TSTP Solution File: HAL002+1 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : HAL002+1 : TPTP v8.1.0. Released v2.6.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n019.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 : Sat Jul 16 12:45:59 EDT 2022
% Result : Theorem 2.54s 2.71s
% Output : Refutation 2.54s
% Verified :
% SZS Type : Refutation
% Derivation depth : 29
% Number of leaves : 18
% Syntax : Number of clauses : 67 ( 18 unt; 15 nHn; 67 RR)
% Number of literals : 182 ( 0 equ; 104 neg)
% Maximal clause size : 8 ( 2 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-3 aty)
% Number of functors : 15 ( 15 usr; 9 con; 0-3 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
( injection_2(x__dfg)
| injection(x__dfg) ),
file('HAL002+1.p',unknown),
[] ).
cnf(2,axiom,
morphism(x__dfg,any1,any2),
file('HAL002+1.p',unknown),
[] ).
cnf(3,axiom,
( ~ injection_2(x__dfg)
| ~ injection(x__dfg) ),
file('HAL002+1.p',unknown),
[] ).
cnf(4,axiom,
( ~ element(u,v)
| equal(subtract(v,u,u),zero(v)) ),
file('HAL002+1.p',unknown),
[] ).
cnf(5,axiom,
( ~ morphism(u,v,w)
| equal(apply(u,zero(v)),zero(w)) ),
file('HAL002+1.p',unknown),
[] ).
cnf(6,axiom,
( ~ morphism(u,v,w)
| injection(u)
| element(skf11(v,x),v) ),
file('HAL002+1.p',unknown),
[] ).
cnf(7,axiom,
( ~ morphism(u,v,w)
| injection(u)
| element(skf10(v,x),v) ),
file('HAL002+1.p',unknown),
[] ).
cnf(8,axiom,
( ~ morphism(u,v,w)
| injection_2(u)
| element(skf9(v,x,y),v) ),
file('HAL002+1.p',unknown),
[] ).
cnf(10,axiom,
( ~ element(u,v)
| ~ morphism(w,v,x)
| element(apply(w,u),x) ),
file('HAL002+1.p',unknown),
[] ).
cnf(11,axiom,
( ~ element(u,v)
| ~ element(w,v)
| element(subtract(v,w,u),v) ),
file('HAL002+1.p',unknown),
[] ).
cnf(12,axiom,
( ~ equal(skf9(u,v,w),zero(u))
| ~ morphism(x,u,y)
| injection_2(x) ),
file('HAL002+1.p',unknown),
[] ).
cnf(13,axiom,
( ~ equal(skf11(u,v),skf10(u,v))
| ~ morphism(v,u,w)
| injection(v) ),
file('HAL002+1.p',unknown),
[] ).
cnf(14,axiom,
( ~ morphism(u,v,w)
| injection_2(u)
| equal(apply(u,skf9(v,w,u)),zero(w)) ),
file('HAL002+1.p',unknown),
[] ).
cnf(15,axiom,
( ~ element(u,v)
| ~ element(w,v)
| equal(subtract(v,w,subtract(v,w,u)),u) ),
file('HAL002+1.p',unknown),
[] ).
cnf(16,axiom,
( ~ morphism(u,v,w)
| injection(u)
| equal(apply(u,skf11(v,u)),apply(u,skf10(v,u))) ),
file('HAL002+1.p',unknown),
[] ).
cnf(20,axiom,
( ~ injection_2(u)
| ~ element(v,w)
| ~ equal(apply(u,v),zero(x))
| ~ morphism(u,w,x)
| equal(v,zero(w)) ),
file('HAL002+1.p',unknown),
[] ).
cnf(22,axiom,
( ~ injection(u)
| ~ element(v,w)
| ~ element(x,w)
| ~ equal(apply(u,x),apply(u,v))
| ~ morphism(u,w,y)
| equal(x,v) ),
file('HAL002+1.p',unknown),
[] ).
cnf(23,axiom,
( ~ element(u,v)
| ~ element(w,v)
| ~ morphism(x,v,y)
| equal(apply(x,subtract(v,w,u)),subtract(y,apply(x,w),apply(x,u))) ),
file('HAL002+1.p',unknown),
[] ).
cnf(35,plain,
injection_2(x__dfg),
inference(spt,[spt(split,[position(s1)])],[1]),
[iquote('1:Spt:1.0')] ).
cnf(36,plain,
~ injection(x__dfg),
inference(mrr,[status(thm)],[3,35]),
[iquote('1:MRR:3.0,35.0')] ).
cnf(38,plain,
equal(apply(x__dfg,zero(any1)),zero(any2)),
inference(res,[status(thm),theory(equality)],[2,5]),
[iquote('0:Res:2.0,5.0')] ).
cnf(40,plain,
( injection(x__dfg)
| element(skf10(any1,u),any1) ),
inference(res,[status(thm),theory(equality)],[2,7]),
[iquote('0:Res:2.0,7.0')] ).
cnf(41,plain,
element(skf10(any1,u),any1),
inference(mrr,[status(thm)],[40,36]),
[iquote('1:MRR:40.0,36.0')] ).
cnf(42,plain,
( injection(x__dfg)
| element(skf11(any1,u),any1) ),
inference(res,[status(thm),theory(equality)],[2,6]),
[iquote('0:Res:2.0,6.0')] ).
cnf(43,plain,
element(skf11(any1,u),any1),
inference(mrr,[status(thm)],[42,36]),
[iquote('1:MRR:42.0,36.0')] ).
cnf(45,plain,
( injection_2(x__dfg)
| element(skf9(any1,u,v),any1) ),
inference(res,[status(thm),theory(equality)],[2,8]),
[iquote('0:Res:2.0,8.0')] ).
cnf(46,plain,
( ~ element(u,v)
| ~ element(u,v)
| ~ element(u,v)
| element(zero(v),v) ),
inference(spr,[status(thm),theory(equality)],[4,11]),
[iquote('0:SpR:4.1,11.2')] ).
cnf(47,plain,
( ~ element(u,v)
| element(zero(v),v) ),
inference(obv,[status(thm),theory(equality)],[46]),
[iquote('0:Obv:46.1')] ).
cnf(48,plain,
( ~ element(u,any1)
| element(apply(x__dfg,u),any2) ),
inference(res,[status(thm),theory(equality)],[2,10]),
[iquote('0:Res:2.0,10.1')] ).
cnf(58,plain,
( ~ equal(skf11(any1,x__dfg),skf10(any1,x__dfg))
| injection(x__dfg) ),
inference(res,[status(thm),theory(equality)],[2,13]),
[iquote('0:Res:2.0,13.1')] ).
cnf(59,plain,
~ equal(skf11(any1,x__dfg),skf10(any1,x__dfg)),
inference(mrr,[status(thm)],[58,36]),
[iquote('1:MRR:58.1,36.0')] ).
cnf(71,plain,
( ~ element(u,v)
| ~ element(u,v)
| ~ element(u,v)
| equal(subtract(v,u,zero(v)),u) ),
inference(spr,[status(thm),theory(equality)],[4,15]),
[iquote('0:SpR:4.1,15.2')] ).
cnf(72,plain,
( ~ element(u,v)
| equal(subtract(v,u,zero(v)),u) ),
inference(obv,[status(thm),theory(equality)],[71]),
[iquote('0:Obv:71.1')] ).
cnf(78,plain,
( injection(x__dfg)
| equal(apply(x__dfg,skf11(any1,x__dfg)),apply(x__dfg,skf10(any1,x__dfg))) ),
inference(res,[status(thm),theory(equality)],[2,16]),
[iquote('0:Res:2.0,16.0')] ).
cnf(79,plain,
equal(apply(x__dfg,skf11(any1,x__dfg)),apply(x__dfg,skf10(any1,x__dfg))),
inference(mrr,[status(thm)],[78,36]),
[iquote('1:MRR:78.0,36.0')] ).
cnf(80,plain,
( ~ element(skf11(any1,x__dfg),any1)
| element(apply(x__dfg,skf10(any1,x__dfg)),any2) ),
inference(spr,[status(thm),theory(equality)],[79,48]),
[iquote('1:SpR:79.0,48.1')] ).
cnf(82,plain,
element(apply(x__dfg,skf10(any1,x__dfg)),any2),
inference(mrr,[status(thm)],[80,43]),
[iquote('1:MRR:80.0,43.0')] ).
cnf(101,plain,
( ~ injection(u)
| ~ morphism(u,v,w)
| ~ element(skf9(v,w,u),x)
| ~ element(y,x)
| ~ equal(apply(u,y),zero(w))
| ~ morphism(u,x,z)
| injection_2(u)
| equal(y,skf9(v,w,u)) ),
inference(spl,[status(thm),theory(equality)],[14,22]),
[iquote('0:SpL:14.2,22.3')] ).
cnf(108,plain,
( ~ element(u,any1)
| ~ element(v,any1)
| equal(subtract(any2,apply(x__dfg,v),apply(x__dfg,u)),apply(x__dfg,subtract(any1,v,u))) ),
inference(res,[status(thm),theory(equality)],[2,23]),
[iquote('0:Res:2.0,23.2')] ).
cnf(121,plain,
( ~ element(u,any1)
| ~ element(skf11(any1,x__dfg),any1)
| equal(subtract(any2,apply(x__dfg,skf10(any1,x__dfg)),apply(x__dfg,u)),apply(x__dfg,subtract(any1,skf11(any1,x__dfg),u))) ),
inference(spr,[status(thm),theory(equality)],[79,108]),
[iquote('1:SpR:79.0,108.2')] ).
cnf(128,plain,
( ~ element(u,any1)
| equal(subtract(any2,apply(x__dfg,skf10(any1,x__dfg)),apply(x__dfg,u)),apply(x__dfg,subtract(any1,skf11(any1,x__dfg),u))) ),
inference(mrr,[status(thm)],[121,43]),
[iquote('1:MRR:121.1,43.0')] ).
cnf(198,plain,
( ~ element(skf10(any1,x__dfg),any1)
| ~ element(apply(x__dfg,skf10(any1,x__dfg)),any2)
| equal(apply(x__dfg,subtract(any1,skf11(any1,x__dfg),skf10(any1,x__dfg))),zero(any2)) ),
inference(spr,[status(thm),theory(equality)],[128,4]),
[iquote('1:SpR:128.1,4.1')] ).
cnf(209,plain,
equal(apply(x__dfg,subtract(any1,skf11(any1,x__dfg),skf10(any1,x__dfg))),zero(any2)),
inference(mrr,[status(thm)],[198,41,82]),
[iquote('1:MRR:198.0,198.1,41.0,82.0')] ).
cnf(232,plain,
( ~ injection_2(x__dfg)
| ~ element(subtract(any1,skf11(any1,x__dfg),skf10(any1,x__dfg)),u)
| ~ equal(zero(any2),zero(v))
| ~ morphism(x__dfg,u,v)
| equal(subtract(any1,skf11(any1,x__dfg),skf10(any1,x__dfg)),zero(u)) ),
inference(spl,[status(thm),theory(equality)],[209,20]),
[iquote('1:SpL:209.0,20.2')] ).
cnf(239,plain,
( ~ element(subtract(any1,skf11(any1,x__dfg),skf10(any1,x__dfg)),u)
| ~ equal(zero(any2),zero(v))
| ~ morphism(x__dfg,u,v)
| equal(subtract(any1,skf11(any1,x__dfg),skf10(any1,x__dfg)),zero(u)) ),
inference(ssi,[status(thm)],[232,35]),
[iquote('1:SSi:232.0,35.0')] ).
cnf(4479,plain,
( ~ element(skf10(any1,x__dfg),any1)
| ~ element(skf11(any1,x__dfg),any1)
| ~ equal(zero(any2),zero(u))
| ~ morphism(x__dfg,any1,u)
| equal(subtract(any1,skf11(any1,x__dfg),skf10(any1,x__dfg)),zero(any1)) ),
inference(res,[status(thm),theory(equality)],[11,239]),
[iquote('1:Res:11.2,239.0')] ).
cnf(4480,plain,
( ~ equal(zero(any2),zero(u))
| ~ morphism(x__dfg,any1,u)
| equal(subtract(any1,skf11(any1,x__dfg),skf10(any1,x__dfg)),zero(any1)) ),
inference(mrr,[status(thm)],[4479,41,43]),
[iquote('1:MRR:4479.0,4479.1,41.0,43.0')] ).
cnf(4481,plain,
( ~ morphism(x__dfg,any1,any2)
| equal(subtract(any1,skf11(any1,x__dfg),skf10(any1,x__dfg)),zero(any1)) ),
inference(eqr,[status(thm),theory(equality)],[4480]),
[iquote('1:EqR:4480.0')] ).
cnf(4482,plain,
equal(subtract(any1,skf11(any1,x__dfg),skf10(any1,x__dfg)),zero(any1)),
inference(mrr,[status(thm)],[4481,2]),
[iquote('1:MRR:4481.0,2.0')] ).
cnf(4621,plain,
( ~ element(skf10(any1,x__dfg),any1)
| ~ element(skf11(any1,x__dfg),any1)
| equal(subtract(any1,skf11(any1,x__dfg),zero(any1)),skf10(any1,x__dfg)) ),
inference(spr,[status(thm),theory(equality)],[4482,15]),
[iquote('1:SpR:4482.0,15.2')] ).
cnf(4637,plain,
( ~ element(skf10(any1,x__dfg),any1)
| ~ element(skf11(any1,x__dfg),any1)
| equal(skf11(any1,x__dfg),skf10(any1,x__dfg)) ),
inference(rew,[status(thm),theory(equality)],[72,4621]),
[iquote('1:Rew:72.1,4621.2')] ).
cnf(4638,plain,
$false,
inference(mrr,[status(thm)],[4637,41,43,59]),
[iquote('1:MRR:4637.0,4637.1,4637.2,41.0,43.0,59.0')] ).
cnf(4643,plain,
~ injection_2(x__dfg),
inference(spt,[spt(split,[position(sa)])],[4638,35]),
[iquote('1:Spt:4638.0,1.0,35.0')] ).
cnf(4644,plain,
injection(x__dfg),
inference(spt,[spt(split,[position(s2)])],[1]),
[iquote('1:Spt:4638.0,1.1')] ).
cnf(4646,plain,
element(skf9(any1,u,v),any1),
inference(mrr,[status(thm)],[45,4643]),
[iquote('1:MRR:45.0,4643.0')] ).
cnf(4663,plain,
element(zero(any1),any1),
inference(res,[status(thm),theory(equality)],[4646,47]),
[iquote('1:Res:4646.0,47.0')] ).
cnf(4664,plain,
( ~ injection(u)
| ~ morphism(u,any1,v)
| ~ element(w,any1)
| ~ equal(apply(u,w),zero(v))
| ~ morphism(u,any1,x)
| injection_2(u)
| equal(w,skf9(any1,v,u)) ),
inference(res,[status(thm),theory(equality)],[4646,101]),
[iquote('1:Res:4646.0,101.2')] ).
cnf(4669,plain,
( ~ injection(u)
| ~ morphism(u,any1,v)
| ~ element(w,any1)
| ~ equal(apply(u,w),zero(v))
| injection_2(u)
| equal(w,skf9(any1,v,u)) ),
inference(con,[status(thm)],[4664]),
[iquote('1:Con:4664.4')] ).
cnf(5058,plain,
( ~ injection(x__dfg)
| ~ morphism(x__dfg,any1,u)
| ~ element(zero(any1),any1)
| ~ equal(zero(any2),zero(u))
| injection_2(x__dfg)
| equal(skf9(any1,u,x__dfg),zero(any1)) ),
inference(spl,[status(thm),theory(equality)],[38,4669]),
[iquote('1:SpL:38.0,4669.3')] ).
cnf(5117,plain,
( ~ morphism(x__dfg,any1,u)
| ~ element(zero(any1),any1)
| ~ equal(zero(any2),zero(u))
| injection_2(x__dfg)
| equal(skf9(any1,u,x__dfg),zero(any1)) ),
inference(ssi,[status(thm)],[5058,4644]),
[iquote('1:SSi:5058.0,4644.0')] ).
cnf(5118,plain,
( ~ morphism(x__dfg,any1,u)
| ~ equal(zero(any2),zero(u))
| equal(skf9(any1,u,x__dfg),zero(any1)) ),
inference(mrr,[status(thm)],[5117,4663,4643]),
[iquote('1:MRR:5117.1,5117.3,4663.0,4643.0')] ).
cnf(5133,plain,
( ~ morphism(x__dfg,any1,u)
| ~ equal(zero(any2),zero(u))
| ~ equal(zero(any1),zero(any1))
| ~ morphism(v,any1,w)
| injection_2(v) ),
inference(spl,[status(thm),theory(equality)],[5118,12]),
[iquote('1:SpL:5118.2,12.0')] ).
cnf(5138,plain,
( ~ morphism(x__dfg,any1,u)
| ~ equal(zero(any2),zero(u))
| ~ morphism(v,any1,w)
| injection_2(v) ),
inference(obv,[status(thm),theory(equality)],[5133]),
[iquote('1:Obv:5133.2')] ).
cnf(5163,plain,
( ~ morphism(x__dfg,any1,any2)
| ~ morphism(u,any1,v)
| injection_2(u) ),
inference(eqr,[status(thm),theory(equality)],[5138]),
[iquote('1:EqR:5138.1')] ).
cnf(5164,plain,
( ~ morphism(u,any1,v)
| injection_2(u) ),
inference(mrr,[status(thm)],[5163,2]),
[iquote('1:MRR:5163.0,2.0')] ).
cnf(5165,plain,
injection_2(x__dfg),
inference(res,[status(thm),theory(equality)],[2,5164]),
[iquote('1:Res:2.0,5164.0')] ).
cnf(5166,plain,
$false,
inference(mrr,[status(thm)],[5165,4643]),
[iquote('1:MRR:5165.0,4643.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : HAL002+1 : TPTP v8.1.0. Released v2.6.0.
% 0.08/0.13 % Command : run_spass %d %s
% 0.14/0.35 % Computer : n019.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 : Tue Jun 7 21:24:10 EDT 2022
% 0.14/0.35 % CPUTime :
% 2.54/2.71
% 2.54/2.71 SPASS V 3.9
% 2.54/2.71 SPASS beiseite: Proof found.
% 2.54/2.71 % SZS status Theorem
% 2.54/2.71 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.54/2.71 SPASS derived 3095 clauses, backtracked 51 clauses, performed 3 splits and kept 1302 clauses.
% 2.54/2.71 SPASS allocated 103516 KBytes.
% 2.54/2.71 SPASS spent 0:00:02.25 on the problem.
% 2.54/2.71 0:00:00.04 for the input.
% 2.54/2.71 0:00:00.11 for the FLOTTER CNF translation.
% 2.54/2.71 0:00:00.09 for inferences.
% 2.54/2.71 0:00:00.11 for the backtracking.
% 2.54/2.71 0:00:01.86 for the reduction.
% 2.54/2.71
% 2.54/2.71
% 2.54/2.71 Here is a proof with depth 7, length 67 :
% 2.54/2.71 % SZS output start Refutation
% See solution above
% 2.54/2.71 Formulae used in the proof : my x_morphism subtract_to_0 morphism properties_for_injection properties_for_injection_2 subtract_in_domain subtract_cancellation injection_properties_2 injection_properties subtract_distribution
% 2.54/2.71
%------------------------------------------------------------------------------