%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : BOO016-2 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n021.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 23:49:27 EDT 2022
% Result : Unsatisfiable 0.21s 0.49s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 10
% Syntax : Number of clauses : 28 ( 28 unt; 0 nHn; 28 RR)
% Number of literals : 28 ( 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 : 11 ( 11 usr; 8 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
equal(multiply(x__dfg,y__dfg),z__dfg),
file('BOO016-2.p',unknown),
[] ).
cnf(2,axiom,
~ equal(add(x__dfg,z__dfg),x__dfg),
file('BOO016-2.p',unknown),
[] ).
cnf(3,axiom,
equal(add(u,v),add(v,u)),
file('BOO016-2.p',unknown),
[] ).
cnf(4,axiom,
equal(multiply(u,v),multiply(v,u)),
file('BOO016-2.p',unknown),
[] ).
cnf(5,axiom,
equal(multiply(add(u,v),add(w,v)),add(multiply(u,w),v)),
file('BOO016-2.p',unknown),
[] ).
cnf(8,axiom,
equal(add(multiply(u,v),multiply(u,w)),multiply(u,add(v,w))),
file('BOO016-2.p',unknown),
[] ).
cnf(9,axiom,
equal(add(u,inverse(u)),multiplicative_identity),
file('BOO016-2.p',unknown),
[] ).
cnf(11,axiom,
equal(multiply(u,inverse(u)),additive_identity),
file('BOO016-2.p',unknown),
[] ).
cnf(13,axiom,
equal(multiply(u,multiplicative_identity),u),
file('BOO016-2.p',unknown),
[] ).
cnf(16,axiom,
equal(add(additive_identity,u),u),
file('BOO016-2.p',unknown),
[] ).
cnf(89,plain,
equal(multiply(add(u,v),v),add(multiply(u,additive_identity),v)),
inference(spr,[status(thm),theory(equality)],[16,5]),
[iquote('0:SpR:16.0,5.0')] ).
cnf(103,plain,
equal(multiply(u,add(v,u)),add(multiply(v,additive_identity),u)),
inference(rew,[status(thm),theory(equality)],[4,89]),
[iquote('0:Rew:4.0,89.0')] ).
cnf(171,plain,
equal(add(multiply(u,v),u),multiply(u,add(v,multiplicative_identity))),
inference(spr,[status(thm),theory(equality)],[13,8]),
[iquote('0:SpR:13.0,8.0')] ).
cnf(172,plain,
equal(multiply(u,add(v,inverse(u))),add(multiply(u,v),additive_identity)),
inference(spr,[status(thm),theory(equality)],[11,8]),
[iquote('0:SpR:11.0,8.0')] ).
cnf(192,plain,
equal(add(u,multiply(u,v)),multiply(u,add(v,multiplicative_identity))),
inference(rew,[status(thm),theory(equality)],[3,171]),
[iquote('0:Rew:3.0,171.0')] ).
cnf(196,plain,
equal(multiply(u,add(v,inverse(u))),multiply(u,v)),
inference(rew,[status(thm),theory(equality)],[16,172,3]),
[iquote('0:Rew:16.0,172.0,3.0,172.0')] ).
cnf(219,plain,
equal(multiply(u,inverse(u)),multiply(u,additive_identity)),
inference(spr,[status(thm),theory(equality)],[16,196]),
[iquote('0:SpR:16.0,196.0')] ).
cnf(221,plain,
equal(multiply(u,multiplicative_identity),multiply(u,u)),
inference(spr,[status(thm),theory(equality)],[9,196]),
[iquote('0:SpR:9.0,196.0')] ).
cnf(223,plain,
equal(multiply(u,u),u),
inference(rew,[status(thm),theory(equality)],[13,221]),
[iquote('0:Rew:13.0,221.0')] ).
cnf(225,plain,
equal(multiply(u,additive_identity),additive_identity),
inference(rew,[status(thm),theory(equality)],[11,219]),
[iquote('0:Rew:11.0,219.0')] ).
cnf(226,plain,
equal(multiply(u,add(v,u)),add(additive_identity,u)),
inference(rew,[status(thm),theory(equality)],[225,103]),
[iquote('0:Rew:225.0,103.0')] ).
cnf(228,plain,
equal(multiply(u,add(v,u)),u),
inference(rew,[status(thm),theory(equality)],[16,226]),
[iquote('0:Rew:16.0,226.0')] ).
cnf(278,plain,
equal(add(multiply(u,v),u),multiply(u,add(v,u))),
inference(spr,[status(thm),theory(equality)],[223,8]),
[iquote('0:SpR:223.0,8.0')] ).
cnf(296,plain,
equal(add(u,multiply(u,v)),multiply(u,add(v,u))),
inference(rew,[status(thm),theory(equality)],[3,278]),
[iquote('0:Rew:3.0,278.0')] ).
cnf(297,plain,
equal(multiply(u,add(v,multiplicative_identity)),u),
inference(rew,[status(thm),theory(equality)],[192,296,228]),
[iquote('0:Rew:192.0,296.0,228.0,296.0')] ).
cnf(298,plain,
equal(add(u,multiply(u,v)),u),
inference(rew,[status(thm),theory(equality)],[297,192]),
[iquote('0:Rew:297.0,192.0')] ).
cnf(550,plain,
equal(add(x__dfg,z__dfg),x__dfg),
inference(spr,[status(thm),theory(equality)],[1,298]),
[iquote('0:SpR:1.0,298.0')] ).
cnf(567,plain,
$false,
inference(mrr,[status(thm)],[550,2]),
[iquote('0:MRR:550.0,2.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : BOO016-2 : TPTP v8.1.0. Released v1.0.0.
% 0.12/0.14 % Command : run_spass %d %s
% 0.13/0.35 % Computer : n021.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 600
% 0.13/0.35 % DateTime : Wed Jun 1 15:32:45 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.21/0.49
% 0.21/0.49 SPASS V 3.9
% 0.21/0.49 SPASS beiseite: Proof found.
% 0.21/0.49 % SZS status Theorem
% 0.21/0.49 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.21/0.49 SPASS derived 380 clauses, backtracked 0 clauses, performed 0 splits and kept 152 clauses.
% 0.21/0.49 SPASS allocated 63688 KBytes.
% 0.21/0.49 SPASS spent 0:00:00.12 on the problem.
% 0.21/0.49 0:00:00.03 for the input.
% 0.21/0.49 0:00:00.00 for the FLOTTER CNF translation.
% 0.21/0.49 0:00:00.00 for inferences.
% 0.21/0.49 0:00:00.00 for the backtracking.
% 0.21/0.49 0:00:00.06 for the reduction.
% 0.21/0.49
% 0.21/0.49
% 0.21/0.49 Here is a proof with depth 3, length 28 :
% 0.21/0.49 % SZS output start Refutation
% See solution above
% 0.21/0.49 Formulae used in the proof : x_times_y prove_sum commutativity_of_add commutativity_of_multiply distributivity1 distributivity4 additive_inverse1 multiplicative_inverse1 multiplicative_id1 additive_id2
% 0.21/0.49
%------------------------------------------------------------------------------