TSTP Solution File: GRP039-3 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP039-3 : TPTP v8.1.0. Released v1.0.0.
% 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 11:44:56 EDT 2022
% Result : Unsatisfiable 0.59s 0.81s
% Output : Refutation 0.59s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 18
% Syntax : Number of clauses : 50 ( 18 unt; 7 nHn; 50 RR)
% Number of literals : 104 ( 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(1,axiom,
( ~ product(u,v,w)
| ~ product(u,x,w)
| equal(v,x) ),
file('GRP039-3.p',unknown),
[] ).
cnf(2,axiom,
( ~ product(u,v,w)
| ~ product(x,v,w)
| equal(u,x) ),
file('GRP039-3.p',unknown),
[] ).
cnf(3,axiom,
equal(inverse(inverse(u)),u),
file('GRP039-3.p',unknown),
[] ).
cnf(5,axiom,
( ~ subgroup_member(u)
| subgroup_member(inverse(u)) ),
file('GRP039-3.p',unknown),
[] ).
cnf(6,axiom,
( subgroup_member(u)
| subgroup_member(v)
| subgroup_member(element_in_O2(u,v)) ),
file('GRP039-3.p',unknown),
[] ).
cnf(7,axiom,
( subgroup_member(u)
| subgroup_member(v)
| product(u,element_in_O2(u,v),v) ),
file('GRP039-3.p',unknown),
[] ).
cnf(8,axiom,
subgroup_member(b),
file('GRP039-3.p',unknown),
[] ).
cnf(9,axiom,
product(b,inverse(a),c),
file('GRP039-3.p',unknown),
[] ).
cnf(10,axiom,
product(a,c,d),
file('GRP039-3.p',unknown),
[] ).
cnf(11,axiom,
~ subgroup_member(d),
file('GRP039-3.p',unknown),
[] ).
cnf(13,axiom,
product(u,identity,u),
file('GRP039-3.p',unknown),
[] ).
cnf(14,axiom,
product(inverse(u),u,identity),
file('GRP039-3.p',unknown),
[] ).
cnf(15,axiom,
product(u,inverse(u),identity),
file('GRP039-3.p',unknown),
[] ).
cnf(16,axiom,
product(u,v,multiply(u,v)),
file('GRP039-3.p',unknown),
[] ).
cnf(17,axiom,
( ~ product(u,v,w)
| ~ product(u,v,x)
| equal(x,w) ),
file('GRP039-3.p',unknown),
[] ).
cnf(18,axiom,
( ~ product(u,v,w)
| ~ product(x,v,y)
| ~ product(z,x,u)
| product(z,y,w) ),
file('GRP039-3.p',unknown),
[] ).
cnf(19,axiom,
( ~ product(u,v,w)
| ~ product(x,y,v)
| ~ product(u,x,z)
| product(z,y,w) ),
file('GRP039-3.p',unknown),
[] ).
cnf(20,axiom,
( ~ subgroup_member(u)
| ~ subgroup_member(v)
| ~ product(v,inverse(u),w)
| subgroup_member(w) ),
file('GRP039-3.p',unknown),
[] ).
cnf(21,plain,
( ~ subgroup_member(u)
| ~ product(b,inverse(u),v)
| subgroup_member(v) ),
inference(res,[status(thm),theory(equality)],[8,20]),
[iquote('0:Res:8.0,20.0')] ).
cnf(22,plain,
subgroup_member(inverse(b)),
inference(res,[status(thm),theory(equality)],[8,5]),
[iquote('0:Res:8.0,5.0')] ).
cnf(26,plain,
( subgroup_member(u)
| product(u,element_in_O2(u,d),d) ),
inference(res,[status(thm),theory(equality)],[7,11]),
[iquote('0:Res:7.1,11.0')] ).
cnf(27,plain,
( subgroup_member(u)
| subgroup_member(element_in_O2(u,d)) ),
inference(res,[status(thm),theory(equality)],[6,11]),
[iquote('0:Res:6.1,11.0')] ).
cnf(31,plain,
( ~ product(a,u,d)
| equal(u,c) ),
inference(res,[status(thm),theory(equality)],[10,1]),
[iquote('0:Res:10.0,1.0')] ).
cnf(33,plain,
( ~ product(a,c,u)
| equal(d,u) ),
inference(res,[status(thm),theory(equality)],[10,17]),
[iquote('0:Res:10.0,17.0')] ).
cnf(49,plain,
equal(multiply(a,c),d),
inference(res,[status(thm),theory(equality)],[16,33]),
[iquote('0:Res:16.0,33.0')] ).
cnf(54,plain,
( subgroup_member(a)
| equal(element_in_O2(a,d),c) ),
inference(res,[status(thm),theory(equality)],[26,31]),
[iquote('0:Res:26.1,31.0')] ).
cnf(55,plain,
( subgroup_member(a)
| subgroup_member(a)
| subgroup_member(c) ),
inference(spr,[status(thm),theory(equality)],[54,27]),
[iquote('0:SpR:54.1,27.1')] ).
cnf(59,plain,
( subgroup_member(a)
| subgroup_member(c) ),
inference(obv,[status(thm),theory(equality)],[55]),
[iquote('0:Obv:55.0')] ).
cnf(66,plain,
( ~ subgroup_member(a)
| subgroup_member(c) ),
inference(res,[status(thm),theory(equality)],[9,21]),
[iquote('0:Res:9.0,21.1')] ).
cnf(69,plain,
subgroup_member(c),
inference(mrr,[status(thm)],[66,59]),
[iquote('0:MRR:66.0,59.0')] ).
cnf(94,plain,
( ~ product(u,v,identity)
| equal(inverse(v),u) ),
inference(res,[status(thm),theory(equality)],[14,2]),
[iquote('0:Res:14.0,2.0')] ).
cnf(141,plain,
( ~ subgroup_member(inverse(u))
| ~ subgroup_member(v)
| ~ product(v,u,w)
| subgroup_member(w) ),
inference(spl,[status(thm),theory(equality)],[3,20]),
[iquote('0:SpL:3.0,20.2')] ).
cnf(147,plain,
( ~ subgroup_member(u)
| ~ subgroup_member(v)
| subgroup_member(multiply(v,inverse(u))) ),
inference(res,[status(thm),theory(equality)],[16,20]),
[iquote('0:Res:16.0,20.2')] ).
cnf(182,plain,
( ~ product(u,v,identity)
| ~ product(w,u,x)
| product(x,v,w) ),
inference(res,[status(thm),theory(equality)],[13,19]),
[iquote('0:Res:13.0,19.0')] ).
cnf(209,plain,
( ~ product(u,inverse(v),w)
| ~ product(x,u,v)
| product(x,w,identity) ),
inference(res,[status(thm),theory(equality)],[15,18]),
[iquote('0:Res:15.0,18.0')] ).
cnf(336,plain,
( ~ subgroup_member(inverse(u))
| ~ subgroup_member(v)
| subgroup_member(multiply(v,u)) ),
inference(spr,[status(thm),theory(equality)],[3,147]),
[iquote('0:SpR:3.0,147.2')] ).
cnf(344,plain,
( ~ subgroup_member(u)
| ~ subgroup_member(v)
| subgroup_member(multiply(u,v)) ),
inference(sor,[status(thm)],[336,5]),
[iquote('0:SoR:336.0,5.1')] ).
cnf(351,plain,
( ~ subgroup_member(a)
| ~ subgroup_member(c)
| subgroup_member(d) ),
inference(spr,[status(thm),theory(equality)],[49,344]),
[iquote('0:SpR:49.0,344.2')] ).
cnf(356,plain,
( ~ subgroup_member(a)
| subgroup_member(d) ),
inference(ssi,[status(thm)],[351,69]),
[iquote('0:SSi:351.1,69.0')] ).
cnf(357,plain,
~ subgroup_member(a),
inference(mrr,[status(thm)],[356,11]),
[iquote('0:MRR:356.1,11.0')] ).
cnf(520,plain,
( ~ subgroup_member(u)
| ~ product(u,b,v)
| subgroup_member(v) ),
inference(sor,[status(thm)],[141,22]),
[iquote('0:SoR:141.0,22.0')] ).
cnf(718,plain,
( ~ product(u,inverse(v),w)
| product(w,v,u) ),
inference(res,[status(thm),theory(equality)],[14,182]),
[iquote('0:Res:14.0,182.0')] ).
cnf(974,plain,
( ~ product(u,b,a)
| product(u,c,identity) ),
inference(res,[status(thm),theory(equality)],[9,209]),
[iquote('0:Res:9.0,209.0')] ).
cnf(1010,plain,
( ~ product(u,b,a)
| equal(inverse(c),u) ),
inference(res,[status(thm),theory(equality)],[974,94]),
[iquote('0:Res:974.1,94.0')] ).
cnf(2029,plain,
product(multiply(u,inverse(v)),v,u),
inference(res,[status(thm),theory(equality)],[16,718]),
[iquote('0:Res:16.0,718.0')] ).
cnf(2114,plain,
equal(multiply(a,inverse(b)),inverse(c)),
inference(res,[status(thm),theory(equality)],[2029,1010]),
[iquote('0:Res:2029.0,1010.0')] ).
cnf(2235,plain,
product(inverse(c),b,a),
inference(spr,[status(thm),theory(equality)],[2114,2029]),
[iquote('0:SpR:2114.0,2029.0')] ).
cnf(2251,plain,
( ~ subgroup_member(inverse(c))
| subgroup_member(a) ),
inference(res,[status(thm),theory(equality)],[2235,520]),
[iquote('0:Res:2235.0,520.1')] ).
cnf(2256,plain,
subgroup_member(a),
inference(ssi,[status(thm)],[2251,5,69]),
[iquote('0:SSi:2251.0,5.0,69.1')] ).
cnf(2257,plain,
$false,
inference(mrr,[status(thm)],[2256,357]),
[iquote('0:MRR:2256.0,357.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : GRP039-3 : TPTP v8.1.0. Released v1.0.0.
% 0.13/0.13 % Command : run_spass %d %s
% 0.13/0.35 % Computer : n019.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 600
% 0.13/0.35 % DateTime : Mon Jun 13 18:58:39 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.59/0.81
% 0.59/0.81 SPASS V 3.9
% 0.59/0.81 SPASS beiseite: Proof found.
% 0.59/0.81 % SZS status Theorem
% 0.59/0.81 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.59/0.81 SPASS derived 1897 clauses, backtracked 0 clauses, performed 0 splits and kept 918 clauses.
% 0.59/0.81 SPASS allocated 77112 KBytes.
% 0.59/0.81 SPASS spent 0:00:00.44 on the problem.
% 0.59/0.81 0:00:00.04 for the input.
% 0.59/0.81 0:00:00.00 for the FLOTTER CNF translation.
% 0.59/0.81 0:00:00.03 for inferences.
% 0.59/0.81 0:00:00.00 for the backtracking.
% 0.59/0.81 0:00:00.35 for the reduction.
% 0.59/0.81
% 0.59/0.81
% 0.59/0.81 Here is a proof with depth 6, length 50 :
% 0.59/0.81 % SZS output start Refutation
% See solution above
% 0.59/0.81 Formulae used in the proof : product_right_cancellation product_left_cancellation inverse_is_self_cancelling subgroup_member_inverse_are_in_subgroup an_element_in_O2 property_of_O2 b_is_in_subgroup b_times_a_inverse_is_c a_times_c_is_d prove_d_is_in_subgroup right_identity left_inverse right_inverse total_function1 total_function2 associativity1 associativity2 closure_of_product_and_inverse
% 0.59/0.81
%------------------------------------------------------------------------------