TSTP Solution File: ALG005-1 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : ALG005-1 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n020.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 18:01:56 EDT 2022
% Result : Unsatisfiable 2.22s 2.46s
% Output : Refutation 2.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 5
% Syntax : Number of clauses : 72 ( 72 unt; 0 nHn; 72 RR)
% Number of literals : 72 ( 0 equ; 2 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 : 8 ( 8 usr; 6 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
equal(difference(u,difference(v,u)),u),
file('ALG005-1.p',unknown),
[] ).
cnf(2,axiom,
equal(difference(u,difference(u,v)),difference(v,difference(v,u))),
file('ALG005-1.p',unknown),
[] ).
cnf(3,axiom,
equal(difference(difference(u,v),difference(w,v)),difference(difference(u,w),v)),
file('ALG005-1.p',unknown),
[] ).
cnf(4,axiom,
equal(difference(u,difference(u,v)),multiply(u,v)),
file('ALG005-1.p',unknown),
[] ).
cnf(5,axiom,
~ equal(multiply(multiply(a,b),c),multiply(a,multiply(b,c))),
file('ALG005-1.p',unknown),
[] ).
cnf(6,plain,
equal(multiply(u,v),multiply(v,u)),
inference(rew,[status(thm),theory(equality)],[4,2]),
[iquote('0:Rew:4.0,2.0,4.0,2.0')] ).
cnf(7,plain,
~ equal(multiply(c,multiply(a,b)),multiply(a,multiply(b,c))),
inference(rew,[status(thm),theory(equality)],[6,5]),
[iquote('0:Rew:6.0,5.0')] ).
cnf(8,plain,
equal(difference(difference(u,v),v),difference(u,v)),
inference(spr,[status(thm),theory(equality)],[1]),
[iquote('0:SpR:1.0,1.0')] ).
cnf(14,plain,
equal(difference(difference(u,v),multiply(u,v)),difference(u,v)),
inference(spr,[status(thm),theory(equality)],[4,1]),
[iquote('0:SpR:4.0,1.0')] ).
cnf(15,plain,
equal(multiply(u,u),u),
inference(spr,[status(thm),theory(equality)],[4,1]),
[iquote('0:SpR:4.0,1.0')] ).
cnf(17,plain,
equal(multiply(u,difference(u,v)),difference(u,multiply(u,v))),
inference(spr,[status(thm),theory(equality)],[4]),
[iquote('0:SpR:4.0,4.0')] ).
cnf(18,plain,
equal(multiply(u,difference(v,u)),difference(u,u)),
inference(spr,[status(thm),theory(equality)],[1,4]),
[iquote('0:SpR:1.0,4.0')] ).
cnf(23,plain,
equal(difference(difference(u,v),difference(u,v)),multiply(difference(u,v),v)),
inference(spr,[status(thm),theory(equality)],[8,4]),
[iquote('0:SpR:8.0,4.0')] ).
cnf(27,plain,
equal(difference(multiply(u,v),difference(u,v)),multiply(u,v)),
inference(spr,[status(thm),theory(equality)],[4,8]),
[iquote('0:SpR:4.0,8.0')] ).
cnf(28,plain,
equal(difference(difference(u,v),difference(u,v)),multiply(v,difference(u,v))),
inference(rew,[status(thm),theory(equality)],[6,23]),
[iquote('0:Rew:6.0,23.0')] ).
cnf(29,plain,
equal(difference(difference(u,u),v),difference(v,v)),
inference(rew,[status(thm),theory(equality)],[3,28,18]),
[iquote('0:Rew:3.0,28.0,18.0,28.0')] ).
cnf(39,plain,
equal(difference(difference(u,u),difference(v,v)),multiply(difference(u,u),v)),
inference(spr,[status(thm),theory(equality)],[29,4]),
[iquote('0:SpR:29.0,4.0')] ).
cnf(51,plain,
equal(difference(difference(u,u),v),difference(difference(w,w),v)),
inference(spr,[status(thm),theory(equality)],[29]),
[iquote('0:SpR:29.0,29.0')] ).
cnf(81,plain,
equal(difference(difference(u,difference(u,v)),v),multiply(difference(u,v),v)),
inference(spr,[status(thm),theory(equality)],[3,4]),
[iquote('0:SpR:3.0,4.0')] ).
cnf(82,plain,
equal(difference(difference(u,v),difference(difference(u,w),v)),multiply(difference(u,v),difference(w,v))),
inference(spr,[status(thm),theory(equality)],[3,4]),
[iquote('0:SpR:3.0,4.0')] ).
cnf(94,plain,
equal(difference(difference(u,v),difference(v,v)),difference(difference(u,difference(w,w)),v)),
inference(spr,[status(thm),theory(equality)],[29,3]),
[iquote('0:SpR:29.0,3.0')] ).
cnf(97,plain,
equal(difference(difference(u,v),difference(w,u)),difference(u,difference(v,difference(w,u)))),
inference(spr,[status(thm),theory(equality)],[1,3]),
[iquote('0:SpR:1.0,3.0')] ).
cnf(98,plain,
equal(difference(multiply(u,v),difference(w,difference(u,v))),difference(difference(u,w),difference(u,v))),
inference(spr,[status(thm),theory(equality)],[4,3]),
[iquote('0:SpR:4.0,3.0')] ).
cnf(104,plain,
equal(difference(multiply(u,v),v),difference(v,v)),
inference(rew,[status(thm),theory(equality)],[4,81,18,6]),
[iquote('0:Rew:4.0,81.0,18.0,81.0,6.0,81.0')] ).
cnf(109,plain,
equal(difference(difference(u,difference(v,v)),w),difference(u,w)),
inference(rew,[status(thm),theory(equality)],[8,94,3]),
[iquote('0:Rew:8.0,94.0,3.0,94.0')] ).
cnf(115,plain,
equal(multiply(difference(u,v),difference(w,v)),difference(multiply(u,w),v)),
inference(rew,[status(thm),theory(equality)],[4,82,3]),
[iquote('0:Rew:4.0,82.0,3.0,82.0')] ).
cnf(129,plain,
equal(difference(multiply(u,v),u),difference(u,u)),
inference(spr,[status(thm),theory(equality)],[6,104]),
[iquote('0:SpR:6.0,104.0')] ).
cnf(144,plain,
equal(difference(difference(u,v),difference(v,v)),difference(difference(u,multiply(v,w)),v)),
inference(spr,[status(thm),theory(equality)],[129,3]),
[iquote('0:SpR:129.0,3.0')] ).
cnf(153,plain,
equal(difference(difference(u,multiply(v,w)),v),difference(u,v)),
inference(rew,[status(thm),theory(equality)],[8,144,3]),
[iquote('0:Rew:8.0,144.0,3.0,144.0')] ).
cnf(188,plain,
equal(difference(difference(multiply(u,v),w),difference(u,v)),difference(multiply(u,v),difference(w,difference(u,v)))),
inference(spr,[status(thm),theory(equality)],[27,3]),
[iquote('0:SpR:27.0,3.0')] ).
cnf(196,plain,
equal(difference(multiply(difference(u,v),v),difference(u,v)),multiply(difference(u,v),v)),
inference(spr,[status(thm),theory(equality)],[8,27]),
[iquote('0:SpR:8.0,27.0')] ).
cnf(218,plain,
equal(difference(difference(u,v),u),difference(u,u)),
inference(rew,[status(thm),theory(equality)],[3,196,18,6]),
[iquote('0:Rew:3.0,196.0,18.0,196.0,6.0,196.0')] ).
cnf(227,plain,
equal(difference(difference(multiply(u,v),w),difference(u,v)),difference(difference(u,w),difference(u,v))),
inference(rew,[status(thm),theory(equality)],[98,188]),
[iquote('0:Rew:98.0,188.0')] ).
cnf(303,plain,
equal(difference(difference(u,v),difference(u,u)),multiply(difference(u,v),u)),
inference(spr,[status(thm),theory(equality)],[218,4]),
[iquote('0:SpR:218.0,4.0')] ).
cnf(312,plain,
equal(difference(difference(u,v),difference(v,v)),difference(difference(u,difference(v,w)),v)),
inference(spr,[status(thm),theory(equality)],[218,3]),
[iquote('0:SpR:218.0,3.0')] ).
cnf(328,plain,
equal(difference(difference(u,v),difference(u,u)),difference(u,multiply(u,v))),
inference(rew,[status(thm),theory(equality)],[17,303,6]),
[iquote('0:Rew:17.0,303.0,6.0,303.0')] ).
cnf(329,plain,
equal(difference(u,difference(v,difference(u,u))),difference(u,multiply(u,v))),
inference(rew,[status(thm),theory(equality)],[97,328]),
[iquote('0:Rew:97.0,328.0')] ).
cnf(335,plain,
equal(difference(difference(u,difference(v,w)),v),difference(u,v)),
inference(rew,[status(thm),theory(equality)],[8,312,3]),
[iquote('0:Rew:8.0,312.0,3.0,312.0')] ).
cnf(440,plain,
equal(difference(difference(u,u),difference(v,w)),difference(difference(w,v),w)),
inference(spr,[status(thm),theory(equality)],[51,3]),
[iquote('0:SpR:51.0,3.0')] ).
cnf(489,plain,
equal(difference(difference(u,u),difference(v,w)),difference(w,w)),
inference(rew,[status(thm),theory(equality)],[218,440]),
[iquote('0:Rew:218.0,440.0')] ).
cnf(490,plain,
equal(difference(u,u),multiply(difference(v,v),u)),
inference(rew,[status(thm),theory(equality)],[489,39]),
[iquote('0:Rew:489.0,39.0')] ).
cnf(532,plain,
equal(multiply(u,difference(v,v)),difference(u,u)),
inference(spr,[status(thm),theory(equality)],[490,6]),
[iquote('0:SpR:490.0,6.0')] ).
cnf(560,plain,
equal(multiply(difference(u,v),difference(w,v)),difference(multiply(w,u),v)),
inference(spr,[status(thm),theory(equality)],[115,6]),
[iquote('0:SpR:115.0,6.0')] ).
cnf(591,plain,
equal(multiply(difference(u,v),difference(w,v)),difference(multiply(difference(u,v),w),v)),
inference(spr,[status(thm),theory(equality)],[8,115]),
[iquote('0:SpR:8.0,115.0')] ).
cnf(605,plain,
equal(difference(multiply(u,v),w),difference(multiply(v,u),w)),
inference(rew,[status(thm),theory(equality)],[115,560]),
[iquote('0:Rew:115.0,560.0')] ).
cnf(620,plain,
equal(difference(multiply(difference(u,v),w),v),difference(multiply(u,w),v)),
inference(rew,[status(thm),theory(equality)],[115,591]),
[iquote('0:Rew:115.0,591.0')] ).
cnf(736,plain,
equal(difference(difference(u,difference(v,v)),difference(u,u)),difference(u,difference(v,v))),
inference(spr,[status(thm),theory(equality)],[532,14]),
[iquote('0:SpR:532.0,14.0')] ).
cnf(790,plain,
equal(difference(u,difference(u,u)),difference(u,difference(v,v))),
inference(rew,[status(thm),theory(equality)],[109,736]),
[iquote('0:Rew:109.0,736.0')] ).
cnf(791,plain,
equal(difference(u,difference(v,v)),u),
inference(rew,[status(thm),theory(equality)],[15,790,4]),
[iquote('0:Rew:15.0,790.0,4.0,790.0')] ).
cnf(792,plain,
equal(difference(u,multiply(u,v)),difference(u,v)),
inference(rew,[status(thm),theory(equality)],[791,329]),
[iquote('0:Rew:791.0,329.0')] ).
cnf(798,plain,
equal(multiply(u,difference(u,v)),difference(u,v)),
inference(rew,[status(thm),theory(equality)],[792,17]),
[iquote('0:Rew:792.0,17.0')] ).
cnf(1118,plain,
equal(multiply(difference(u,v),difference(u,difference(v,difference(w,u)))),difference(u,difference(v,difference(w,u)))),
inference(spr,[status(thm),theory(equality)],[97,798]),
[iquote('0:SpR:97.0,798.0')] ).
cnf(2418,plain,
equal(multiply(difference(u,difference(v,w)),difference(u,v)),difference(u,v)),
inference(spr,[status(thm),theory(equality)],[335,798]),
[iquote('0:SpR:335.0,798.0')] ).
cnf(2498,plain,
equal(multiply(difference(u,v),difference(u,difference(v,w))),difference(u,v)),
inference(rew,[status(thm),theory(equality)],[6,2418]),
[iquote('0:Rew:6.0,2418.0')] ).
cnf(2499,plain,
equal(difference(u,difference(v,difference(w,u))),difference(u,v)),
inference(rew,[status(thm),theory(equality)],[2498,1118]),
[iquote('0:Rew:2498.0,1118.0')] ).
cnf(2500,plain,
equal(difference(difference(u,v),difference(w,u)),difference(u,v)),
inference(rew,[status(thm),theory(equality)],[2499,97]),
[iquote('0:Rew:2499.0,97.0')] ).
cnf(2630,plain,
equal(difference(multiply(u,v),difference(multiply(v,u),w)),multiply(multiply(v,u),w)),
inference(spr,[status(thm),theory(equality)],[605,4]),
[iquote('0:SpR:605.0,4.0')] ).
cnf(2631,plain,
equal(difference(multiply(u,v),difference(multiply(v,u),w)),multiply(multiply(u,v),w)),
inference(spr,[status(thm),theory(equality)],[605,4]),
[iquote('0:SpR:605.0,4.0')] ).
cnf(2760,plain,
equal(multiply(multiply(u,v),w),multiply(multiply(v,u),w)),
inference(rew,[status(thm),theory(equality)],[2630,2631]),
[iquote('0:Rew:2630.0,2631.0')] ).
cnf(2820,plain,
equal(difference(u,multiply(difference(v,u),w)),difference(u,difference(v,u))),
inference(spr,[status(thm),theory(equality)],[2500,153]),
[iquote('0:SpR:2500.0,153.0')] ).
cnf(2841,plain,
equal(difference(difference(multiply(u,v),w),difference(u,v)),difference(multiply(u,v),w)),
inference(spr,[status(thm),theory(equality)],[792,2500]),
[iquote('0:SpR:792.0,2500.0')] ).
cnf(2910,plain,
equal(difference(u,multiply(difference(v,u),w)),u),
inference(rew,[status(thm),theory(equality)],[1,2820]),
[iquote('0:Rew:1.0,2820.0')] ).
cnf(2954,plain,
equal(difference(difference(u,v),difference(u,w)),difference(multiply(u,w),v)),
inference(rew,[status(thm),theory(equality)],[227,2841]),
[iquote('0:Rew:227.0,2841.0')] ).
cnf(3032,plain,
equal(difference(multiply(difference(u,v),w),v),multiply(difference(u,v),w)),
inference(spr,[status(thm),theory(equality)],[2910,1]),
[iquote('0:SpR:2910.0,1.0')] ).
cnf(3095,plain,
equal(multiply(difference(u,v),w),difference(multiply(u,w),v)),
inference(rew,[status(thm),theory(equality)],[620,3032]),
[iquote('0:Rew:620.0,3032.0')] ).
cnf(5325,plain,
equal(difference(multiply(u,v),difference(u,w)),multiply(multiply(u,w),v)),
inference(spr,[status(thm),theory(equality)],[4,3095]),
[iquote('0:SpR:4.0,3095.0')] ).
cnf(11711,plain,
equal(difference(multiply(u,v),difference(u,w)),difference(multiply(u,w),difference(u,v))),
inference(spr,[status(thm),theory(equality)],[4,2954]),
[iquote('0:SpR:4.0,2954.0')] ).
cnf(11815,plain,
equal(multiply(multiply(u,v),w),multiply(multiply(u,w),v)),
inference(rew,[status(thm),theory(equality)],[5325,11711]),
[iquote('0:Rew:5325.0,11711.0,5325.0,11711.0')] ).
cnf(12467,plain,
equal(multiply(multiply(u,v),w),multiply(v,multiply(u,w))),
inference(spr,[status(thm),theory(equality)],[11815,6]),
[iquote('0:SpR:11815.0,6.0')] ).
cnf(12522,plain,
equal(multiply(multiply(u,v),w),multiply(multiply(w,u),v)),
inference(spr,[status(thm),theory(equality)],[11815,2760]),
[iquote('0:SpR:11815.0,2760.0')] ).
cnf(12830,plain,
equal(multiply(u,multiply(v,w)),multiply(v,multiply(w,u))),
inference(rew,[status(thm),theory(equality)],[12467,12522]),
[iquote('0:Rew:12467.0,12522.0,12467.0,12522.0')] ).
cnf(12831,plain,
$false,
inference(unc,[status(thm)],[12830,7]),
[iquote('0:UnC:12830.0,7.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.14 % Problem : ALG005-1 : TPTP v8.1.0. Released v2.2.0.
% 0.13/0.15 % Command : run_spass %d %s
% 0.16/0.36 % Computer : n020.cluster.edu
% 0.16/0.36 % Model : x86_64 x86_64
% 0.16/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.36 % Memory : 8042.1875MB
% 0.16/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.36 % CPULimit : 300
% 0.16/0.36 % WCLimit : 600
% 0.16/0.36 % DateTime : Wed Jun 8 11:06:36 EDT 2022
% 0.16/0.37 % CPUTime :
% 2.22/2.46
% 2.22/2.46 SPASS V 3.9
% 2.22/2.46 SPASS beiseite: Proof found.
% 2.22/2.46 % SZS status Theorem
% 2.22/2.46 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.22/2.46 SPASS derived 8359 clauses, backtracked 0 clauses, performed 0 splits and kept 1042 clauses.
% 2.22/2.46 SPASS allocated 73135 KBytes.
% 2.22/2.46 SPASS spent 0:00:02.03 on the problem.
% 2.22/2.46 0:00:00.03 for the input.
% 2.22/2.46 0:00:00.00 for the FLOTTER CNF translation.
% 2.22/2.46 0:00:00.06 for inferences.
% 2.22/2.46 0:00:00.00 for the backtracking.
% 2.22/2.46 0:00:01.91 for the reduction.
% 2.22/2.46
% 2.22/2.46
% 2.22/2.46 Here is a proof with depth 7, length 72 :
% 2.22/2.46 % SZS output start Refutation
% See solution above
% 2.22/2.46 Formulae used in the proof : set_difference_1 set_difference_2 set_difference_3 intersection prove_associativity_of_multiply
% 2.22/2.46
%------------------------------------------------------------------------------