TSTP Solution File: GRP775+1 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP775+1 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n006.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 11:49:21 EDT 2022
% Result : Theorem 7.44s 7.66s
% Output : Refutation 7.44s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 14
% Syntax : Number of clauses : 96 ( 24 unt; 2 nHn; 96 RR)
% Number of literals : 196 ( 0 equ; 108 neg)
% Maximal clause size : 4 ( 2 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 6 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
equal(product(u,u),u),
file('GRP775+1.p',unknown),
[] ).
cnf(2,axiom,
r(u,skf1(v,u)),
file('GRP775+1.p',unknown),
[] ).
cnf(3,axiom,
( ~ l(u,v)
| equal(product(u,v),u) ),
file('GRP775+1.p',unknown),
[] ).
cnf(4,axiom,
( ~ l(u,v)
| equal(product(v,u),v) ),
file('GRP775+1.p',unknown),
[] ).
cnf(5,axiom,
( ~ r(u,v)
| equal(product(u,v),v) ),
file('GRP775+1.p',unknown),
[] ).
cnf(6,axiom,
( ~ r(u,v)
| equal(product(v,u),u) ),
file('GRP775+1.p',unknown),
[] ).
cnf(7,axiom,
( ~ d(u,v)
| l(skf1(v,u),v) ),
file('GRP775+1.p',unknown),
[] ).
cnf(8,axiom,
( d(skc2,skc3)
| equal(product(skc2,product(skc3,skc2)),skc2) ),
file('GRP775+1.p',unknown),
[] ).
cnf(9,axiom,
( d(skc2,skc3)
| equal(product(skc3,product(skc2,skc3)),skc3) ),
file('GRP775+1.p',unknown),
[] ).
cnf(10,axiom,
equal(product(product(u,v),w),product(u,product(v,w))),
file('GRP775+1.p',unknown),
[] ).
cnf(11,axiom,
( ~ l(u,v)
| ~ r(w,u)
| d(w,v) ),
file('GRP775+1.p',unknown),
[] ).
cnf(12,axiom,
( ~ equal(product(u,v),u)
| ~ equal(product(v,u),v)
| l(v,u) ),
file('GRP775+1.p',unknown),
[] ).
cnf(13,axiom,
( ~ equal(product(u,v),v)
| ~ equal(product(v,u),u)
| r(v,u) ),
file('GRP775+1.p',unknown),
[] ).
cnf(14,axiom,
( ~ d(skc2,skc3)
| ~ equal(product(skc3,product(skc2,skc3)),skc3)
| ~ equal(product(skc2,product(skc3,skc2)),skc2) ),
file('GRP775+1.p',unknown),
[] ).
cnf(15,plain,
d(skc2,skc3),
inference(spt,[spt(split,[position(s1)])],[9]),
[iquote('1:Spt:9.0')] ).
cnf(16,plain,
( ~ equal(product(skc3,product(skc2,skc3)),skc3)
| ~ equal(product(skc2,product(skc3,skc2)),skc2) ),
inference(mrr,[status(thm)],[14,15]),
[iquote('1:MRR:14.0,15.0')] ).
cnf(32,plain,
equal(product(u,product(v,product(u,v))),product(u,v)),
inference(spr,[status(thm),theory(equality)],[10,1]),
[iquote('0:SpR:10.0,1.0')] ).
cnf(33,plain,
( ~ r(u,product(v,w))
| equal(product(v,product(w,u)),u) ),
inference(spr,[status(thm),theory(equality)],[10,6]),
[iquote('0:SpR:10.0,6.1')] ).
cnf(35,plain,
( ~ r(product(u,v),w)
| equal(product(u,product(v,w)),w) ),
inference(spr,[status(thm),theory(equality)],[10,5]),
[iquote('0:SpR:10.0,5.1')] ).
cnf(39,plain,
equal(product(u,product(u,v)),product(u,v)),
inference(spr,[status(thm),theory(equality)],[1,10]),
[iquote('0:SpR:1.0,10.0')] ).
cnf(40,plain,
( ~ l(u,v)
| equal(product(v,product(u,w)),product(v,w)) ),
inference(spr,[status(thm),theory(equality)],[4,10]),
[iquote('0:SpR:4.1,10.0')] ).
cnf(42,plain,
( ~ l(u,v)
| equal(product(u,product(v,w)),product(u,w)) ),
inference(spr,[status(thm),theory(equality)],[3,10]),
[iquote('0:SpR:3.1,10.0')] ).
cnf(108,plain,
( ~ equal(u,u)
| ~ equal(product(u,u),u)
| r(u,u) ),
inference(spl,[status(thm),theory(equality)],[1,13]),
[iquote('0:SpL:1.0,13.0')] ).
cnf(112,plain,
( ~ r(u,v)
| ~ equal(v,v)
| ~ equal(product(v,u),u)
| r(v,u) ),
inference(spl,[status(thm),theory(equality)],[5,13]),
[iquote('0:SpL:5.1,13.0')] ).
cnf(114,plain,
( ~ equal(product(u,v),product(u,v))
| ~ equal(product(product(u,v),u),u)
| r(product(u,v),u) ),
inference(spl,[status(thm),theory(equality)],[39,13]),
[iquote('0:SpL:39.0,13.0')] ).
cnf(116,plain,
( ~ equal(product(u,u),u)
| r(u,u) ),
inference(obv,[status(thm),theory(equality)],[108]),
[iquote('0:Obv:108.0')] ).
cnf(117,plain,
( ~ equal(u,u)
| r(u,u) ),
inference(rew,[status(thm),theory(equality)],[1,116]),
[iquote('0:Rew:1.0,116.0')] ).
cnf(118,plain,
r(u,u),
inference(obv,[status(thm),theory(equality)],[117]),
[iquote('0:Obv:117.0')] ).
cnf(123,plain,
( ~ r(u,v)
| ~ equal(product(v,u),u)
| r(v,u) ),
inference(obv,[status(thm),theory(equality)],[112]),
[iquote('0:Obv:112.1')] ).
cnf(124,plain,
( ~ r(u,v)
| ~ equal(u,u)
| r(v,u) ),
inference(rew,[status(thm),theory(equality)],[6,123]),
[iquote('0:Rew:6.1,123.1')] ).
cnf(125,plain,
( ~ r(u,v)
| r(v,u) ),
inference(obv,[status(thm),theory(equality)],[124]),
[iquote('0:Obv:124.1')] ).
cnf(126,plain,
( ~ equal(product(product(u,v),u),u)
| r(product(u,v),u) ),
inference(obv,[status(thm),theory(equality)],[114]),
[iquote('0:Obv:114.0')] ).
cnf(127,plain,
( ~ equal(product(u,product(v,u)),u)
| r(product(u,v),u) ),
inference(rew,[status(thm),theory(equality)],[10,126]),
[iquote('0:Rew:10.0,126.0')] ).
cnf(129,plain,
r(skf1(u,v),v),
inference(res,[status(thm),theory(equality)],[2,125]),
[iquote('0:Res:2.0,125.0')] ).
cnf(145,plain,
( ~ l(u,v)
| ~ equal(u,u)
| ~ equal(product(v,u),v)
| l(v,u) ),
inference(spl,[status(thm),theory(equality)],[3,12]),
[iquote('0:SpL:3.1,12.0')] ).
cnf(149,plain,
( ~ equal(product(u,product(v,w)),product(u,v))
| ~ equal(product(w,product(u,v)),w)
| l(w,product(u,v)) ),
inference(spl,[status(thm),theory(equality)],[10,12]),
[iquote('0:SpL:10.0,12.0')] ).
cnf(155,plain,
( ~ l(u,v)
| ~ equal(product(v,u),v)
| l(v,u) ),
inference(obv,[status(thm),theory(equality)],[145]),
[iquote('0:Obv:145.1')] ).
cnf(156,plain,
( ~ l(u,v)
| ~ equal(v,v)
| l(v,u) ),
inference(rew,[status(thm),theory(equality)],[4,155]),
[iquote('0:Rew:4.1,155.1')] ).
cnf(157,plain,
( ~ l(u,v)
| l(v,u) ),
inference(obv,[status(thm),theory(equality)],[156]),
[iquote('0:Obv:156.1')] ).
cnf(165,plain,
( ~ d(u,v)
| l(v,skf1(v,u)) ),
inference(res,[status(thm),theory(equality)],[7,157]),
[iquote('0:Res:7.1,157.0')] ).
cnf(226,plain,
( ~ r(u,product(v,w))
| equal(product(v,u),u) ),
inference(spr,[status(thm),theory(equality)],[33,39]),
[iquote('0:SpR:33.1,39.0')] ).
cnf(245,plain,
( ~ r(skc3,product(skc3,skc2))
| ~ equal(skc3,skc3)
| ~ equal(product(skc2,product(skc3,skc2)),skc2) ),
inference(spl,[status(thm),theory(equality)],[33,16]),
[iquote('1:SpL:33.1,16.0')] ).
cnf(253,plain,
( ~ r(skc3,product(skc3,skc2))
| ~ equal(product(skc2,product(skc3,skc2)),skc2) ),
inference(obv,[status(thm),theory(equality)],[245]),
[iquote('1:Obv:245.1')] ).
cnf(263,plain,
( ~ r(product(u,v),w)
| equal(product(u,product(product(v,w),x)),product(w,x)) ),
inference(spr,[status(thm),theory(equality)],[35,10]),
[iquote('0:SpR:35.1,10.0')] ).
cnf(264,plain,
( ~ r(product(u,v),w)
| equal(product(u,w),w) ),
inference(spr,[status(thm),theory(equality)],[35,39]),
[iquote('0:SpR:35.1,39.0')] ).
cnf(290,plain,
( ~ r(product(u,v),w)
| equal(product(u,product(v,product(w,x))),product(w,x)) ),
inference(rew,[status(thm),theory(equality)],[10,263]),
[iquote('0:Rew:10.0,263.1')] ).
cnf(300,plain,
( ~ r(u,v)
| ~ r(w,u)
| equal(product(v,w),w) ),
inference(spl,[status(thm),theory(equality)],[6,226]),
[iquote('0:SpL:6.1,226.0')] ).
cnf(313,plain,
( ~ r(u,v)
| ~ r(u,w)
| equal(product(v,w),w) ),
inference(spl,[status(thm),theory(equality)],[6,264]),
[iquote('0:SpL:6.1,264.0')] ).
cnf(444,plain,
( ~ l(u,v)
| equal(product(u,product(w,product(v,w))),product(u,product(v,w))) ),
inference(spr,[status(thm),theory(equality)],[32,42]),
[iquote('0:SpR:32.0,42.1')] ).
cnf(462,plain,
( ~ l(u,v)
| equal(product(u,product(w,product(v,w))),product(u,w)) ),
inference(rew,[status(thm),theory(equality)],[42,444]),
[iquote('0:Rew:42.1,444.1')] ).
cnf(1100,plain,
( ~ equal(product(product(u,v),product(u,v)),product(u,v))
| r(product(product(u,v),u),product(u,v)) ),
inference(spl,[status(thm),theory(equality)],[39,127]),
[iquote('0:SpL:39.0,127.0')] ).
cnf(1103,plain,
( ~ l(u,v)
| ~ equal(product(product(u,w),product(v,w)),product(u,w))
| r(product(product(u,w),v),product(u,w)) ),
inference(spl,[status(thm),theory(equality)],[40,127]),
[iquote('0:SpL:40.1,127.0')] ).
cnf(1145,plain,
( ~ equal(product(u,v),product(u,v))
| r(product(u,product(v,u)),product(u,v)) ),
inference(rew,[status(thm),theory(equality)],[10,1100,32]),
[iquote('0:Rew:10.0,1100.1,32.0,1100.0,10.0,1100.0')] ).
cnf(1146,plain,
r(product(u,product(v,u)),product(u,v)),
inference(obv,[status(thm),theory(equality)],[1145]),
[iquote('0:Obv:1145.0')] ).
cnf(1150,plain,
( ~ l(u,v)
| ~ equal(product(u,product(w,product(v,w))),product(u,w))
| r(product(u,product(w,v)),product(u,w)) ),
inference(rew,[status(thm),theory(equality)],[10,1103]),
[iquote('0:Rew:10.0,1103.2,10.0,1103.1')] ).
cnf(1151,plain,
( ~ l(u,v)
| ~ equal(product(u,w),product(u,w))
| r(product(u,product(w,v)),product(u,w)) ),
inference(rew,[status(thm),theory(equality)],[462,1150]),
[iquote('0:Rew:462.1,1150.1')] ).
cnf(1152,plain,
( ~ l(u,v)
| r(product(u,product(w,v)),product(u,w)) ),
inference(obv,[status(thm),theory(equality)],[1151]),
[iquote('0:Obv:1151.1')] ).
cnf(1176,plain,
( ~ r(product(u,v),w)
| r(product(u,product(product(v,w),u)),w) ),
inference(spr,[status(thm),theory(equality)],[35,1146]),
[iquote('0:SpR:35.1,1146.0')] ).
cnf(1235,plain,
( ~ r(product(u,v),w)
| r(product(u,product(v,product(w,u))),w) ),
inference(rew,[status(thm),theory(equality)],[10,1176]),
[iquote('0:Rew:10.0,1176.1')] ).
cnf(1236,plain,
( ~ r(product(u,v),w)
| r(product(w,u),w) ),
inference(rew,[status(thm),theory(equality)],[290,1235]),
[iquote('0:Rew:290.1,1235.1')] ).
cnf(1382,plain,
( ~ equal(product(u,v),product(u,v))
| ~ equal(product(v,product(u,v)),v)
| l(v,product(u,v)) ),
inference(spl,[status(thm),theory(equality)],[1,149]),
[iquote('0:SpL:1.0,149.0')] ).
cnf(1415,plain,
( ~ equal(product(u,product(v,u)),u)
| l(u,product(v,u)) ),
inference(obv,[status(thm),theory(equality)],[1382]),
[iquote('0:Obv:1382.0')] ).
cnf(1540,plain,
( ~ r(u,v)
| ~ r(u,w)
| r(product(w,v),w) ),
inference(spl,[status(thm),theory(equality)],[6,1236]),
[iquote('0:SpL:6.1,1236.0')] ).
cnf(1562,plain,
( ~ r(u,v)
| ~ r(u,w)
| r(v,w) ),
inference(rew,[status(thm),theory(equality)],[313,1540]),
[iquote('0:Rew:313.2,1540.2')] ).
cnf(1657,plain,
( ~ r(skf1(u,v),w)
| r(v,w) ),
inference(res,[status(thm),theory(equality)],[129,1562]),
[iquote('0:Res:129.0,1562.0')] ).
cnf(1671,plain,
r(u,skf1(v,skf1(w,u))),
inference(res,[status(thm),theory(equality)],[2,1657]),
[iquote('0:Res:2.0,1657.0')] ).
cnf(2074,plain,
( ~ equal(product(product(u,product(v,u)),product(v,u)),product(u,product(v,u)))
| l(product(u,product(v,u)),product(v,product(u,product(v,u)))) ),
inference(spl,[status(thm),theory(equality)],[32,1415]),
[iquote('0:SpL:32.0,1415.0')] ).
cnf(2078,plain,
( ~ l(u,v)
| ~ equal(product(product(u,w),product(v,w)),product(u,w))
| l(product(u,w),product(v,product(u,w))) ),
inference(spl,[status(thm),theory(equality)],[40,1415]),
[iquote('0:SpL:40.1,1415.0')] ).
cnf(2125,plain,
( ~ l(u,v)
| ~ equal(product(u,product(w,product(v,w))),product(u,w))
| l(product(u,w),product(v,w)) ),
inference(rew,[status(thm),theory(equality)],[40,2078,10]),
[iquote('0:Rew:40.1,2078.2,10.0,2078.1')] ).
cnf(2126,plain,
( ~ l(u,v)
| ~ equal(product(u,w),product(u,w))
| l(product(u,w),product(v,w)) ),
inference(rew,[status(thm),theory(equality)],[462,2125]),
[iquote('0:Rew:462.1,2125.1')] ).
cnf(2127,plain,
( ~ l(u,v)
| l(product(u,w),product(v,w)) ),
inference(obv,[status(thm),theory(equality)],[2126]),
[iquote('0:Obv:2126.1')] ).
cnf(2141,plain,
( ~ equal(product(u,product(v,u)),product(u,product(v,u)))
| l(product(u,product(v,u)),product(v,u)) ),
inference(rew,[status(thm),theory(equality)],[32,2074,10]),
[iquote('0:Rew:32.0,2074.1,32.0,2074.0,10.0,2074.0,10.0,2074.0')] ).
cnf(2142,plain,
l(product(u,product(v,u)),product(v,u)),
inference(obv,[status(thm),theory(equality)],[2141]),
[iquote('0:Obv:2141.0')] ).
cnf(2198,plain,
( ~ l(product(skc3,skc2),skc2)
| ~ r(skc3,product(skc3,skc2))
| ~ equal(skc2,skc2) ),
inference(spl,[status(thm),theory(equality)],[4,253]),
[iquote('1:SpL:4.1,253.1')] ).
cnf(2210,plain,
( ~ l(product(skc3,skc2),skc2)
| ~ r(skc3,product(skc3,skc2)) ),
inference(obv,[status(thm),theory(equality)],[2198]),
[iquote('1:Obv:2198.2')] ).
cnf(2655,plain,
l(product(u,v),product(v,product(u,v))),
inference(res,[status(thm),theory(equality)],[2142,157]),
[iquote('0:Res:2142.0,157.0')] ).
cnf(7341,plain,
( ~ r(u,skf1(v,w))
| equal(product(w,u),u) ),
inference(res,[status(thm),theory(equality)],[129,300]),
[iquote('0:Res:129.0,300.0')] ).
cnf(7564,plain,
equal(product(skf1(u,v),v),v),
inference(res,[status(thm),theory(equality)],[1671,7341]),
[iquote('0:Res:1671.0,7341.0')] ).
cnf(7569,plain,
equal(product(u,skf1(v,u)),skf1(v,u)),
inference(res,[status(thm),theory(equality)],[118,7341]),
[iquote('0:Res:118.0,7341.0')] ).
cnf(7618,plain,
( ~ l(u,skf1(v,w))
| l(product(u,w),w) ),
inference(spr,[status(thm),theory(equality)],[7564,2127]),
[iquote('0:SpR:7564.0,2127.1')] ).
cnf(9342,plain,
( ~ d(u,v)
| l(product(v,u),u) ),
inference(res,[status(thm),theory(equality)],[165,7618]),
[iquote('0:Res:165.1,7618.0')] ).
cnf(9404,plain,
( ~ d(skc2,skc3)
| ~ r(skc3,product(skc3,skc2)) ),
inference(res,[status(thm),theory(equality)],[9342,2210]),
[iquote('1:Res:9342.1,2210.0')] ).
cnf(9415,plain,
~ r(skc3,product(skc3,skc2)),
inference(mrr,[status(thm)],[9404,15]),
[iquote('1:MRR:9404.0,15.0')] ).
cnf(15772,plain,
( ~ l(u,skf1(v,w))
| r(product(u,skf1(v,w)),product(u,w)) ),
inference(spr,[status(thm),theory(equality)],[7569,1152]),
[iquote('0:SpR:7569.0,1152.1')] ).
cnf(15888,plain,
( ~ l(u,skf1(v,w))
| r(u,product(u,w)) ),
inference(rew,[status(thm),theory(equality)],[3,15772]),
[iquote('0:Rew:3.1,15772.1')] ).
cnf(16307,plain,
( ~ d(u,v)
| r(v,product(v,u)) ),
inference(res,[status(thm),theory(equality)],[165,15888]),
[iquote('0:Res:165.1,15888.0')] ).
cnf(16399,plain,
~ d(skc2,skc3),
inference(res,[status(thm),theory(equality)],[16307,9415]),
[iquote('1:Res:16307.1,9415.0')] ).
cnf(16416,plain,
$false,
inference(mrr,[status(thm)],[16399,15]),
[iquote('1:MRR:16399.0,15.0')] ).
cnf(16440,plain,
~ d(skc2,skc3),
inference(spt,[spt(split,[position(sa)])],[16416,15]),
[iquote('1:Spt:16416.0,9.0,15.0')] ).
cnf(16441,plain,
equal(product(skc3,product(skc2,skc3)),skc3),
inference(spt,[spt(split,[position(s2)])],[9]),
[iquote('1:Spt:16416.0,9.1')] ).
cnf(16442,plain,
equal(product(skc2,product(skc3,skc2)),skc2),
inference(mrr,[status(thm)],[8,16440]),
[iquote('1:MRR:8.0,16440.0')] ).
cnf(16513,plain,
l(product(skc2,skc3),skc3),
inference(spr,[status(thm),theory(equality)],[16441,2655]),
[iquote('1:SpR:16441.0,2655.0')] ).
cnf(16718,plain,
( ~ r(u,product(skc2,skc3))
| d(u,skc3) ),
inference(res,[status(thm),theory(equality)],[16513,11]),
[iquote('1:Res:16513.0,11.0')] ).
cnf(20206,plain,
d(product(skc2,product(skc3,skc2)),skc3),
inference(res,[status(thm),theory(equality)],[1146,16718]),
[iquote('1:Res:1146.0,16718.0')] ).
cnf(20213,plain,
d(skc2,skc3),
inference(rew,[status(thm),theory(equality)],[16442,20206]),
[iquote('1:Rew:16442.0,20206.0')] ).
cnf(20214,plain,
$false,
inference(mrr,[status(thm)],[20213,16440]),
[iquote('1:MRR:20213.0,16440.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : GRP775+1 : TPTP v8.1.0. Released v4.1.0.
% 0.06/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n006.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Tue Jun 14 13:26:56 EDT 2022
% 0.12/0.34 % CPUTime :
% 7.44/7.66
% 7.44/7.66 SPASS V 3.9
% 7.44/7.66 SPASS beiseite: Proof found.
% 7.44/7.66 % SZS status Theorem
% 7.44/7.66 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 7.44/7.66 SPASS derived 14948 clauses, backtracked 4 clauses, performed 1 splits and kept 4230 clauses.
% 7.44/7.66 SPASS allocated 98763 KBytes.
% 7.44/7.66 SPASS spent 0:00:07.19 on the problem.
% 7.44/7.66 0:00:00.03 for the input.
% 7.44/7.66 0:00:00.02 for the FLOTTER CNF translation.
% 7.44/7.66 0:00:00.11 for inferences.
% 7.44/7.66 0:00:00.06 for the backtracking.
% 7.44/7.66 0:00:06.91 for the reduction.
% 7.44/7.66
% 7.44/7.66
% 7.44/7.66 Here is a proof with depth 12, length 96 :
% 7.44/7.66 % SZS output start Refutation
% See solution above
% 7.44/7.66 Formulae used in the proof : sos02 sos05 sos03 sos04 goals sos01
% 7.44/7.66
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