TSTP Solution File: RNG007-1 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : RNG007-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n022.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 20:41:11 EDT 2022
% Result : Unsatisfiable 12.08s 12.30s
% Output : Refutation 12.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 14
% Syntax : Number of clauses : 63 ( 22 unt; 0 nHn; 63 RR)
% Number of literals : 132 ( 0 equ; 74 neg)
% Maximal clause size : 5 ( 2 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 12 ( 12 usr; 9 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
product(u,u,u),
file('RNG007-1.p',unknown),
[] ).
cnf(2,axiom,
~ sum__dfg(a,a,additive_identity),
file('RNG007-1.p',unknown),
[] ).
cnf(3,axiom,
sum__dfg(additive_identity,u,u),
file('RNG007-1.p',unknown),
[] ).
cnf(4,axiom,
sum__dfg(u,additive_identity,u),
file('RNG007-1.p',unknown),
[] ).
cnf(5,axiom,
product(u,v,multiply(u,v)),
file('RNG007-1.p',unknown),
[] ).
cnf(6,axiom,
sum__dfg(u,v,add(u,v)),
file('RNG007-1.p',unknown),
[] ).
cnf(7,axiom,
sum__dfg(additive_inverse(u),u,additive_identity),
file('RNG007-1.p',unknown),
[] ).
cnf(8,axiom,
sum__dfg(u,additive_inverse(u),additive_identity),
file('RNG007-1.p',unknown),
[] ).
cnf(9,axiom,
( ~ sum__dfg(u,v,w)
| ~ sum__dfg(x,v,y)
| ~ sum__dfg(z,x,u)
| sum__dfg(z,y,w) ),
file('RNG007-1.p',unknown),
[] ).
cnf(10,axiom,
( ~ sum__dfg(u,v,w)
| ~ sum__dfg(x,y,v)
| ~ sum__dfg(u,x,z)
| sum__dfg(z,y,w) ),
file('RNG007-1.p',unknown),
[] ).
cnf(11,axiom,
( ~ sum__dfg(u,v,w)
| sum__dfg(v,u,w) ),
file('RNG007-1.p',unknown),
[] ).
cnf(14,axiom,
( ~ product(u,v,w)
| ~ sum__dfg(x,y,v)
| ~ product(u,y,z)
| ~ product(u,x,x1)
| sum__dfg(x1,z,w) ),
file('RNG007-1.p',unknown),
[] ).
cnf(16,axiom,
( ~ product(u,v,w)
| ~ sum__dfg(x,y,u)
| ~ product(y,v,z)
| ~ product(x,v,x1)
| sum__dfg(x1,z,w) ),
file('RNG007-1.p',unknown),
[] ).
cnf(18,axiom,
( ~ sum__dfg(u,v,w)
| ~ sum__dfg(u,v,x)
| equal(x,w) ),
file('RNG007-1.p',unknown),
[] ).
cnf(24,plain,
( ~ sum__dfg(u,v,w)
| ~ product(x,w,additive_identity)
| ~ product(x,v,a)
| ~ product(x,u,a) ),
inference(res,[status(thm),theory(equality)],[14,2]),
[iquote('0:Res:14.4,2.0')] ).
cnf(29,plain,
sum__dfg(u,v,add(v,u)),
inference(res,[status(thm),theory(equality)],[6,11]),
[iquote('0:Res:6.0,11.0')] ).
cnf(39,plain,
( ~ sum__dfg(additive_identity,u,v)
| equal(v,u) ),
inference(res,[status(thm),theory(equality)],[3,18]),
[iquote('0:Res:3.0,18.0')] ).
cnf(40,plain,
( ~ sum__dfg(u,additive_identity,v)
| equal(v,u) ),
inference(res,[status(thm),theory(equality)],[4,18]),
[iquote('0:Res:4.0,18.0')] ).
cnf(42,plain,
( ~ sum__dfg(u,additive_inverse(u),v)
| equal(v,additive_identity) ),
inference(res,[status(thm),theory(equality)],[8,18]),
[iquote('0:Res:8.0,18.0')] ).
cnf(44,plain,
( ~ sum__dfg(u,v,w)
| equal(w,add(v,u)) ),
inference(res,[status(thm),theory(equality)],[29,18]),
[iquote('0:Res:29.0,18.0')] ).
cnf(49,plain,
equal(add(u,additive_identity),u),
inference(res,[status(thm),theory(equality)],[29,39]),
[iquote('0:Res:29.0,39.0')] ).
cnf(115,plain,
( ~ sum__dfg(u,v,w)
| ~ sum__dfg(additive_identity,u,x)
| sum__dfg(x,v,w) ),
inference(res,[status(thm),theory(equality)],[3,10]),
[iquote('0:Res:3.0,10.0')] ).
cnf(116,plain,
( ~ sum__dfg(u,v,additive_identity)
| ~ sum__dfg(w,u,x)
| sum__dfg(x,v,w) ),
inference(res,[status(thm),theory(equality)],[4,10]),
[iquote('0:Res:4.0,10.0')] ).
cnf(119,plain,
( ~ sum__dfg(u,v,w)
| ~ sum__dfg(x,u,y)
| sum__dfg(y,v,add(x,w)) ),
inference(res,[status(thm),theory(equality)],[6,10]),
[iquote('0:Res:6.0,10.0')] ).
cnf(124,plain,
( ~ sum__dfg(additive_identity,u,v)
| sum__dfg(v,additive_inverse(u),additive_identity) ),
inference(res,[status(thm),theory(equality)],[8,115]),
[iquote('0:Res:8.0,115.0')] ).
cnf(148,plain,
( ~ sum__dfg(u,v,w)
| ~ sum__dfg(x,u,additive_identity)
| sum__dfg(x,w,v) ),
inference(res,[status(thm),theory(equality)],[3,9]),
[iquote('0:Res:3.0,9.0')] ).
cnf(158,plain,
( ~ sum__dfg(additive_identity,u,v)
| equal(add(additive_inverse(u),v),additive_identity) ),
inference(res,[status(thm),theory(equality)],[124,44]),
[iquote('0:Res:124.1,44.0')] ).
cnf(307,plain,
( ~ sum__dfg(u,v,w)
| ~ product(v,w,x)
| ~ product(u,w,y)
| sum__dfg(y,x,w) ),
inference(res,[status(thm),theory(equality)],[1,16]),
[iquote('0:Res:1.0,16.0')] ).
cnf(308,plain,
( ~ sum__dfg(u,v,w)
| ~ product(v,x,y)
| ~ product(u,x,z)
| sum__dfg(z,y,multiply(w,x)) ),
inference(res,[status(thm),theory(equality)],[5,16]),
[iquote('0:Res:5.0,16.0')] ).
cnf(369,plain,
( ~ sum__dfg(u,v,w)
| ~ product(w,v,x)
| ~ product(w,u,y)
| sum__dfg(y,x,w) ),
inference(res,[status(thm),theory(equality)],[1,14]),
[iquote('0:Res:1.0,14.0')] ).
cnf(433,plain,
( ~ sum__dfg(u,additive_inverse(v),w)
| sum__dfg(w,v,u) ),
inference(res,[status(thm),theory(equality)],[7,116]),
[iquote('0:Res:7.0,116.0')] ).
cnf(435,plain,
( ~ sum__dfg(u,v,w)
| sum__dfg(w,additive_inverse(v),u) ),
inference(res,[status(thm),theory(equality)],[8,116]),
[iquote('0:Res:8.0,116.0')] ).
cnf(479,plain,
( ~ sum__dfg(u,additive_inverse(v),additive_identity)
| sum__dfg(u,additive_identity,v) ),
inference(res,[status(thm),theory(equality)],[7,148]),
[iquote('0:Res:7.0,148.0')] ).
cnf(498,plain,
sum__dfg(additive_inverse(additive_inverse(u)),additive_identity,u),
inference(res,[status(thm),theory(equality)],[7,479]),
[iquote('0:Res:7.0,479.0')] ).
cnf(516,plain,
equal(additive_inverse(additive_inverse(u)),u),
inference(res,[status(thm),theory(equality)],[498,40]),
[iquote('0:Res:498.0,40.0')] ).
cnf(826,plain,
sum__dfg(add(u,additive_inverse(v)),v,u),
inference(res,[status(thm),theory(equality)],[6,433]),
[iquote('0:Res:6.0,433.0')] ).
cnf(853,plain,
equal(add(u,add(v,additive_inverse(u))),v),
inference(res,[status(thm),theory(equality)],[826,44]),
[iquote('0:Res:826.0,44.0')] ).
cnf(1273,plain,
( ~ sum__dfg(additive_identity,u,additive_inverse(v))
| equal(add(v,additive_identity),additive_inverse(u)) ),
inference(spr,[status(thm),theory(equality)],[158,853]),
[iquote('0:SpR:158.1,853.0')] ).
cnf(1283,plain,
( ~ sum__dfg(additive_identity,u,additive_inverse(v))
| equal(v,additive_inverse(u)) ),
inference(rew,[status(thm),theory(equality)],[49,1273]),
[iquote('0:Rew:49.0,1273.1')] ).
cnf(2327,plain,
( ~ sum__dfg(u,v,w)
| sum__dfg(w,x,add(u,add(v,x))) ),
inference(res,[status(thm),theory(equality)],[6,119]),
[iquote('0:Res:6.0,119.0')] ).
cnf(3630,plain,
( ~ product(u,u,v)
| ~ product(additive_identity,u,w)
| sum__dfg(w,v,u) ),
inference(res,[status(thm),theory(equality)],[3,307]),
[iquote('0:Res:3.0,307.0')] ).
cnf(3997,plain,
( ~ product(u,u,v)
| ~ product(u,additive_identity,w)
| sum__dfg(w,v,u) ),
inference(res,[status(thm),theory(equality)],[3,369]),
[iquote('0:Res:3.0,369.0')] ).
cnf(4332,plain,
( ~ product(u,additive_identity,additive_identity)
| ~ product(u,v,a)
| ~ product(u,additive_inverse(v),a) ),
inference(res,[status(thm),theory(equality)],[7,24]),
[iquote('0:Res:7.0,24.0')] ).
cnf(5240,plain,
( ~ sum__dfg(u,v,v)
| equal(u,additive_identity) ),
inference(res,[status(thm),theory(equality)],[435,42]),
[iquote('0:Res:435.1,42.0')] ).
cnf(5857,plain,
( ~ product(additive_inverse(u),v,w)
| ~ product(u,v,x)
| sum__dfg(x,w,multiply(additive_identity,v)) ),
inference(res,[status(thm),theory(equality)],[8,308]),
[iquote('0:Res:8.0,308.0')] ).
cnf(8888,plain,
( ~ sum__dfg(u,v,w)
| sum__dfg(w,additive_inverse(u),v) ),
inference(spr,[status(thm),theory(equality)],[853,2327]),
[iquote('0:SpR:853.0,2327.1')] ).
cnf(9796,plain,
( ~ sum__dfg(u,additive_inverse(v),additive_identity)
| equal(v,additive_inverse(additive_inverse(u))) ),
inference(res,[status(thm),theory(equality)],[8888,1283]),
[iquote('0:Res:8888.1,1283.0')] ).
cnf(9864,plain,
( ~ sum__dfg(u,additive_inverse(v),additive_identity)
| equal(v,u) ),
inference(rew,[status(thm),theory(equality)],[516,9796]),
[iquote('0:Rew:516.0,9796.1')] ).
cnf(10225,plain,
( ~ product(additive_identity,u,v)
| sum__dfg(v,u,u) ),
inference(res,[status(thm),theory(equality)],[1,3630]),
[iquote('0:Res:1.0,3630.0')] ).
cnf(10298,plain,
( ~ product(additive_identity,u,v)
| equal(v,additive_identity) ),
inference(res,[status(thm),theory(equality)],[10225,5240]),
[iquote('0:Res:10225.1,5240.0')] ).
cnf(10392,plain,
equal(multiply(additive_identity,u),additive_identity),
inference(res,[status(thm),theory(equality)],[5,10298]),
[iquote('0:Res:5.0,10298.0')] ).
cnf(10403,plain,
( ~ product(additive_inverse(u),v,w)
| ~ product(u,v,x)
| sum__dfg(x,w,additive_identity) ),
inference(rew,[status(thm),theory(equality)],[10392,5857]),
[iquote('0:Rew:10392.0,5857.2')] ).
cnf(10422,plain,
( ~ product(u,additive_identity,v)
| sum__dfg(v,u,u) ),
inference(res,[status(thm),theory(equality)],[1,3997]),
[iquote('0:Res:1.0,3997.0')] ).
cnf(10995,plain,
( ~ product(u,additive_identity,v)
| equal(v,additive_identity) ),
inference(res,[status(thm),theory(equality)],[10422,5240]),
[iquote('0:Res:10422.1,5240.0')] ).
cnf(11089,plain,
equal(multiply(u,additive_identity),additive_identity),
inference(res,[status(thm),theory(equality)],[5,10995]),
[iquote('0:Res:5.0,10995.0')] ).
cnf(11130,plain,
product(u,additive_identity,additive_identity),
inference(spr,[status(thm),theory(equality)],[11089,5]),
[iquote('0:SpR:11089.0,5.0')] ).
cnf(11144,plain,
( ~ product(u,v,a)
| ~ product(u,additive_inverse(v),a) ),
inference(mrr,[status(thm)],[4332,11130]),
[iquote('0:MRR:4332.0,11130.0')] ).
cnf(11632,plain,
( ~ product(u,additive_inverse(u),v)
| sum__dfg(v,additive_inverse(u),additive_identity) ),
inference(res,[status(thm),theory(equality)],[1,10403]),
[iquote('0:Res:1.0,10403.0')] ).
cnf(22864,plain,
sum__dfg(multiply(u,additive_inverse(u)),additive_inverse(u),additive_identity),
inference(res,[status(thm),theory(equality)],[5,11632]),
[iquote('0:Res:5.0,11632.0')] ).
cnf(22933,plain,
equal(multiply(u,additive_inverse(u)),u),
inference(res,[status(thm),theory(equality)],[22864,9864]),
[iquote('0:Res:22864.0,9864.0')] ).
cnf(22991,plain,
product(u,additive_inverse(u),u),
inference(spr,[status(thm),theory(equality)],[22933,5]),
[iquote('0:SpR:22933.0,5.0')] ).
cnf(23043,plain,
~ product(a,a,a),
inference(res,[status(thm),theory(equality)],[22991,11144]),
[iquote('0:Res:22991.0,11144.1')] ).
cnf(23072,plain,
$false,
inference(mrr,[status(thm)],[23043,1]),
[iquote('0:MRR:23043.0,1.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : RNG007-1 : TPTP v8.1.0. Released v1.0.0.
% 0.07/0.13 % Command : run_spass %d %s
% 0.13/0.35 % Computer : n022.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 : Mon May 30 08:13:07 EDT 2022
% 0.13/0.35 % CPUTime :
% 12.08/12.30
% 12.08/12.30 SPASS V 3.9
% 12.08/12.30 SPASS beiseite: Proof found.
% 12.08/12.30 % SZS status Theorem
% 12.08/12.30 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 12.08/12.30 SPASS derived 17473 clauses, backtracked 0 clauses, performed 0 splits and kept 5262 clauses.
% 12.08/12.30 SPASS allocated 76700 KBytes.
% 12.08/12.30 SPASS spent 0:0:11.82 on the problem.
% 12.08/12.30 0:00:00.04 for the input.
% 12.08/12.30 0:00:00.00 for the FLOTTER CNF translation.
% 12.08/12.30 0:00:00.18 for inferences.
% 12.08/12.30 0:00:00.00 for the backtracking.
% 12.08/12.30 0:0:11.52 for the reduction.
% 12.08/12.30
% 12.08/12.30
% 12.08/12.30 Here is a proof with depth 9, length 63 :
% 12.08/12.30 % SZS output start Refutation
% See solution above
% 12.08/12.30 Formulae used in the proof : x_squared_is_x prove_a_plus_a_is_id additive_identity1 additive_identity2 closure_of_multiplication closure_of_addition left_inverse right_inverse associativity_of_addition1 associativity_of_addition2 commutativity_of_addition distributivity1 distributivity3 addition_is_well_defined
% 12.08/12.30
%------------------------------------------------------------------------------