TSTP Solution File: GRP539-1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP539-1 : TPTP v8.1.0. Released v2.6.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n008.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 11:47:57 EDT 2022
% Result : Unsatisfiable 0.18s 0.52s
% Output : Refutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 5
% Syntax : Number of clauses : 55 ( 55 unt; 0 nHn; 55 RR)
% Number of literals : 55 ( 0 equ; 5 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(divide(divide(u,v),divide(divide(u,w),v)),w),
file('GRP539-1.p',unknown),
[] ).
cnf(2,axiom,
equal(divide(u,divide(divide(v,v),w)),multiply(u,w)),
file('GRP539-1.p',unknown),
[] ).
cnf(3,axiom,
equal(divide(divide(u,u),v),inverse(v)),
file('GRP539-1.p',unknown),
[] ).
cnf(4,axiom,
equal(divide(u,u),identity),
file('GRP539-1.p',unknown),
[] ).
cnf(5,axiom,
~ equal(multiply(multiply(a3,b3),c3),multiply(a3,multiply(b3,c3))),
file('GRP539-1.p',unknown),
[] ).
cnf(6,plain,
equal(divide(identity,u),inverse(u)),
inference(rew,[status(thm),theory(equality)],[4,3]),
[iquote('0:Rew:4.0,3.0')] ).
cnf(7,plain,
equal(divide(u,inverse(v)),multiply(u,v)),
inference(rew,[status(thm),theory(equality)],[6,2,4]),
[iquote('0:Rew:6.0,2.0,4.0,2.0')] ).
cnf(9,plain,
equal(inverse(identity),identity),
inference(spr,[status(thm),theory(equality)],[6,4]),
[iquote('0:SpR:6.0,4.0')] ).
cnf(13,plain,
equal(multiply(identity,u),inverse(inverse(u))),
inference(spr,[status(thm),theory(equality)],[7,6]),
[iquote('0:SpR:7.0,6.0')] ).
cnf(15,plain,
equal(divide(u,identity),multiply(u,identity)),
inference(spr,[status(thm),theory(equality)],[9,7]),
[iquote('0:SpR:9.0,7.0')] ).
cnf(20,plain,
equal(divide(divide(u,v),divide(identity,v)),u),
inference(spr,[status(thm),theory(equality)],[4,1]),
[iquote('0:SpR:4.0,1.0')] ).
cnf(23,plain,
equal(divide(divide(u,divide(u,v)),identity),v),
inference(spr,[status(thm),theory(equality)],[4,1]),
[iquote('0:SpR:4.0,1.0')] ).
cnf(24,plain,
equal(divide(divide(u,inverse(v)),multiply(divide(u,w),v)),w),
inference(spr,[status(thm),theory(equality)],[7,1]),
[iquote('0:SpR:7.0,1.0')] ).
cnf(25,plain,
equal(divide(identity,divide(divide(u,v),u)),v),
inference(spr,[status(thm),theory(equality)],[4,1]),
[iquote('0:SpR:4.0,1.0')] ).
cnf(28,plain,
equal(multiply(divide(u,v),v),u),
inference(rew,[status(thm),theory(equality)],[7,20,6]),
[iquote('0:Rew:7.0,20.0,6.0,20.0')] ).
cnf(29,plain,
equal(multiply(divide(u,divide(u,v)),identity),v),
inference(rew,[status(thm),theory(equality)],[15,23]),
[iquote('0:Rew:15.0,23.0')] ).
cnf(30,plain,
equal(inverse(divide(divide(u,v),u)),v),
inference(rew,[status(thm),theory(equality)],[6,25]),
[iquote('0:Rew:6.0,25.0')] ).
cnf(33,plain,
equal(divide(multiply(u,v),multiply(divide(u,w),v)),w),
inference(rew,[status(thm),theory(equality)],[7,24]),
[iquote('0:Rew:7.0,24.0')] ).
cnf(52,plain,
equal(multiply(identity,u),u),
inference(spr,[status(thm),theory(equality)],[4,28]),
[iquote('0:SpR:4.0,28.0')] ).
cnf(54,plain,
equal(multiply(multiply(u,v),inverse(v)),u),
inference(spr,[status(thm),theory(equality)],[7,28]),
[iquote('0:SpR:7.0,28.0')] ).
cnf(57,plain,
equal(inverse(inverse(u)),u),
inference(rew,[status(thm),theory(equality)],[13,52]),
[iquote('0:Rew:13.0,52.0')] ).
cnf(61,plain,
equal(multiply(u,inverse(v)),divide(u,v)),
inference(spr,[status(thm),theory(equality)],[57,7]),
[iquote('0:SpR:57.0,7.0')] ).
cnf(64,plain,
equal(divide(multiply(u,v),v),u),
inference(rew,[status(thm),theory(equality)],[61,54]),
[iquote('0:Rew:61.0,54.0')] ).
cnf(85,plain,
equal(divide(divide(u,v),u),inverse(v)),
inference(spr,[status(thm),theory(equality)],[30,57]),
[iquote('0:SpR:30.0,57.0')] ).
cnf(89,plain,
equal(inverse(divide(inverse(u),identity)),u),
inference(spr,[status(thm),theory(equality)],[6,30]),
[iquote('0:SpR:6.0,30.0')] ).
cnf(97,plain,
equal(inverse(multiply(inverse(u),identity)),u),
inference(rew,[status(thm),theory(equality)],[15,89]),
[iquote('0:Rew:15.0,89.0')] ).
cnf(104,plain,
equal(multiply(inverse(u),identity),inverse(u)),
inference(spr,[status(thm),theory(equality)],[97,57]),
[iquote('0:SpR:97.0,57.0')] ).
cnf(121,plain,
equal(multiply(u,identity),u),
inference(spr,[status(thm),theory(equality)],[57,104]),
[iquote('0:SpR:57.0,104.0')] ).
cnf(124,plain,
equal(divide(u,divide(u,v)),v),
inference(rew,[status(thm),theory(equality)],[121,29]),
[iquote('0:Rew:121.0,29.0')] ).
cnf(144,plain,
equal(multiply(u,divide(v,u)),v),
inference(spr,[status(thm),theory(equality)],[124,28]),
[iquote('0:SpR:124.0,28.0')] ).
cnf(151,plain,
equal(divide(u,multiply(u,v)),inverse(v)),
inference(spr,[status(thm),theory(equality)],[7,124]),
[iquote('0:SpR:7.0,124.0')] ).
cnf(174,plain,
equal(multiply(u,v),multiply(v,u)),
inference(spr,[status(thm),theory(equality)],[64,144]),
[iquote('0:SpR:64.0,144.0')] ).
cnf(176,plain,
~ equal(multiply(c3,multiply(a3,b3)),multiply(a3,multiply(b3,c3))),
inference(rew,[status(thm),theory(equality)],[174,5]),
[iquote('0:Rew:174.0,5.0')] ).
cnf(205,plain,
equal(multiply(inverse(u),v),divide(v,u)),
inference(spr,[status(thm),theory(equality)],[61,174]),
[iquote('0:SpR:61.0,174.0')] ).
cnf(226,plain,
equal(inverse(divide(u,v)),divide(v,u)),
inference(spr,[status(thm),theory(equality)],[124,85]),
[iquote('0:SpR:124.0,85.0')] ).
cnf(238,plain,
equal(divide(inverse(u),v),inverse(multiply(v,u))),
inference(spr,[status(thm),theory(equality)],[151,85]),
[iquote('0:SpR:151.0,85.0')] ).
cnf(261,plain,
equal(divide(inverse(u),v),divide(inverse(v),u)),
inference(spr,[status(thm),theory(equality)],[205,61]),
[iquote('0:SpR:205.0,61.0')] ).
cnf(272,plain,
equal(inverse(multiply(u,v)),inverse(multiply(v,u))),
inference(rew,[status(thm),theory(equality)],[238,261]),
[iquote('0:Rew:238.0,261.0,238.0,261.0')] ).
cnf(294,plain,
equal(multiply(multiply(divide(u,v),w),v),multiply(u,w)),
inference(spr,[status(thm),theory(equality)],[33,144]),
[iquote('0:SpR:33.0,144.0')] ).
cnf(295,plain,
equal(divide(multiply(u,v),w),multiply(divide(u,w),v)),
inference(spr,[status(thm),theory(equality)],[33,124]),
[iquote('0:SpR:33.0,124.0')] ).
cnf(326,plain,
equal(multiply(u,multiply(divide(v,u),w)),multiply(v,w)),
inference(rew,[status(thm),theory(equality)],[174,294]),
[iquote('0:Rew:174.0,294.0')] ).
cnf(374,plain,
equal(divide(u,divide(v,w)),multiply(divide(w,v),u)),
inference(spr,[status(thm),theory(equality)],[226,205]),
[iquote('0:SpR:226.0,205.0')] ).
cnf(437,plain,
equal(divide(u,inverse(multiply(v,w))),multiply(u,multiply(w,v))),
inference(spr,[status(thm),theory(equality)],[272,7]),
[iquote('0:SpR:272.0,7.0')] ).
cnf(471,plain,
equal(multiply(u,multiply(v,w)),multiply(u,multiply(w,v))),
inference(rew,[status(thm),theory(equality)],[7,437]),
[iquote('0:Rew:7.0,437.0')] ).
cnf(646,plain,
equal(multiply(u,multiply(divide(v,divide(u,w)),x)),multiply(w,multiply(v,x))),
inference(spr,[status(thm),theory(equality)],[326]),
[iquote('0:SpR:326.0,326.0')] ).
cnf(678,plain,
equal(multiply(u,multiply(multiply(divide(v,u),w),x)),multiply(v,multiply(w,x))),
inference(rew,[status(thm),theory(equality)],[374,646]),
[iquote('0:Rew:374.0,646.0')] ).
cnf(683,plain,
equal(multiply(u,multiply(multiply(divide(v,u),w),x)),multiply(multiply(v,w),x)),
inference(spr,[status(thm),theory(equality)],[295,326]),
[iquote('0:SpR:295.0,326.0')] ).
cnf(714,plain,
equal(multiply(multiply(u,v),w),multiply(u,multiply(v,w))),
inference(rew,[status(thm),theory(equality)],[678,683]),
[iquote('0:Rew:678.0,683.0')] ).
cnf(1006,plain,
equal(multiply(u,multiply(v,w)),multiply(multiply(w,v),u)),
inference(spr,[status(thm),theory(equality)],[471,174]),
[iquote('0:SpR:471.0,174.0')] ).
cnf(1062,plain,
equal(multiply(u,multiply(v,w)),multiply(w,multiply(v,u))),
inference(rew,[status(thm),theory(equality)],[714,1006]),
[iquote('0:Rew:714.0,1006.0')] ).
cnf(1063,plain,
~ equal(multiply(b3,multiply(a3,c3)),multiply(a3,multiply(b3,c3))),
inference(rew,[status(thm),theory(equality)],[1062,176]),
[iquote('0:Rew:1062.0,176.0')] ).
cnf(1430,plain,
equal(multiply(u,multiply(v,w)),multiply(w,multiply(u,v))),
inference(spr,[status(thm),theory(equality)],[714,174]),
[iquote('0:SpR:714.0,174.0')] ).
cnf(1467,plain,
~ equal(multiply(a3,multiply(c3,b3)),multiply(a3,multiply(b3,c3))),
inference(rew,[status(thm),theory(equality)],[1430,1063]),
[iquote('0:Rew:1430.0,1063.0')] ).
cnf(1479,plain,
~ equal(multiply(a3,multiply(b3,c3)),multiply(a3,multiply(b3,c3))),
inference(rew,[status(thm),theory(equality)],[174,1467]),
[iquote('0:Rew:174.0,1467.0')] ).
cnf(1480,plain,
$false,
inference(obv,[status(thm),theory(equality)],[1479]),
[iquote('0:Obv:1479.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : GRP539-1 : TPTP v8.1.0. Released v2.6.0.
% 0.00/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n008.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 20:56:52 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.18/0.52
% 0.18/0.52 SPASS V 3.9
% 0.18/0.52 SPASS beiseite: Proof found.
% 0.18/0.52 % SZS status Theorem
% 0.18/0.52 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/0.52 SPASS derived 794 clauses, backtracked 0 clauses, performed 0 splits and kept 158 clauses.
% 0.18/0.52 SPASS allocated 64293 KBytes.
% 0.18/0.52 SPASS spent 0:00:00.17 on the problem.
% 0.18/0.52 0:00:00.03 for the input.
% 0.18/0.52 0:00:00.00 for the FLOTTER CNF translation.
% 0.18/0.52 0:00:00.01 for inferences.
% 0.18/0.52 0:00:00.00 for the backtracking.
% 0.18/0.52 0:00:00.11 for the reduction.
% 0.18/0.52
% 0.18/0.52
% 0.18/0.52 Here is a proof with depth 7, length 55 :
% 0.18/0.52 % SZS output start Refutation
% See solution above
% 0.18/0.52 Formulae used in the proof : single_axiom multiply inverse identity prove_these_axioms_3
% 0.18/0.52
%------------------------------------------------------------------------------