TSTP Solution File: BOO029-1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : BOO029-1 : 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 23:49:29 EDT 2022
% Result : Unsatisfiable 0.36s 0.54s
% Output : Refutation 0.36s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 9
% Syntax : Number of clauses : 29 ( 29 unt; 0 nHn; 29 RR)
% Number of literals : 29 ( 0 equ; 1 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; 5 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
equal(add(u,multiply(v,multiply(u,w))),u),
file('BOO029-1.p',unknown),
[] ).
cnf(3,axiom,
equal(multiply(add(u,v),add(u,inverse(v))),u),
file('BOO029-1.p',unknown),
[] ).
cnf(4,axiom,
equal(multiply(u,add(v,add(u,w))),u),
file('BOO029-1.p',unknown),
[] ).
cnf(6,axiom,
equal(add(multiply(u,v),multiply(u,inverse(v))),u),
file('BOO029-1.p',unknown),
[] ).
cnf(7,axiom,
equal(add(u,v),add(v,u)),
file('BOO029-1.p',unknown),
[] ).
cnf(8,axiom,
equal(multiply(u,v),multiply(v,u)),
file('BOO029-1.p',unknown),
[] ).
cnf(9,axiom,
equal(add(add(u,v),w),add(u,add(v,w))),
file('BOO029-1.p',unknown),
[] ).
cnf(10,axiom,
equal(multiply(multiply(u,v),w),multiply(u,multiply(v,w))),
file('BOO029-1.p',unknown),
[] ).
cnf(11,axiom,
~ equal(add(a,inverse(a)),add(b,inverse(b))),
file('BOO029-1.p',unknown),
[] ).
cnf(29,plain,
equal(multiply(u,add(v,u)),u),
inference(spr,[status(thm),theory(equality)],[1,4]),
[iquote('0:SpR:1.0,4.0')] ).
cnf(40,plain,
equal(multiply(u,add(u,v)),u),
inference(spr,[status(thm),theory(equality)],[7,29]),
[iquote('0:SpR:7.0,29.0')] ).
cnf(76,plain,
equal(multiply(multiply(u,v),add(w,u)),multiply(u,v)),
inference(spr,[status(thm),theory(equality)],[6,4]),
[iquote('0:SpR:6.0,4.0')] ).
cnf(81,plain,
equal(add(multiply(u,v),multiply(v,inverse(u))),v),
inference(spr,[status(thm),theory(equality)],[8,6]),
[iquote('0:SpR:8.0,6.0')] ).
cnf(90,plain,
equal(multiply(u,multiply(v,add(w,u))),multiply(u,v)),
inference(rew,[status(thm),theory(equality)],[10,76]),
[iquote('0:Rew:10.0,76.0')] ).
cnf(378,plain,
equal(add(u,multiply(add(v,u),inverse(u))),add(v,u)),
inference(spr,[status(thm),theory(equality)],[29,81]),
[iquote('0:SpR:29.0,81.0')] ).
cnf(391,plain,
equal(add(u,multiply(inverse(u),add(v,u))),add(v,u)),
inference(rew,[status(thm),theory(equality)],[8,378]),
[iquote('0:Rew:8.0,378.0')] ).
cnf(495,plain,
equal(add(u,add(v,w)),add(v,add(w,u))),
inference(spr,[status(thm),theory(equality)],[9,7]),
[iquote('0:SpR:9.0,7.0')] ).
cnf(685,plain,
equal(multiply(inverse(u),add(v,u)),multiply(inverse(u),v)),
inference(spr,[status(thm),theory(equality)],[3,90]),
[iquote('0:SpR:3.0,90.0')] ).
cnf(695,plain,
equal(add(u,multiply(inverse(u),v)),add(v,u)),
inference(rew,[status(thm),theory(equality)],[685,391]),
[iquote('0:Rew:685.0,391.0')] ).
cnf(753,plain,
equal(add(add(u,inverse(v)),v),add(v,inverse(v))),
inference(spr,[status(thm),theory(equality)],[29,695]),
[iquote('0:SpR:29.0,695.0')] ).
cnf(754,plain,
equal(add(add(inverse(u),v),u),add(u,inverse(u))),
inference(spr,[status(thm),theory(equality)],[40,695]),
[iquote('0:SpR:40.0,695.0')] ).
cnf(763,plain,
equal(add(u,add(v,inverse(v))),add(v,inverse(v))),
inference(rew,[status(thm),theory(equality)],[7,753,9]),
[iquote('0:Rew:7.0,753.0,9.0,753.0')] ).
cnf(764,plain,
equal(add(inverse(u),add(v,u)),add(u,inverse(u))),
inference(rew,[status(thm),theory(equality)],[9,754]),
[iquote('0:Rew:9.0,754.0')] ).
cnf(765,plain,
equal(add(u,add(inverse(u),v)),add(u,inverse(u))),
inference(rew,[status(thm),theory(equality)],[495,764]),
[iquote('0:Rew:495.0,764.0')] ).
cnf(1084,plain,
equal(multiply(u,add(v,inverse(v))),u),
inference(spr,[status(thm),theory(equality)],[763,40]),
[iquote('0:SpR:763.0,40.0')] ).
cnf(1219,plain,
equal(add(u,inverse(u)),add(add(v,inverse(v)),u)),
inference(spr,[status(thm),theory(equality)],[1084,695]),
[iquote('0:SpR:1084.0,695.0')] ).
cnf(1228,plain,
equal(add(u,inverse(u)),add(v,add(inverse(v),u))),
inference(rew,[status(thm),theory(equality)],[9,1219]),
[iquote('0:Rew:9.0,1219.0')] ).
cnf(1229,plain,
equal(add(u,inverse(u)),add(v,inverse(v))),
inference(rew,[status(thm),theory(equality)],[765,1228]),
[iquote('0:Rew:765.0,1228.0')] ).
cnf(1230,plain,
$false,
inference(unc,[status(thm)],[1229,11]),
[iquote('0:UnC:1229.0,11.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : BOO029-1 : TPTP v8.1.0. Released v2.2.0.
% 0.03/0.12 % Command : run_spass %d %s
% 0.13/0.33 % Computer : n026.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Thu Jun 2 00:25:12 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.36/0.54
% 0.36/0.54 SPASS V 3.9
% 0.36/0.54 SPASS beiseite: Proof found.
% 0.36/0.54 % SZS status Theorem
% 0.36/0.54 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.36/0.54 SPASS derived 837 clauses, backtracked 0 clauses, performed 0 splits and kept 219 clauses.
% 0.36/0.54 SPASS allocated 64337 KBytes.
% 0.36/0.54 SPASS spent 0:00:00.17 on the problem.
% 0.36/0.54 0:00:00.03 for the input.
% 0.36/0.54 0:00:00.00 for the FLOTTER CNF translation.
% 0.36/0.54 0:00:00.01 for inferences.
% 0.36/0.54 0:00:00.00 for the backtracking.
% 0.36/0.54 0:00:00.11 for the reduction.
% 0.36/0.54
% 0.36/0.54
% 0.36/0.54 Here is a proof with depth 5, length 29 :
% 0.36/0.54 % SZS output start Refutation
% See solution above
% 0.36/0.54 Formulae used in the proof : l1 b1 l2 b2 commutativity_of_add commutativity_of_multiply associativity_of_add associativity_of_multiply prove_equal_inverse
% 0.36/0.54
%------------------------------------------------------------------------------