%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : RNG020-6 : TPTP v8.1.0. Released v1.0.0.
% 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 : Mon Jul 18 20:41:13 EDT 2022
% Result : Unsatisfiable 0.19s 0.55s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 10
% Syntax : Number of clauses : 34 ( 34 unt; 0 nHn; 34 RR)
% Number of literals : 34 ( 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(1,axiom,
~ equal(add(associator(x__dfg,u__dfg,y__dfg),associator(x__dfg,v__dfg,y__dfg)),associator(x__dfg,add(u__dfg,v__dfg),y__dfg)),
file('RNG020-6.p',unknown),
[] ).
cnf(2,axiom,
equal(add(additive_identity,u),u),
file('RNG020-6.p',unknown),
[] ).
cnf(3,axiom,
equal(add(u,additive_identity),u),
file('RNG020-6.p',unknown),
[] ).
cnf(7,axiom,
equal(add(u,additive_inverse(u)),additive_identity),
file('RNG020-6.p',unknown),
[] ).
cnf(8,axiom,
equal(additive_inverse(additive_inverse(u)),u),
file('RNG020-6.p',unknown),
[] ).
cnf(9,axiom,
equal(multiply(u,add(v,w)),add(multiply(u,v),multiply(u,w))),
file('RNG020-6.p',unknown),
[] ).
cnf(10,axiom,
equal(multiply(add(u,v),w),add(multiply(u,w),multiply(v,w))),
file('RNG020-6.p',unknown),
[] ).
cnf(11,axiom,
equal(add(u,v),add(v,u)),
file('RNG020-6.p',unknown),
[] ).
cnf(12,axiom,
equal(add(add(u,v),w),add(u,add(v,w))),
file('RNG020-6.p',unknown),
[] ).
cnf(15,axiom,
equal(add(multiply(multiply(u,v),w),additive_inverse(multiply(u,multiply(v,w)))),associator(u,v,w)),
file('RNG020-6.p',unknown),
[] ).
cnf(18,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)],[11,15]),
[iquote('0:Rew:11.0,15.0')] ).
cnf(64,plain,
equal(add(u,add(v,additive_inverse(add(u,v)))),additive_identity),
inference(spr,[status(thm),theory(equality)],[12,7]),
[iquote('0:SpR:12.0,7.0')] ).
cnf(69,plain,
equal(add(add(u,v),w),add(v,add(u,w))),
inference(spr,[status(thm),theory(equality)],[11,12]),
[iquote('0:SpR:11.0,12.0')] ).
cnf(71,plain,
equal(add(u,add(additive_inverse(u),v)),add(additive_identity,v)),
inference(spr,[status(thm),theory(equality)],[7,12]),
[iquote('0:SpR:7.0,12.0')] ).
cnf(75,plain,
equal(add(u,add(additive_inverse(u),v)),v),
inference(rew,[status(thm),theory(equality)],[2,71]),
[iquote('0:Rew:2.0,71.0')] ).
cnf(76,plain,
equal(add(u,add(v,w)),add(v,add(u,w))),
inference(rew,[status(thm),theory(equality)],[12,69]),
[iquote('0:Rew:12.0,69.0')] ).
cnf(120,plain,
equal(add(u,additive_inverse(add(additive_inverse(v),u))),add(v,additive_identity)),
inference(spr,[status(thm),theory(equality)],[64,75]),
[iquote('0:SpR:64.0,75.0')] ).
cnf(136,plain,
equal(add(u,additive_inverse(add(additive_inverse(v),u))),v),
inference(rew,[status(thm),theory(equality)],[3,120]),
[iquote('0:Rew:3.0,120.0')] ).
cnf(185,plain,
equal(add(u,additive_inverse(add(v,u))),additive_inverse(v)),
inference(spr,[status(thm),theory(equality)],[8,136]),
[iquote('0:SpR:8.0,136.0')] ).
cnf(245,plain,
equal(add(u,additive_inverse(v)),additive_inverse(add(v,additive_inverse(u)))),
inference(spr,[status(thm),theory(equality)],[185,75]),
[iquote('0:SpR:185.0,75.0')] ).
cnf(249,plain,
equal(add(u,additive_inverse(add(u,v))),additive_inverse(v)),
inference(spr,[status(thm),theory(equality)],[11,185]),
[iquote('0:SpR:11.0,185.0')] ).
cnf(255,plain,
equal(add(u,additive_inverse(add(v,add(w,u)))),additive_inverse(add(v,w))),
inference(spr,[status(thm),theory(equality)],[12,185]),
[iquote('0:SpR:12.0,185.0')] ).
cnf(390,plain,
equal(add(additive_inverse(u),v),additive_inverse(add(u,additive_inverse(v)))),
inference(spr,[status(thm),theory(equality)],[245,11]),
[iquote('0:SpR:245.0,11.0')] ).
cnf(440,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)],[390,18]),
[iquote('0:Rew:390.0,18.0')] ).
cnf(1015,plain,
equal(add(u,additive_inverse(add(v,add(u,w)))),additive_inverse(add(v,w))),
inference(spr,[status(thm),theory(equality)],[76,249]),
[iquote('0:SpR:76.0,249.0')] ).
cnf(1197,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)],[440,249]),
[iquote('0:SpR:440.0,249.0')] ).
cnf(1221,plain,
equal(additive_inverse(add(multiply(u,add(multiply(v,w),multiply(x,w))),additive_inverse(multiply(multiply(u,add(v,x)),w)))),associator(u,add(v,x),w)),
inference(spr,[status(thm),theory(equality)],[10,440]),
[iquote('0:SpR:10.0,440.0')] ).
cnf(1239,plain,
equal(multiply(multiply(u,v),w),add(associator(u,v,w),multiply(u,multiply(v,w)))),
inference(rew,[status(thm),theory(equality)],[8,1197,11]),
[iquote('0:Rew:8.0,1197.0,11.0,1197.0')] ).
cnf(1326,plain,
equal(additive_inverse(add(multiply(u,multiply(v,w)),add(multiply(u,multiply(x,w)),additive_inverse(add(multiply(multiply(u,v),w),multiply(multiply(u,x),w)))))),associator(u,add(v,x),w)),
inference(rew,[status(thm),theory(equality)],[12,1221,9,10]),
[iquote('0:Rew:12.0,1221.0,9.0,1221.0,10.0,1221.0,9.0,1221.0')] ).
cnf(1327,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,x,w))))),associator(u,add(v,x),w)),
inference(rew,[status(thm),theory(equality)],[255,1326,1239]),
[iquote('0:Rew:255.0,1326.0,1239.0,1326.0,1239.0,1326.0')] ).
cnf(1328,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,x,w)))))),associator(u,add(v,x),w)),
inference(rew,[status(thm),theory(equality)],[12,1327]),
[iquote('0:Rew:12.0,1327.0')] ).
cnf(1329,plain,
equal(additive_inverse(additive_inverse(add(associator(u,v,w),associator(u,x,w)))),associator(u,add(v,x),w)),
inference(rew,[status(thm),theory(equality)],[1015,1328]),
[iquote('0:Rew:1015.0,1328.0')] ).
cnf(1330,plain,
equal(add(associator(u,v,w),associator(u,x,w)),associator(u,add(v,x),w)),
inference(rew,[status(thm),theory(equality)],[8,1329]),
[iquote('0:Rew:8.0,1329.0')] ).
cnf(1331,plain,
$false,
inference(unc,[status(thm)],[1330,1]),
[iquote('0:UnC:1330.0,1.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11 % Problem : RNG020-6 : TPTP v8.1.0. Released v1.0.0.
% 0.11/0.12 % Command : run_spass %d %s
% 0.11/0.33 % Computer : n020.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 600
% 0.11/0.33 % DateTime : Mon May 30 05:13:24 EDT 2022
% 0.11/0.33 % CPUTime :
% 0.19/0.55
% 0.19/0.55 SPASS V 3.9
% 0.19/0.55 SPASS beiseite: Proof found.
% 0.19/0.55 % SZS status Theorem
% 0.19/0.55 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.55 SPASS derived 715 clauses, backtracked 0 clauses, performed 0 splits and kept 205 clauses.
% 0.19/0.55 SPASS allocated 65219 KBytes.
% 0.19/0.55 SPASS spent 0:00:00.20 on the problem.
% 0.19/0.55 0:00:00.04 for the input.
% 0.19/0.55 0:00:00.00 for the FLOTTER CNF translation.
% 0.19/0.55 0:00:00.01 for inferences.
% 0.19/0.55 0:00:00.00 for the backtracking.
% 0.19/0.55 0:00:00.14 for the reduction.
% 0.19/0.55
% 0.19/0.55
% 0.19/0.55 Here is a proof with depth 5, length 34 :
% 0.19/0.55 % SZS output start Refutation
% See solution above
% 0.19/0.55 Formulae used in the proof : prove_linearised_form2 left_additive_identity right_additive_identity right_additive_inverse additive_inverse_additive_inverse distribute1 distribute2 commutativity_for_addition associativity_for_addition associator
% 0.19/0.55
%------------------------------------------------------------------------------