TSTP Solution File: GRP703-12 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP703-12 : TPTP v8.1.0. Released v8.1.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n023.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 11:49:04 EDT 2022
% Result : Unsatisfiable 0.20s 0.43s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 10
% Syntax : Number of clauses : 20 ( 20 unt; 0 nHn; 20 RR)
% Number of literals : 20 ( 0 equ; 3 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 : 11 ( 11 usr; 8 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
equal(mult(u,ld(u,v)),v),
file('GRP703-12.p',unknown),
[] ).
cnf(2,axiom,
equal(ld(u,mult(u,v)),v),
file('GRP703-12.p',unknown),
[] ).
cnf(3,axiom,
equal(mult(rd(u,v),v),u),
file('GRP703-12.p',unknown),
[] ).
cnf(5,axiom,
equal(mult(u,unit),u),
file('GRP703-12.p',unknown),
[] ).
cnf(6,axiom,
equal(mult(unit,u),u),
file('GRP703-12.p',unknown),
[] ).
cnf(8,axiom,
equal(mult(mult(op_c,u),v),mult(op_c,mult(u,v))),
file('GRP703-12.p',unknown),
[] ).
cnf(10,axiom,
equal(mult(mult(u,op_c),v),mult(u,mult(op_c,v))),
file('GRP703-12.p',unknown),
[] ).
cnf(11,axiom,
equal(ld(u,mult(op_c,u)),op_d),
file('GRP703-12.p',unknown),
[] ).
cnf(12,axiom,
equal(mult(mult(rd(op_c,mult(u,v)),v),u),op_e),
file('GRP703-12.p',unknown),
[] ).
cnf(14,axiom,
~ equal(mult(mult(x2__dfg,op_e),x3__dfg),mult(x2__dfg,mult(op_e,x3__dfg))),
file('GRP703-12.p',unknown),
[] ).
cnf(34,plain,
equal(op_d,op_c),
inference(spr,[status(thm),theory(equality)],[2,11]),
[iquote('0:SpR:2.0,11.0')] ).
cnf(39,plain,
equal(ld(u,mult(op_c,u)),op_c),
inference(rew,[status(thm),theory(equality)],[34,11]),
[iquote('0:Rew:34.0,11.0')] ).
cnf(56,plain,
equal(mult(u,op_c),mult(op_c,u)),
inference(spr,[status(thm),theory(equality)],[39,1]),
[iquote('0:SpR:39.0,1.0')] ).
cnf(61,plain,
equal(mult(rd(op_c,mult(unit,u)),u),op_e),
inference(spr,[status(thm),theory(equality)],[12,5]),
[iquote('0:SpR:12.0,5.0')] ).
cnf(70,plain,
equal(op_e,op_c),
inference(rew,[status(thm),theory(equality)],[3,61,6]),
[iquote('0:Rew:3.0,61.0,6.0,61.0')] ).
cnf(72,plain,
~ equal(mult(mult(x2__dfg,op_c),x3__dfg),mult(x2__dfg,mult(op_c,x3__dfg))),
inference(rew,[status(thm),theory(equality)],[70,14]),
[iquote('0:Rew:70.0,14.0')] ).
cnf(81,plain,
~ equal(mult(x2__dfg,mult(op_c,x3__dfg)),mult(op_c,mult(x2__dfg,x3__dfg))),
inference(rew,[status(thm),theory(equality)],[8,72,56]),
[iquote('0:Rew:8.0,72.0,56.0,72.0')] ).
cnf(117,plain,
equal(mult(mult(u,op_c),v),mult(op_c,mult(u,v))),
inference(spr,[status(thm),theory(equality)],[56,8]),
[iquote('0:SpR:56.0,8.0')] ).
cnf(123,plain,
equal(mult(u,mult(op_c,v)),mult(op_c,mult(u,v))),
inference(rew,[status(thm),theory(equality)],[10,117]),
[iquote('0:Rew:10.0,117.0')] ).
cnf(124,plain,
$false,
inference(unc,[status(thm)],[123,81]),
[iquote('0:UnC:123.0,81.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP703-12 : TPTP v8.1.0. Released v8.1.0.
% 0.07/0.13 % Command : run_spass %d %s
% 0.13/0.34 % Computer : n023.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Tue Jun 14 00:06:51 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.20/0.43
% 0.20/0.43 SPASS V 3.9
% 0.20/0.43 SPASS beiseite: Proof found.
% 0.20/0.43 % SZS status Theorem
% 0.20/0.43 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.20/0.43 SPASS derived 94 clauses, backtracked 0 clauses, performed 0 splits and kept 41 clauses.
% 0.20/0.43 SPASS allocated 63201 KBytes.
% 0.20/0.43 SPASS spent 0:00:00.07 on the problem.
% 0.20/0.43 0:00:00.04 for the input.
% 0.20/0.43 0:00:00.00 for the FLOTTER CNF translation.
% 0.20/0.43 0:00:00.00 for inferences.
% 0.20/0.43 0:00:00.00 for the backtracking.
% 0.20/0.43 0:00:00.00 for the reduction.
% 0.20/0.43
% 0.20/0.43
% 0.20/0.43 Here is a proof with depth 2, length 20 :
% 0.20/0.43 % SZS output start Refutation
% See solution above
% 0.20/0.43 Formulae used in the proof : f01 f02 f03 f05 f06 f08 f10 f11 f12 goal
% 0.20/0.43
%------------------------------------------------------------------------------