%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP009-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n013.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 11:44:43 EDT 2022
% Result : Unsatisfiable 0.19s 0.46s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 8
% Syntax : Number of clauses : 21 ( 11 unt; 0 nHn; 21 RR)
% Number of literals : 36 ( 0 equ; 19 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 11 ( 11 usr; 10 con; 0-1 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
product(a,b,identity),
file('GRP009-1.p',unknown),
[] ).
cnf(2,axiom,
product(c,b,identity),
file('GRP009-1.p',unknown),
[] ).
cnf(3,axiom,
~ equal(c,a),
file('GRP009-1.p',unknown),
[] ).
cnf(4,axiom,
product(identity,u,u),
file('GRP009-1.p',unknown),
[] ).
cnf(5,axiom,
product(u,identity,u),
file('GRP009-1.p',unknown),
[] ).
cnf(6,axiom,
product(inverse(u),u,identity),
file('GRP009-1.p',unknown),
[] ).
cnf(9,axiom,
( ~ product(u,v,w)
| ~ product(u,v,x)
| equal(x,w) ),
file('GRP009-1.p',unknown),
[] ).
cnf(10,axiom,
( ~ product(u,v,w)
| ~ product(x,v,y)
| ~ product(z,x,u)
| product(z,y,w) ),
file('GRP009-1.p',unknown),
[] ).
cnf(12,plain,
( ~ product(u,v,a)
| ~ product(u,v,c) ),
inference(res,[status(thm),theory(equality)],[9,3]),
[iquote('0:Res:9.2,3.0')] ).
cnf(21,plain,
( ~ product(u,identity,v)
| equal(v,u) ),
inference(res,[status(thm),theory(equality)],[5,9]),
[iquote('0:Res:5.0,9.0')] ).
cnf(46,plain,
( ~ product(u,b,v)
| ~ product(w,u,a)
| product(w,v,identity) ),
inference(res,[status(thm),theory(equality)],[1,10]),
[iquote('0:Res:1.0,10.0')] ).
cnf(49,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(119,plain,
( ~ product(u,identity,a)
| product(u,b,identity) ),
inference(res,[status(thm),theory(equality)],[4,46]),
[iquote('0:Res:4.0,46.0')] ).
cnf(211,plain,
( ~ product(u,c,identity)
| product(u,identity,b) ),
inference(res,[status(thm),theory(equality)],[2,49]),
[iquote('0:Res:2.0,49.0')] ).
cnf(224,plain,
product(inverse(c),identity,b),
inference(res,[status(thm),theory(equality)],[6,211]),
[iquote('0:Res:6.0,211.0')] ).
cnf(233,plain,
equal(inverse(c),b),
inference(res,[status(thm),theory(equality)],[224,21]),
[iquote('0:Res:224.0,21.0')] ).
cnf(243,plain,
product(b,c,identity),
inference(spr,[status(thm),theory(equality)],[233,6]),
[iquote('0:SpR:233.0,6.0')] ).
cnf(250,plain,
( ~ product(u,b,identity)
| product(u,identity,c) ),
inference(res,[status(thm),theory(equality)],[243,49]),
[iquote('0:Res:243.0,49.0')] ).
cnf(332,plain,
( ~ product(u,b,identity)
| ~ product(u,identity,a) ),
inference(res,[status(thm),theory(equality)],[250,12]),
[iquote('0:Res:250.1,12.1')] ).
cnf(346,plain,
~ product(u,identity,a),
inference(mrr,[status(thm)],[332,119]),
[iquote('0:MRR:332.0,119.1')] ).
cnf(347,plain,
$false,
inference(unc,[status(thm)],[346,5]),
[iquote('0:UnC:346.0,5.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : GRP009-1 : TPTP v8.1.0. Released v1.0.0.
% 0.10/0.12 % Command : run_spass %d %s
% 0.12/0.34 % Computer : n013.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Mon Jun 13 21:23:29 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.19/0.46
% 0.19/0.46 SPASS V 3.9
% 0.19/0.46 SPASS beiseite: Proof found.
% 0.19/0.46 % SZS status Theorem
% 0.19/0.46 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.46 SPASS derived 289 clauses, backtracked 0 clauses, performed 0 splits and kept 174 clauses.
% 0.19/0.46 SPASS allocated 63319 KBytes.
% 0.19/0.46 SPASS spent 0:00:00.10 on the problem.
% 0.19/0.46 0:00:00.04 for the input.
% 0.19/0.46 0:00:00.00 for the FLOTTER CNF translation.
% 0.19/0.46 0:00:00.00 for inferences.
% 0.19/0.46 0:00:00.00 for the backtracking.
% 0.19/0.46 0:00:00.04 for the reduction.
% 0.19/0.46
% 0.19/0.46
% 0.19/0.46 Here is a proof with depth 7, length 21 :
% 0.19/0.46 % SZS output start Refutation
% See solution above
% 0.19/0.46 Formulae used in the proof : a_is_an_inverse_of_b c_is_an_inverse_of_b prove_a_equals_c left_identity right_identity left_inverse total_function2 associativity1
% 0.19/0.46
%------------------------------------------------------------------------------