TSTP Solution File: BOO025-1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : BOO025-1 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n026.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 23:49:28 EDT 2022
% Result : Unsatisfiable 0.51s 0.71s
% Output : Refutation 0.51s
% Verified :
% SZS Type : Refutation
% Derivation depth : 34
% Number of leaves : 8
% Syntax : Number of clauses : 67 ( 67 unt; 0 nHn; 67 RR)
% Number of literals : 67 ( 0 equ; 3 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 : 10 ( 10 usr; 6 con; 0-3 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
equal(multiply(add(u,v),v),v),
file('BOO025-1.p',unknown),
[] ).
cnf(2,axiom,
equal(add(multiply(u,v),multiply(w,v)),multiply(v,add(u,w))),
file('BOO025-1.p',unknown),
[] ).
cnf(3,axiom,
equal(add(u,inverse(u)),n1),
file('BOO025-1.p',unknown),
[] ).
cnf(4,axiom,
equal(add(multiply(u,inverse(v)),add(multiply(u,w),multiply(inverse(v),w))),pixley(u,v,w)),
file('BOO025-1.p',unknown),
[] ).
cnf(5,axiom,
equal(pixley(u,u,v),v),
file('BOO025-1.p',unknown),
[] ).
cnf(6,axiom,
equal(pixley(u,v,v),u),
file('BOO025-1.p',unknown),
[] ).
cnf(7,axiom,
equal(pixley(u,v,u),u),
file('BOO025-1.p',unknown),
[] ).
cnf(8,axiom,
~ equal(multiply(a,inverse(a)),multiply(b,inverse(b))),
file('BOO025-1.p',unknown),
[] ).
cnf(9,plain,
equal(add(multiply(u,inverse(v)),multiply(w,add(u,inverse(v)))),pixley(u,v,w)),
inference(rew,[status(thm),theory(equality)],[2,4]),
[iquote('0:Rew:2.0,4.0')] ).
cnf(18,plain,
equal(multiply(n1,inverse(u)),inverse(u)),
inference(spr,[status(thm),theory(equality)],[3,1]),
[iquote('0:SpR:3.0,1.0')] ).
cnf(20,plain,
equal(multiply(multiply(u,add(v,w)),multiply(w,u)),multiply(w,u)),
inference(spr,[status(thm),theory(equality)],[2,1]),
[iquote('0:SpR:2.0,1.0')] ).
cnf(22,plain,
equal(multiply(u,add(v,add(w,u))),add(multiply(v,u),u)),
inference(spr,[status(thm),theory(equality)],[1,2]),
[iquote('0:SpR:1.0,2.0')] ).
cnf(23,plain,
equal(add(multiply(u,inverse(v)),inverse(v)),multiply(inverse(v),add(u,n1))),
inference(spr,[status(thm),theory(equality)],[18,2]),
[iquote('0:SpR:18.0,2.0')] ).
cnf(24,plain,
equal(multiply(u,add(add(v,u),w)),add(u,multiply(w,u))),
inference(spr,[status(thm),theory(equality)],[1,2]),
[iquote('0:SpR:1.0,2.0')] ).
cnf(31,plain,
equal(multiply(multiply(inverse(u),add(v,n1)),inverse(u)),inverse(u)),
inference(spr,[status(thm),theory(equality)],[18,20]),
[iquote('0:SpR:18.0,20.0')] ).
cnf(32,plain,
equal(multiply(multiply(u,n1),multiply(inverse(v),u)),multiply(inverse(v),u)),
inference(spr,[status(thm),theory(equality)],[3,20]),
[iquote('0:SpR:3.0,20.0')] ).
cnf(34,plain,
equal(multiply(add(u,v),multiply(v,add(w,add(u,v)))),multiply(v,add(w,add(u,v)))),
inference(spr,[status(thm),theory(equality)],[1,20]),
[iquote('0:SpR:1.0,20.0')] ).
cnf(36,plain,
equal(multiply(add(u,v),add(multiply(w,v),v)),add(multiply(w,v),v)),
inference(rew,[status(thm),theory(equality)],[22,34]),
[iquote('0:Rew:22.0,34.0')] ).
cnf(38,plain,
equal(multiply(pixley(u,v,w),multiply(w,add(u,inverse(v)))),multiply(w,add(u,inverse(v)))),
inference(spr,[status(thm),theory(equality)],[9,1]),
[iquote('0:SpR:9.0,1.0')] ).
cnf(41,plain,
equal(add(multiply(u,inverse(u)),multiply(v,n1)),pixley(u,u,v)),
inference(spr,[status(thm),theory(equality)],[3,9]),
[iquote('0:SpR:3.0,9.0')] ).
cnf(42,plain,
equal(add(multiply(u,inverse(v)),add(u,inverse(v))),pixley(u,v,add(w,add(u,inverse(v))))),
inference(spr,[status(thm),theory(equality)],[1,9]),
[iquote('0:SpR:1.0,9.0')] ).
cnf(45,plain,
equal(add(multiply(u,inverse(u)),multiply(v,n1)),v),
inference(rew,[status(thm),theory(equality)],[5,41]),
[iquote('0:Rew:5.0,41.0')] ).
cnf(50,plain,
equal(add(inverse(n1),multiply(u,n1)),u),
inference(spr,[status(thm),theory(equality)],[18,45]),
[iquote('0:SpR:18.0,45.0')] ).
cnf(54,plain,
equal(add(inverse(n1),n1),add(u,n1)),
inference(spr,[status(thm),theory(equality)],[1,50]),
[iquote('0:SpR:1.0,50.0')] ).
cnf(59,plain,
equal(add(u,n1),add(v,n1)),
inference(spr,[status(thm),theory(equality)],[54]),
[iquote('0:SpR:54.0,54.0')] ).
cnf(90,plain,
equal(multiply(inverse(u),add(v,multiply(inverse(u),add(w,n1)))),add(multiply(v,inverse(u)),inverse(u))),
inference(spr,[status(thm),theory(equality)],[31,2]),
[iquote('0:SpR:31.0,2.0')] ).
cnf(97,plain,
equal(multiply(inverse(u),add(v,multiply(inverse(u),add(w,n1)))),multiply(inverse(u),add(v,n1))),
inference(rew,[status(thm),theory(equality)],[23,90]),
[iquote('0:Rew:23.0,90.0')] ).
cnf(125,plain,
equal(multiply(u,add(v,n1)),add(u,multiply(n1,u))),
inference(spr,[status(thm),theory(equality)],[59,24]),
[iquote('0:SpR:59.0,24.0')] ).
cnf(138,plain,
equal(multiply(u,multiply(v,add(u,inverse(v)))),multiply(v,add(u,inverse(v)))),
inference(spr,[status(thm),theory(equality)],[6,38]),
[iquote('0:SpR:6.0,38.0')] ).
cnf(149,plain,
equal(multiply(multiply(add(u,n1),n1),add(inverse(v),multiply(n1,inverse(v)))),add(inverse(v),multiply(n1,inverse(v)))),
inference(spr,[status(thm),theory(equality)],[125,32]),
[iquote('0:SpR:125.0,32.0')] ).
cnf(159,plain,
equal(multiply(inverse(u),add(v,n1)),add(inverse(u),inverse(u))),
inference(spr,[status(thm),theory(equality)],[18,125]),
[iquote('0:SpR:18.0,125.0')] ).
cnf(165,plain,
equal(multiply(n1,add(inverse(u),inverse(u))),add(inverse(u),inverse(u))),
inference(rew,[status(thm),theory(equality)],[1,149,18]),
[iquote('0:Rew:1.0,149.0,18.0,149.0')] ).
cnf(258,plain,
equal(multiply(inverse(u),pixley(v,u,add(w,add(v,inverse(u))))),add(multiply(multiply(v,inverse(u)),inverse(u)),inverse(u))),
inference(spr,[status(thm),theory(equality)],[42,22]),
[iquote('0:SpR:42.0,22.0')] ).
cnf(277,plain,
equal(multiply(inverse(u),pixley(v,u,add(w,add(v,inverse(u))))),multiply(inverse(u),add(multiply(v,inverse(u)),n1))),
inference(rew,[status(thm),theory(equality)],[23,258]),
[iquote('0:Rew:23.0,258.0')] ).
cnf(278,plain,
equal(multiply(inverse(u),pixley(v,u,add(w,add(v,inverse(u))))),add(inverse(u),inverse(u))),
inference(rew,[status(thm),theory(equality)],[18,277,125]),
[iquote('0:Rew:18.0,277.0,125.0,277.0')] ).
cnf(302,plain,
equal(add(multiply(inverse(u),inverse(u)),add(inverse(u),inverse(u))),pixley(inverse(u),u,n1)),
inference(spr,[status(thm),theory(equality)],[165,9]),
[iquote('0:SpR:165.0,9.0')] ).
cnf(818,plain,
equal(multiply(add(u,v),add(v,v)),add(v,v)),
inference(spr,[status(thm),theory(equality)],[1,36]),
[iquote('0:SpR:1.0,36.0')] ).
cnf(1034,plain,
equal(multiply(u,add(multiply(u,n1),multiply(u,n1))),add(multiply(u,n1),multiply(u,n1))),
inference(spr,[status(thm),theory(equality)],[45,818]),
[iquote('0:SpR:45.0,818.0')] ).
cnf(1052,plain,
equal(multiply(u,multiply(n1,add(u,u))),multiply(n1,add(u,u))),
inference(rew,[status(thm),theory(equality)],[2,1034]),
[iquote('0:Rew:2.0,1034.0')] ).
cnf(1134,plain,
equal(multiply(inverse(u),add(inverse(u),inverse(u))),add(inverse(u),inverse(u))),
inference(spr,[status(thm),theory(equality)],[165,1052]),
[iquote('0:SpR:165.0,1052.0')] ).
cnf(1351,plain,
equal(add(multiply(inverse(u),inverse(u)),add(inverse(u),inverse(u))),pixley(inverse(u),u,inverse(u))),
inference(spr,[status(thm),theory(equality)],[1134,9]),
[iquote('0:SpR:1134.0,9.0')] ).
cnf(1355,plain,
equal(add(multiply(inverse(u),inverse(u)),add(inverse(u),inverse(u))),inverse(u)),
inference(rew,[status(thm),theory(equality)],[7,1351]),
[iquote('0:Rew:7.0,1351.0')] ).
cnf(1356,plain,
equal(pixley(inverse(u),u,n1),inverse(u)),
inference(rew,[status(thm),theory(equality)],[302,1355]),
[iquote('0:Rew:302.0,1355.0')] ).
cnf(1357,plain,
equal(add(multiply(inverse(u),inverse(u)),add(inverse(u),inverse(u))),inverse(u)),
inference(rew,[status(thm),theory(equality)],[1356,302]),
[iquote('0:Rew:1356.0,302.0')] ).
cnf(1429,plain,
equal(multiply(inverse(u),pixley(inverse(u),u,inverse(u))),add(inverse(u),inverse(u))),
inference(spr,[status(thm),theory(equality)],[1357,278]),
[iquote('0:SpR:1357.0,278.0')] ).
cnf(1433,plain,
equal(add(inverse(u),inverse(u)),multiply(inverse(u),inverse(u))),
inference(rew,[status(thm),theory(equality)],[7,1429]),
[iquote('0:Rew:7.0,1429.0')] ).
cnf(1434,plain,
equal(multiply(inverse(u),add(v,n1)),multiply(inverse(u),inverse(u))),
inference(rew,[status(thm),theory(equality)],[1433,159]),
[iquote('0:Rew:1433.0,159.0')] ).
cnf(1437,plain,
equal(multiply(inverse(u),multiply(inverse(u),inverse(u))),multiply(inverse(u),inverse(u))),
inference(rew,[status(thm),theory(equality)],[1433,1134]),
[iquote('0:Rew:1433.0,1134.0')] ).
cnf(1438,plain,
equal(add(multiply(inverse(u),inverse(u)),multiply(inverse(u),inverse(u))),inverse(u)),
inference(rew,[status(thm),theory(equality)],[1433,1357]),
[iquote('0:Rew:1433.0,1357.0')] ).
cnf(1471,plain,
equal(multiply(inverse(u),add(inverse(u),inverse(u))),inverse(u)),
inference(rew,[status(thm),theory(equality)],[2,1438]),
[iquote('0:Rew:2.0,1438.0')] ).
cnf(1472,plain,
equal(multiply(inverse(u),inverse(u)),inverse(u)),
inference(rew,[status(thm),theory(equality)],[1437,1471,1433]),
[iquote('0:Rew:1437.0,1471.0,1433.0,1471.0')] ).
cnf(1476,plain,
equal(multiply(inverse(u),add(v,n1)),inverse(u)),
inference(rew,[status(thm),theory(equality)],[1472,1434]),
[iquote('0:Rew:1472.0,1434.0')] ).
cnf(1501,plain,
equal(multiply(inverse(u),add(v,inverse(u))),multiply(inverse(u),add(v,n1))),
inference(rew,[status(thm),theory(equality)],[1476,97]),
[iquote('0:Rew:1476.0,97.0')] ).
cnf(1530,plain,
equal(multiply(inverse(u),add(v,inverse(u))),inverse(u)),
inference(rew,[status(thm),theory(equality)],[1476,1501]),
[iquote('0:Rew:1476.0,1501.0')] ).
cnf(1852,plain,
equal(multiply(inverse(u),n1),inverse(u)),
inference(spr,[status(thm),theory(equality)],[3,1530]),
[iquote('0:SpR:3.0,1530.0')] ).
cnf(1893,plain,
equal(add(inverse(n1),inverse(u)),inverse(u)),
inference(spr,[status(thm),theory(equality)],[1852,50]),
[iquote('0:SpR:1852.0,50.0')] ).
cnf(1910,plain,
equal(inverse(inverse(n1)),n1),
inference(spr,[status(thm),theory(equality)],[1893,3]),
[iquote('0:SpR:1893.0,3.0')] ).
cnf(1915,plain,
equal(multiply(inverse(n1),multiply(u,inverse(u))),multiply(u,inverse(u))),
inference(spr,[status(thm),theory(equality)],[1893,138]),
[iquote('0:SpR:1893.0,138.0')] ).
cnf(1958,plain,
equal(multiply(u,multiply(inverse(n1),add(u,n1))),multiply(inverse(n1),add(u,n1))),
inference(spr,[status(thm),theory(equality)],[1910,138]),
[iquote('0:SpR:1910.0,138.0')] ).
cnf(2008,plain,
equal(multiply(u,inverse(n1)),inverse(n1)),
inference(rew,[status(thm),theory(equality)],[1476,1958]),
[iquote('0:Rew:1476.0,1958.0')] ).
cnf(2355,plain,
equal(add(multiply(u,inverse(n1)),inverse(n1)),multiply(inverse(n1),add(u,v))),
inference(spr,[status(thm),theory(equality)],[2008,2]),
[iquote('0:SpR:2008.0,2.0')] ).
cnf(2375,plain,
equal(multiply(inverse(n1),add(u,v)),inverse(n1)),
inference(rew,[status(thm),theory(equality)],[1893,2355,2008]),
[iquote('0:Rew:1893.0,2355.0,2008.0,2355.0')] ).
cnf(2453,plain,
equal(multiply(inverse(n1),u),inverse(n1)),
inference(spr,[status(thm),theory(equality)],[45,2375]),
[iquote('0:SpR:45.0,2375.0')] ).
cnf(2461,plain,
equal(multiply(u,inverse(u)),inverse(n1)),
inference(rew,[status(thm),theory(equality)],[2453,1915]),
[iquote('0:Rew:2453.0,1915.0')] ).
cnf(2464,plain,
~ equal(multiply(b,inverse(b)),inverse(n1)),
inference(rew,[status(thm),theory(equality)],[2461,8]),
[iquote('0:Rew:2461.0,8.0')] ).
cnf(2469,plain,
~ equal(inverse(n1),inverse(n1)),
inference(rew,[status(thm),theory(equality)],[2461,2464]),
[iquote('0:Rew:2461.0,2464.0')] ).
cnf(2470,plain,
$false,
inference(obv,[status(thm),theory(equality)],[2469]),
[iquote('0:Obv:2469.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : BOO025-1 : TPTP v8.1.0. Released v2.2.0.
% 0.03/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n026.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 : Wed Jun 1 16:50:56 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.51/0.71
% 0.51/0.71 SPASS V 3.9
% 0.51/0.71 SPASS beiseite: Proof found.
% 0.51/0.71 % SZS status Theorem
% 0.51/0.71 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.51/0.71 SPASS derived 1818 clauses, backtracked 0 clauses, performed 0 splits and kept 590 clauses.
% 0.51/0.71 SPASS allocated 65965 KBytes.
% 0.51/0.71 SPASS spent 0:00:00.35 on the problem.
% 0.51/0.71 0:00:00.03 for the input.
% 0.51/0.71 0:00:00.00 for the FLOTTER CNF translation.
% 0.51/0.71 0:00:00.02 for inferences.
% 0.51/0.71 0:00:00.00 for the backtracking.
% 0.51/0.71 0:00:00.28 for the reduction.
% 0.51/0.71
% 0.51/0.71
% 0.51/0.71 Here is a proof with depth 9, length 67 :
% 0.51/0.71 % SZS output start Refutation
% See solution above
% 0.51/0.71 Formulae used in the proof : multiply_add multiply_add_property additive_inverse pixley_defn pixley1 pixley2 pixley3 prove_equal_identity
% 0.51/0.71
%------------------------------------------------------------------------------