%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP012-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n021.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 11:44:44 EDT 2022
% Result : Unsatisfiable 0.22s 0.48s
% Output : Refutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 10
% Syntax : Number of clauses : 25 ( 13 unt; 0 nHn; 25 RR)
% Number of literals : 44 ( 0 equ; 20 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('GRP012-1.p',unknown),
[] ).
cnf(2,axiom,
product(inverse(b),inverse(a),d),
file('GRP012-1.p',unknown),
[] ).
cnf(3,axiom,
~ product(c,d,identity),
file('GRP012-1.p',unknown),
[] ).
cnf(4,axiom,
product(identity,u,u),
file('GRP012-1.p',unknown),
[] ).
cnf(5,axiom,
product(u,identity,u),
file('GRP012-1.p',unknown),
[] ).
cnf(6,axiom,
product(inverse(u),u,identity),
file('GRP012-1.p',unknown),
[] ).
cnf(8,axiom,
product(u,v,multiply(u,v)),
file('GRP012-1.p',unknown),
[] ).
cnf(9,axiom,
( ~ product(u,v,w)
| ~ product(u,v,x)
| equal(x,w) ),
file('GRP012-1.p',unknown),
[] ).
cnf(10,axiom,
( ~ product(u,v,w)
| ~ product(x,v,y)
| ~ product(z,x,u)
| product(z,y,w) ),
file('GRP012-1.p',unknown),
[] ).
cnf(11,axiom,
( ~ product(u,v,w)
| ~ product(x,y,v)
| ~ product(u,x,z)
| product(z,y,w) ),
file('GRP012-1.p',unknown),
[] ).
cnf(16,plain,
( ~ product(u,identity,v)
| equal(v,u) ),
inference(res,[status(thm),theory(equality)],[5,9]),
[iquote('0:Res:5.0,9.0')] ).
cnf(20,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(24,plain,
( ~ product(u,v,w)
| ~ product(inverse(w),u,x)
| product(x,v,identity) ),
inference(res,[status(thm),theory(equality)],[6,11]),
[iquote('0:Res:6.0,11.0')] ).
cnf(40,plain,
( ~ product(u,v,w)
| ~ product(x,u,identity)
| product(x,w,v) ),
inference(res,[status(thm),theory(equality)],[4,10]),
[iquote('0:Res:4.0,10.0')] ).
cnf(133,plain,
( ~ product(u,a,identity)
| product(u,c,b) ),
inference(res,[status(thm),theory(equality)],[1,40]),
[iquote('0:Res:1.0,40.0')] ).
cnf(143,plain,
( ~ product(u,a,identity)
| equal(multiply(u,c),b) ),
inference(res,[status(thm),theory(equality)],[133,20]),
[iquote('0:Res:133.1,20.0')] ).
cnf(163,plain,
equal(multiply(inverse(a),c),b),
inference(res,[status(thm),theory(equality)],[6,143]),
[iquote('0:Res:6.0,143.0')] ).
cnf(164,plain,
product(inverse(a),c,b),
inference(spr,[status(thm),theory(equality)],[163,8]),
[iquote('0:SpR:163.0,8.0')] ).
cnf(207,plain,
( ~ product(inverse(a),u,b)
| product(d,u,identity) ),
inference(res,[status(thm),theory(equality)],[2,24]),
[iquote('0:Res:2.0,24.1')] ).
cnf(286,plain,
product(d,c,identity),
inference(res,[status(thm),theory(equality)],[164,207]),
[iquote('0:Res:164.0,207.0')] ).
cnf(288,plain,
( ~ product(u,d,identity)
| product(u,identity,c) ),
inference(res,[status(thm),theory(equality)],[286,40]),
[iquote('0:Res:286.0,40.0')] ).
cnf(321,plain,
( ~ product(u,d,identity)
| equal(c,u) ),
inference(res,[status(thm),theory(equality)],[288,16]),
[iquote('0:Res:288.1,16.0')] ).
cnf(331,plain,
equal(inverse(d),c),
inference(res,[status(thm),theory(equality)],[6,321]),
[iquote('0:Res:6.0,321.0')] ).
cnf(332,plain,
product(c,d,identity),
inference(spr,[status(thm),theory(equality)],[331,6]),
[iquote('0:SpR:331.0,6.0')] ).
cnf(343,plain,
$false,
inference(mrr,[status(thm)],[332,3]),
[iquote('0:MRR:332.0,3.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.14 % Problem : GRP012-1 : TPTP v8.1.0. Released v1.0.0.
% 0.08/0.14 % Command : run_spass %d %s
% 0.14/0.36 % Computer : n021.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 600
% 0.14/0.36 % DateTime : Tue Jun 14 04:14:42 EDT 2022
% 0.14/0.36 % CPUTime :
% 0.22/0.48
% 0.22/0.48 SPASS V 3.9
% 0.22/0.48 SPASS beiseite: Proof found.
% 0.22/0.48 % SZS status Theorem
% 0.22/0.48 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.22/0.48 SPASS derived 289 clauses, backtracked 0 clauses, performed 0 splits and kept 169 clauses.
% 0.22/0.48 SPASS allocated 63335 KBytes.
% 0.22/0.48 SPASS spent 0:00:00.10 on the problem.
% 0.22/0.48 0:00:00.03 for the input.
% 0.22/0.48 0:00:00.00 for the FLOTTER CNF translation.
% 0.22/0.48 0:00:00.01 for inferences.
% 0.22/0.48 0:00:00.00 for the backtracking.
% 0.22/0.48 0:00:00.03 for the reduction.
% 0.22/0.48
% 0.22/0.48
% 0.22/0.48 Here is a proof with depth 10, length 25 :
% 0.22/0.48 % SZS output start Refutation
% See solution above
% 0.22/0.48 Formulae used in the proof : a_multiply_b_is_c inverse_b_multiply_inverse_a_is_d prove_c_multiply_d_is_identity left_identity right_identity left_inverse total_function1 total_function2 associativity1 associativity2
% 0.22/0.48
%------------------------------------------------------------------------------