%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP040-4 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n018.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 11:44:57 EDT 2022
% Result : Unsatisfiable 0.49s 0.67s
% Output : Refutation 0.49s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 19
% Syntax : Number of clauses : 46 ( 19 unt; 4 nHn; 46 RR)
% Number of literals : 97 ( 0 equ; 46 neg)
% Maximal clause size : 4 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 14 ( 14 usr; 11 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(2,axiom,
( ~ subgroup_member(u)
| subgroup_member(inverse(u)) ),
file('GRP040-4.p',unknown),
[] ).
cnf(3,axiom,
( ~ product(u,v,w)
| ~ product(u,x,w)
| equal(v,x) ),
file('GRP040-4.p',unknown),
[] ).
cnf(4,axiom,
( ~ product(u,v,w)
| ~ product(x,v,w)
| equal(u,x) ),
file('GRP040-4.p',unknown),
[] ).
cnf(5,axiom,
( subgroup_member(u)
| subgroup_member(v)
| subgroup_member(element_in_O2(u,v)) ),
file('GRP040-4.p',unknown),
[] ).
cnf(6,axiom,
( subgroup_member(u)
| subgroup_member(v)
| product(u,element_in_O2(u,v),v) ),
file('GRP040-4.p',unknown),
[] ).
cnf(7,axiom,
~ subgroup_member(a),
file('GRP040-4.p',unknown),
[] ).
cnf(8,axiom,
subgroup_member(b),
file('GRP040-4.p',unknown),
[] ).
cnf(9,axiom,
~ subgroup_member(d),
file('GRP040-4.p',unknown),
[] ).
cnf(10,axiom,
product(b,inverse(a),c),
file('GRP040-4.p',unknown),
[] ).
cnf(11,axiom,
product(a,c,d),
file('GRP040-4.p',unknown),
[] ).
cnf(12,axiom,
equal(inverse(inverse(u)),u),
file('GRP040-4.p',unknown),
[] ).
cnf(14,axiom,
product(u,identity,u),
file('GRP040-4.p',unknown),
[] ).
cnf(15,axiom,
product(inverse(u),u,identity),
file('GRP040-4.p',unknown),
[] ).
cnf(16,axiom,
product(u,inverse(u),identity),
file('GRP040-4.p',unknown),
[] ).
cnf(17,axiom,
product(u,v,multiply(u,v)),
file('GRP040-4.p',unknown),
[] ).
cnf(18,axiom,
( ~ product(u,v,w)
| ~ product(u,v,x)
| equal(x,w) ),
file('GRP040-4.p',unknown),
[] ).
cnf(19,axiom,
( ~ product(u,v,w)
| ~ product(x,v,y)
| ~ product(z,x,u)
| product(z,y,w) ),
file('GRP040-4.p',unknown),
[] ).
cnf(20,axiom,
( ~ product(u,v,w)
| ~ product(x,y,v)
| ~ product(u,x,z)
| product(z,y,w) ),
file('GRP040-4.p',unknown),
[] ).
cnf(21,axiom,
( ~ subgroup_member(u)
| ~ subgroup_member(v)
| ~ product(v,inverse(u),w)
| subgroup_member(w) ),
file('GRP040-4.p',unknown),
[] ).
cnf(28,plain,
( ~ product(a,c,u)
| equal(u,d) ),
inference(res,[status(thm),theory(equality)],[11,18]),
[iquote('0:Res:11.0,18.0')] ).
cnf(37,plain,
equal(multiply(a,c),d),
inference(res,[status(thm),theory(equality)],[17,28]),
[iquote('0:Res:17.0,28.0')] ).
cnf(44,plain,
( ~ product(u,v,identity)
| equal(inverse(v),u) ),
inference(res,[status(thm),theory(equality)],[15,4]),
[iquote('0:Res:15.0,4.0')] ).
cnf(61,plain,
( ~ product(a,u,d)
| equal(c,u) ),
inference(res,[status(thm),theory(equality)],[11,3]),
[iquote('0:Res:11.0,3.0')] ).
cnf(70,plain,
( subgroup_member(a)
| subgroup_member(d)
| equal(element_in_O2(a,d),c) ),
inference(res,[status(thm),theory(equality)],[6,61]),
[iquote('0:Res:6.2,61.0')] ).
cnf(71,plain,
equal(element_in_O2(a,d),c),
inference(mrr,[status(thm)],[70,7,9]),
[iquote('0:MRR:70.0,70.1,7.0,9.0')] ).
cnf(72,plain,
( subgroup_member(a)
| subgroup_member(d)
| subgroup_member(c) ),
inference(spr,[status(thm),theory(equality)],[71,5]),
[iquote('0:SpR:71.0,5.2')] ).
cnf(75,plain,
subgroup_member(c),
inference(mrr,[status(thm)],[72,7,9]),
[iquote('0:MRR:72.0,72.1,7.0,9.0')] ).
cnf(80,plain,
( ~ subgroup_member(inverse(u))
| ~ subgroup_member(v)
| ~ product(v,u,w)
| subgroup_member(w) ),
inference(spl,[status(thm),theory(equality)],[12,21]),
[iquote('0:SpL:12.0,21.2')] ).
cnf(86,plain,
( ~ subgroup_member(u)
| ~ subgroup_member(v)
| subgroup_member(multiply(v,inverse(u))) ),
inference(res,[status(thm),theory(equality)],[17,21]),
[iquote('0:Res:17.0,21.2')] ).
cnf(108,plain,
( ~ product(u,v,identity)
| ~ product(w,u,x)
| product(x,v,w) ),
inference(res,[status(thm),theory(equality)],[14,20]),
[iquote('0:Res:14.0,20.0')] ).
cnf(126,plain,
( ~ product(u,inverse(v),w)
| ~ product(x,u,v)
| product(x,w,identity) ),
inference(res,[status(thm),theory(equality)],[16,19]),
[iquote('0:Res:16.0,19.0')] ).
cnf(198,plain,
( ~ subgroup_member(inverse(u))
| ~ subgroup_member(v)
| subgroup_member(multiply(v,u)) ),
inference(spr,[status(thm),theory(equality)],[12,86]),
[iquote('0:SpR:12.0,86.2')] ).
cnf(206,plain,
( ~ subgroup_member(u)
| ~ subgroup_member(v)
| subgroup_member(multiply(u,v)) ),
inference(sor,[status(thm)],[198,2]),
[iquote('0:SoR:198.0,2.1')] ).
cnf(207,plain,
( ~ subgroup_member(u)
| ~ subgroup_member(v)
| ~ product(u,v,w)
| subgroup_member(w) ),
inference(sor,[status(thm)],[80,2]),
[iquote('0:SoR:80.0,2.1')] ).
cnf(210,plain,
( ~ subgroup_member(a)
| ~ subgroup_member(c)
| subgroup_member(d) ),
inference(spr,[status(thm),theory(equality)],[37,206]),
[iquote('0:SpR:37.0,206.2')] ).
cnf(214,plain,
( ~ subgroup_member(a)
| subgroup_member(d) ),
inference(ssi,[status(thm)],[210,75]),
[iquote('0:SSi:210.1,75.0')] ).
cnf(215,plain,
~ subgroup_member(a),
inference(mrr,[status(thm)],[214,9]),
[iquote('0:MRR:214.1,9.0')] ).
cnf(375,plain,
( ~ product(u,inverse(v),w)
| product(w,v,u) ),
inference(res,[status(thm),theory(equality)],[15,108]),
[iquote('0:Res:15.0,108.0')] ).
cnf(604,plain,
( ~ product(u,b,a)
| product(u,c,identity) ),
inference(res,[status(thm),theory(equality)],[10,126]),
[iquote('0:Res:10.0,126.0')] ).
cnf(663,plain,
( ~ product(u,b,a)
| equal(inverse(c),u) ),
inference(res,[status(thm),theory(equality)],[604,44]),
[iquote('0:Res:604.1,44.0')] ).
cnf(1339,plain,
product(multiply(u,inverse(v)),v,u),
inference(res,[status(thm),theory(equality)],[17,375]),
[iquote('0:Res:17.0,375.0')] ).
cnf(1427,plain,
equal(multiply(a,inverse(b)),inverse(c)),
inference(res,[status(thm),theory(equality)],[1339,663]),
[iquote('0:Res:1339.0,663.0')] ).
cnf(1552,plain,
product(inverse(c),b,a),
inference(spr,[status(thm),theory(equality)],[1427,1339]),
[iquote('0:SpR:1427.0,1339.0')] ).
cnf(1561,plain,
( ~ subgroup_member(inverse(c))
| ~ subgroup_member(b)
| subgroup_member(a) ),
inference(res,[status(thm),theory(equality)],[1552,207]),
[iquote('0:Res:1552.0,207.2')] ).
cnf(1572,plain,
subgroup_member(a),
inference(ssi,[status(thm)],[1561,8,2,75]),
[iquote('0:SSi:1561.1,1561.0,8.0,2.1,75.0')] ).
cnf(1573,plain,
$false,
inference(mrr,[status(thm)],[1572,215]),
[iquote('0:MRR:1572.0,215.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13 % Problem : GRP040-4 : TPTP v8.1.0. Released v1.0.0.
% 0.04/0.14 % Command : run_spass %d %s
% 0.14/0.35 % Computer : n018.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 600
% 0.14/0.35 % DateTime : Mon Jun 13 23:05:13 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.49/0.67
% 0.49/0.67 SPASS V 3.9
% 0.49/0.67 SPASS beiseite: Proof found.
% 0.49/0.67 % SZS status Theorem
% 0.49/0.67 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.49/0.67 SPASS derived 1319 clauses, backtracked 0 clauses, performed 0 splits and kept 652 clauses.
% 0.49/0.67 SPASS allocated 76652 KBytes.
% 0.49/0.67 SPASS spent 0:00:00.30 on the problem.
% 0.49/0.67 0:00:00.04 for the input.
% 0.49/0.67 0:00:00.00 for the FLOTTER CNF translation.
% 0.49/0.67 0:00:00.02 for inferences.
% 0.49/0.67 0:00:00.00 for the backtracking.
% 0.49/0.67 0:00:00.22 for the reduction.
% 0.49/0.67
% 0.49/0.67
% 0.49/0.67 Here is a proof with depth 6, length 46 :
% 0.49/0.67 % SZS output start Refutation
% See solution above
% 0.49/0.67 Formulae used in the proof : closure_of_inverse product_right_cancellation product_left_cancellation an_element_in_O2 property_of_O2 a_in_subgroup b_is_in_subgroup d_in_subgroup b_times_a_inverse_is_c a_times_c_is_d prove_inverse_is_self_cancelling right_identity left_inverse right_inverse total_function1 total_function2 associativity1 associativity2 closure_of_product_and_inverse
% 0.49/0.67
%------------------------------------------------------------------------------