TSTP Solution File: GRP012-2 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP012-2 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n027.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 11:44:45 EDT 2022
% Result : Unsatisfiable 0.20s 0.49s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 10
% Syntax : Number of clauses : 35 ( 26 unt; 0 nHn; 35 RR)
% Number of literals : 49 ( 0 equ; 15 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 13 ( 13 usr; 11 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
product(a,b,c),
file('GRP012-2.p',unknown),
[] ).
cnf(2,axiom,
product(inverse(b),inverse(a),d),
file('GRP012-2.p',unknown),
[] ).
cnf(3,axiom,
~ equal(inverse(c),d),
file('GRP012-2.p',unknown),
[] ).
cnf(4,axiom,
product(identity,u,u),
file('GRP012-2.p',unknown),
[] ).
cnf(5,axiom,
product(u,identity,u),
file('GRP012-2.p',unknown),
[] ).
cnf(6,axiom,
product(inverse(u),u,identity),
file('GRP012-2.p',unknown),
[] ).
cnf(7,axiom,
product(u,inverse(u),identity),
file('GRP012-2.p',unknown),
[] ).
cnf(8,axiom,
product(u,v,multiply(u,v)),
file('GRP012-2.p',unknown),
[] ).
cnf(9,axiom,
( ~ product(u,v,w)
| ~ product(u,v,x)
| equal(x,w) ),
file('GRP012-2.p',unknown),
[] ).
cnf(11,axiom,
( ~ product(u,v,w)
| ~ product(x,y,v)
| ~ product(u,x,z)
| product(z,y,w) ),
file('GRP012-2.p',unknown),
[] ).
cnf(17,plain,
( ~ product(identity,u,v)
| equal(v,u) ),
inference(res,[status(thm),theory(equality)],[4,9]),
[iquote('0:Res:4.0,9.0')] ).
cnf(22,plain,
( ~ product(u,v,w)
| equal(w,multiply(u,v)) ),
inference(res,[status(thm),theory(equality)],[8,9]),
[iquote('0:Res:8.0,9.0')] ).
cnf(29,plain,
( ~ product(u,v,identity)
| ~ product(w,u,x)
| product(x,v,w) ),
inference(res,[status(thm),theory(equality)],[5,11]),
[iquote('0:Res:5.0,11.0')] ).
cnf(31,plain,
( ~ product(u,v,inverse(w))
| ~ product(w,u,x)
| product(x,v,identity) ),
inference(res,[status(thm),theory(equality)],[7,11]),
[iquote('0:Res:7.0,11.0')] ).
cnf(37,plain,
equal(multiply(identity,u),u),
inference(res,[status(thm),theory(equality)],[8,17]),
[iquote('0:Res:8.0,17.0')] ).
cnf(127,plain,
( ~ product(u,inverse(v),w)
| product(w,v,u) ),
inference(res,[status(thm),theory(equality)],[6,29]),
[iquote('0:Res:6.0,29.0')] ).
cnf(138,plain,
product(identity,u,inverse(inverse(u))),
inference(res,[status(thm),theory(equality)],[6,127]),
[iquote('0:Res:6.0,127.0')] ).
cnf(140,plain,
product(d,a,inverse(b)),
inference(res,[status(thm),theory(equality)],[2,127]),
[iquote('0:Res:2.0,127.0')] ).
cnf(141,plain,
product(multiply(u,inverse(v)),v,u),
inference(res,[status(thm),theory(equality)],[8,127]),
[iquote('0:Res:8.0,127.0')] ).
cnf(173,plain,
equal(inverse(inverse(u)),u),
inference(res,[status(thm),theory(equality)],[138,17]),
[iquote('0:Res:138.0,17.0')] ).
cnf(207,plain,
product(multiply(u,v),inverse(v),u),
inference(spr,[status(thm),theory(equality)],[173,141]),
[iquote('0:SpR:173.0,141.0')] ).
cnf(251,plain,
equal(multiply(multiply(u,v),inverse(v)),u),
inference(res,[status(thm),theory(equality)],[207,22]),
[iquote('0:Res:207.0,22.0')] ).
cnf(347,plain,
( ~ product(b,d,u)
| product(u,a,identity) ),
inference(res,[status(thm),theory(equality)],[140,31]),
[iquote('0:Res:140.0,31.0')] ).
cnf(371,plain,
product(multiply(b,d),a,identity),
inference(res,[status(thm),theory(equality)],[8,347]),
[iquote('0:Res:8.0,347.0')] ).
cnf(374,plain,
equal(multiply(multiply(b,d),a),identity),
inference(res,[status(thm),theory(equality)],[371,22]),
[iquote('0:Res:371.0,22.0')] ).
cnf(381,plain,
equal(multiply(identity,inverse(a)),multiply(b,d)),
inference(spr,[status(thm),theory(equality)],[374,251]),
[iquote('0:SpR:374.0,251.0')] ).
cnf(383,plain,
equal(multiply(b,d),inverse(a)),
inference(rew,[status(thm),theory(equality)],[37,381]),
[iquote('0:Rew:37.0,381.0')] ).
cnf(404,plain,
product(b,d,inverse(a)),
inference(spr,[status(thm),theory(equality)],[383,8]),
[iquote('0:SpR:383.0,8.0')] ).
cnf(416,plain,
( ~ product(a,b,u)
| product(u,d,identity) ),
inference(res,[status(thm),theory(equality)],[404,31]),
[iquote('0:Res:404.0,31.0')] ).
cnf(623,plain,
product(c,d,identity),
inference(res,[status(thm),theory(equality)],[1,416]),
[iquote('0:Res:1.0,416.0')] ).
cnf(630,plain,
equal(multiply(c,d),identity),
inference(res,[status(thm),theory(equality)],[623,22]),
[iquote('0:Res:623.0,22.0')] ).
cnf(638,plain,
equal(multiply(identity,inverse(d)),c),
inference(spr,[status(thm),theory(equality)],[630,251]),
[iquote('0:SpR:630.0,251.0')] ).
cnf(640,plain,
equal(inverse(d),c),
inference(rew,[status(thm),theory(equality)],[37,638]),
[iquote('0:Rew:37.0,638.0')] ).
cnf(663,plain,
equal(inverse(c),d),
inference(spr,[status(thm),theory(equality)],[640,173]),
[iquote('0:SpR:640.0,173.0')] ).
cnf(678,plain,
$false,
inference(mrr,[status(thm)],[663,3]),
[iquote('0:MRR:663.0,3.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : GRP012-2 : TPTP v8.1.0. Released v1.0.0.
% 0.10/0.13 % Command : run_spass %d %s
% 0.13/0.34 % Computer : n027.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 : Tue Jun 14 10:07:33 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.20/0.49
% 0.20/0.49 SPASS V 3.9
% 0.20/0.49 SPASS beiseite: Proof found.
% 0.20/0.49 % SZS status Theorem
% 0.20/0.49 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.20/0.49 SPASS derived 567 clauses, backtracked 0 clauses, performed 0 splits and kept 297 clauses.
% 0.20/0.49 SPASS allocated 63577 KBytes.
% 0.20/0.49 SPASS spent 0:00:00.14 on the problem.
% 0.20/0.49 0:00:00.04 for the input.
% 0.20/0.49 0:00:00.00 for the FLOTTER CNF translation.
% 0.20/0.49 0:00:00.01 for inferences.
% 0.20/0.49 0:00:00.00 for the backtracking.
% 0.20/0.49 0:00:00.07 for the reduction.
% 0.20/0.49
% 0.20/0.49
% 0.20/0.49 Here is a proof with depth 13, length 35 :
% 0.20/0.49 % SZS output start Refutation
% See solution above
% 0.20/0.49 Formulae used in the proof : a_multiply_b_is_c inverse_b_multiply_inverse_a_is_d prove_c_inverse_equals_d left_identity right_identity left_inverse right_inverse total_function1 total_function2 associativity2
% 0.20/0.49
%------------------------------------------------------------------------------