TSTP Solution File: GRP605-1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP605-1 : TPTP v8.1.0. Released v2.6.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n010.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 11:48:15 EDT 2022
% Result : Unsatisfiable 0.38s 0.58s
% Output : Refutation 0.38s
% Verified :
% SZS Type : Refutation
% Derivation depth : 28
% Number of leaves : 3
% Syntax : Number of clauses : 51 ( 51 unt; 0 nHn; 51 RR)
% Number of literals : 51 ( 0 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 6 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
equal(double_divide(inverse(double_divide(u,inverse(double_divide(inverse(v),double_divide(u,w))))),w),v),
file('GRP605-1.p',unknown),
[] ).
cnf(2,axiom,
equal(inverse(double_divide(u,v)),multiply(v,u)),
file('GRP605-1.p',unknown),
[] ).
cnf(3,axiom,
~ equal(multiply(inverse(b1),b1),multiply(inverse(a1),a1)),
file('GRP605-1.p',unknown),
[] ).
cnf(4,plain,
equal(double_divide(multiply(multiply(double_divide(u,v),inverse(w)),u),v),w),
inference(rew,[status(thm),theory(equality)],[2,1]),
[iquote('0:Rew:2.0,1.0,2.0,1.0')] ).
cnf(6,plain,
equal(multiply(u,multiply(multiply(double_divide(v,u),inverse(w)),v)),inverse(w)),
inference(spr,[status(thm),theory(equality)],[4,2]),
[iquote('0:SpR:4.0,2.0')] ).
cnf(7,plain,
equal(double_divide(multiply(multiply(u,inverse(v)),multiply(multiply(double_divide(w,x),inverse(u)),w)),x),v),
inference(spr,[status(thm),theory(equality)],[4]),
[iquote('0:SpR:4.0,4.0')] ).
cnf(9,plain,
equal(double_divide(multiply(multiply(double_divide(u,v),multiply(w,x)),u),v),double_divide(x,w)),
inference(spr,[status(thm),theory(equality)],[2,4]),
[iquote('0:SpR:2.0,4.0')] ).
cnf(11,plain,
equal(multiply(u,multiply(multiply(double_divide(v,u),multiply(w,x)),v)),multiply(w,x)),
inference(spr,[status(thm),theory(equality)],[2,6]),
[iquote('0:SpR:2.0,6.0')] ).
cnf(20,plain,
equal(double_divide(u,multiply(double_divide(u,double_divide(v,w)),inverse(x))),double_divide(multiply(inverse(x),v),w)),
inference(spr,[status(thm),theory(equality)],[6,9]),
[iquote('0:SpR:6.0,9.0')] ).
cnf(44,plain,
equal(double_divide(inverse(u),multiply(u,inverse(v))),v),
inference(spr,[status(thm),theory(equality)],[6,7]),
[iquote('0:SpR:6.0,7.0')] ).
cnf(45,plain,
equal(multiply(multiply(u,inverse(v)),inverse(u)),inverse(v)),
inference(spr,[status(thm),theory(equality)],[44,2]),
[iquote('0:SpR:44.0,2.0')] ).
cnf(55,plain,
equal(double_divide(inverse(multiply(u,inverse(v))),inverse(v)),u),
inference(spr,[status(thm),theory(equality)],[45,44]),
[iquote('0:SpR:45.0,44.0')] ).
cnf(56,plain,
equal(multiply(inverse(u),inverse(multiply(v,inverse(u)))),inverse(v)),
inference(spr,[status(thm),theory(equality)],[45]),
[iquote('0:SpR:45.0,45.0')] ).
cnf(95,plain,
equal(double_divide(inverse(inverse(u)),inverse(v)),multiply(v,inverse(u))),
inference(spr,[status(thm),theory(equality)],[45,55]),
[iquote('0:SpR:45.0,55.0')] ).
cnf(98,plain,
equal(multiply(inverse(u),inverse(inverse(v))),inverse(multiply(u,inverse(v)))),
inference(spr,[status(thm),theory(equality)],[56,45]),
[iquote('0:SpR:56.0,45.0')] ).
cnf(120,plain,
equal(double_divide(inverse(multiply(u,v)),inverse(w)),multiply(w,multiply(u,v))),
inference(spr,[status(thm),theory(equality)],[2,95]),
[iquote('0:SpR:2.0,95.0')] ).
cnf(121,plain,
equal(multiply(u,multiply(v,inverse(u))),v),
inference(rew,[status(thm),theory(equality)],[120,55]),
[iquote('0:Rew:120.0,55.0')] ).
cnf(123,plain,
equal(multiply(double_divide(inverse(u),u),inverse(v)),inverse(v)),
inference(spr,[status(thm),theory(equality)],[121,6]),
[iquote('0:SpR:121.0,6.0')] ).
cnf(127,plain,
equal(multiply(u,inverse(double_divide(v,w))),multiply(w,multiply(u,v))),
inference(spr,[status(thm),theory(equality)],[121,11]),
[iquote('0:SpR:121.0,11.0')] ).
cnf(139,plain,
equal(multiply(u,multiply(v,w)),multiply(v,multiply(u,w))),
inference(rew,[status(thm),theory(equality)],[2,127]),
[iquote('0:Rew:2.0,127.0')] ).
cnf(179,plain,
equal(double_divide(inverse(double_divide(inverse(u),u)),inverse(v)),v),
inference(spr,[status(thm),theory(equality)],[123,44]),
[iquote('0:SpR:123.0,44.0')] ).
cnf(181,plain,
equal(multiply(inverse(u),inverse(inverse(u))),inverse(double_divide(inverse(v),v))),
inference(spr,[status(thm),theory(equality)],[123,56]),
[iquote('0:SpR:123.0,56.0')] ).
cnf(182,plain,
equal(multiply(u,inverse(u)),double_divide(inverse(v),v)),
inference(spr,[status(thm),theory(equality)],[123,121]),
[iquote('0:SpR:123.0,121.0')] ).
cnf(188,plain,
equal(double_divide(multiply(u,inverse(u)),inverse(v)),v),
inference(rew,[status(thm),theory(equality)],[2,179]),
[iquote('0:Rew:2.0,179.0')] ).
cnf(190,plain,
equal(multiply(inverse(u),inverse(inverse(u))),multiply(v,inverse(v))),
inference(rew,[status(thm),theory(equality)],[2,181]),
[iquote('0:Rew:2.0,181.0')] ).
cnf(191,plain,
equal(inverse(multiply(u,inverse(u))),multiply(v,inverse(v))),
inference(rew,[status(thm),theory(equality)],[98,190]),
[iquote('0:Rew:98.0,190.0')] ).
cnf(205,plain,
equal(multiply(u,double_divide(inverse(v),v)),u),
inference(spr,[status(thm),theory(equality)],[182,121]),
[iquote('0:SpR:182.0,121.0')] ).
cnf(237,plain,
equal(multiply(u,multiply(v,inverse(v))),u),
inference(spr,[status(thm),theory(equality)],[95,205]),
[iquote('0:SpR:95.0,205.0')] ).
cnf(279,plain,
equal(double_divide(u,multiply(double_divide(u,v),inverse(w))),double_divide(multiply(inverse(w),multiply(x,inverse(x))),inverse(v))),
inference(spr,[status(thm),theory(equality)],[188,20]),
[iquote('0:SpR:188.0,20.0')] ).
cnf(280,plain,
equal(double_divide(multiply(multiply(u,inverse(v)),multiply(multiply(w,inverse(u)),multiply(x,inverse(x)))),inverse(w)),v),
inference(spr,[status(thm),theory(equality)],[188,7]),
[iquote('0:SpR:188.0,7.0')] ).
cnf(292,plain,
equal(double_divide(u,multiply(double_divide(u,v),inverse(w))),double_divide(inverse(w),inverse(v))),
inference(rew,[status(thm),theory(equality)],[237,279]),
[iquote('0:Rew:237.0,279.0')] ).
cnf(293,plain,
equal(double_divide(inverse(u),inverse(double_divide(v,w))),double_divide(multiply(inverse(u),v),w)),
inference(rew,[status(thm),theory(equality)],[292,20]),
[iquote('0:Rew:292.0,20.0')] ).
cnf(299,plain,
equal(double_divide(multiply(inverse(u),v),w),double_divide(inverse(u),multiply(w,v))),
inference(rew,[status(thm),theory(equality)],[2,293]),
[iquote('0:Rew:2.0,293.0')] ).
cnf(322,plain,
equal(double_divide(multiply(multiply(u,inverse(v)),multiply(w,inverse(u))),inverse(w)),v),
inference(rew,[status(thm),theory(equality)],[237,280]),
[iquote('0:Rew:237.0,280.0')] ).
cnf(431,plain,
equal(inverse(double_divide(inverse(u),multiply(v,w))),multiply(v,multiply(inverse(u),w))),
inference(spr,[status(thm),theory(equality)],[299,2]),
[iquote('0:SpR:299.0,2.0')] ).
cnf(438,plain,
equal(double_divide(multiply(multiply(u,v),w),x),double_divide(multiply(u,v),multiply(x,w))),
inference(spr,[status(thm),theory(equality)],[2,299]),
[iquote('0:SpR:2.0,299.0')] ).
cnf(448,plain,
equal(multiply(multiply(u,v),inverse(w)),multiply(u,multiply(inverse(w),v))),
inference(rew,[status(thm),theory(equality)],[2,431]),
[iquote('0:Rew:2.0,431.0')] ).
cnf(449,plain,
equal(multiply(u,multiply(inverse(u),inverse(v))),inverse(v)),
inference(rew,[status(thm),theory(equality)],[448,45]),
[iquote('0:Rew:448.0,45.0')] ).
cnf(473,plain,
equal(double_divide(multiply(u,inverse(v)),multiply(inverse(w),multiply(w,inverse(u)))),v),
inference(rew,[status(thm),theory(equality)],[438,322]),
[iquote('0:Rew:438.0,322.0')] ).
cnf(490,plain,
equal(double_divide(multiply(u,inverse(v)),inverse(u)),v),
inference(rew,[status(thm),theory(equality)],[449,473,139]),
[iquote('0:Rew:449.0,473.0,139.0,473.0')] ).
cnf(586,plain,
equal(double_divide(multiply(u,multiply(v,inverse(v))),inverse(u)),multiply(w,inverse(w))),
inference(spr,[status(thm),theory(equality)],[191,490]),
[iquote('0:SpR:191.0,490.0')] ).
cnf(607,plain,
equal(multiply(u,inverse(multiply(v,inverse(v)))),u),
inference(spr,[status(thm),theory(equality)],[191,237]),
[iquote('0:SpR:191.0,237.0')] ).
cnf(653,plain,
equal(double_divide(u,inverse(u)),multiply(v,inverse(v))),
inference(rew,[status(thm),theory(equality)],[237,586]),
[iquote('0:Rew:237.0,586.0')] ).
cnf(871,plain,
equal(inverse(multiply(u,inverse(u))),multiply(inverse(v),v)),
inference(spr,[status(thm),theory(equality)],[653,2]),
[iquote('0:SpR:653.0,2.0')] ).
cnf(888,plain,
equal(multiply(u,inverse(double_divide(v,inverse(v)))),u),
inference(spr,[status(thm),theory(equality)],[653,607]),
[iquote('0:SpR:653.0,607.0')] ).
cnf(909,plain,
equal(multiply(u,multiply(inverse(v),v)),u),
inference(rew,[status(thm),theory(equality)],[2,888]),
[iquote('0:Rew:2.0,888.0')] ).
cnf(1076,plain,
equal(inverse(inverse(u)),u),
inference(spr,[status(thm),theory(equality)],[909,121]),
[iquote('0:SpR:909.0,121.0')] ).
cnf(1090,plain,
equal(multiply(u,inverse(v)),double_divide(v,inverse(u))),
inference(rew,[status(thm),theory(equality)],[1076,95]),
[iquote('0:Rew:1076.0,95.0')] ).
cnf(1160,plain,
equal(inverse(double_divide(u,inverse(u))),multiply(inverse(v),v)),
inference(rew,[status(thm),theory(equality)],[1090,871]),
[iquote('0:Rew:1090.0,871.0')] ).
cnf(1218,plain,
equal(multiply(inverse(u),u),multiply(inverse(v),v)),
inference(rew,[status(thm),theory(equality)],[2,1160]),
[iquote('0:Rew:2.0,1160.0')] ).
cnf(1219,plain,
$false,
inference(unc,[status(thm)],[1218,3]),
[iquote('0:UnC:1218.0,3.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP605-1 : TPTP v8.1.0. Released v2.6.0.
% 0.07/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n010.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 07:23:40 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.38/0.58
% 0.38/0.58 SPASS V 3.9
% 0.38/0.58 SPASS beiseite: Proof found.
% 0.38/0.58 % SZS status Theorem
% 0.38/0.58 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.38/0.58 SPASS derived 908 clauses, backtracked 0 clauses, performed 0 splits and kept 366 clauses.
% 0.38/0.58 SPASS allocated 64954 KBytes.
% 0.38/0.58 SPASS spent 0:00:00.23 on the problem.
% 0.38/0.58 0:00:00.03 for the input.
% 0.38/0.58 0:00:00.00 for the FLOTTER CNF translation.
% 0.38/0.58 0:00:00.01 for inferences.
% 0.38/0.58 0:00:00.00 for the backtracking.
% 0.38/0.58 0:00:00.17 for the reduction.
% 0.38/0.58
% 0.38/0.58
% 0.38/0.58 Here is a proof with depth 11, length 51 :
% 0.38/0.58 % SZS output start Refutation
% See solution above
% 0.38/0.58 Formulae used in the proof : single_axiom multiply prove_these_axioms_1
% 0.38/0.58
%------------------------------------------------------------------------------