TSTP Solution File: GRP776+1 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP776+1 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n026.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 11:49:22 EDT 2022
% Result : Theorem 201.13s 201.31s
% Output : Refutation 236.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 35
% Number of leaves : 20
% Syntax : Number of clauses : 145 ( 32 unt; 0 nHn; 145 RR)
% Number of literals : 381 ( 0 equ; 239 neg)
% Maximal clause size : 6 ( 2 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 6 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
g(skc1),
file('GRP776+1.p',unknown),
[] ).
cnf(2,axiom,
g(eh),
file('GRP776+1.p',unknown),
[] ).
cnf(3,axiom,
h(eg),
file('GRP776+1.p',unknown),
[] ).
cnf(4,axiom,
( ~ g(u)
| g(inv(u)) ),
file('GRP776+1.p',unknown),
[] ).
cnf(5,axiom,
( ~ h(u)
| h(opp(v)) ),
file('GRP776+1.p',unknown),
[] ).
cnf(6,axiom,
( ~ g(u)
| h(f(u)) ),
file('GRP776+1.p',unknown),
[] ).
cnf(7,axiom,
( ~ g(u)
| equal(product(eh,u),u) ),
file('GRP776+1.p',unknown),
[] ).
cnf(8,axiom,
( ~ g(u)
| equal(product(u,eh),u) ),
file('GRP776+1.p',unknown),
[] ).
cnf(9,axiom,
( ~ h(u)
| equal(sum__dfg(eg,u),u) ),
file('GRP776+1.p',unknown),
[] ).
cnf(10,axiom,
( ~ h(u)
| equal(sum__dfg(u,eg),u) ),
file('GRP776+1.p',unknown),
[] ).
cnf(11,axiom,
( ~ g(u)
| equal(product(u,inv(u)),eh) ),
file('GRP776+1.p',unknown),
[] ).
cnf(12,axiom,
( ~ g(u)
| equal(product(inv(u),u),eh) ),
file('GRP776+1.p',unknown),
[] ).
cnf(13,axiom,
( ~ h(u)
| equal(sum__dfg(u,opp(u)),eg) ),
file('GRP776+1.p',unknown),
[] ).
cnf(14,axiom,
( ~ h(u)
| equal(sum__dfg(opp(u),u),eg) ),
file('GRP776+1.p',unknown),
[] ).
cnf(15,axiom,
( ~ g(u)
| ~ g(v)
| g(product(u,v)) ),
file('GRP776+1.p',unknown),
[] ).
cnf(16,axiom,
( ~ h(u)
| ~ h(v)
| h(sum__dfg(u,v)) ),
file('GRP776+1.p',unknown),
[] ).
cnf(17,axiom,
equal(sum__dfg(f(u),f(v)),f(product(u,v))),
file('GRP776+1.p',unknown),
[] ).
cnf(18,axiom,
( ~ equal(f(eh),eg)
| ~ equal(f(inv(skc1)),opp(f(skc1))) ),
file('GRP776+1.p',unknown),
[] ).
cnf(19,axiom,
( ~ h(u)
| ~ h(v)
| ~ h(w)
| equal(sum__dfg(sum__dfg(u,v),w),sum__dfg(u,sum__dfg(v,w))) ),
file('GRP776+1.p',unknown),
[] ).
cnf(20,axiom,
( ~ g(u)
| ~ g(v)
| ~ g(w)
| equal(product(product(u,v),w),product(u,product(v,w))) ),
file('GRP776+1.p',unknown),
[] ).
cnf(21,plain,
( ~ g(u)
| ~ g(v)
| equal(product(product(u,v),skc1),product(u,product(v,skc1))) ),
inference(res,[status(thm),theory(equality)],[1,20]),
[iquote('0:Res:1.0,20.0')] ).
cnf(22,plain,
( ~ g(u)
| g(product(u,skc1)) ),
inference(res,[status(thm),theory(equality)],[1,15]),
[iquote('0:Res:1.0,15.0')] ).
cnf(23,plain,
equal(product(skc1,inv(skc1)),eh),
inference(res,[status(thm),theory(equality)],[1,11]),
[iquote('0:Res:1.0,11.0')] ).
cnf(24,plain,
equal(product(inv(skc1),skc1),eh),
inference(res,[status(thm),theory(equality)],[1,12]),
[iquote('0:Res:1.0,12.0')] ).
cnf(25,plain,
equal(product(eh,skc1),skc1),
inference(res,[status(thm),theory(equality)],[1,7]),
[iquote('0:Res:1.0,7.0')] ).
cnf(26,plain,
equal(product(skc1,eh),skc1),
inference(res,[status(thm),theory(equality)],[1,8]),
[iquote('0:Res:1.0,8.0')] ).
cnf(27,plain,
g(inv(skc1)),
inference(res,[status(thm),theory(equality)],[1,4]),
[iquote('0:Res:1.0,4.0')] ).
cnf(28,plain,
h(f(skc1)),
inference(res,[status(thm),theory(equality)],[1,6]),
[iquote('0:Res:1.0,6.0')] ).
cnf(30,plain,
( ~ g(u)
| g(product(skc1,u)) ),
inference(res,[status(thm),theory(equality)],[1,15]),
[iquote('0:Res:1.0,15.1')] ).
cnf(31,plain,
( ~ g(u)
| ~ g(v)
| equal(product(product(skc1,u),v),product(skc1,product(u,v))) ),
inference(res,[status(thm),theory(equality)],[1,20]),
[iquote('0:Res:1.0,20.2')] ).
cnf(35,plain,
g(product(skc1,skc1)),
inference(res,[status(thm),theory(equality)],[1,30]),
[iquote('0:Res:1.0,30.0')] ).
cnf(37,plain,
( ~ g(u)
| equal(product(product(skc1,skc1),u),product(skc1,product(skc1,u))) ),
inference(res,[status(thm),theory(equality)],[1,31]),
[iquote('0:Res:1.0,31.1')] ).
cnf(45,plain,
h(opp(u)),
inference(ems,[status(thm)],[5,28]),
[iquote('0:EmS:5.0,28.0')] ).
cnf(88,plain,
( ~ h(f(u))
| ~ h(f(v))
| h(f(product(u,v))) ),
inference(spr,[status(thm),theory(equality)],[17,16]),
[iquote('0:SpR:17.0,16.2')] ).
cnf(102,plain,
( ~ h(f(u))
| h(f(product(skc1,u))) ),
inference(sor,[status(thm)],[88,28]),
[iquote('0:SoR:88.0,28.0')] ).
cnf(103,plain,
( ~ g(u)
| h(f(product(skc1,u))) ),
inference(sor,[status(thm)],[102,6]),
[iquote('0:SoR:102.0,6.1')] ).
cnf(112,plain,
( ~ h(u)
| ~ h(v)
| ~ h(opp(sum__dfg(u,v)))
| ~ h(sum__dfg(u,v))
| equal(sum__dfg(u,sum__dfg(v,opp(sum__dfg(u,v)))),eg) ),
inference(spr,[status(thm),theory(equality)],[19,13]),
[iquote('0:SpR:19.3,13.1')] ).
cnf(117,plain,
( ~ h(u)
| ~ h(opp(u))
| ~ h(u)
| ~ h(v)
| equal(sum__dfg(opp(u),sum__dfg(u,v)),sum__dfg(eg,v)) ),
inference(spr,[status(thm),theory(equality)],[14,19]),
[iquote('0:SpR:14.1,19.3')] ).
cnf(119,plain,
( ~ h(u)
| ~ h(u)
| ~ h(opp(u))
| ~ h(v)
| equal(sum__dfg(u,sum__dfg(opp(u),v)),sum__dfg(eg,v)) ),
inference(spr,[status(thm),theory(equality)],[13,19]),
[iquote('0:SpR:13.1,19.3')] ).
cnf(125,plain,
( ~ h(u)
| ~ h(opp(u))
| ~ h(v)
| equal(sum__dfg(u,sum__dfg(opp(u),v)),sum__dfg(eg,v)) ),
inference(obv,[status(thm),theory(equality)],[119]),
[iquote('0:Obv:119.0')] ).
cnf(126,plain,
( ~ h(u)
| ~ h(opp(u))
| ~ h(v)
| equal(sum__dfg(u,sum__dfg(opp(u),v)),v) ),
inference(rew,[status(thm),theory(equality)],[9,125]),
[iquote('0:Rew:9.1,125.3')] ).
cnf(127,plain,
( ~ h(u)
| ~ h(v)
| equal(sum__dfg(u,sum__dfg(opp(u),v)),v) ),
inference(ssi,[status(thm)],[126,45]),
[iquote('0:SSi:126.1,45.0')] ).
cnf(128,plain,
( ~ h(opp(u))
| ~ h(u)
| ~ h(v)
| equal(sum__dfg(opp(u),sum__dfg(u,v)),sum__dfg(eg,v)) ),
inference(obv,[status(thm),theory(equality)],[117]),
[iquote('0:Obv:117.0')] ).
cnf(129,plain,
( ~ h(opp(u))
| ~ h(u)
| ~ h(v)
| equal(sum__dfg(opp(u),sum__dfg(u,v)),v) ),
inference(rew,[status(thm),theory(equality)],[9,128]),
[iquote('0:Rew:9.1,128.3')] ).
cnf(130,plain,
( ~ h(u)
| ~ h(v)
| equal(sum__dfg(opp(u),sum__dfg(u,v)),v) ),
inference(ssi,[status(thm)],[129,45]),
[iquote('0:SSi:129.0,45.0')] ).
cnf(134,plain,
( ~ h(u)
| ~ h(v)
| equal(sum__dfg(u,sum__dfg(v,opp(sum__dfg(u,v)))),eg) ),
inference(ssi,[status(thm)],[112,16,45]),
[iquote('0:SSi:112.3,112.2,16.2,45.0,16.2')] ).
cnf(141,plain,
( ~ g(inv(skc1))
| h(f(eh)) ),
inference(spr,[status(thm),theory(equality)],[23,103]),
[iquote('0:SpR:23.0,103.1')] ).
cnf(144,plain,
h(f(eh)),
inference(ssi,[status(thm)],[141,27]),
[iquote('0:SSi:141.0,27.0')] ).
cnf(163,plain,
( ~ g(u)
| ~ g(v)
| ~ g(inv(product(u,v)))
| ~ g(product(u,v))
| equal(product(u,product(v,inv(product(u,v)))),eh) ),
inference(spr,[status(thm),theory(equality)],[20,11]),
[iquote('0:SpR:20.3,11.1')] ).
cnf(170,plain,
( ~ g(inv(skc1))
| ~ g(skc1)
| ~ g(u)
| equal(product(inv(skc1),product(skc1,u)),product(eh,u)) ),
inference(spr,[status(thm),theory(equality)],[24,20]),
[iquote('0:SpR:24.0,20.3')] ).
cnf(172,plain,
( ~ g(u)
| ~ g(inv(u))
| ~ g(u)
| ~ g(v)
| equal(product(inv(u),product(u,v)),product(eh,v)) ),
inference(spr,[status(thm),theory(equality)],[12,20]),
[iquote('0:SpR:12.1,20.3')] ).
cnf(174,plain,
( ~ g(u)
| ~ g(u)
| ~ g(inv(u))
| ~ g(v)
| equal(product(u,product(inv(u),v)),product(eh,v)) ),
inference(spr,[status(thm),theory(equality)],[11,20]),
[iquote('0:SpR:11.1,20.3')] ).
cnf(178,plain,
( ~ g(inv(skc1))
| ~ g(skc1)
| ~ g(u)
| equal(product(inv(skc1),product(skc1,u)),u) ),
inference(rew,[status(thm),theory(equality)],[7,170]),
[iquote('0:Rew:7.1,170.3')] ).
cnf(179,plain,
( ~ g(u)
| equal(product(inv(skc1),product(skc1,u)),u) ),
inference(ssi,[status(thm)],[178,1,27]),
[iquote('0:SSi:178.1,178.0,1.0,27.0')] ).
cnf(187,plain,
( ~ g(u)
| ~ g(inv(u))
| ~ g(v)
| equal(product(u,product(inv(u),v)),product(eh,v)) ),
inference(obv,[status(thm),theory(equality)],[174]),
[iquote('0:Obv:174.0')] ).
cnf(188,plain,
( ~ g(u)
| ~ g(inv(u))
| ~ g(v)
| equal(product(u,product(inv(u),v)),v) ),
inference(rew,[status(thm),theory(equality)],[7,187]),
[iquote('0:Rew:7.1,187.3')] ).
cnf(189,plain,
( ~ g(u)
| ~ g(v)
| equal(product(u,product(inv(u),v)),v) ),
inference(ssi,[status(thm)],[188,4]),
[iquote('0:SSi:188.1,4.1')] ).
cnf(190,plain,
( ~ g(inv(u))
| ~ g(u)
| ~ g(v)
| equal(product(inv(u),product(u,v)),product(eh,v)) ),
inference(obv,[status(thm),theory(equality)],[172]),
[iquote('0:Obv:172.0')] ).
cnf(191,plain,
( ~ g(inv(u))
| ~ g(u)
| ~ g(v)
| equal(product(inv(u),product(u,v)),v) ),
inference(rew,[status(thm),theory(equality)],[7,190]),
[iquote('0:Rew:7.1,190.3')] ).
cnf(192,plain,
( ~ g(u)
| ~ g(v)
| equal(product(inv(u),product(u,v)),v) ),
inference(ssi,[status(thm)],[191,4]),
[iquote('0:SSi:191.0,4.1')] ).
cnf(196,plain,
( ~ g(u)
| ~ g(v)
| equal(product(u,product(v,inv(product(u,v)))),eh) ),
inference(ssi,[status(thm)],[163,15,4]),
[iquote('0:SSi:163.3,163.2,15.2,4.1,15.2')] ).
cnf(232,plain,
( ~ h(opp(u))
| ~ h(u)
| ~ h(opp(opp(u)))
| equal(sum__dfg(u,eg),opp(opp(u))) ),
inference(spr,[status(thm),theory(equality)],[13,127]),
[iquote('0:SpR:13.1,127.2')] ).
cnf(236,plain,
( ~ h(opp(u))
| ~ h(u)
| ~ h(opp(opp(u)))
| equal(opp(opp(u)),u) ),
inference(rew,[status(thm),theory(equality)],[10,232]),
[iquote('0:Rew:10.1,232.3')] ).
cnf(237,plain,
( ~ h(u)
| equal(opp(opp(u)),u) ),
inference(ssi,[status(thm)],[236,45]),
[iquote('0:SSi:236.2,236.0,45.0,45.0,45.0')] ).
cnf(275,plain,
( ~ h(f(u))
| ~ h(f(v))
| equal(sum__dfg(opp(f(u)),f(product(u,v))),f(v)) ),
inference(spr,[status(thm),theory(equality)],[17,130]),
[iquote('0:SpR:17.0,130.2')] ).
cnf(333,plain,
( ~ g(inv(u))
| ~ g(u)
| ~ g(inv(inv(u)))
| equal(product(u,eh),inv(inv(u))) ),
inference(spr,[status(thm),theory(equality)],[11,189]),
[iquote('0:SpR:11.1,189.2')] ).
cnf(338,plain,
( ~ g(inv(u))
| ~ g(u)
| ~ g(inv(inv(u)))
| equal(inv(inv(u)),u) ),
inference(rew,[status(thm),theory(equality)],[8,333]),
[iquote('0:Rew:8.1,333.3')] ).
cnf(339,plain,
( ~ g(u)
| equal(inv(inv(u)),u) ),
inference(ssi,[status(thm)],[338,4]),
[iquote('0:SSi:338.2,338.0,4.1,4.1,4.1')] ).
cnf(938,plain,
( ~ h(u)
| ~ h(v)
| ~ h(u)
| ~ h(sum__dfg(v,opp(sum__dfg(u,v))))
| ~ h(w)
| equal(sum__dfg(u,sum__dfg(sum__dfg(v,opp(sum__dfg(u,v))),w)),sum__dfg(eg,w)) ),
inference(spr,[status(thm),theory(equality)],[134,19]),
[iquote('0:SpR:134.2,19.3')] ).
cnf(939,plain,
( ~ h(u)
| ~ h(v)
| ~ h(u)
| ~ h(sum__dfg(v,opp(sum__dfg(u,v))))
| equal(sum__dfg(v,opp(sum__dfg(u,v))),sum__dfg(opp(u),eg)) ),
inference(spr,[status(thm),theory(equality)],[134,130]),
[iquote('0:SpR:134.2,130.2')] ).
cnf(952,plain,
( ~ h(u)
| ~ h(u)
| ~ h(eg)
| equal(sum__dfg(u,sum__dfg(eg,opp(u))),eg) ),
inference(spr,[status(thm),theory(equality)],[10,134]),
[iquote('0:SpR:10.1,134.2')] ).
cnf(966,plain,
( ~ h(u)
| ~ h(eg)
| equal(sum__dfg(u,sum__dfg(eg,opp(u))),eg) ),
inference(obv,[status(thm),theory(equality)],[952]),
[iquote('0:Obv:952.0')] ).
cnf(967,plain,
( ~ h(u)
| equal(sum__dfg(u,sum__dfg(eg,opp(u))),eg) ),
inference(ssi,[status(thm)],[966,3]),
[iquote('0:SSi:966.1,3.0')] ).
cnf(989,plain,
( ~ h(u)
| ~ h(v)
| ~ h(sum__dfg(u,opp(sum__dfg(v,u))))
| equal(sum__dfg(u,opp(sum__dfg(v,u))),sum__dfg(opp(v),eg)) ),
inference(obv,[status(thm),theory(equality)],[939]),
[iquote('0:Obv:939.0')] ).
cnf(990,plain,
( ~ h(u)
| ~ h(v)
| equal(sum__dfg(u,opp(sum__dfg(v,u))),sum__dfg(opp(v),eg)) ),
inference(ssi,[status(thm)],[989,16,45]),
[iquote('0:SSi:989.2,16.2,45.0,16.2')] ).
cnf(1001,plain,
( ~ h(u)
| ~ h(v)
| ~ h(sum__dfg(u,opp(sum__dfg(v,u))))
| ~ h(w)
| equal(sum__dfg(v,sum__dfg(sum__dfg(u,opp(sum__dfg(v,u))),w)),sum__dfg(eg,w)) ),
inference(obv,[status(thm),theory(equality)],[938]),
[iquote('0:Obv:938.0')] ).
cnf(1002,plain,
( ~ h(u)
| ~ h(v)
| ~ h(sum__dfg(u,opp(sum__dfg(v,u))))
| ~ h(w)
| equal(sum__dfg(v,sum__dfg(sum__dfg(u,opp(sum__dfg(v,u))),w)),w) ),
inference(rew,[status(thm),theory(equality)],[9,1001]),
[iquote('0:Rew:9.1,1001.4')] ).
cnf(1003,plain,
( ~ h(u)
| ~ h(v)
| ~ h(sum__dfg(u,opp(sum__dfg(v,u))))
| ~ h(w)
| equal(sum__dfg(v,sum__dfg(sum__dfg(opp(v),eg),w)),w) ),
inference(rew,[status(thm),theory(equality)],[990,1002]),
[iquote('0:Rew:990.2,1002.4')] ).
cnf(1004,plain,
( ~ h(u)
| ~ h(v)
| ~ h(w)
| equal(sum__dfg(v,sum__dfg(sum__dfg(opp(v),eg),w)),w) ),
inference(ssi,[status(thm)],[1003,16,45]),
[iquote('0:SSi:1003.2,16.2,45.0,16.2')] ).
cnf(1151,plain,
( ~ g(u)
| ~ g(v)
| ~ g(u)
| ~ g(product(v,inv(product(u,v))))
| equal(product(v,inv(product(u,v))),product(inv(u),eh)) ),
inference(spr,[status(thm),theory(equality)],[196,192]),
[iquote('0:SpR:196.2,192.2')] ).
cnf(1162,plain,
( ~ g(skc1)
| ~ g(eh)
| equal(product(skc1,product(eh,inv(skc1))),eh) ),
inference(spr,[status(thm),theory(equality)],[26,196]),
[iquote('0:SpR:26.0,196.2')] ).
cnf(1168,plain,
( ~ g(u)
| ~ g(u)
| ~ g(eh)
| equal(product(u,product(eh,inv(u))),eh) ),
inference(spr,[status(thm),theory(equality)],[8,196]),
[iquote('0:SpR:8.1,196.2')] ).
cnf(1177,plain,
equal(product(skc1,product(eh,inv(skc1))),eh),
inference(ssi,[status(thm)],[1162,2,1]),
[iquote('0:SSi:1162.1,1162.0,2.0,1.0')] ).
cnf(1186,plain,
( ~ g(u)
| ~ g(eh)
| equal(product(u,product(eh,inv(u))),eh) ),
inference(obv,[status(thm),theory(equality)],[1168]),
[iquote('0:Obv:1168.0')] ).
cnf(1187,plain,
( ~ g(u)
| equal(product(u,product(eh,inv(u))),eh) ),
inference(ssi,[status(thm)],[1186,2]),
[iquote('0:SSi:1186.1,2.0')] ).
cnf(1211,plain,
( ~ g(u)
| ~ g(v)
| ~ g(product(u,inv(product(v,u))))
| equal(product(u,inv(product(v,u))),product(inv(v),eh)) ),
inference(obv,[status(thm),theory(equality)],[1151]),
[iquote('0:Obv:1151.0')] ).
cnf(1212,plain,
( ~ g(u)
| ~ g(v)
| equal(product(u,inv(product(v,u))),product(inv(v),eh)) ),
inference(ssi,[status(thm)],[1211,15,4]),
[iquote('0:SSi:1211.2,15.2,4.1,15.2')] ).
cnf(1213,plain,
( ~ g(u)
| ~ g(v)
| equal(product(u,product(inv(u),eh)),eh) ),
inference(rew,[status(thm),theory(equality)],[1212,196]),
[iquote('0:Rew:1212.2,196.2')] ).
cnf(1214,plain,
( ~ g(u)
| equal(product(u,product(inv(u),eh)),eh) ),
inference(con,[status(thm)],[1213]),
[iquote('0:Con:1213.1')] ).
cnf(1236,plain,
( ~ g(skc1)
| ~ g(product(eh,inv(skc1)))
| equal(product(inv(skc1),eh),product(eh,inv(skc1))) ),
inference(spr,[status(thm),theory(equality)],[1177,192]),
[iquote('0:SpR:1177.0,192.2')] ).
cnf(1244,plain,
equal(product(inv(skc1),eh),product(eh,inv(skc1))),
inference(ssi,[status(thm)],[1236,15,2,27,1]),
[iquote('0:SSi:1236.1,1236.0,15.0,2.0,27.0,1.2')] ).
cnf(1613,plain,
( ~ g(u)
| ~ g(inv(u))
| ~ g(u)
| equal(product(inv(u),product(u,skc1)),product(eh,skc1)) ),
inference(spr,[status(thm),theory(equality)],[12,21]),
[iquote('0:SpR:12.1,21.2')] ).
cnf(1617,plain,
( ~ g(u)
| ~ g(u)
| ~ g(product(inv(u),eh))
| equal(product(u,product(product(inv(u),eh),skc1)),product(eh,skc1)) ),
inference(spr,[status(thm),theory(equality)],[1214,21]),
[iquote('0:SpR:1214.1,21.2')] ).
cnf(1652,plain,
( ~ g(inv(u))
| ~ g(u)
| equal(product(inv(u),product(u,skc1)),product(eh,skc1)) ),
inference(obv,[status(thm),theory(equality)],[1613]),
[iquote('0:Obv:1613.0')] ).
cnf(1653,plain,
( ~ g(inv(u))
| ~ g(u)
| equal(product(inv(u),product(u,skc1)),skc1) ),
inference(rew,[status(thm),theory(equality)],[25,1652]),
[iquote('0:Rew:25.0,1652.2')] ).
cnf(1654,plain,
( ~ g(u)
| equal(product(inv(u),product(u,skc1)),skc1) ),
inference(ssi,[status(thm)],[1653,4]),
[iquote('0:SSi:1653.0,4.1')] ).
cnf(1657,plain,
( ~ g(u)
| ~ g(product(inv(u),eh))
| equal(product(u,product(product(inv(u),eh),skc1)),product(eh,skc1)) ),
inference(obv,[status(thm),theory(equality)],[1617]),
[iquote('0:Obv:1617.0')] ).
cnf(1658,plain,
( ~ g(u)
| ~ g(product(inv(u),eh))
| equal(product(u,product(product(inv(u),eh),skc1)),skc1) ),
inference(rew,[status(thm),theory(equality)],[25,1657]),
[iquote('0:Rew:25.0,1657.2')] ).
cnf(1659,plain,
( ~ g(u)
| equal(product(u,product(product(inv(u),eh),skc1)),skc1) ),
inference(ssi,[status(thm)],[1658,15,4,2]),
[iquote('0:SSi:1658.1,15.0,4.1,2.2')] ).
cnf(2912,plain,
( ~ h(u)
| ~ h(u)
| ~ h(sum__dfg(eg,opp(u)))
| equal(sum__dfg(opp(u),eg),sum__dfg(eg,opp(u))) ),
inference(spr,[status(thm),theory(equality)],[967,130]),
[iquote('0:SpR:967.1,130.2')] ).
cnf(2936,plain,
( ~ h(u)
| ~ h(sum__dfg(eg,opp(u)))
| equal(sum__dfg(opp(u),eg),sum__dfg(eg,opp(u))) ),
inference(obv,[status(thm),theory(equality)],[2912]),
[iquote('0:Obv:2912.0')] ).
cnf(2937,plain,
( ~ h(u)
| equal(sum__dfg(opp(u),eg),sum__dfg(eg,opp(u))) ),
inference(ssi,[status(thm)],[2936,16,3,45]),
[iquote('0:SSi:2936.1,16.0,3.0,45.2')] ).
cnf(2940,plain,
( ~ h(u)
| ~ h(v)
| ~ h(w)
| equal(sum__dfg(v,sum__dfg(sum__dfg(eg,opp(v)),w)),w) ),
inference(rew,[status(thm),theory(equality)],[2937,1004]),
[iquote('0:Rew:2937.1,1004.3')] ).
cnf(2942,plain,
( ~ h(u)
| ~ h(v)
| equal(sum__dfg(u,sum__dfg(sum__dfg(eg,opp(u)),v)),v) ),
inference(con,[status(thm)],[2940]),
[iquote('0:Con:2940.0')] ).
cnf(3032,plain,
( ~ g(u)
| ~ g(u)
| ~ g(product(eh,inv(u)))
| equal(product(inv(u),eh),product(eh,inv(u))) ),
inference(spr,[status(thm),theory(equality)],[1187,192]),
[iquote('0:SpR:1187.1,192.2')] ).
cnf(3064,plain,
( ~ g(u)
| ~ g(product(eh,inv(u)))
| equal(product(inv(u),eh),product(eh,inv(u))) ),
inference(obv,[status(thm),theory(equality)],[3032]),
[iquote('0:Obv:3032.0')] ).
cnf(3065,plain,
( ~ g(u)
| equal(product(inv(u),eh),product(eh,inv(u))) ),
inference(ssi,[status(thm)],[3064,15,2,4]),
[iquote('0:SSi:3064.1,15.1,2.0,4.2')] ).
cnf(3067,plain,
( ~ g(u)
| equal(product(u,product(product(eh,inv(u)),skc1)),skc1) ),
inference(rew,[status(thm),theory(equality)],[3065,1659]),
[iquote('0:Rew:3065.1,1659.1')] ).
cnf(5431,plain,
( ~ g(skc1)
| ~ g(product(product(eh,inv(skc1)),skc1))
| equal(product(product(eh,inv(skc1)),skc1),product(inv(skc1),skc1)) ),
inference(spr,[status(thm),theory(equality)],[3067,179]),
[iquote('0:SpR:3067.1,179.1')] ).
cnf(5483,plain,
( ~ g(skc1)
| ~ g(product(product(eh,inv(skc1)),skc1))
| equal(product(product(eh,inv(skc1)),skc1),eh) ),
inference(rew,[status(thm),theory(equality)],[12,5431]),
[iquote('0:Rew:12.1,5431.2')] ).
cnf(5484,plain,
equal(product(product(eh,inv(skc1)),skc1),eh),
inference(ssi,[status(thm)],[5483,22,15,2,27,1]),
[iquote('0:SSi:5483.1,5483.0,22.0,15.0,2.0,27.2,1.1')] ).
cnf(5510,plain,
( ~ g(product(eh,inv(skc1)))
| equal(product(inv(product(eh,inv(skc1))),eh),skc1) ),
inference(spr,[status(thm),theory(equality)],[5484,1654]),
[iquote('0:SpR:5484.0,1654.1')] ).
cnf(5530,plain,
( ~ g(product(eh,inv(skc1)))
| equal(product(eh,inv(product(eh,inv(skc1)))),skc1) ),
inference(rew,[status(thm),theory(equality)],[3065,5510]),
[iquote('0:Rew:3065.1,5510.1')] ).
cnf(5531,plain,
equal(product(eh,inv(product(eh,inv(skc1)))),skc1),
inference(ssi,[status(thm)],[5530,15,2,27]),
[iquote('0:SSi:5530.0,15.0,2.0,27.2')] ).
cnf(5543,plain,
( ~ g(inv(product(eh,inv(skc1))))
| equal(inv(product(eh,inv(skc1))),skc1) ),
inference(spr,[status(thm),theory(equality)],[5531,7]),
[iquote('0:SpR:5531.0,7.1')] ).
cnf(5557,plain,
equal(inv(product(eh,inv(skc1))),skc1),
inference(ssi,[status(thm)],[5543,4,15,2,27]),
[iquote('0:SSi:5543.0,4.0,15.0,2.2,27.1')] ).
cnf(5570,plain,
( ~ g(product(eh,inv(skc1)))
| equal(product(eh,inv(skc1)),inv(skc1)) ),
inference(spr,[status(thm),theory(equality)],[5557,339]),
[iquote('0:SpR:5557.0,339.1')] ).
cnf(5577,plain,
equal(product(eh,inv(skc1)),inv(skc1)),
inference(ssi,[status(thm)],[5570,15,2,27]),
[iquote('0:SSi:5570.0,15.0,2.0,27.2')] ).
cnf(5579,plain,
equal(product(inv(skc1),eh),inv(skc1)),
inference(rew,[status(thm),theory(equality)],[5577,1244]),
[iquote('0:Rew:5577.0,1244.0')] ).
cnf(5620,plain,
( ~ g(inv(product(skc1,skc1)))
| ~ g(product(skc1,skc1))
| equal(product(skc1,product(skc1,inv(product(skc1,skc1)))),eh) ),
inference(spr,[status(thm),theory(equality)],[37,11]),
[iquote('0:SpR:37.1,11.1')] ).
cnf(5684,plain,
equal(product(skc1,product(skc1,inv(product(skc1,skc1)))),eh),
inference(ssi,[status(thm)],[5620,35,4]),
[iquote('0:SSi:5620.1,5620.0,35.0,4.1,35.0')] ).
cnf(5763,plain,
( ~ g(product(skc1,inv(product(skc1,skc1))))
| equal(product(skc1,inv(product(skc1,skc1))),product(inv(skc1),eh)) ),
inference(spr,[status(thm),theory(equality)],[5684,179]),
[iquote('0:SpR:5684.0,179.1')] ).
cnf(5795,plain,
( ~ g(product(skc1,inv(product(skc1,skc1))))
| equal(product(skc1,inv(product(skc1,skc1))),inv(skc1)) ),
inference(rew,[status(thm),theory(equality)],[5579,5763]),
[iquote('0:Rew:5579.0,5763.1')] ).
cnf(5796,plain,
equal(product(skc1,inv(product(skc1,skc1))),inv(skc1)),
inference(ssi,[status(thm)],[5795,30,4,35]),
[iquote('0:SSi:5795.0,30.0,4.1,35.1')] ).
cnf(5812,plain,
( ~ g(inv(product(skc1,skc1)))
| h(f(inv(skc1))) ),
inference(spr,[status(thm),theory(equality)],[5796,103]),
[iquote('0:SpR:5796.0,103.1')] ).
cnf(5831,plain,
h(f(inv(skc1))),
inference(ssi,[status(thm)],[5812,4,35]),
[iquote('0:SSi:5812.0,4.0,35.1')] ).
cnf(6500,plain,
( ~ h(sum__dfg(eg,opp(u)))
| ~ h(u)
| ~ h(opp(sum__dfg(eg,opp(u))))
| equal(opp(sum__dfg(eg,opp(u))),sum__dfg(u,eg)) ),
inference(spr,[status(thm),theory(equality)],[13,2942]),
[iquote('0:SpR:13.1,2942.2')] ).
cnf(6513,plain,
( ~ h(sum__dfg(eg,opp(u)))
| ~ h(u)
| ~ h(opp(sum__dfg(eg,opp(u))))
| equal(opp(sum__dfg(eg,opp(u))),u) ),
inference(rew,[status(thm),theory(equality)],[10,6500]),
[iquote('0:Rew:10.1,6500.3')] ).
cnf(6514,plain,
( ~ h(u)
| equal(opp(sum__dfg(eg,opp(u))),u) ),
inference(ssi,[status(thm)],[6513,45,16,3]),
[iquote('0:SSi:6513.2,6513.0,45.0,16.0,3.2,45.0,16.0,3.2,45.0')] ).
cnf(7145,plain,
( ~ h(u)
| ~ h(sum__dfg(eg,opp(u)))
| equal(sum__dfg(eg,opp(u)),opp(u)) ),
inference(spr,[status(thm),theory(equality)],[6514,237]),
[iquote('0:SpR:6514.1,237.1')] ).
cnf(7157,plain,
( ~ h(u)
| equal(sum__dfg(eg,opp(u)),opp(u)) ),
inference(ssi,[status(thm)],[7145,16,3,45]),
[iquote('0:SSi:7145.1,16.0,3.0,45.2')] ).
cnf(7163,plain,
( ~ h(u)
| equal(sum__dfg(opp(u),eg),opp(u)) ),
inference(rew,[status(thm),theory(equality)],[7157,2937]),
[iquote('0:Rew:7157.1,2937.1')] ).
cnf(11910,plain,
( ~ h(f(u))
| equal(sum__dfg(opp(f(skc1)),f(product(skc1,u))),f(u)) ),
inference(sor,[status(thm)],[275,28]),
[iquote('0:SoR:275.0,28.0')] ).
cnf(73230,plain,
equal(sum__dfg(opp(f(skc1)),f(product(skc1,inv(skc1)))),f(inv(skc1))),
inference(sor,[status(thm)],[11910,5831]),
[iquote('0:SoR:11910.0,5831.0')] ).
cnf(73231,plain,
equal(sum__dfg(opp(f(skc1)),f(product(skc1,eh))),f(eh)),
inference(sor,[status(thm)],[11910,144]),
[iquote('0:SoR:11910.0,144.0')] ).
cnf(73427,plain,
equal(sum__dfg(opp(f(skc1)),f(skc1)),f(eh)),
inference(rew,[status(thm),theory(equality)],[26,73231]),
[iquote('0:Rew:26.0,73231.0')] ).
cnf(73428,plain,
equal(sum__dfg(opp(f(skc1)),f(eh)),f(inv(skc1))),
inference(rew,[status(thm),theory(equality)],[23,73230]),
[iquote('0:Rew:23.0,73230.0')] ).
cnf(73466,plain,
( ~ h(f(skc1))
| equal(f(eh),eg) ),
inference(spr,[status(thm),theory(equality)],[73427,14]),
[iquote('0:SpR:73427.0,14.1')] ).
cnf(73504,plain,
equal(f(eh),eg),
inference(ssi,[status(thm)],[73466,28]),
[iquote('0:SSi:73466.0,28.0')] ).
cnf(73505,plain,
( ~ equal(eg,eg)
| ~ equal(f(inv(skc1)),opp(f(skc1))) ),
inference(rew,[status(thm),theory(equality)],[73504,18]),
[iquote('0:Rew:73504.0,18.0')] ).
cnf(73516,plain,
equal(sum__dfg(opp(f(skc1)),eg),f(inv(skc1))),
inference(rew,[status(thm),theory(equality)],[73504,73428]),
[iquote('0:Rew:73504.0,73428.0')] ).
cnf(73521,plain,
~ equal(f(inv(skc1)),opp(f(skc1))),
inference(obv,[status(thm),theory(equality)],[73505]),
[iquote('0:Obv:73505.0')] ).
cnf(74321,plain,
( ~ h(f(skc1))
| equal(f(inv(skc1)),opp(f(skc1))) ),
inference(spr,[status(thm),theory(equality)],[73516,7163]),
[iquote('0:SpR:73516.0,7163.1')] ).
cnf(74335,plain,
equal(f(inv(skc1)),opp(f(skc1))),
inference(ssi,[status(thm)],[74321,28]),
[iquote('0:SSi:74321.0,28.0')] ).
cnf(74336,plain,
$false,
inference(mrr,[status(thm)],[74335,73521]),
[iquote('0:MRR:74335.0,73521.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : GRP776+1 : TPTP v8.1.0. Released v4.1.0.
% 0.06/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n026.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 : Mon Jun 13 06:57:35 EDT 2022
% 0.12/0.34 % CPUTime :
% 201.13/201.31
% 201.13/201.31 SPASS V 3.9
% 201.13/201.31 SPASS beiseite: Proof found.
% 201.13/201.31 % SZS status Theorem
% 201.13/201.31 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 201.13/201.31 SPASS derived 46432 clauses, backtracked 0 clauses, performed 0 splits and kept 15163 clauses.
% 201.13/201.31 SPASS allocated 192825 KBytes.
% 201.13/201.31 SPASS spent 0:3:20.89 on the problem.
% 201.13/201.31 0:00:00.03 for the input.
% 201.13/201.31 0:00:00.04 for the FLOTTER CNF translation.
% 201.13/201.31 0:00:00.59 for inferences.
% 201.13/201.31 0:00:00.00 for the backtracking.
% 201.13/201.31 0:3:19.98 for the reduction.
% 201.13/201.31
% 201.13/201.31
% 201.13/201.31 Here is a proof with depth 7, length 145 :
% 201.13/201.31 % SZS output start Refutation
% See solution above
% 236.20/236.39 Formulae used in the proof : goals sos03 sos11 sos02 sos10 sos17 sos05 sos06 sos13 sos14 sos07 sos08 sos15 sos16 sos01 sos09 sos18 sos12 sos04
% 236.20/236.39
%------------------------------------------------------------------------------