TSTP Solution File: BOO007-4 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : BOO007-4 : TPTP v8.1.0. Released v1.1.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n022.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 : Thu Jul 14 23:49:23 EDT 2022
% Result : Unsatisfiable 7.21s 7.47s
% Output : Refutation 7.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 9
% Syntax : Number of clauses : 57 ( 57 unt; 0 nHn; 57 RR)
% Number of literals : 57 ( 0 equ; 2 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 6 ( 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(multiply(multiply(a,b),c),multiply(a,multiply(b,c))),
file('BOO007-4.p',unknown),
[] ).
cnf(2,axiom,
equal(add(u,v),add(v,u)),
file('BOO007-4.p',unknown),
[] ).
cnf(3,axiom,
equal(multiply(u,v),multiply(v,u)),
file('BOO007-4.p',unknown),
[] ).
cnf(4,axiom,
equal(multiply(add(u,v),add(u,w)),add(u,multiply(v,w))),
file('BOO007-4.p',unknown),
[] ).
cnf(5,axiom,
equal(add(multiply(u,v),multiply(u,w)),multiply(u,add(v,w))),
file('BOO007-4.p',unknown),
[] ).
cnf(6,axiom,
equal(add(u,additive_identity),u),
file('BOO007-4.p',unknown),
[] ).
cnf(7,axiom,
equal(multiply(u,multiplicative_identity),u),
file('BOO007-4.p',unknown),
[] ).
cnf(8,axiom,
equal(add(u,inverse(u)),multiplicative_identity),
file('BOO007-4.p',unknown),
[] ).
cnf(9,axiom,
equal(multiply(u,inverse(u)),additive_identity),
file('BOO007-4.p',unknown),
[] ).
cnf(10,plain,
~ equal(multiply(c,multiply(a,b)),multiply(a,multiply(b,c))),
inference(rew,[status(thm),theory(equality)],[3,1]),
[iquote('0:Rew:3.0,1.0')] ).
cnf(15,plain,
equal(multiply(multiplicative_identity,u),u),
inference(spr,[status(thm),theory(equality)],[3,7]),
[iquote('0:SpR:3.0,7.0')] ).
cnf(29,plain,
equal(add(additive_identity,u),u),
inference(spr,[status(thm),theory(equality)],[2,6]),
[iquote('0:SpR:2.0,6.0')] ).
cnf(46,plain,
equal(add(multiply(u,v),u),multiply(u,add(v,multiplicative_identity))),
inference(spr,[status(thm),theory(equality)],[7,5]),
[iquote('0:SpR:7.0,5.0')] ).
cnf(47,plain,
equal(multiply(u,add(v,inverse(u))),add(multiply(u,v),additive_identity)),
inference(spr,[status(thm),theory(equality)],[9,5]),
[iquote('0:SpR:9.0,5.0')] ).
cnf(52,plain,
equal(multiply(u,add(inverse(u),v)),add(additive_identity,multiply(u,v))),
inference(spr,[status(thm),theory(equality)],[9,5]),
[iquote('0:SpR:9.0,5.0')] ).
cnf(56,plain,
equal(add(u,multiply(u,v)),multiply(u,add(v,multiplicative_identity))),
inference(rew,[status(thm),theory(equality)],[2,46]),
[iquote('0:Rew:2.0,46.0')] ).
cnf(60,plain,
equal(multiply(u,add(v,inverse(u))),multiply(u,v)),
inference(rew,[status(thm),theory(equality)],[29,47,2]),
[iquote('0:Rew:29.0,47.0,2.0,47.0')] ).
cnf(61,plain,
equal(multiply(u,add(inverse(u),v)),multiply(u,v)),
inference(rew,[status(thm),theory(equality)],[29,52]),
[iquote('0:Rew:29.0,52.0')] ).
cnf(70,plain,
equal(multiply(u,multiplicative_identity),multiply(u,u)),
inference(spr,[status(thm),theory(equality)],[8,60]),
[iquote('0:SpR:8.0,60.0')] ).
cnf(73,plain,
equal(multiply(u,inverse(u)),multiply(u,additive_identity)),
inference(spr,[status(thm),theory(equality)],[29,60]),
[iquote('0:SpR:29.0,60.0')] ).
cnf(74,plain,
equal(multiply(u,u),u),
inference(rew,[status(thm),theory(equality)],[7,70]),
[iquote('0:Rew:7.0,70.0')] ).
cnf(76,plain,
equal(multiply(u,additive_identity),additive_identity),
inference(rew,[status(thm),theory(equality)],[9,73]),
[iquote('0:Rew:9.0,73.0')] ).
cnf(89,plain,
equal(multiply(add(u,v),add(u,w)),add(u,multiply(w,v))),
inference(spr,[status(thm),theory(equality)],[4,3]),
[iquote('0:SpR:4.0,3.0')] ).
cnf(95,plain,
equal(multiply(add(u,v),u),add(u,multiply(v,additive_identity))),
inference(spr,[status(thm),theory(equality)],[6,4]),
[iquote('0:SpR:6.0,4.0')] ).
cnf(96,plain,
equal(add(u,multiply(v,inverse(u))),multiply(add(u,v),multiplicative_identity)),
inference(spr,[status(thm),theory(equality)],[8,4]),
[iquote('0:SpR:8.0,4.0')] ).
cnf(102,plain,
equal(add(u,multiply(inverse(u),v)),multiply(multiplicative_identity,add(u,v))),
inference(spr,[status(thm),theory(equality)],[8,4]),
[iquote('0:SpR:8.0,4.0')] ).
cnf(107,plain,
equal(multiply(u,add(u,v)),u),
inference(rew,[status(thm),theory(equality)],[3,95,6,76]),
[iquote('0:Rew:3.0,95.0,6.0,95.0,76.0,95.0')] ).
cnf(111,plain,
equal(add(u,multiply(v,inverse(u))),add(u,v)),
inference(rew,[status(thm),theory(equality)],[15,96,3]),
[iquote('0:Rew:15.0,96.0,3.0,96.0')] ).
cnf(112,plain,
equal(add(u,multiply(inverse(u),v)),add(u,v)),
inference(rew,[status(thm),theory(equality)],[15,102]),
[iquote('0:Rew:15.0,102.0')] ).
cnf(113,plain,
equal(add(u,multiply(v,w)),add(u,multiply(w,v))),
inference(rew,[status(thm),theory(equality)],[4,89]),
[iquote('0:Rew:4.0,89.0')] ).
cnf(130,plain,
equal(add(u,multiply(u,v)),multiply(u,add(u,v))),
inference(spr,[status(thm),theory(equality)],[74,5]),
[iquote('0:SpR:74.0,5.0')] ).
cnf(131,plain,
equal(add(multiply(u,v),u),multiply(u,add(v,u))),
inference(spr,[status(thm),theory(equality)],[74,5]),
[iquote('0:SpR:74.0,5.0')] ).
cnf(139,plain,
equal(multiply(u,add(v,multiplicative_identity)),u),
inference(rew,[status(thm),theory(equality)],[56,130,107]),
[iquote('0:Rew:56.0,130.0,107.0,130.0')] ).
cnf(140,plain,
equal(add(u,multiply(u,v)),u),
inference(rew,[status(thm),theory(equality)],[139,56]),
[iquote('0:Rew:139.0,56.0')] ).
cnf(141,plain,
equal(add(u,multiply(u,v)),multiply(u,add(v,u))),
inference(rew,[status(thm),theory(equality)],[2,131]),
[iquote('0:Rew:2.0,131.0')] ).
cnf(142,plain,
equal(multiply(u,add(v,u)),u),
inference(rew,[status(thm),theory(equality)],[140,141]),
[iquote('0:Rew:140.0,141.0')] ).
cnf(207,plain,
equal(add(u,multiply(v,u)),u),
inference(spr,[status(thm),theory(equality)],[3,140]),
[iquote('0:SpR:3.0,140.0')] ).
cnf(266,plain,
equal(multiply(u,inverse(inverse(u))),multiply(u,multiplicative_identity)),
inference(spr,[status(thm),theory(equality)],[8,61]),
[iquote('0:SpR:8.0,61.0')] ).
cnf(276,plain,
equal(multiply(u,inverse(inverse(u))),u),
inference(rew,[status(thm),theory(equality)],[7,266]),
[iquote('0:Rew:7.0,266.0')] ).
cnf(292,plain,
equal(add(u,multiply(multiply(v,u),w)),multiply(u,add(u,w))),
inference(spr,[status(thm),theory(equality)],[207,4]),
[iquote('0:SpR:207.0,4.0')] ).
cnf(304,plain,
equal(add(inverse(inverse(u)),u),inverse(inverse(u))),
inference(spr,[status(thm),theory(equality)],[276,207]),
[iquote('0:SpR:276.0,207.0')] ).
cnf(317,plain,
equal(add(u,inverse(inverse(u))),inverse(inverse(u))),
inference(rew,[status(thm),theory(equality)],[2,304]),
[iquote('0:Rew:2.0,304.0')] ).
cnf(322,plain,
equal(add(u,multiply(multiply(v,u),w)),u),
inference(rew,[status(thm),theory(equality)],[107,292]),
[iquote('0:Rew:107.0,292.0')] ).
cnf(374,plain,
equal(add(u,multiply(multiply(v,inverse(u)),w)),multiply(add(u,v),add(u,w))),
inference(spr,[status(thm),theory(equality)],[111,4]),
[iquote('0:SpR:111.0,4.0')] ).
cnf(401,plain,
equal(add(u,multiply(multiply(v,inverse(u)),w)),add(u,multiply(v,w))),
inference(rew,[status(thm),theory(equality)],[4,374]),
[iquote('0:Rew:4.0,374.0')] ).
cnf(494,plain,
equal(add(u,inverse(inverse(u))),add(u,additive_identity)),
inference(spr,[status(thm),theory(equality)],[9,112]),
[iquote('0:SpR:9.0,112.0')] ).
cnf(513,plain,
equal(inverse(inverse(u)),u),
inference(rew,[status(thm),theory(equality)],[317,494,6]),
[iquote('0:Rew:317.0,494.0,6.0,494.0')] ).
cnf(927,plain,
equal(multiply(u,add(inverse(u),multiply(v,w))),multiply(u,multiply(w,v))),
inference(spr,[status(thm),theory(equality)],[113,61]),
[iquote('0:SpR:113.0,61.0')] ).
cnf(989,plain,
equal(multiply(u,multiply(v,w)),multiply(u,multiply(w,v))),
inference(rew,[status(thm),theory(equality)],[61,927]),
[iquote('0:Rew:61.0,927.0')] ).
cnf(2717,plain,
equal(multiply(multiply(multiply(u,v),w),v),multiply(multiply(u,v),w)),
inference(spr,[status(thm),theory(equality)],[322,142]),
[iquote('0:SpR:322.0,142.0')] ).
cnf(2798,plain,
equal(multiply(u,multiply(multiply(v,u),w)),multiply(multiply(v,u),w)),
inference(rew,[status(thm),theory(equality)],[3,2717]),
[iquote('0:Rew:3.0,2717.0')] ).
cnf(9842,plain,
equal(multiply(u,multiply(v,w)),multiply(multiply(w,v),u)),
inference(spr,[status(thm),theory(equality)],[989,3]),
[iquote('0:SpR:989.0,3.0')] ).
cnf(25800,plain,
equal(multiply(u,multiply(multiply(v,inverse(inverse(u))),w)),multiply(u,add(inverse(u),multiply(v,w)))),
inference(spr,[status(thm),theory(equality)],[401,61]),
[iquote('0:SpR:401.0,61.0')] ).
cnf(26032,plain,
equal(multiply(u,multiply(multiply(v,u),w)),multiply(u,multiply(v,w))),
inference(rew,[status(thm),theory(equality)],[513,25800,61]),
[iquote('0:Rew:513.0,25800.0,61.0,25800.0')] ).
cnf(26033,plain,
equal(multiply(multiply(u,v),w),multiply(v,multiply(u,w))),
inference(rew,[status(thm),theory(equality)],[2798,26032]),
[iquote('0:Rew:2798.0,26032.0')] ).
cnf(26125,plain,
equal(multiply(u,multiply(v,w)),multiply(v,multiply(w,u))),
inference(rew,[status(thm),theory(equality)],[26033,9842]),
[iquote('0:Rew:26033.0,9842.0')] ).
cnf(26529,plain,
$false,
inference(unc,[status(thm)],[26125,10]),
[iquote('0:UnC:26125.0,10.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.13 % Problem : BOO007-4 : TPTP v8.1.0. Released v1.1.0.
% 0.13/0.14 % Command : run_spass %d %s
% 0.13/0.35 % Computer : n022.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 : Wed Jun 1 17:49:52 EDT 2022
% 0.13/0.35 % CPUTime :
% 7.21/7.47
% 7.21/7.47 SPASS V 3.9
% 7.21/7.47 SPASS beiseite: Proof found.
% 7.21/7.47 % SZS status Theorem
% 7.21/7.47 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 7.21/7.47 SPASS derived 17922 clauses, backtracked 0 clauses, performed 0 splits and kept 2643 clauses.
% 7.21/7.47 SPASS allocated 82693 KBytes.
% 7.21/7.47 SPASS spent 0:00:06.94 on the problem.
% 7.21/7.47 0:00:00.04 for the input.
% 7.21/7.47 0:00:00.00 for the FLOTTER CNF translation.
% 7.21/7.47 0:00:00.11 for inferences.
% 7.21/7.47 0:00:00.00 for the backtracking.
% 7.21/7.47 0:00:06.77 for the reduction.
% 7.21/7.47
% 7.21/7.47
% 7.21/7.47 Here is a proof with depth 4, length 57 :
% 7.21/7.47 % SZS output start Refutation
% See solution above
% 7.21/7.47 Formulae used in the proof : prove_associativity commutativity_of_add commutativity_of_multiply distributivity1 distributivity2 additive_id1 multiplicative_id1 additive_inverse1 multiplicative_inverse1
% 7.21/7.47
%------------------------------------------------------------------------------