TSTP Solution File: GRP003-2 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP003-2 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n008.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 11:44:42 EDT 2022
% Result : Unsatisfiable 1.20s 1.41s
% Output : Refutation 1.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 8
% Syntax : Number of clauses : 30 ( 12 unt; 0 nHn; 30 RR)
% Number of literals : 57 ( 0 equ; 32 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 10 ( 10 usr; 8 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
~ product(a,identity,a),
file('GRP003-2.p',unknown),
[] ).
cnf(2,axiom,
product(identity,u,u),
file('GRP003-2.p',unknown),
[] ).
cnf(3,axiom,
product(inverse(u),u,identity),
file('GRP003-2.p',unknown),
[] ).
cnf(4,axiom,
product(u,v,multiply(u,v)),
file('GRP003-2.p',unknown),
[] ).
cnf(5,axiom,
( ~ product(u,v,w)
| ~ product(u,v,x)
| equalish(x,w) ),
file('GRP003-2.p',unknown),
[] ).
cnf(6,axiom,
( ~ product(u,v,w)
| ~ product(x,v,y)
| ~ product(z,x,u)
| product(z,y,w) ),
file('GRP003-2.p',unknown),
[] ).
cnf(7,axiom,
( ~ product(u,v,w)
| ~ product(x,y,v)
| ~ product(u,x,z)
| product(z,y,w) ),
file('GRP003-2.p',unknown),
[] ).
cnf(8,axiom,
( ~ equalish(u,v)
| ~ product(w,x,u)
| product(w,x,v) ),
file('GRP003-2.p',unknown),
[] ).
cnf(10,plain,
( ~ equalish(u,a)
| ~ product(a,identity,u) ),
inference(res,[status(thm),theory(equality)],[8,1]),
[iquote('0:Res:8.2,1.0')] ).
cnf(12,plain,
( ~ equalish(u,v)
| product(identity,u,v) ),
inference(res,[status(thm),theory(equality)],[2,8]),
[iquote('0:Res:2.0,8.1')] ).
cnf(14,plain,
( ~ equalish(multiply(u,v),w)
| product(u,v,w) ),
inference(res,[status(thm),theory(equality)],[4,8]),
[iquote('0:Res:4.0,8.1')] ).
cnf(18,plain,
( ~ product(identity,u,v)
| equalish(v,u) ),
inference(res,[status(thm),theory(equality)],[2,5]),
[iquote('0:Res:2.0,5.0')] ).
cnf(21,plain,
( ~ product(u,v,w)
| equalish(w,multiply(u,v)) ),
inference(res,[status(thm),theory(equality)],[4,5]),
[iquote('0:Res:4.0,5.0')] ).
cnf(24,plain,
( ~ equalish(u,v)
| equalish(v,u) ),
inference(res,[status(thm),theory(equality)],[12,18]),
[iquote('0:Res:12.1,18.0')] ).
cnf(25,plain,
equalish(multiply(identity,u),u),
inference(res,[status(thm),theory(equality)],[4,18]),
[iquote('0:Res:4.0,18.0')] ).
cnf(27,plain,
equalish(u,multiply(identity,u)),
inference(res,[status(thm),theory(equality)],[25,24]),
[iquote('0:Res:25.0,24.0')] ).
cnf(28,plain,
( ~ product(u,v,w)
| ~ product(identity,u,x)
| product(x,v,w) ),
inference(res,[status(thm),theory(equality)],[2,7]),
[iquote('0:Res:2.0,7.0')] ).
cnf(31,plain,
( ~ product(u,v,w)
| ~ product(x,u,y)
| product(y,v,multiply(x,w)) ),
inference(res,[status(thm),theory(equality)],[4,7]),
[iquote('0:Res:4.0,7.0')] ).
cnf(39,plain,
( ~ product(u,v,w)
| ~ product(x,u,identity)
| product(x,w,v) ),
inference(res,[status(thm),theory(equality)],[2,6]),
[iquote('0:Res:2.0,6.0')] ).
cnf(44,plain,
product(u,v,multiply(identity,multiply(u,v))),
inference(res,[status(thm),theory(equality)],[27,14]),
[iquote('0:Res:27.0,14.0')] ).
cnf(62,plain,
( ~ product(u,v,w)
| equalish(multiply(u,v),w) ),
inference(res,[status(thm),theory(equality)],[21,24]),
[iquote('0:Res:21.1,24.0')] ).
cnf(75,plain,
( ~ product(identity,inverse(u),v)
| product(v,u,identity) ),
inference(res,[status(thm),theory(equality)],[3,28]),
[iquote('0:Res:3.0,28.0')] ).
cnf(98,plain,
( ~ product(u,inverse(v),identity)
| product(u,identity,v) ),
inference(res,[status(thm),theory(equality)],[3,39]),
[iquote('0:Res:3.0,39.0')] ).
cnf(238,plain,
( ~ product(u,identity,v)
| product(v,w,multiply(u,w)) ),
inference(res,[status(thm),theory(equality)],[2,31]),
[iquote('0:Res:2.0,31.0')] ).
cnf(373,plain,
product(multiply(identity,multiply(identity,inverse(u))),u,identity),
inference(res,[status(thm),theory(equality)],[44,75]),
[iquote('0:Res:44.0,75.0')] ).
cnf(586,plain,
( ~ product(u,identity,a)
| ~ equalish(multiply(u,identity),a) ),
inference(res,[status(thm),theory(equality)],[238,10]),
[iquote('0:Res:238.1,10.1')] ).
cnf(598,plain,
~ equalish(multiply(u,identity),a),
inference(mrr,[status(thm)],[586,14]),
[iquote('0:MRR:586.0,14.1')] ).
cnf(820,plain,
product(multiply(identity,multiply(identity,inverse(inverse(u)))),identity,u),
inference(res,[status(thm),theory(equality)],[373,98]),
[iquote('0:Res:373.0,98.0')] ).
cnf(2949,plain,
~ product(u,identity,a),
inference(res,[status(thm),theory(equality)],[62,598]),
[iquote('0:Res:62.1,598.0')] ).
cnf(2958,plain,
$false,
inference(unc,[status(thm)],[2949,820]),
[iquote('0:UnC:2949.0,820.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : GRP003-2 : TPTP v8.1.0. Released v1.0.0.
% 0.11/0.13 % Command : run_spass %d %s
% 0.13/0.33 % Computer : n008.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Tue Jun 14 08:43:22 EDT 2022
% 0.13/0.34 % CPUTime :
% 1.20/1.41
% 1.20/1.41 SPASS V 3.9
% 1.20/1.41 SPASS beiseite: Proof found.
% 1.20/1.41 % SZS status Theorem
% 1.20/1.41 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 1.20/1.41 SPASS derived 2941 clauses, backtracked 0 clauses, performed 0 splits and kept 1930 clauses.
% 1.20/1.41 SPASS allocated 65101 KBytes.
% 1.20/1.41 SPASS spent 0:00:01.05 on the problem.
% 1.20/1.41 0:00:00.04 for the input.
% 1.20/1.41 0:00:00.00 for the FLOTTER CNF translation.
% 1.20/1.41 0:00:00.04 for inferences.
% 1.20/1.41 0:00:00.00 for the backtracking.
% 1.20/1.41 0:00:00.95 for the reduction.
% 1.20/1.41
% 1.20/1.41
% 1.20/1.41 Here is a proof with depth 6, length 30 :
% 1.20/1.41 % SZS output start Refutation
% See solution above
% 1.20/1.41 Formulae used in the proof : prove_right_identity left_identity left_inverse total_function1 total_function2 associativity1 associativity2 product_substitution3
% 1.20/1.41
%------------------------------------------------------------------------------