TSTP Solution File: BOO022-1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : BOO022-1 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n032.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 5.94s 6.14s
% Output : Refutation 5.94s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 5
% Syntax : Number of clauses : 36 ( 36 unt; 0 nHn; 36 RR)
% Number of literals : 36 ( 0 equ; 2 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 4 ( 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(multiply(add(u,v),v),v),
file('BOO022-1.p',unknown),
[] ).
cnf(2,axiom,
equal(add(multiply(u,v),multiply(w,v)),multiply(v,add(u,w))),
file('BOO022-1.p',unknown),
[] ).
cnf(4,axiom,
equal(add(multiply(u,v),v),v),
file('BOO022-1.p',unknown),
[] ).
cnf(5,axiom,
equal(multiply(add(u,v),add(w,v)),add(v,multiply(u,w))),
file('BOO022-1.p',unknown),
[] ).
cnf(7,axiom,
~ equal(multiply(multiply(a,b),c),multiply(a,multiply(b,c))),
file('BOO022-1.p',unknown),
[] ).
cnf(14,plain,
equal(add(u,u),u),
inference(spr,[status(thm),theory(equality)],[1,4]),
[iquote('0:SpR:1.0,4.0')] ).
cnf(18,plain,
equal(multiply(u,u),u),
inference(spr,[status(thm),theory(equality)],[4,1]),
[iquote('0:SpR:4.0,1.0')] ).
cnf(43,plain,
equal(add(u,multiply(v,v)),add(v,u)),
inference(spr,[status(thm),theory(equality)],[5,18]),
[iquote('0:SpR:5.0,18.0')] ).
cnf(54,plain,
equal(multiply(u,add(v,u)),add(u,multiply(u,v))),
inference(spr,[status(thm),theory(equality)],[14,5]),
[iquote('0:SpR:14.0,5.0')] ).
cnf(55,plain,
equal(add(u,v),add(v,u)),
inference(rew,[status(thm),theory(equality)],[18,43]),
[iquote('0:Rew:18.0,43.0')] ).
cnf(57,plain,
equal(add(u,multiply(v,u)),u),
inference(rew,[status(thm),theory(equality)],[55,4]),
[iquote('0:Rew:55.0,4.0')] ).
cnf(90,plain,
equal(multiply(u,add(v,multiply(w,u))),add(multiply(w,u),multiply(u,v))),
inference(spr,[status(thm),theory(equality)],[57,5]),
[iquote('0:SpR:57.0,5.0')] ).
cnf(91,plain,
equal(multiply(add(u,multiply(v,w)),w),add(multiply(v,w),multiply(u,w))),
inference(spr,[status(thm),theory(equality)],[57,5]),
[iquote('0:SpR:57.0,5.0')] ).
cnf(101,plain,
equal(multiply(add(u,multiply(v,w)),w),multiply(w,add(v,u))),
inference(rew,[status(thm),theory(equality)],[2,91]),
[iquote('0:Rew:2.0,91.0')] ).
cnf(102,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(106,plain,
equal(multiply(u,add(v,v)),multiply(v,u)),
inference(spr,[status(thm),theory(equality)],[2,14]),
[iquote('0:SpR:2.0,14.0')] ).
cnf(123,plain,
equal(multiply(u,v),multiply(v,u)),
inference(rew,[status(thm),theory(equality)],[14,106]),
[iquote('0:Rew:14.0,106.0')] ).
cnf(124,plain,
~ equal(multiply(c,multiply(a,b)),multiply(a,multiply(b,c))),
inference(rew,[status(thm),theory(equality)],[123,7]),
[iquote('0:Rew:123.0,7.0')] ).
cnf(126,plain,
equal(multiply(u,add(v,u)),u),
inference(rew,[status(thm),theory(equality)],[123,1]),
[iquote('0:Rew:123.0,1.0')] ).
cnf(127,plain,
equal(multiply(u,add(v,multiply(w,u))),multiply(u,add(w,v))),
inference(rew,[status(thm),theory(equality)],[123,101]),
[iquote('0:Rew:123.0,101.0')] ).
cnf(132,plain,
equal(add(u,multiply(u,v)),u),
inference(rew,[status(thm),theory(equality)],[54,126]),
[iquote('0:Rew:54.0,126.0')] ).
cnf(144,plain,
equal(multiply(multiply(u,v),multiply(v,add(w,u))),multiply(u,v)),
inference(rew,[status(thm),theory(equality)],[123,102]),
[iquote('0:Rew:123.0,102.0')] ).
cnf(150,plain,
equal(add(multiply(u,v),multiply(v,w)),multiply(v,add(u,w))),
inference(rew,[status(thm),theory(equality)],[90,127]),
[iquote('0:Rew:90.0,127.0')] ).
cnf(151,plain,
equal(multiply(u,add(v,multiply(w,u))),multiply(u,add(w,v))),
inference(rew,[status(thm),theory(equality)],[150,90]),
[iquote('0:Rew:150.0,90.0')] ).
cnf(1965,plain,
equal(multiply(multiply(multiply(u,v),w),multiply(w,v)),multiply(multiply(u,v),w)),
inference(spr,[status(thm),theory(equality)],[57,144]),
[iquote('0:SpR:57.0,144.0')] ).
cnf(2047,plain,
equal(multiply(multiply(u,v),multiply(multiply(w,v),u)),multiply(multiply(w,v),u)),
inference(rew,[status(thm),theory(equality)],[123,1965]),
[iquote('0:Rew:123.0,1965.0')] ).
cnf(3128,plain,
equal(multiply(u,multiply(v,add(w,u))),multiply(u,add(v,multiply(w,v)))),
inference(spr,[status(thm),theory(equality)],[150,151]),
[iquote('0:SpR:150.0,151.0')] ).
cnf(3149,plain,
equal(multiply(u,multiply(v,add(w,u))),multiply(u,v)),
inference(rew,[status(thm),theory(equality)],[57,3128]),
[iquote('0:Rew:57.0,3128.0')] ).
cnf(22264,plain,
equal(multiply(multiply(u,v),multiply(w,v)),multiply(multiply(u,v),w)),
inference(spr,[status(thm),theory(equality)],[57,3149]),
[iquote('0:SpR:57.0,3149.0')] ).
cnf(22267,plain,
equal(multiply(multiply(u,v),multiply(w,u)),multiply(multiply(u,v),w)),
inference(spr,[status(thm),theory(equality)],[132,3149]),
[iquote('0:SpR:132.0,3149.0')] ).
cnf(22392,plain,
equal(multiply(multiply(u,v),multiply(w,v)),multiply(multiply(w,v),u)),
inference(rew,[status(thm),theory(equality)],[22267,2047]),
[iquote('0:Rew:22267.0,2047.0')] ).
cnf(22415,plain,
equal(multiply(multiply(u,v),w),multiply(multiply(w,v),u)),
inference(rew,[status(thm),theory(equality)],[22264,22392]),
[iquote('0:Rew:22264.0,22392.0')] ).
cnf(26919,plain,
equal(multiply(multiply(u,v),w),multiply(u,multiply(w,v))),
inference(spr,[status(thm),theory(equality)],[22415,123]),
[iquote('0:SpR:22415.0,123.0')] ).
cnf(27174,plain,
equal(multiply(multiply(u,v),w),multiply(multiply(w,u),v)),
inference(spr,[status(thm),theory(equality)],[123,22415]),
[iquote('0:SpR:123.0,22415.0')] ).
cnf(28026,plain,
equal(multiply(u,multiply(v,w)),multiply(v,multiply(w,u))),
inference(rew,[status(thm),theory(equality)],[26919,27174]),
[iquote('0:Rew:26919.0,27174.0,26919.0,27174.0')] ).
cnf(28027,plain,
$false,
inference(unc,[status(thm)],[28026,124]),
[iquote('0:UnC:28026.0,124.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.10 % Problem : BOO022-1 : TPTP v8.1.0. Released v2.2.0.
% 0.10/0.11 % Command : run_spass %d %s
% 0.11/0.30 % Computer : n032.cluster.edu
% 0.11/0.30 % Model : x86_64 x86_64
% 0.11/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.30 % Memory : 8042.1875MB
% 0.11/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.30 % CPULimit : 300
% 0.11/0.30 % WCLimit : 600
% 0.11/0.30 % DateTime : Wed Jun 1 22:53:15 EDT 2022
% 0.11/0.30 % CPUTime :
% 5.94/6.14
% 5.94/6.14 SPASS V 3.9
% 5.94/6.14 SPASS beiseite: Proof found.
% 5.94/6.14 % SZS status Theorem
% 5.94/6.14 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 5.94/6.14 SPASS derived 19649 clauses, backtracked 0 clauses, performed 0 splits and kept 2608 clauses.
% 5.94/6.14 SPASS allocated 84375 KBytes.
% 5.94/6.14 SPASS spent 0:00:05.64 on the problem.
% 5.94/6.14 0:00:00.03 for the input.
% 5.94/6.14 0:00:00.00 for the FLOTTER CNF translation.
% 5.94/6.14 0:00:00.11 for inferences.
% 5.94/6.14 0:00:00.00 for the backtracking.
% 5.94/6.14 0:00:05.48 for the reduction.
% 5.94/6.14
% 5.94/6.14
% 5.94/6.14 Here is a proof with depth 3, length 36 :
% 5.94/6.14 % SZS output start Refutation
% See solution above
% 5.94/6.14 Formulae used in the proof : multiply_add multiply_add_property add_multiply add_multiply_property prove_associativity_of_multiply
% 5.94/6.14
%------------------------------------------------------------------------------