TSTP Solution File: GRP715-10 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP715-10 : TPTP v8.1.0. Released v8.1.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n019.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 11:49:08 EDT 2022
% Result : Unsatisfiable 1.99s 2.20s
% Output : Refutation 1.99s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 7
% Syntax : Number of clauses : 17 ( 17 unt; 0 nHn; 17 RR)
% Number of literals : 17 ( 0 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 7 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(6,axiom,
equal(mult(mult(mult(u,v),w),v),mult(u,mult(mult(v,w),v))),
file('GRP715-10.p',unknown),
[] ).
cnf(7,axiom,
equal(mult(mult(u,v),v),mult(u,mult(v,v))),
file('GRP715-10.p',unknown),
[] ).
cnf(8,axiom,
equal(mult(u,unit),u),
file('GRP715-10.p',unknown),
[] ).
cnf(9,axiom,
equal(mult(unit,u),u),
file('GRP715-10.p',unknown),
[] ).
cnf(10,axiom,
equal(mult(op_a,op_b),unit),
file('GRP715-10.p',unknown),
[] ).
cnf(11,axiom,
equal(mult(op_b,op_a),unit),
file('GRP715-10.p',unknown),
[] ).
cnf(12,axiom,
~ equal(mult(mult(x0__dfg,op_a),op_b),x0__dfg),
file('GRP715-10.p',unknown),
[] ).
cnf(37,plain,
equal(mult(op_a,mult(op_b,op_b)),mult(unit,op_b)),
inference(spr,[status(thm),theory(equality)],[10,7]),
[iquote('0:SpR:10.0,7.0')] ).
cnf(42,plain,
equal(mult(op_a,mult(op_b,op_b)),op_b),
inference(rew,[status(thm),theory(equality)],[9,37]),
[iquote('0:Rew:9.0,37.0')] ).
cnf(157,plain,
equal(mult(mult(u,mult(mult(v,w),v)),v),mult(mult(mult(u,v),w),mult(v,v))),
inference(spr,[status(thm),theory(equality)],[6,7]),
[iquote('0:SpR:6.0,7.0')] ).
cnf(1580,plain,
equal(mult(mult(mult(u,op_b),op_a),mult(op_b,op_b)),mult(mult(u,mult(unit,op_b)),op_b)),
inference(spr,[status(thm),theory(equality)],[11,157]),
[iquote('0:SpR:11.0,157.0')] ).
cnf(1662,plain,
equal(mult(mult(mult(u,op_b),op_a),mult(op_b,op_b)),mult(u,mult(op_b,op_b))),
inference(rew,[status(thm),theory(equality)],[7,1580,9]),
[iquote('0:Rew:7.0,1580.0,9.0,1580.0')] ).
cnf(7267,plain,
equal(mult(mult(u,mult(op_b,op_b)),op_a),mult(mult(u,op_b),mult(mult(op_a,mult(op_b,op_b)),op_a))),
inference(spr,[status(thm),theory(equality)],[1662,6]),
[iquote('0:SpR:1662.0,6.0')] ).
cnf(7298,plain,
equal(mult(mult(u,mult(op_b,op_b)),op_a),mult(u,op_b)),
inference(rew,[status(thm),theory(equality)],[8,7267,11,42]),
[iquote('0:Rew:8.0,7267.0,11.0,7267.0,42.0,7267.0')] ).
cnf(7364,plain,
equal(mult(mult(u,op_a),op_b),mult(u,mult(mult(op_a,mult(op_b,op_b)),op_a))),
inference(spr,[status(thm),theory(equality)],[7298,6]),
[iquote('0:SpR:7298.0,6.0')] ).
cnf(7398,plain,
equal(mult(mult(u,op_a),op_b),u),
inference(rew,[status(thm),theory(equality)],[8,7364,11,42]),
[iquote('0:Rew:8.0,7364.0,11.0,7364.0,42.0,7364.0')] ).
cnf(7399,plain,
$false,
inference(unc,[status(thm)],[7398,12]),
[iquote('0:UnC:7398.0,12.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : GRP715-10 : TPTP v8.1.0. Released v8.1.0.
% 0.07/0.14 % Command : run_spass %d %s
% 0.13/0.35 % Computer : n019.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 08:20:54 EDT 2022
% 0.13/0.35 % CPUTime :
% 1.99/2.20
% 1.99/2.20 SPASS V 3.9
% 1.99/2.20 SPASS beiseite: Proof found.
% 1.99/2.20 % SZS status Theorem
% 1.99/2.20 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 1.99/2.20 SPASS derived 4163 clauses, backtracked 0 clauses, performed 0 splits and kept 1176 clauses.
% 1.99/2.20 SPASS allocated 75322 KBytes.
% 1.99/2.20 SPASS spent 0:00:01.77 on the problem.
% 1.99/2.20 0:00:00.03 for the input.
% 1.99/2.20 0:00:00.00 for the FLOTTER CNF translation.
% 1.99/2.20 0:00:00.04 for inferences.
% 1.99/2.20 0:00:00.00 for the backtracking.
% 1.99/2.20 0:00:01.67 for the reduction.
% 1.99/2.20
% 1.99/2.20
% 1.99/2.20 Here is a proof with depth 4, length 17 :
% 1.99/2.20 % SZS output start Refutation
% See solution above
% 1.99/2.20 Formulae used in the proof : f06 f07 f08 f09 f10 f11 goal
% 1.99/2.20
%------------------------------------------------------------------------------