TSTP Solution File: RNG008-7 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : RNG008-7 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n027.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 : Mon Jul 18 20:41:12 EDT 2022
% Result : Unsatisfiable 0.38s 0.55s
% Output : Refutation 0.38s
% Verified :
% SZS Type : Refutation
% Derivation depth : 28
% Number of leaves : 11
% 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; 7 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
equal(multiply(u,u),u),
file('RNG008-7.p',unknown),
[] ).
cnf(2,axiom,
equal(multiply(a,b),c),
file('RNG008-7.p',unknown),
[] ).
cnf(3,axiom,
~ equal(multiply(b,a),c),
file('RNG008-7.p',unknown),
[] ).
cnf(4,axiom,
equal(add(additive_identity,u),u),
file('RNG008-7.p',unknown),
[] ).
cnf(5,axiom,
equal(add(u,additive_identity),u),
file('RNG008-7.p',unknown),
[] ).
cnf(7,axiom,
equal(add(u,additive_inverse(u)),additive_identity),
file('RNG008-7.p',unknown),
[] ).
cnf(8,axiom,
equal(add(add(u,v),w),add(u,add(v,w))),
file('RNG008-7.p',unknown),
[] ).
cnf(9,axiom,
equal(add(u,v),add(v,u)),
file('RNG008-7.p',unknown),
[] ).
cnf(10,axiom,
equal(multiply(multiply(u,v),w),multiply(u,multiply(v,w))),
file('RNG008-7.p',unknown),
[] ).
cnf(11,axiom,
equal(multiply(u,add(v,w)),add(multiply(u,v),multiply(u,w))),
file('RNG008-7.p',unknown),
[] ).
cnf(12,axiom,
equal(multiply(add(u,v),w),add(multiply(u,w),multiply(v,w))),
file('RNG008-7.p',unknown),
[] ).
cnf(19,plain,
equal(additive_inverse(additive_identity),additive_identity),
inference(spr,[status(thm),theory(equality)],[7,4]),
[iquote('0:SpR:7.0,4.0')] ).
cnf(31,plain,
equal(multiply(u,multiply(v,multiply(u,v))),multiply(u,v)),
inference(spr,[status(thm),theory(equality)],[10,1]),
[iquote('0:SpR:10.0,1.0')] ).
cnf(35,plain,
equal(multiply(u,multiply(u,v)),multiply(u,v)),
inference(spr,[status(thm),theory(equality)],[1,10]),
[iquote('0:SpR:1.0,10.0')] ).
cnf(39,plain,
equal(add(u,add(v,additive_inverse(add(u,v)))),additive_identity),
inference(spr,[status(thm),theory(equality)],[8,7]),
[iquote('0:SpR:8.0,7.0')] ).
cnf(44,plain,
equal(add(add(u,v),w),add(v,add(u,w))),
inference(spr,[status(thm),theory(equality)],[9,8]),
[iquote('0:SpR:9.0,8.0')] ).
cnf(46,plain,
equal(add(u,add(additive_inverse(u),v)),add(additive_identity,v)),
inference(spr,[status(thm),theory(equality)],[7,8]),
[iquote('0:SpR:7.0,8.0')] ).
cnf(50,plain,
equal(add(u,add(additive_inverse(u),v)),v),
inference(rew,[status(thm),theory(equality)],[4,46]),
[iquote('0:Rew:4.0,46.0')] ).
cnf(51,plain,
equal(add(u,add(v,w)),add(v,add(u,w))),
inference(rew,[status(thm),theory(equality)],[8,44]),
[iquote('0:Rew:8.0,44.0')] ).
cnf(62,plain,
equal(add(u,additive_identity),additive_inverse(additive_inverse(u))),
inference(spr,[status(thm),theory(equality)],[7,50]),
[iquote('0:SpR:7.0,50.0')] ).
cnf(66,plain,
equal(additive_inverse(additive_inverse(u)),u),
inference(rew,[status(thm),theory(equality)],[5,62]),
[iquote('0:Rew:5.0,62.0')] ).
cnf(98,plain,
equal(add(multiply(u,add(u,v)),multiply(v,add(u,v))),add(u,v)),
inference(spr,[status(thm),theory(equality)],[12,1]),
[iquote('0:SpR:12.0,1.0')] ).
cnf(101,plain,
equal(add(multiply(additive_identity,u),multiply(v,u)),multiply(v,u)),
inference(spr,[status(thm),theory(equality)],[4,12]),
[iquote('0:SpR:4.0,12.0')] ).
cnf(104,plain,
equal(add(multiply(u,v),multiply(additive_inverse(u),v)),multiply(additive_identity,v)),
inference(spr,[status(thm),theory(equality)],[7,12]),
[iquote('0:SpR:7.0,12.0')] ).
cnf(113,plain,
equal(add(add(multiply(u,u),multiply(u,v)),add(multiply(v,u),multiply(v,v))),add(u,v)),
inference(rew,[status(thm),theory(equality)],[11,98]),
[iquote('0:Rew:11.0,98.0,11.0,98.0')] ).
cnf(114,plain,
equal(add(u,add(multiply(u,v),add(v,multiply(v,u)))),add(u,v)),
inference(rew,[status(thm),theory(equality)],[8,113,1,9]),
[iquote('0:Rew:8.0,113.0,1.0,113.0,9.0,113.0,1.0,113.0')] ).
cnf(115,plain,
equal(add(u,add(v,add(multiply(u,v),multiply(v,u)))),add(u,v)),
inference(rew,[status(thm),theory(equality)],[51,114]),
[iquote('0:Rew:51.0,114.0')] ).
cnf(157,plain,
equal(add(u,additive_inverse(add(additive_inverse(v),u))),add(v,additive_identity)),
inference(spr,[status(thm),theory(equality)],[39,50]),
[iquote('0:SpR:39.0,50.0')] ).
cnf(173,plain,
equal(add(u,additive_inverse(add(additive_inverse(v),u))),v),
inference(rew,[status(thm),theory(equality)],[5,157]),
[iquote('0:Rew:5.0,157.0')] ).
cnf(188,plain,
equal(add(multiply(u,additive_identity),multiply(u,v)),multiply(u,v)),
inference(spr,[status(thm),theory(equality)],[4,11]),
[iquote('0:SpR:4.0,11.0')] ).
cnf(191,plain,
equal(add(multiply(u,v),multiply(u,additive_inverse(v))),multiply(u,additive_identity)),
inference(spr,[status(thm),theory(equality)],[7,11]),
[iquote('0:SpR:7.0,11.0')] ).
cnf(222,plain,
equal(add(u,additive_inverse(add(v,u))),additive_inverse(v)),
inference(spr,[status(thm),theory(equality)],[66,173]),
[iquote('0:SpR:66.0,173.0')] ).
cnf(255,plain,
equal(add(u,additive_inverse(add(u,v))),additive_inverse(v)),
inference(spr,[status(thm),theory(equality)],[9,222]),
[iquote('0:SpR:9.0,222.0')] ).
cnf(398,plain,
equal(add(multiply(u,v),additive_inverse(multiply(u,v))),additive_inverse(multiply(additive_identity,v))),
inference(spr,[status(thm),theory(equality)],[101,222]),
[iquote('0:SpR:101.0,222.0')] ).
cnf(421,plain,
equal(additive_inverse(multiply(additive_identity,u)),additive_identity),
inference(rew,[status(thm),theory(equality)],[7,398]),
[iquote('0:Rew:7.0,398.0')] ).
cnf(427,plain,
equal(multiply(additive_identity,u),additive_inverse(additive_identity)),
inference(spr,[status(thm),theory(equality)],[421,66]),
[iquote('0:SpR:421.0,66.0')] ).
cnf(434,plain,
equal(multiply(additive_identity,u),additive_identity),
inference(rew,[status(thm),theory(equality)],[19,427]),
[iquote('0:Rew:19.0,427.0')] ).
cnf(445,plain,
equal(add(multiply(u,v),multiply(additive_inverse(u),v)),additive_identity),
inference(rew,[status(thm),theory(equality)],[434,104]),
[iquote('0:Rew:434.0,104.0')] ).
cnf(557,plain,
equal(add(multiply(additive_inverse(u),v),additive_inverse(additive_identity)),additive_inverse(multiply(u,v))),
inference(spr,[status(thm),theory(equality)],[445,222]),
[iquote('0:SpR:445.0,222.0')] ).
cnf(585,plain,
equal(multiply(additive_inverse(u),v),additive_inverse(multiply(u,v))),
inference(rew,[status(thm),theory(equality)],[4,557,9,19]),
[iquote('0:Rew:4.0,557.0,9.0,557.0,19.0,557.0')] ).
cnf(645,plain,
equal(additive_inverse(multiply(u,additive_inverse(u))),additive_inverse(u)),
inference(spr,[status(thm),theory(equality)],[585,1]),
[iquote('0:SpR:585.0,1.0')] ).
cnf(670,plain,
equal(multiply(u,additive_inverse(u)),additive_inverse(additive_inverse(u))),
inference(spr,[status(thm),theory(equality)],[645,66]),
[iquote('0:SpR:645.0,66.0')] ).
cnf(689,plain,
equal(multiply(u,additive_inverse(u)),u),
inference(rew,[status(thm),theory(equality)],[66,670]),
[iquote('0:Rew:66.0,670.0')] ).
cnf(736,plain,
equal(add(multiply(u,v),additive_inverse(multiply(u,v))),additive_inverse(multiply(u,additive_identity))),
inference(spr,[status(thm),theory(equality)],[188,222]),
[iquote('0:SpR:188.0,222.0')] ).
cnf(771,plain,
equal(additive_inverse(multiply(u,additive_identity)),additive_identity),
inference(rew,[status(thm),theory(equality)],[7,736]),
[iquote('0:Rew:7.0,736.0')] ).
cnf(784,plain,
equal(multiply(u,additive_identity),additive_inverse(additive_identity)),
inference(spr,[status(thm),theory(equality)],[771,66]),
[iquote('0:SpR:771.0,66.0')] ).
cnf(797,plain,
equal(multiply(u,additive_identity),additive_identity),
inference(rew,[status(thm),theory(equality)],[19,784]),
[iquote('0:Rew:19.0,784.0')] ).
cnf(804,plain,
equal(add(multiply(u,v),multiply(u,additive_inverse(v))),additive_identity),
inference(rew,[status(thm),theory(equality)],[797,191]),
[iquote('0:Rew:797.0,191.0')] ).
cnf(842,plain,
equal(add(multiply(u,additive_inverse(v)),additive_inverse(additive_identity)),additive_inverse(multiply(u,v))),
inference(spr,[status(thm),theory(equality)],[804,222]),
[iquote('0:SpR:804.0,222.0')] ).
cnf(854,plain,
equal(add(multiply(u,u),u),additive_identity),
inference(spr,[status(thm),theory(equality)],[689,804]),
[iquote('0:SpR:689.0,804.0')] ).
cnf(874,plain,
equal(add(u,u),additive_identity),
inference(rew,[status(thm),theory(equality)],[1,854]),
[iquote('0:Rew:1.0,854.0')] ).
cnf(883,plain,
equal(multiply(u,additive_inverse(v)),additive_inverse(multiply(u,v))),
inference(rew,[status(thm),theory(equality)],[4,842,9,19]),
[iquote('0:Rew:4.0,842.0,9.0,842.0,19.0,842.0')] ).
cnf(886,plain,
equal(additive_inverse(multiply(u,u)),u),
inference(rew,[status(thm),theory(equality)],[883,689]),
[iquote('0:Rew:883.0,689.0')] ).
cnf(902,plain,
equal(additive_inverse(u),u),
inference(rew,[status(thm),theory(equality)],[1,886]),
[iquote('0:Rew:1.0,886.0')] ).
cnf(905,plain,
equal(add(u,add(u,v)),additive_inverse(v)),
inference(rew,[status(thm),theory(equality)],[902,255]),
[iquote('0:Rew:902.0,255.0')] ).
cnf(931,plain,
equal(add(u,add(u,v)),v),
inference(rew,[status(thm),theory(equality)],[902,905]),
[iquote('0:Rew:902.0,905.0')] ).
cnf(1763,plain,
equal(add(u,add(multiply(v,u),multiply(u,v))),add(v,add(v,u))),
inference(spr,[status(thm),theory(equality)],[115,931]),
[iquote('0:SpR:115.0,931.0')] ).
cnf(1825,plain,
equal(add(u,add(multiply(v,u),multiply(u,v))),u),
inference(rew,[status(thm),theory(equality)],[931,1763]),
[iquote('0:Rew:931.0,1763.0')] ).
cnf(1911,plain,
equal(add(multiply(u,multiply(v,u)),add(multiply(v,u),multiply(multiply(u,multiply(v,u)),v))),multiply(u,multiply(v,u))),
inference(spr,[status(thm),theory(equality)],[31,1825]),
[iquote('0:SpR:31.0,1825.0')] ).
cnf(1912,plain,
equal(add(multiply(u,v),add(multiply(u,v),multiply(multiply(u,v),u))),multiply(u,v)),
inference(spr,[status(thm),theory(equality)],[35,1825]),
[iquote('0:SpR:35.0,1825.0')] ).
cnf(1982,plain,
equal(multiply(u,multiply(v,u)),multiply(u,v)),
inference(rew,[status(thm),theory(equality)],[931,1912,10]),
[iquote('0:Rew:931.0,1912.0,10.0,1912.0')] ).
cnf(1995,plain,
equal(add(multiply(u,v),add(multiply(v,multiply(u,v)),multiply(v,multiply(u,multiply(v,u))))),multiply(v,multiply(u,v))),
inference(rew,[status(thm),theory(equality)],[51,1911,10]),
[iquote('0:Rew:51.0,1911.0,10.0,1911.0,10.0,1911.0')] ).
cnf(1996,plain,
equal(add(multiply(u,v),add(multiply(v,u),multiply(v,u))),multiply(v,u)),
inference(rew,[status(thm),theory(equality)],[1982,1995]),
[iquote('0:Rew:1982.0,1995.0,1982.0,1995.0,1982.0,1995.0')] ).
cnf(1997,plain,
equal(multiply(u,v),multiply(v,u)),
inference(rew,[status(thm),theory(equality)],[4,1996,9,874]),
[iquote('0:Rew:4.0,1996.0,9.0,1996.0,874.0,1996.0')] ).
cnf(1998,plain,
~ equal(multiply(a,b),c),
inference(rew,[status(thm),theory(equality)],[1997,3]),
[iquote('0:Rew:1997.0,3.0')] ).
cnf(2002,plain,
~ equal(c,c),
inference(rew,[status(thm),theory(equality)],[2,1998]),
[iquote('0:Rew:2.0,1998.0')] ).
cnf(2003,plain,
$false,
inference(obv,[status(thm),theory(equality)],[2002]),
[iquote('0:Obv:2002.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : RNG008-7 : TPTP v8.1.0. Released v1.0.0.
% 0.03/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n027.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 May 30 11:43:46 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.38/0.55
% 0.38/0.55 SPASS V 3.9
% 0.38/0.55 SPASS beiseite: Proof found.
% 0.38/0.55 % SZS status Theorem
% 0.38/0.55 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.38/0.55 SPASS derived 1131 clauses, backtracked 0 clauses, performed 0 splits and kept 202 clauses.
% 0.38/0.55 SPASS allocated 64819 KBytes.
% 0.38/0.55 SPASS spent 0:00:00.20 on the problem.
% 0.38/0.55 0:00:00.04 for the input.
% 0.38/0.55 0:00:00.00 for the FLOTTER CNF translation.
% 0.38/0.55 0:00:00.01 for inferences.
% 0.38/0.55 0:00:00.00 for the backtracking.
% 0.38/0.55 0:00:00.13 for the reduction.
% 0.38/0.55
% 0.38/0.55
% 0.38/0.55 Here is a proof with depth 7, length 67 :
% 0.38/0.55 % SZS output start Refutation
% See solution above
% 0.38/0.55 Formulae used in the proof : boolean_ring a_times_b_is_c prove_commutativity left_additive_identity right_additive_identity right_additive_inverse associativity_for_addition commutativity_for_addition associativity_for_multiplication distribute1 distribute2
% 0.38/0.55
%------------------------------------------------------------------------------