TSTP Solution File: GRP452-1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP452-1 : TPTP v8.1.0. Released v2.6.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n009.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 11:47:32 EDT 2022
% Result : Unsatisfiable 0.19s 0.50s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 4
% Syntax : Number of clauses : 34 ( 34 unt; 0 nHn; 34 RR)
% Number of literals : 34 ( 0 equ; 2 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 7 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
equal(divide(divide(divide(u,u),divide(u,divide(v,divide(divide(divide(u,u),u),w)))),w),v),
file('GRP452-1.p',unknown),
[] ).
cnf(2,axiom,
equal(divide(u,divide(divide(v,v),w)),multiply(u,w)),
file('GRP452-1.p',unknown),
[] ).
cnf(3,axiom,
equal(divide(divide(u,u),v),inverse(v)),
file('GRP452-1.p',unknown),
[] ).
cnf(4,axiom,
~ equal(multiply(multiply(inverse(b2),b2),a2),a2),
file('GRP452-1.p',unknown),
[] ).
cnf(5,plain,
equal(divide(u,inverse(v)),multiply(u,v)),
inference(rew,[status(thm),theory(equality)],[3,2]),
[iquote('0:Rew:3.0,2.0')] ).
cnf(6,plain,
equal(divide(inverse(divide(u,divide(v,divide(inverse(u),w)))),w),v),
inference(rew,[status(thm),theory(equality)],[3,1]),
[iquote('0:Rew:3.0,1.0,3.0,1.0')] ).
cnf(7,plain,
equal(divide(inverse(divide(u,u)),v),inverse(v)),
inference(spr,[status(thm),theory(equality)],[3]),
[iquote('0:SpR:3.0,3.0')] ).
cnf(9,plain,
equal(divide(multiply(inverse(u),u),v),inverse(v)),
inference(spr,[status(thm),theory(equality)],[5,3]),
[iquote('0:SpR:5.0,3.0')] ).
cnf(11,plain,
equal(multiply(divide(u,u),v),inverse(inverse(v))),
inference(spr,[status(thm),theory(equality)],[5,3]),
[iquote('0:SpR:5.0,3.0')] ).
cnf(12,plain,
equal(divide(inverse(inverse(divide(u,u))),v),inverse(v)),
inference(spr,[status(thm),theory(equality)],[7,3]),
[iquote('0:SpR:7.0,3.0')] ).
cnf(18,plain,
equal(multiply(inverse(divide(u,divide(v,divide(inverse(u),inverse(w))))),w),v),
inference(spr,[status(thm),theory(equality)],[6,5]),
[iquote('0:SpR:6.0,5.0')] ).
cnf(19,plain,
equal(divide(inverse(divide(divide(u,divide(v,divide(inverse(u),w))),divide(x,v))),w),x),
inference(spr,[status(thm),theory(equality)],[6]),
[iquote('0:SpR:6.0,6.0')] ).
cnf(23,plain,
equal(divide(inverse(divide(divide(u,u),divide(v,inverse(w)))),w),v),
inference(spr,[status(thm),theory(equality)],[7,6]),
[iquote('0:SpR:7.0,6.0')] ).
cnf(24,plain,
equal(divide(inverse(divide(u,inverse(divide(inverse(u),v)))),v),divide(w,w)),
inference(spr,[status(thm),theory(equality)],[3,6]),
[iquote('0:SpR:3.0,6.0')] ).
cnf(28,plain,
equal(divide(inverse(inverse(multiply(u,v))),v),u),
inference(rew,[status(thm),theory(equality)],[3,23,5]),
[iquote('0:Rew:3.0,23.0,5.0,23.0')] ).
cnf(29,plain,
equal(multiply(inverse(divide(u,divide(v,multiply(inverse(u),w)))),w),v),
inference(rew,[status(thm),theory(equality)],[5,18]),
[iquote('0:Rew:5.0,18.0')] ).
cnf(31,plain,
equal(divide(inverse(multiply(u,divide(inverse(u),v))),v),divide(w,w)),
inference(rew,[status(thm),theory(equality)],[5,24]),
[iquote('0:Rew:5.0,24.0')] ).
cnf(38,plain,
equal(multiply(multiply(inverse(u),u),v),inverse(inverse(v))),
inference(spr,[status(thm),theory(equality)],[9,5]),
[iquote('0:SpR:9.0,5.0')] ).
cnf(42,plain,
~ equal(inverse(inverse(a2)),a2),
inference(rew,[status(thm),theory(equality)],[38,4]),
[iquote('0:Rew:38.0,4.0')] ).
cnf(55,plain,
equal(divide(inverse(inverse(inverse(inverse(u)))),u),divide(v,v)),
inference(spr,[status(thm),theory(equality)],[11,28]),
[iquote('0:SpR:11.0,28.0')] ).
cnf(56,plain,
equal(inverse(divide(u,divide(v,multiply(inverse(u),w)))),divide(inverse(inverse(v)),w)),
inference(spr,[status(thm),theory(equality)],[29,28]),
[iquote('0:SpR:29.0,28.0')] ).
cnf(70,plain,
equal(multiply(divide(inverse(inverse(u)),v),v),u),
inference(rew,[status(thm),theory(equality)],[56,29]),
[iquote('0:Rew:56.0,29.0')] ).
cnf(78,plain,
equal(inverse(inverse(inverse(inverse(u)))),u),
inference(spr,[status(thm),theory(equality)],[70,11]),
[iquote('0:SpR:70.0,11.0')] ).
cnf(82,plain,
equal(divide(u,u),divide(v,v)),
inference(rew,[status(thm),theory(equality)],[78,55]),
[iquote('0:Rew:78.0,55.0')] ).
cnf(345,plain,
equal(divide(inverse(divide(divide(u,divide(v,divide(inverse(u),w))),x)),w),inverse(inverse(multiply(x,v)))),
inference(spr,[status(thm),theory(equality)],[28,19]),
[iquote('0:SpR:28.0,19.0')] ).
cnf(346,plain,
equal(divide(inverse(divide(divide(u,divide(v,divide(inverse(u),w))),divide(x,x))),w),inverse(multiply(y,divide(inverse(y),v)))),
inference(spr,[status(thm),theory(equality)],[31,19]),
[iquote('0:SpR:31.0,19.0')] ).
cnf(432,plain,
equal(inverse(inverse(multiply(divide(u,u),v))),inverse(multiply(w,divide(inverse(w),v)))),
inference(rew,[status(thm),theory(equality)],[345,346]),
[iquote('0:Rew:345.0,346.0')] ).
cnf(433,plain,
equal(inverse(multiply(u,divide(inverse(u),v))),v),
inference(rew,[status(thm),theory(equality)],[78,432,11]),
[iquote('0:Rew:78.0,432.0,11.0,432.0')] ).
cnf(599,plain,
equal(divide(inverse(u),divide(inverse(v),u)),v),
inference(spr,[status(thm),theory(equality)],[433,28]),
[iquote('0:SpR:433.0,28.0')] ).
cnf(612,plain,
equal(inverse(multiply(u,divide(v,v))),inverse(u)),
inference(spr,[status(thm),theory(equality)],[82,433]),
[iquote('0:SpR:82.0,433.0')] ).
cnf(700,plain,
equal(inverse(divide(inverse(u),inverse(divide(v,v)))),u),
inference(spr,[status(thm),theory(equality)],[599,12]),
[iquote('0:SpR:599.0,12.0')] ).
cnf(775,plain,
equal(inverse(multiply(inverse(u),divide(v,v))),u),
inference(rew,[status(thm),theory(equality)],[5,700]),
[iquote('0:Rew:5.0,700.0')] ).
cnf(776,plain,
equal(inverse(inverse(u)),u),
inference(rew,[status(thm),theory(equality)],[612,775]),
[iquote('0:Rew:612.0,775.0')] ).
cnf(777,plain,
$false,
inference(unc,[status(thm)],[776,42]),
[iquote('0:UnC:776.0,42.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GRP452-1 : TPTP v8.1.0. Released v2.6.0.
% 0.03/0.13 % Command : run_spass %d %s
% 0.13/0.34 % Computer : n009.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 : Mon Jun 13 19:35:08 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.19/0.50
% 0.19/0.50 SPASS V 3.9
% 0.19/0.50 SPASS beiseite: Proof found.
% 0.19/0.50 % SZS status Theorem
% 0.19/0.50 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.50 SPASS derived 582 clauses, backtracked 0 clauses, performed 0 splits and kept 194 clauses.
% 0.19/0.50 SPASS allocated 64146 KBytes.
% 0.19/0.50 SPASS spent 0:00:00.15 on the problem.
% 0.19/0.50 0:00:00.04 for the input.
% 0.19/0.50 0:00:00.00 for the FLOTTER CNF translation.
% 0.19/0.50 0:00:00.01 for inferences.
% 0.19/0.50 0:00:00.00 for the backtracking.
% 0.19/0.50 0:00:00.08 for the reduction.
% 0.19/0.50
% 0.19/0.50
% 0.19/0.50 Here is a proof with depth 4, length 34 :
% 0.19/0.50 % SZS output start Refutation
% See solution above
% 0.19/0.50 Formulae used in the proof : single_axiom multiply inverse prove_these_axioms_2
% 0.19/0.50
%------------------------------------------------------------------------------