TSTP Solution File: GRP013-1 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP013-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n006.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 11:44:46 EDT 2022
% Result : Unsatisfiable 0.18s 0.41s
% Output : Refutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 9
% Syntax : Number of clauses : 21 ( 17 unt; 0 nHn; 21 RR)
% Number of literals : 26 ( 0 equ; 7 neg)
% Maximal clause size : 3 ( 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,
product(u,u,identity),
file('GRP013-1.p',unknown),
[] ).
cnf(2,axiom,
product(a,b,c),
file('GRP013-1.p',unknown),
[] ).
cnf(3,axiom,
product(inverse(a),inverse(b),d),
file('GRP013-1.p',unknown),
[] ).
cnf(4,axiom,
( ~ product(inverse(u),inverse(v),w)
| product(u,w,v) ),
file('GRP013-1.p',unknown),
[] ).
cnf(5,axiom,
~ product(c,d,identity),
file('GRP013-1.p',unknown),
[] ).
cnf(6,axiom,
product(identity,u,u),
file('GRP013-1.p',unknown),
[] ).
cnf(9,axiom,
product(u,inverse(u),identity),
file('GRP013-1.p',unknown),
[] ).
cnf(10,axiom,
product(u,v,multiply(u,v)),
file('GRP013-1.p',unknown),
[] ).
cnf(11,axiom,
( ~ product(u,v,w)
| ~ product(u,v,x)
| equal(x,w) ),
file('GRP013-1.p',unknown),
[] ).
cnf(21,plain,
product(u,multiply(inverse(u),inverse(v)),v),
inference(res,[status(thm),theory(equality)],[10,4]),
[iquote('0:Res:10.0,4.0')] ).
cnf(22,plain,
( ~ product(a,b,u)
| equal(u,c) ),
inference(res,[status(thm),theory(equality)],[2,11]),
[iquote('0:Res:2.0,11.0')] ).
cnf(24,plain,
( ~ product(identity,u,v)
| equal(v,u) ),
inference(res,[status(thm),theory(equality)],[6,11]),
[iquote('0:Res:6.0,11.0')] ).
cnf(57,plain,
equal(inverse(identity),identity),
inference(res,[status(thm),theory(equality)],[9,24]),
[iquote('0:Res:9.0,24.0')] ).
cnf(58,plain,
equal(multiply(identity,u),u),
inference(res,[status(thm),theory(equality)],[10,24]),
[iquote('0:Res:10.0,24.0')] ).
cnf(59,plain,
equal(multiply(inverse(identity),inverse(u)),u),
inference(res,[status(thm),theory(equality)],[21,24]),
[iquote('0:Res:21.0,24.0')] ).
cnf(62,plain,
equal(inverse(u),u),
inference(rew,[status(thm),theory(equality)],[58,59,57]),
[iquote('0:Rew:58.0,59.0,57.0,59.0')] ).
cnf(65,plain,
product(a,inverse(b),d),
inference(rew,[status(thm),theory(equality)],[62,3]),
[iquote('0:Rew:62.0,3.0')] ).
cnf(83,plain,
product(a,b,d),
inference(rew,[status(thm),theory(equality)],[62,65]),
[iquote('0:Rew:62.0,65.0')] ).
cnf(90,plain,
equal(d,c),
inference(res,[status(thm),theory(equality)],[83,22]),
[iquote('0:Res:83.0,22.0')] ).
cnf(93,plain,
~ product(c,c,identity),
inference(rew,[status(thm),theory(equality)],[90,5]),
[iquote('0:Rew:90.0,5.0')] ).
cnf(104,plain,
$false,
inference(mrr,[status(thm)],[93,1]),
[iquote('0:MRR:93.0,1.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : GRP013-1 : TPTP v8.1.0. Released v1.0.0.
% 0.06/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n006.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Mon Jun 13 11:17:26 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.18/0.41
% 0.18/0.41 SPASS V 3.9
% 0.18/0.41 SPASS beiseite: Proof found.
% 0.18/0.41 % SZS status Theorem
% 0.18/0.41 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.18/0.41 SPASS derived 82 clauses, backtracked 0 clauses, performed 0 splits and kept 67 clauses.
% 0.18/0.41 SPASS allocated 63168 KBytes.
% 0.18/0.41 SPASS spent 0:00:00.06 on the problem.
% 0.18/0.41 0:00:00.03 for the input.
% 0.18/0.41 0:00:00.00 for the FLOTTER CNF translation.
% 0.18/0.41 0:00:00.00 for inferences.
% 0.18/0.41 0:00:00.00 for the backtracking.
% 0.18/0.41 0:00:00.01 for the reduction.
% 0.18/0.41
% 0.18/0.41
% 0.18/0.41 Here is a proof with depth 2, length 21 :
% 0.18/0.41 % SZS output start Refutation
% See solution above
% 0.18/0.41 Formulae used in the proof : squareness a_times_b_is_c inverse_a_times_inverse_b_is_d inverses_have_property prove_c_times_d_is_identity left_identity right_inverse total_function1 total_function2
% 0.18/0.41
%------------------------------------------------------------------------------