%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : RNG128-1 : TPTP v8.1.0. Released v5.4.0.
% 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 : Mon Jul 18 20:41:34 EDT 2022
% Result : Unsatisfiable 0.15s 0.39s
% Output : Refutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 8
% Syntax : Number of clauses : 46 ( 46 unt; 0 nHn; 46 RR)
% Number of literals : 46 ( 0 equ; 3 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 7 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
equal(add(add(u,v),w),add(u,add(v,w))),
file('RNG128-1.p',unknown),
[] ).
cnf(2,axiom,
equal(add(u,v),add(v,u)),
file('RNG128-1.p',unknown),
[] ).
cnf(3,axiom,
equal(mult(u,v),mult(v,u)),
file('RNG128-1.p',unknown),
[] ).
cnf(4,axiom,
equal(mult(u,add(v,w)),add(mult(u,v),mult(u,w))),
file('RNG128-1.p',unknown),
[] ).
cnf(5,axiom,
equal(add(zero,u),u),
file('RNG128-1.p',unknown),
[] ).
cnf(6,axiom,
equal(mult(u,unit),u),
file('RNG128-1.p',unknown),
[] ).
cnf(7,axiom,
equal(add(unit,add(u,mult(u,u))),u),
file('RNG128-1.p',unknown),
[] ).
cnf(8,axiom,
~ equal(mult(x0__dfg,x1__dfg),add(x0__dfg,x1__dfg)),
file('RNG128-1.p',unknown),
[] ).
cnf(21,plain,
equal(add(u,zero),u),
inference(spr,[status(thm),theory(equality)],[2,5]),
[iquote('0:SpR:2.0,5.0')] ).
cnf(32,plain,
equal(add(unit,add(unit,unit)),unit),
inference(spr,[status(thm),theory(equality)],[6,7]),
[iquote('0:SpR:6.0,7.0')] ).
cnf(36,plain,
equal(add(unit,mult(zero,zero)),zero),
inference(spr,[status(thm),theory(equality)],[5,7]),
[iquote('0:SpR:5.0,7.0')] ).
cnf(47,plain,
equal(add(add(u,v),w),add(v,add(u,w))),
inference(spr,[status(thm),theory(equality)],[2,1]),
[iquote('0:SpR:2.0,1.0')] ).
cnf(50,plain,
equal(add(unit,add(add(u,mult(u,u)),v)),add(u,v)),
inference(spr,[status(thm),theory(equality)],[7,1]),
[iquote('0:SpR:7.0,1.0')] ).
cnf(54,plain,
equal(add(u,add(v,w)),add(v,add(u,w))),
inference(rew,[status(thm),theory(equality)],[1,47]),
[iquote('0:Rew:1.0,47.0')] ).
cnf(57,plain,
equal(add(unit,add(u,add(mult(u,u),v))),add(u,v)),
inference(rew,[status(thm),theory(equality)],[1,50]),
[iquote('0:Rew:1.0,50.0')] ).
cnf(63,plain,
equal(add(unit,add(mult(zero,zero),u)),add(zero,u)),
inference(spr,[status(thm),theory(equality)],[36,1]),
[iquote('0:SpR:36.0,1.0')] ).
cnf(67,plain,
equal(add(unit,add(mult(zero,zero),u)),u),
inference(rew,[status(thm),theory(equality)],[5,63]),
[iquote('0:Rew:5.0,63.0')] ).
cnf(102,plain,
equal(add(mult(u,zero),mult(u,v)),mult(u,v)),
inference(spr,[status(thm),theory(equality)],[5,4]),
[iquote('0:SpR:5.0,4.0')] ).
cnf(105,plain,
equal(add(mult(u,v),mult(u,zero)),mult(u,v)),
inference(spr,[status(thm),theory(equality)],[21,4]),
[iquote('0:SpR:21.0,4.0')] ).
cnf(108,plain,
equal(add(mult(u,unit),mult(u,add(unit,unit))),mult(u,unit)),
inference(spr,[status(thm),theory(equality)],[32,4]),
[iquote('0:SpR:32.0,4.0')] ).
cnf(115,plain,
equal(add(u,add(u,u)),u),
inference(rew,[status(thm),theory(equality)],[6,108,4]),
[iquote('0:Rew:6.0,108.0,4.0,108.0,6.0,108.0')] ).
cnf(123,plain,
equal(add(mult(zero,zero),mult(zero,zero)),add(unit,mult(zero,zero))),
inference(spr,[status(thm),theory(equality)],[115,67]),
[iquote('0:SpR:115.0,67.0')] ).
cnf(134,plain,
equal(add(mult(zero,zero),mult(zero,zero)),zero),
inference(rew,[status(thm),theory(equality)],[36,123]),
[iquote('0:Rew:36.0,123.0')] ).
cnf(135,plain,
equal(mult(zero,zero),zero),
inference(rew,[status(thm),theory(equality)],[105,134]),
[iquote('0:Rew:105.0,134.0')] ).
cnf(136,plain,
equal(add(unit,zero),zero),
inference(rew,[status(thm),theory(equality)],[135,36]),
[iquote('0:Rew:135.0,36.0')] ).
cnf(145,plain,
equal(unit,zero),
inference(rew,[status(thm),theory(equality)],[21,136]),
[iquote('0:Rew:21.0,136.0')] ).
cnf(146,plain,
equal(mult(u,zero),u),
inference(rew,[status(thm),theory(equality)],[145,6]),
[iquote('0:Rew:145.0,6.0')] ).
cnf(148,plain,
equal(add(zero,add(u,mult(u,u))),u),
inference(rew,[status(thm),theory(equality)],[145,7]),
[iquote('0:Rew:145.0,7.0')] ).
cnf(149,plain,
equal(add(zero,add(u,add(mult(u,u),v))),add(u,v)),
inference(rew,[status(thm),theory(equality)],[145,57]),
[iquote('0:Rew:145.0,57.0')] ).
cnf(151,plain,
equal(add(u,mult(u,v)),mult(u,v)),
inference(rew,[status(thm),theory(equality)],[146,102]),
[iquote('0:Rew:146.0,102.0')] ).
cnf(159,plain,
equal(add(u,mult(u,u)),u),
inference(rew,[status(thm),theory(equality)],[5,148]),
[iquote('0:Rew:5.0,148.0')] ).
cnf(160,plain,
equal(mult(u,u),u),
inference(rew,[status(thm),theory(equality)],[151,159]),
[iquote('0:Rew:151.0,159.0')] ).
cnf(171,plain,
equal(add(u,add(mult(u,u),v)),add(u,v)),
inference(rew,[status(thm),theory(equality)],[5,149]),
[iquote('0:Rew:5.0,149.0')] ).
cnf(172,plain,
equal(add(u,add(u,v)),add(u,v)),
inference(rew,[status(thm),theory(equality)],[160,171]),
[iquote('0:Rew:160.0,171.0')] ).
cnf(190,plain,
equal(add(mult(add(u,v),u),mult(add(u,v),v)),add(u,v)),
inference(spr,[status(thm),theory(equality)],[160,4]),
[iquote('0:SpR:160.0,4.0')] ).
cnf(195,plain,
equal(add(u,add(mult(u,v),add(v,mult(v,u)))),add(u,v)),
inference(rew,[status(thm),theory(equality)],[1,190,160,4,3,2]),
[iquote('0:Rew:1.0,190.0,160.0,190.0,4.0,190.0,3.0,190.0,2.0,190.0,160.0,190.0,4.0,190.0,3.0,190.0')] ).
cnf(196,plain,
equal(add(u,add(mult(u,v),mult(v,u))),add(u,v)),
inference(rew,[status(thm),theory(equality)],[151,195]),
[iquote('0:Rew:151.0,195.0')] ).
cnf(207,plain,
equal(add(u,add(mult(u,v),w)),add(mult(u,v),w)),
inference(spr,[status(thm),theory(equality)],[151,1]),
[iquote('0:SpR:151.0,1.0')] ).
cnf(211,plain,
equal(add(u,mult(v,u)),mult(v,u)),
inference(spr,[status(thm),theory(equality)],[3,151]),
[iquote('0:SpR:3.0,151.0')] ).
cnf(217,plain,
equal(add(mult(u,v),mult(v,u)),add(u,v)),
inference(rew,[status(thm),theory(equality)],[207,196]),
[iquote('0:Rew:207.0,196.0')] ).
cnf(227,plain,
equal(add(u,add(v,u)),add(v,u)),
inference(spr,[status(thm),theory(equality)],[2,172]),
[iquote('0:SpR:2.0,172.0')] ).
cnf(459,plain,
equal(add(mult(u,v),add(v,u)),add(v,u)),
inference(spr,[status(thm),theory(equality)],[217,227]),
[iquote('0:SpR:217.0,227.0')] ).
cnf(490,plain,
equal(mult(u,v),add(v,u)),
inference(rew,[status(thm),theory(equality)],[211,459,151,2,54]),
[iquote('0:Rew:211.0,459.0,151.0,459.0,2.0,459.0,54.0,459.0')] ).
cnf(491,plain,
~ equal(add(x1__dfg,x0__dfg),add(x0__dfg,x1__dfg)),
inference(rew,[status(thm),theory(equality)],[490,8]),
[iquote('0:Rew:490.0,8.0')] ).
cnf(509,plain,
~ equal(add(x0__dfg,x1__dfg),add(x0__dfg,x1__dfg)),
inference(rew,[status(thm),theory(equality)],[2,491]),
[iquote('0:Rew:2.0,491.0')] ).
cnf(510,plain,
$false,
inference(obv,[status(thm),theory(equality)],[509]),
[iquote('0:Obv:509.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.10 % Problem : RNG128-1 : TPTP v8.1.0. Released v5.4.0.
% 0.02/0.11 % Command : run_spass %d %s
% 0.09/0.30 % Computer : n032.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 10:02:42 EDT 2022
% 0.09/0.30 % CPUTime :
% 0.15/0.39
% 0.15/0.39 SPASS V 3.9
% 0.15/0.39 SPASS beiseite: Proof found.
% 0.15/0.39 % SZS status Theorem
% 0.15/0.39 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.15/0.39 SPASS derived 356 clauses, backtracked 0 clauses, performed 0 splits and kept 69 clauses.
% 0.15/0.39 SPASS allocated 63523 KBytes.
% 0.15/0.39 SPASS spent 0:00:00.08 on the problem.
% 0.15/0.39 0:00:00.03 for the input.
% 0.15/0.39 0:00:00.00 for the FLOTTER CNF translation.
% 0.15/0.39 0:00:00.00 for inferences.
% 0.15/0.39 0:00:00.00 for the backtracking.
% 0.15/0.39 0:00:00.02 for the reduction.
% 0.15/0.39
% 0.15/0.39
% 0.15/0.39 Here is a proof with depth 3, length 46 :
% 0.15/0.39 % SZS output start Refutation
% See solution above
% 0.15/0.39 Formulae used in the proof : sos sos_001 sos_002 sos_003 sos_004 sos_005 sos_006 goals
% 0.15/0.39
%------------------------------------------------------------------------------