TSTP Solution File: RNG004-1 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : RNG004-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n023.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 20:41:10 EDT 2022
% Result : Unsatisfiable 6.76s 6.96s
% Output : Refutation 6.76s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 15
% Syntax : Number of clauses : 70 ( 35 unt; 0 nHn; 70 RR)
% Number of literals : 130 ( 0 equ; 69 neg)
% Maximal clause size : 5 ( 1 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 15 ( 15 usr; 12 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
product(a,b,c),
file('RNG004-1.p',unknown),
[] ).
cnf(2,axiom,
product(additive_inverse(a),additive_inverse(b),d),
file('RNG004-1.p',unknown),
[] ).
cnf(3,axiom,
~ equal(d,c),
file('RNG004-1.p',unknown),
[] ).
cnf(4,axiom,
sum__dfg(additive_identity,u,u),
file('RNG004-1.p',unknown),
[] ).
cnf(5,axiom,
sum__dfg(u,additive_identity,u),
file('RNG004-1.p',unknown),
[] ).
cnf(6,axiom,
product(u,v,multiply(u,v)),
file('RNG004-1.p',unknown),
[] ).
cnf(7,axiom,
sum__dfg(u,v,add(u,v)),
file('RNG004-1.p',unknown),
[] ).
cnf(8,axiom,
sum__dfg(additive_inverse(u),u,additive_identity),
file('RNG004-1.p',unknown),
[] ).
cnf(9,axiom,
sum__dfg(u,additive_inverse(u),additive_identity),
file('RNG004-1.p',unknown),
[] ).
cnf(10,axiom,
( ~ sum__dfg(u,v,w)
| ~ sum__dfg(x,v,y)
| ~ sum__dfg(z,x,u)
| sum__dfg(z,y,w) ),
file('RNG004-1.p',unknown),
[] ).
cnf(11,axiom,
( ~ sum__dfg(u,v,w)
| ~ sum__dfg(x,y,v)
| ~ sum__dfg(u,x,z)
| sum__dfg(z,y,w) ),
file('RNG004-1.p',unknown),
[] ).
cnf(12,axiom,
( ~ sum__dfg(u,v,w)
| sum__dfg(v,u,w) ),
file('RNG004-1.p',unknown),
[] ).
cnf(15,axiom,
( ~ product(u,v,w)
| ~ sum__dfg(x,y,v)
| ~ product(u,y,z)
| ~ product(u,x,x1)
| sum__dfg(x1,z,w) ),
file('RNG004-1.p',unknown),
[] ).
cnf(17,axiom,
( ~ product(u,v,w)
| ~ sum__dfg(x,y,u)
| ~ product(y,v,z)
| ~ product(x,v,x1)
| sum__dfg(x1,z,w) ),
file('RNG004-1.p',unknown),
[] ).
cnf(19,axiom,
( ~ sum__dfg(u,v,w)
| ~ sum__dfg(u,v,x)
| equal(x,w) ),
file('RNG004-1.p',unknown),
[] ).
cnf(21,plain,
( ~ sum__dfg(u,v,c)
| ~ sum__dfg(u,v,d) ),
inference(res,[status(thm),theory(equality)],[19,3]),
[iquote('0:Res:19.2,3.0')] ).
cnf(29,plain,
sum__dfg(u,v,add(v,u)),
inference(res,[status(thm),theory(equality)],[7,12]),
[iquote('0:Res:7.0,12.0')] ).
cnf(42,plain,
( ~ sum__dfg(u,additive_identity,v)
| equal(v,u) ),
inference(res,[status(thm),theory(equality)],[5,19]),
[iquote('0:Res:5.0,19.0')] ).
cnf(44,plain,
( ~ sum__dfg(u,additive_inverse(u),v)
| equal(v,additive_identity) ),
inference(res,[status(thm),theory(equality)],[9,19]),
[iquote('0:Res:9.0,19.0')] ).
cnf(45,plain,
( ~ sum__dfg(u,v,w)
| equal(w,add(u,v)) ),
inference(res,[status(thm),theory(equality)],[7,19]),
[iquote('0:Res:7.0,19.0')] ).
cnf(46,plain,
( ~ sum__dfg(u,v,w)
| equal(w,add(v,u)) ),
inference(res,[status(thm),theory(equality)],[29,19]),
[iquote('0:Res:29.0,19.0')] ).
cnf(101,plain,
( ~ sum__dfg(u,v,additive_identity)
| ~ sum__dfg(w,u,x)
| sum__dfg(x,v,w) ),
inference(res,[status(thm),theory(equality)],[5,11]),
[iquote('0:Res:5.0,11.0')] ).
cnf(111,plain,
equal(add(u,v),add(v,u)),
inference(res,[status(thm),theory(equality)],[29,45]),
[iquote('0:Res:29.0,45.0')] ).
cnf(132,plain,
( ~ sum__dfg(u,v,w)
| ~ sum__dfg(x,u,additive_identity)
| sum__dfg(x,w,v) ),
inference(res,[status(thm),theory(equality)],[4,10]),
[iquote('0:Res:4.0,10.0')] ).
cnf(174,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)],[6,17]),
[iquote('0:Res:6.0,17.0')] ).
cnf(260,plain,
( ~ sum__dfg(u,v,w)
| ~ product(x,v,y)
| ~ product(x,u,z)
| sum__dfg(z,y,multiply(x,w)) ),
inference(res,[status(thm),theory(equality)],[6,15]),
[iquote('0:Res:6.0,15.0')] ).
cnf(316,plain,
( ~ sum__dfg(u,additive_inverse(v),w)
| sum__dfg(w,v,u) ),
inference(res,[status(thm),theory(equality)],[8,101]),
[iquote('0:Res:8.0,101.0')] ).
cnf(318,plain,
( ~ sum__dfg(u,v,w)
| sum__dfg(w,additive_inverse(v),u) ),
inference(res,[status(thm),theory(equality)],[9,101]),
[iquote('0:Res:9.0,101.0')] ).
cnf(380,plain,
( ~ sum__dfg(u,additive_inverse(v),additive_identity)
| sum__dfg(u,additive_identity,v) ),
inference(res,[status(thm),theory(equality)],[8,132]),
[iquote('0:Res:8.0,132.0')] ).
cnf(382,plain,
( ~ sum__dfg(u,v,additive_identity)
| sum__dfg(u,additive_identity,additive_inverse(v)) ),
inference(res,[status(thm),theory(equality)],[9,132]),
[iquote('0:Res:9.0,132.0')] ).
cnf(383,plain,
( ~ sum__dfg(u,v,additive_identity)
| sum__dfg(u,add(v,w),w) ),
inference(res,[status(thm),theory(equality)],[7,132]),
[iquote('0:Res:7.0,132.0')] ).
cnf(397,plain,
sum__dfg(additive_inverse(additive_inverse(u)),additive_identity,u),
inference(res,[status(thm),theory(equality)],[8,380]),
[iquote('0:Res:8.0,380.0')] ).
cnf(416,plain,
equal(additive_inverse(additive_inverse(u)),u),
inference(res,[status(thm),theory(equality)],[397,42]),
[iquote('0:Res:397.0,42.0')] ).
cnf(477,plain,
( ~ sum__dfg(u,v,additive_identity)
| sum__dfg(additive_identity,u,additive_inverse(v)) ),
inference(res,[status(thm),theory(equality)],[382,12]),
[iquote('0:Res:382.1,12.0')] ).
cnf(480,plain,
( ~ sum__dfg(u,v,additive_identity)
| equal(additive_inverse(v),u) ),
inference(res,[status(thm),theory(equality)],[382,42]),
[iquote('0:Res:382.1,42.0')] ).
cnf(1308,plain,
sum__dfg(add(u,additive_inverse(v)),v,u),
inference(res,[status(thm),theory(equality)],[7,316]),
[iquote('0:Res:7.0,316.0')] ).
cnf(1309,plain,
sum__dfg(add(additive_inverse(u),v),u,v),
inference(res,[status(thm),theory(equality)],[29,316]),
[iquote('0:Res:29.0,316.0')] ).
cnf(1322,plain,
sum__dfg(add(u,v),additive_inverse(v),u),
inference(spr,[status(thm),theory(equality)],[416,1308]),
[iquote('0:SpR:416.0,1308.0')] ).
cnf(1337,plain,
equal(add(u,add(v,additive_inverse(u))),v),
inference(res,[status(thm),theory(equality)],[1308,46]),
[iquote('0:Res:1308.0,46.0')] ).
cnf(1342,plain,
~ sum__dfg(add(d,additive_inverse(u)),u,c),
inference(res,[status(thm),theory(equality)],[1308,21]),
[iquote('0:Res:1308.0,21.1')] ).
cnf(1398,plain,
equal(add(u,add(additive_inverse(u),v)),v),
inference(res,[status(thm),theory(equality)],[1309,46]),
[iquote('0:Res:1309.0,46.0')] ).
cnf(1462,plain,
equal(add(additive_inverse(u),add(v,u)),v),
inference(res,[status(thm),theory(equality)],[1322,46]),
[iquote('0:Res:1322.0,46.0')] ).
cnf(1943,plain,
equal(add(additive_inverse(add(u,v)),u),additive_inverse(v)),
inference(spr,[status(thm),theory(equality)],[1462]),
[iquote('0:SpR:1462.0,1462.0')] ).
cnf(1967,plain,
equal(add(u,additive_inverse(add(u,v))),additive_inverse(v)),
inference(rew,[status(thm),theory(equality)],[111,1943]),
[iquote('0:Rew:111.0,1943.0')] ).
cnf(2798,plain,
equal(additive_inverse(add(u,additive_inverse(v))),add(v,additive_inverse(u))),
inference(spr,[status(thm),theory(equality)],[1337,1967]),
[iquote('0:SpR:1337.0,1967.0')] ).
cnf(3705,plain,
( ~ product(u,v,w)
| ~ product(additive_identity,v,x)
| sum__dfg(x,w,multiply(u,v)) ),
inference(res,[status(thm),theory(equality)],[4,174]),
[iquote('0:Res:4.0,174.0')] ).
cnf(3712,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)],[9,174]),
[iquote('0:Res:9.0,174.0')] ).
cnf(3990,plain,
( ~ product(u,v,w)
| ~ product(u,additive_identity,x)
| sum__dfg(x,w,multiply(u,v)) ),
inference(res,[status(thm),theory(equality)],[4,260]),
[iquote('0:Res:4.0,260.0')] ).
cnf(3994,plain,
( ~ product(u,v,w)
| ~ product(u,additive_inverse(v),x)
| sum__dfg(x,w,multiply(u,additive_identity)) ),
inference(res,[status(thm),theory(equality)],[8,260]),
[iquote('0:Res:8.0,260.0')] ).
cnf(5167,plain,
( ~ sum__dfg(u,v,v)
| equal(u,additive_identity) ),
inference(res,[status(thm),theory(equality)],[318,44]),
[iquote('0:Res:318.1,44.0')] ).
cnf(5870,plain,
~ sum__dfg(add(d,additive_inverse(add(u,c))),u,additive_identity),
inference(res,[status(thm),theory(equality)],[383,1342]),
[iquote('0:Res:383.1,1342.0')] ).
cnf(5934,plain,
~ sum__dfg(additive_identity,u,add(d,additive_inverse(add(additive_inverse(u),c)))),
inference(res,[status(thm),theory(equality)],[318,5870]),
[iquote('0:Res:318.1,5870.0')] ).
cnf(5939,plain,
~ sum__dfg(additive_identity,u,add(d,add(u,additive_inverse(c)))),
inference(rew,[status(thm),theory(equality)],[2798,5934,111]),
[iquote('0:Rew:2798.0,5934.0,111.0,5934.0')] ).
cnf(6072,plain,
~ sum__dfg(additive_identity,additive_inverse(d),additive_inverse(c)),
inference(spl,[status(thm),theory(equality)],[1398,5939]),
[iquote('0:SpL:1398.0,5939.0')] ).
cnf(6079,plain,
~ sum__dfg(additive_inverse(d),c,additive_identity),
inference(res,[status(thm),theory(equality)],[477,6072]),
[iquote('0:Res:477.1,6072.0')] ).
cnf(10868,plain,
( ~ product(u,v,multiply(u,v))
| ~ product(additive_identity,v,w)
| equal(w,additive_identity) ),
inference(res,[status(thm),theory(equality)],[3705,5167]),
[iquote('0:Res:3705.2,5167.0')] ).
cnf(10908,plain,
( ~ product(additive_identity,u,v)
| equal(v,additive_identity) ),
inference(mrr,[status(thm)],[10868,6]),
[iquote('0:MRR:10868.0,6.0')] ).
cnf(10929,plain,
equal(multiply(additive_identity,u),additive_identity),
inference(res,[status(thm),theory(equality)],[6,10908]),
[iquote('0:Res:6.0,10908.0')] ).
cnf(10962,plain,
( ~ product(additive_inverse(u),v,w)
| ~ product(u,v,x)
| sum__dfg(x,w,additive_identity) ),
inference(rew,[status(thm),theory(equality)],[10929,3712]),
[iquote('0:Rew:10929.0,3712.2')] ).
cnf(11051,plain,
( ~ product(a,additive_inverse(b),u)
| sum__dfg(u,d,additive_identity) ),
inference(res,[status(thm),theory(equality)],[2,10962]),
[iquote('0:Res:2.0,10962.0')] ).
cnf(11785,plain,
( ~ product(u,v,multiply(u,v))
| ~ product(u,additive_identity,w)
| equal(w,additive_identity) ),
inference(res,[status(thm),theory(equality)],[3990,5167]),
[iquote('0:Res:3990.2,5167.0')] ).
cnf(11829,plain,
( ~ product(u,additive_identity,v)
| equal(v,additive_identity) ),
inference(mrr,[status(thm)],[11785,6]),
[iquote('0:MRR:11785.0,6.0')] ).
cnf(11853,plain,
equal(multiply(u,additive_identity),additive_identity),
inference(res,[status(thm),theory(equality)],[6,11829]),
[iquote('0:Res:6.0,11829.0')] ).
cnf(11864,plain,
( ~ product(u,v,w)
| ~ product(u,additive_inverse(v),x)
| sum__dfg(x,w,additive_identity) ),
inference(rew,[status(thm),theory(equality)],[11853,3994]),
[iquote('0:Rew:11853.0,3994.2')] ).
cnf(13970,plain,
sum__dfg(multiply(a,additive_inverse(b)),d,additive_identity),
inference(res,[status(thm),theory(equality)],[6,11051]),
[iquote('0:Res:6.0,11051.0')] ).
cnf(14002,plain,
equal(multiply(a,additive_inverse(b)),additive_inverse(d)),
inference(res,[status(thm),theory(equality)],[13970,480]),
[iquote('0:Res:13970.0,480.0')] ).
cnf(14034,plain,
product(a,additive_inverse(b),additive_inverse(d)),
inference(spr,[status(thm),theory(equality)],[14002,6]),
[iquote('0:SpR:14002.0,6.0')] ).
cnf(14180,plain,
( ~ product(a,b,u)
| sum__dfg(additive_inverse(d),u,additive_identity) ),
inference(res,[status(thm),theory(equality)],[14034,11864]),
[iquote('0:Res:14034.0,11864.1')] ).
cnf(15301,plain,
~ product(a,b,c),
inference(res,[status(thm),theory(equality)],[14180,6079]),
[iquote('0:Res:14180.1,6079.0')] ).
cnf(15354,plain,
$false,
inference(mrr,[status(thm)],[15301,1]),
[iquote('0:MRR:15301.0,1.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : RNG004-1 : TPTP v8.1.0. Released v1.0.0.
% 0.03/0.14 % Command : run_spass %d %s
% 0.14/0.35 % Computer : n023.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 600
% 0.14/0.35 % DateTime : Mon May 30 14:10:27 EDT 2022
% 0.14/0.35 % CPUTime :
% 6.76/6.96
% 6.76/6.96 SPASS V 3.9
% 6.76/6.96 SPASS beiseite: Proof found.
% 6.76/6.96 % SZS status Theorem
% 6.76/6.96 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 6.76/6.96 SPASS derived 11949 clauses, backtracked 0 clauses, performed 0 splits and kept 4188 clauses.
% 6.76/6.96 SPASS allocated 72686 KBytes.
% 6.76/6.96 SPASS spent 0:00:06.53 on the problem.
% 6.76/6.96 0:00:00.03 for the input.
% 6.76/6.96 0:00:00.00 for the FLOTTER CNF translation.
% 6.76/6.96 0:00:00.12 for inferences.
% 6.76/6.96 0:00:00.00 for the backtracking.
% 6.76/6.96 0:00:06.31 for the reduction.
% 6.76/6.96
% 6.76/6.96
% 6.76/6.96 Here is a proof with depth 9, length 70 :
% 6.76/6.96 % SZS output start Refutation
% See solution above
% 6.76/6.96 Formulae used in the proof : a_times_b a_inverse_times_b_inverse prove_c_equals_d 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
% 6.76/6.96
%------------------------------------------------------------------------------