%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : RNG019-7 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n018.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 20:41:13 EDT 2022
% Result : Unsatisfiable 0.14s 0.52s
% Output : Refutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 9
% Syntax : Number of clauses : 33 ( 33 unt; 0 nHn; 33 RR)
% Number of literals : 33 ( 0 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 9 con; 0-3 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(8,axiom,
~ equal(add(associator(x__dfg,y__dfg,u__dfg),associator(x__dfg,y__dfg,v__dfg)),associator(x__dfg,y__dfg,add(u__dfg,v__dfg))),
file('RNG019-7.p',unknown),
[] ).
cnf(9,axiom,
equal(add(additive_identity,u),u),
file('RNG019-7.p',unknown),
[] ).
cnf(10,axiom,
equal(add(u,additive_identity),u),
file('RNG019-7.p',unknown),
[] ).
cnf(14,axiom,
equal(add(u,additive_inverse(u)),additive_identity),
file('RNG019-7.p',unknown),
[] ).
cnf(15,axiom,
equal(additive_inverse(additive_inverse(u)),u),
file('RNG019-7.p',unknown),
[] ).
cnf(16,axiom,
equal(multiply(u,add(v,w)),add(multiply(u,v),multiply(u,w))),
file('RNG019-7.p',unknown),
[] ).
cnf(18,axiom,
equal(add(u,v),add(v,u)),
file('RNG019-7.p',unknown),
[] ).
cnf(19,axiom,
equal(add(add(u,v),w),add(u,add(v,w))),
file('RNG019-7.p',unknown),
[] ).
cnf(22,axiom,
equal(add(multiply(multiply(u,v),w),additive_inverse(multiply(u,multiply(v,w)))),associator(u,v,w)),
file('RNG019-7.p',unknown),
[] ).
cnf(30,plain,
equal(add(additive_inverse(multiply(u,multiply(v,w))),multiply(multiply(u,v),w)),associator(u,v,w)),
inference(rew,[status(thm),theory(equality)],[18,22]),
[iquote('0:Rew:18.0,22.0')] ).
cnf(104,plain,
equal(add(u,add(v,additive_inverse(add(u,v)))),additive_identity),
inference(spr,[status(thm),theory(equality)],[19,14]),
[iquote('0:SpR:19.0,14.0')] ).
cnf(109,plain,
equal(add(add(u,v),w),add(v,add(u,w))),
inference(spr,[status(thm),theory(equality)],[18,19]),
[iquote('0:SpR:18.0,19.0')] ).
cnf(111,plain,
equal(add(u,add(additive_inverse(u),v)),add(additive_identity,v)),
inference(spr,[status(thm),theory(equality)],[14,19]),
[iquote('0:SpR:14.0,19.0')] ).
cnf(115,plain,
equal(add(u,add(additive_inverse(u),v)),v),
inference(rew,[status(thm),theory(equality)],[9,111]),
[iquote('0:Rew:9.0,111.0')] ).
cnf(116,plain,
equal(add(u,add(v,w)),add(v,add(u,w))),
inference(rew,[status(thm),theory(equality)],[19,109]),
[iquote('0:Rew:19.0,109.0')] ).
cnf(287,plain,
equal(add(u,additive_inverse(add(additive_inverse(v),u))),add(v,additive_identity)),
inference(spr,[status(thm),theory(equality)],[104,115]),
[iquote('0:SpR:104.0,115.0')] ).
cnf(304,plain,
equal(add(u,additive_inverse(add(additive_inverse(v),u))),v),
inference(rew,[status(thm),theory(equality)],[10,287]),
[iquote('0:Rew:10.0,287.0')] ).
cnf(362,plain,
equal(add(u,additive_inverse(add(v,u))),additive_inverse(v)),
inference(spr,[status(thm),theory(equality)],[15,304]),
[iquote('0:SpR:15.0,304.0')] ).
cnf(396,plain,
equal(add(u,additive_inverse(v)),additive_inverse(add(v,additive_inverse(u)))),
inference(spr,[status(thm),theory(equality)],[362,115]),
[iquote('0:SpR:362.0,115.0')] ).
cnf(400,plain,
equal(add(u,additive_inverse(add(u,v))),additive_inverse(v)),
inference(spr,[status(thm),theory(equality)],[18,362]),
[iquote('0:SpR:18.0,362.0')] ).
cnf(406,plain,
equal(add(u,additive_inverse(add(v,add(w,u)))),additive_inverse(add(v,w))),
inference(spr,[status(thm),theory(equality)],[19,362]),
[iquote('0:SpR:19.0,362.0')] ).
cnf(462,plain,
equal(add(additive_inverse(u),v),additive_inverse(add(u,additive_inverse(v)))),
inference(spr,[status(thm),theory(equality)],[396,18]),
[iquote('0:SpR:396.0,18.0')] ).
cnf(515,plain,
equal(additive_inverse(add(multiply(u,multiply(v,w)),additive_inverse(multiply(multiply(u,v),w)))),associator(u,v,w)),
inference(rew,[status(thm),theory(equality)],[462,30]),
[iquote('0:Rew:462.0,30.0')] ).
cnf(1005,plain,
equal(add(u,additive_inverse(add(v,add(u,w)))),additive_inverse(add(v,w))),
inference(spr,[status(thm),theory(equality)],[116,400]),
[iquote('0:SpR:116.0,400.0')] ).
cnf(1126,plain,
equal(additive_inverse(additive_inverse(multiply(multiply(u,v),w))),add(multiply(u,multiply(v,w)),associator(u,v,w))),
inference(spr,[status(thm),theory(equality)],[515,400]),
[iquote('0:SpR:515.0,400.0')] ).
cnf(1144,plain,
equal(additive_inverse(add(multiply(u,add(multiply(v,w),multiply(v,x))),additive_inverse(multiply(multiply(u,v),add(w,x))))),associator(u,v,add(w,x))),
inference(spr,[status(thm),theory(equality)],[16,515]),
[iquote('0:SpR:16.0,515.0')] ).
cnf(1164,plain,
equal(multiply(multiply(u,v),w),add(associator(u,v,w),multiply(u,multiply(v,w)))),
inference(rew,[status(thm),theory(equality)],[15,1126,18]),
[iquote('0:Rew:15.0,1126.0,18.0,1126.0')] ).
cnf(1241,plain,
equal(additive_inverse(add(multiply(u,multiply(v,w)),add(multiply(u,multiply(v,x)),additive_inverse(add(multiply(multiply(u,v),w),multiply(multiply(u,v),x)))))),associator(u,v,add(w,x))),
inference(rew,[status(thm),theory(equality)],[19,1144,16]),
[iquote('0:Rew:19.0,1144.0,16.0,1144.0,16.0,1144.0')] ).
cnf(1242,plain,
equal(additive_inverse(add(multiply(u,multiply(v,w)),additive_inverse(add(add(associator(u,v,w),multiply(u,multiply(v,w))),associator(u,v,x))))),associator(u,v,add(w,x))),
inference(rew,[status(thm),theory(equality)],[406,1241,1164]),
[iquote('0:Rew:406.0,1241.0,1164.0,1241.0,1164.0,1241.0')] ).
cnf(1243,plain,
equal(additive_inverse(add(multiply(u,multiply(v,w)),additive_inverse(add(associator(u,v,w),add(multiply(u,multiply(v,w)),associator(u,v,x)))))),associator(u,v,add(w,x))),
inference(rew,[status(thm),theory(equality)],[19,1242]),
[iquote('0:Rew:19.0,1242.0')] ).
cnf(1244,plain,
equal(additive_inverse(additive_inverse(add(associator(u,v,w),associator(u,v,x)))),associator(u,v,add(w,x))),
inference(rew,[status(thm),theory(equality)],[1005,1243]),
[iquote('0:Rew:1005.0,1243.0')] ).
cnf(1245,plain,
equal(add(associator(u,v,w),associator(u,v,x)),associator(u,v,add(w,x))),
inference(rew,[status(thm),theory(equality)],[15,1244]),
[iquote('0:Rew:15.0,1244.0')] ).
cnf(1246,plain,
$false,
inference(unc,[status(thm)],[1245,8]),
[iquote('0:UnC:1245.0,8.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : RNG019-7 : TPTP v8.1.0. Released v1.0.0.
% 0.00/0.10 % Command : run_spass %d %s
% 0.09/0.30 % Computer : n018.cluster.edu
% 0.09/0.30 % Model : x86_64 x86_64
% 0.09/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.30 % Memory : 8042.1875MB
% 0.09/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.30 % CPULimit : 300
% 0.09/0.30 % WCLimit : 600
% 0.09/0.30 % DateTime : Mon May 30 16:34:12 EDT 2022
% 0.09/0.30 % CPUTime :
% 0.14/0.52
% 0.14/0.52 SPASS V 3.9
% 0.14/0.52 SPASS beiseite: Proof found.
% 0.14/0.52 % SZS status Theorem
% 0.14/0.52 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.14/0.52 SPASS derived 675 clauses, backtracked 0 clauses, performed 0 splits and kept 180 clauses.
% 0.14/0.52 SPASS allocated 65001 KBytes.
% 0.14/0.52 SPASS spent 0:00:00.20 on the problem.
% 0.14/0.52 0:00:00.03 for the input.
% 0.14/0.52 0:00:00.00 for the FLOTTER CNF translation.
% 0.14/0.52 0:00:00.01 for inferences.
% 0.14/0.52 0:00:00.00 for the backtracking.
% 0.14/0.52 0:00:00.14 for the reduction.
% 0.14/0.52
% 0.14/0.52
% 0.14/0.52 Here is a proof with depth 5, length 33 :
% 0.14/0.52 % SZS output start Refutation
% See solution above
% 0.14/0.52 Formulae used in the proof : prove_linearised_form1 left_additive_identity right_additive_identity right_additive_inverse additive_inverse_additive_inverse distribute1 commutativity_for_addition associativity_for_addition associator
% 0.14/0.52
%------------------------------------------------------------------------------