TSTP Solution File: GRP012-3 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP012-3 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n017.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 0.44s 0.62s
% Output : Refutation 0.44s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 9
% Syntax : Number of clauses : 26 ( 11 unt; 0 nHn; 26 RR)
% Number of literals : 50 ( 0 equ; 30 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 : 11 ( 11 usr; 9 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
~ equal(multiply(inverse(b),inverse(a)),inverse(multiply(a,b))),
file('GRP012-3.p',unknown),
[] ).
cnf(2,axiom,
product(identity,u,u),
file('GRP012-3.p',unknown),
[] ).
cnf(3,axiom,
product(u,identity,u),
file('GRP012-3.p',unknown),
[] ).
cnf(4,axiom,
product(inverse(u),u,identity),
file('GRP012-3.p',unknown),
[] ).
cnf(5,axiom,
product(u,inverse(u),identity),
file('GRP012-3.p',unknown),
[] ).
cnf(6,axiom,
product(u,v,multiply(u,v)),
file('GRP012-3.p',unknown),
[] ).
cnf(7,axiom,
( ~ product(u,v,w)
| ~ product(u,v,x)
| equal(x,w) ),
file('GRP012-3.p',unknown),
[] ).
cnf(8,axiom,
( ~ product(u,v,w)
| ~ product(x,v,y)
| ~ product(z,x,u)
| product(z,y,w) ),
file('GRP012-3.p',unknown),
[] ).
cnf(9,axiom,
( ~ product(u,v,w)
| ~ product(x,y,v)
| ~ product(u,x,z)
| product(z,y,w) ),
file('GRP012-3.p',unknown),
[] ).
cnf(10,plain,
( ~ product(u,v,inverse(multiply(a,b)))
| ~ product(u,v,multiply(inverse(b),inverse(a))) ),
inference(res,[status(thm),theory(equality)],[7,1]),
[iquote('0:Res:7.2,1.0')] ).
cnf(25,plain,
( ~ product(u,v,identity)
| ~ product(w,u,x)
| product(x,v,w) ),
inference(res,[status(thm),theory(equality)],[3,9]),
[iquote('0:Res:3.0,9.0')] ).
cnf(26,plain,
( ~ product(u,v,w)
| ~ product(inverse(w),u,x)
| product(x,v,identity) ),
inference(res,[status(thm),theory(equality)],[4,9]),
[iquote('0:Res:4.0,9.0')] ).
cnf(27,plain,
( ~ product(u,v,inverse(w))
| ~ product(w,u,x)
| product(x,v,identity) ),
inference(res,[status(thm),theory(equality)],[5,9]),
[iquote('0:Res:5.0,9.0')] ).
cnf(42,plain,
( ~ product(u,v,w)
| ~ product(x,u,identity)
| product(x,w,v) ),
inference(res,[status(thm),theory(equality)],[2,8]),
[iquote('0:Res:2.0,8.0')] ).
cnf(98,plain,
( ~ product(u,inverse(v),w)
| product(w,v,u) ),
inference(res,[status(thm),theory(equality)],[4,25]),
[iquote('0:Res:4.0,25.0')] ).
cnf(144,plain,
( ~ product(u,v,identity)
| product(u,identity,inverse(v)) ),
inference(res,[status(thm),theory(equality)],[5,42]),
[iquote('0:Res:5.0,42.0')] ).
cnf(145,plain,
( ~ product(u,v,identity)
| product(u,multiply(v,w),w) ),
inference(res,[status(thm),theory(equality)],[6,42]),
[iquote('0:Res:6.0,42.0')] ).
cnf(274,plain,
( ~ product(u,v,w)
| product(multiply(inverse(w),u),v,identity) ),
inference(res,[status(thm),theory(equality)],[6,26]),
[iquote('0:Res:6.0,26.1')] ).
cnf(330,plain,
( ~ product(u,identity,v)
| product(v,inverse(u),identity) ),
inference(res,[status(thm),theory(equality)],[2,27]),
[iquote('0:Res:2.0,27.0')] ).
cnf(399,plain,
( ~ product(u,identity,v)
| product(identity,u,v) ),
inference(res,[status(thm),theory(equality)],[330,98]),
[iquote('0:Res:330.1,98.0')] ).
cnf(427,plain,
( ~ product(u,v,identity)
| product(identity,u,inverse(v)) ),
inference(res,[status(thm),theory(equality)],[144,399]),
[iquote('0:Res:144.1,399.0')] ).
cnf(647,plain,
~ product(identity,multiply(inverse(b),inverse(a)),inverse(multiply(a,b))),
inference(res,[status(thm),theory(equality)],[2,10]),
[iquote('0:Res:2.0,10.1')] ).
cnf(1438,plain,
~ product(multiply(inverse(b),inverse(a)),multiply(a,b),identity),
inference(res,[status(thm),theory(equality)],[427,647]),
[iquote('0:Res:427.1,647.0')] ).
cnf(1599,plain,
~ product(inverse(a),multiply(a,b),b),
inference(res,[status(thm),theory(equality)],[274,1438]),
[iquote('0:Res:274.1,1438.0')] ).
cnf(1640,plain,
~ product(inverse(a),a,identity),
inference(res,[status(thm),theory(equality)],[145,1599]),
[iquote('0:Res:145.1,1599.0')] ).
cnf(1641,plain,
$false,
inference(mrr,[status(thm)],[1640,4]),
[iquote('0:MRR:1640.0,4.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : GRP012-3 : TPTP v8.1.0. Released v1.0.0.
% 0.07/0.13 % Command : run_spass %d %s
% 0.13/0.35 % Computer : n017.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 : Tue Jun 14 01:22:08 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.44/0.62
% 0.44/0.62 SPASS V 3.9
% 0.44/0.62 SPASS beiseite: Proof found.
% 0.44/0.62 % SZS status Theorem
% 0.44/0.62 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.44/0.62 SPASS derived 1331 clauses, backtracked 0 clauses, performed 0 splits and kept 455 clauses.
% 0.44/0.62 SPASS allocated 64006 KBytes.
% 0.44/0.62 SPASS spent 0:00:00.26 on the problem.
% 0.44/0.62 0:00:00.04 for the input.
% 0.44/0.62 0:00:00.00 for the FLOTTER CNF translation.
% 0.44/0.62 0:00:00.02 for inferences.
% 0.44/0.62 0:00:00.00 for the backtracking.
% 0.44/0.62 0:00:00.18 for the reduction.
% 0.44/0.62
% 0.44/0.62
% 0.44/0.62 Here is a proof with depth 7, length 26 :
% 0.44/0.62 % SZS output start Refutation
% See solution above
% 0.44/0.62 Formulae used in the proof : prove_inverse_of_product_is_product_of_inverses left_identity right_identity left_inverse right_inverse total_function1 total_function2 associativity1 associativity2
% 0.44/0.62
%------------------------------------------------------------------------------