,[status(thm),theory(equality)],[26,65]),
[iquote('0:Res:26.4,65.0')] ).
cnf(77,plain,
( ~ group_element(u)
| product(u,e_1,e_3)
| product(u,e_1,e_2)
| equalish(u,e_1) ),
inference(ssi,[status(thm)],[74,17]),
[iquote('0:SSi:74.0,17.0')] ).
cnf(79,plain,
( ~ group_element(u)
| product(u,u,e_3)
| product(u,u,e_2)
| equalish(e_1,u) ),
inference(obv,[status(thm),theory(equality)],[76]),
[iquote('0:Obv:76.0')] ).
cnf(85,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)],[77,63]),
[iquote('0:Res:77.2,63.0')] ).
cnf(87,plain,
( product(e_2,e_1,e_3)
| equalish(e_2,e_1)
| equalish(e_1,e_2) ),
inference(ssi,[status(thm)],[85,18]),
[iquote('0:SSi:85.0,18.0')] ).
cnf(88,plain,
product(e_2,e_1,e_3),
inference(mrr,[status(thm)],[87,22,20]),
[iquote('0:MRR:87.1,87.2,22.0,20.0')] ).
cnf(145,plain,
( ~ group_element(u)
| product(u,u,e_3)
| equalish(e_1,u)
| equalish(e_2,u) ),
inference(res,[status(thm),theory(equality)],[79,65]),
[iquote('0:Res:79.2,65.0')] ).
cnf(150,plain,
( ~ group_element(u)
| ~ product(u,v,e_3)
| equalish(e_1,u)
| equalish(e_2,u)
| equalish(v,u) ),
inference(res,[status(thm),theory(equality)],[145,28]),
[iquote('0:Res:145.1,28.0')] ).
cnf(208,plain,
( ~ product(u,v,w)
| ~ product(w,v,u)
| equalish(w,u) ),
inference(res,[status(thm),theory(equality)],[30,44]),
[iquote('0:Res:30.0,44.0')] ).
cnf(219,plain,
( ~ product(e_3,e_1,e_2)
| equalish(e_3,e_2) ),
inference(res,[status(thm),theory(equality)],[88,208]),
[iquote('0:Res:88.0,208.0')] ).
cnf(222,plain,
~ product(e_3,e_1,e_2),
inference(mrr,[status(thm)],[219,25]),
[iquote('0:MRR:219.1,25.0')] ).
cnf(225,plain,
( ~ group_element(e_3)
| product(e_3,e_1,e_3)
| equalish(e_3,e_1) ),
inference(res,[status(thm),theory(equality)],[77,222]),
[iquote('0:Res:77.2,222.0')] ).
cnf(226,plain,
( product(e_3,e_1,e_3)
| equalish(e_3,e_1) ),
inference(ssi,[status(thm)],[225,19]),
[iquote('0:SSi:225.0,19.0')] ).
cnf(227,plain,
product(e_3,e_1,e_3),
inference(mrr,[status(thm)],[226,24]),
[iquote('0:MRR:226.1,24.0')] ).
cnf(239,plain,
( ~ group_element(e_3)
| equalish(e_1,e_3)
| equalish(e_2,e_3)
| equalish(e_1,e_3) ),
inference(res,[status(thm),theory(equality)],[227,150]),
[iquote('0:Res:227.0,150.1')] ).
cnf(243,plain,
( ~ group_element(e_3)
| equalish(e_2,e_3)
| equalish(e_1,e_3) ),
inference(obv,[status(thm),theory(equality)],[239]),
[iquote('0:Obv:239.1')] ).
cnf(244,plain,
( equalish(e_2,e_3)
| equalish(e_1,e_3) ),
inference(ssi,[status(thm)],[243,19]),
[iquote('0:SSi:243.0,19.0')] ).
cnf(245,plain,
$false,
inference(mrr,[status(thm)],[244,23,21]),
[iquote('0:MRR:244.0,244.1,23.0,21.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP123-3.003 : TPTP v8.1.0. Released v1.2.0.
% 0.07/0.13 % Command : run_spass %d %s
% 0.13/0.34 % Computer : n024.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 16:45:48 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.20/0.44
% 0.20/0.44 SPASS V 3.9
% 0.20/0.44 SPASS beiseite: Proof found.
% 0.20/0.44 % SZS status Theorem
% 0.20/0.44 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.20/0.44 SPASS derived 172 clauses, backtracked 0 clauses, performed 1 splits and kept 136 clauses.
% 0.20/0.44 SPASS allocated 75802 KBytes.
% 0.20/0.44 SPASS spent 0:00:00.09 on the problem.
% 0.20/0.44 0:00:00.04 for the input.
% 0.20/0.44 0:00:00.00 for the FLOTTER CNF translation.
% 0.20/0.44 0:00:00.00 for inferences.
% 0.20/0.44 0:00:00.00 for the backtracking.
% 0.20/0.44 0:00:00.02 for the reduction.
% 0.20/0.44
% 0.20/0.44
% 0.20/0.44 Here is a proof with depth 6, length 38 :
% 0.20/0.44 % SZS output start Refutation
% See solution above
% 0.20/0.44 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_2_is_not_e_3 e_3_is_not_e_1 e_3_is_not_e_2 product_total_function1 product_total_function2 product_right_cancellation product_left_cancellation product_idempotence qg1_1
% 0.20/0.44
%------------------------------------------------------------------------------