TSTP Solution File: CAT002-1 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : CAT002-1 : TPTP v8.1.0. Released v1.0.0.
% 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 : Fri Jul 15 00:07:27 EDT 2022
% Result : Unsatisfiable 30.49s 30.72s
% Output : Refutation 32.03s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 23
% Syntax : Number of clauses : 156 ( 43 unt; 0 nHn; 156 RR)
% Number of literals : 341 ( 0 equ; 190 neg)
% Maximal clause size : 4 ( 2 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 5 ( 4 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,u,v)
| ~ product(a,w,v)
| equal(w,u) ),
file('CAT002-1.p',unknown),
[] ).
cnf(2,axiom,
( ~ product(b,u,v)
| ~ product(b,w,v)
| equal(w,u) ),
file('CAT002-1.p',unknown),
[] ).
cnf(3,axiom,
product(a,b,c),
file('CAT002-1.p',unknown),
[] ).
cnf(4,axiom,
product(c,h,d),
file('CAT002-1.p',unknown),
[] ).
cnf(5,axiom,
product(c,g,d),
file('CAT002-1.p',unknown),
[] ).
cnf(6,axiom,
~ equal(g,h),
file('CAT002-1.p',unknown),
[] ).
cnf(7,axiom,
( ~ defined(u,v)
| product(u,v,compose(u,v)) ),
file('CAT002-1.p',unknown),
[] ).
cnf(8,axiom,
( ~ product(u,v,w)
| defined(u,v) ),
file('CAT002-1.p',unknown),
[] ).
cnf(9,axiom,
( ~ defined(u,v)
| ~ product(w,x,u)
| defined(x,v) ),
file('CAT002-1.p',unknown),
[] ).
cnf(10,axiom,
( ~ defined(u,v)
| ~ product(w,v,x)
| ~ product(y,w,u)
| defined(y,x) ),
file('CAT002-1.p',unknown),
[] ).
cnf(12,axiom,
( ~ defined(u,v)
| ~ product(w,x,v)
| defined(u,w) ),
file('CAT002-1.p',unknown),
[] ).
cnf(13,axiom,
( ~ defined(u,v)
| ~ product(u,w,x)
| ~ product(w,y,v)
| defined(x,y) ),
file('CAT002-1.p',unknown),
[] ).
cnf(14,axiom,
( ~ product(u,v,w)
| ~ product(u,x,y)
| ~ product(v,z,x)
| product(w,z,y) ),
file('CAT002-1.p',unknown),
[] ).
cnf(15,axiom,
( ~ identity_map(u)
| ~ defined(v,u)
| ~ defined(u,w)
| defined(v,w) ),
file('CAT002-1.p',unknown),
[] ).
cnf(16,axiom,
identity_map(domain__dfg(u)),
file('CAT002-1.p',unknown),
[] ).
cnf(17,axiom,
identity_map(codomain(u)),
file('CAT002-1.p',unknown),
[] ).
cnf(18,axiom,
defined(u,domain__dfg(u)),
file('CAT002-1.p',unknown),
[] ).
cnf(19,axiom,
defined(codomain(u),u),
file('CAT002-1.p',unknown),
[] ).
cnf(20,axiom,
product(u,domain__dfg(u),u),
file('CAT002-1.p',unknown),
[] ).
cnf(21,axiom,
product(codomain(u),u,u),
file('CAT002-1.p',unknown),
[] ).
cnf(22,axiom,
( ~ identity_map(u)
| ~ defined(u,v)
| product(u,v,v) ),
file('CAT002-1.p',unknown),
[] ).
cnf(23,axiom,
( ~ identity_map(u)
| ~ defined(v,u)
| product(v,u,v) ),
file('CAT002-1.p',unknown),
[] ).
cnf(24,axiom,
( ~ product(u,v,w)
| ~ product(u,v,x)
| equal(x,w) ),
file('CAT002-1.p',unknown),
[] ).
cnf(27,plain,
( ~ product(b,h,u)
| ~ product(b,g,u) ),
inference(res,[status(thm),theory(equality)],[2,6]),
[iquote('0:Res:2.2,6.0')] ).
cnf(31,plain,
defined(c,g),
inference(res,[status(thm),theory(equality)],[5,8]),
[iquote('0:Res:5.0,8.0')] ).
cnf(32,plain,
defined(c,h),
inference(res,[status(thm),theory(equality)],[4,8]),
[iquote('0:Res:4.0,8.0')] ).
cnf(33,plain,
defined(a,b),
inference(res,[status(thm),theory(equality)],[3,8]),
[iquote('0:Res:3.0,8.0')] ).
cnf(37,plain,
( ~ defined(b,g)
| ~ product(b,h,compose(b,g)) ),
inference(res,[status(thm),theory(equality)],[7,27]),
[iquote('0:Res:7.1,27.1')] ).
cnf(56,plain,
( ~ defined(u,v)
| defined(u,codomain(v)) ),
inference(res,[status(thm),theory(equality)],[21,12]),
[iquote('0:Res:21.0,12.1')] ).
cnf(58,plain,
( ~ defined(u,v)
| ~ defined(w,compose(u,v))
| defined(w,u) ),
inference(res,[status(thm),theory(equality)],[7,12]),
[iquote('0:Res:7.1,12.1')] ).
cnf(66,plain,
( ~ defined(c,u)
| defined(b,u) ),
inference(res,[status(thm),theory(equality)],[3,9]),
[iquote('0:Res:3.0,9.1')] ).
cnf(68,plain,
( ~ defined(u,v)
| defined(domain__dfg(u),v) ),
inference(res,[status(thm),theory(equality)],[20,9]),
[iquote('0:Res:20.0,9.1')] ).
cnf(75,plain,
( ~ product(b,u,b)
| equal(u,domain__dfg(b)) ),
inference(res,[status(thm),theory(equality)],[20,2]),
[iquote('0:Res:20.0,2.0')] ).
cnf(80,plain,
defined(b,domain__dfg(c)),
inference(res,[status(thm),theory(equality)],[18,66]),
[iquote('0:Res:18.0,66.0')] ).
cnf(81,plain,
defined(b,g),
inference(res,[status(thm),theory(equality)],[31,66]),
[iquote('0:Res:31.0,66.0')] ).
cnf(82,plain,
defined(b,h),
inference(res,[status(thm),theory(equality)],[32,66]),
[iquote('0:Res:32.0,66.0')] ).
cnf(83,plain,
~ product(b,h,compose(b,g)),
inference(mrr,[status(thm)],[37,81]),
[iquote('0:MRR:37.0,81.0')] ).
cnf(87,plain,
( ~ product(a,u,a)
| equal(u,domain__dfg(a)) ),
inference(res,[status(thm),theory(equality)],[20,1]),
[iquote('0:Res:20.0,1.0')] ).
cnf(88,plain,
( ~ defined(a,u)
| ~ product(a,v,compose(a,u))
| equal(v,u) ),
inference(res,[status(thm),theory(equality)],[7,1]),
[iquote('0:Res:7.1,1.0')] ).
cnf(91,plain,
( ~ product(c,g,u)
| equal(u,d) ),
inference(res,[status(thm),theory(equality)],[5,24]),
[iquote('0:Res:5.0,24.0')] ).
cnf(92,plain,
( ~ product(c,h,u)
| equal(u,d) ),
inference(res,[status(thm),theory(equality)],[4,24]),
[iquote('0:Res:4.0,24.0')] ).
cnf(94,plain,
( ~ product(codomain(u),u,v)
| equal(v,u) ),
inference(res,[status(thm),theory(equality)],[21,24]),
[iquote('0:Res:21.0,24.0')] ).
cnf(96,plain,
( ~ defined(u,v)
| ~ product(u,v,w)
| equal(w,compose(u,v)) ),
inference(res,[status(thm),theory(equality)],[7,24]),
[iquote('0:Res:7.1,24.0')] ).
cnf(97,plain,
( ~ identity_map(u)
| ~ defined(u,v)
| ~ product(u,v,w)
| equal(w,v) ),
inference(res,[status(thm),theory(equality)],[22,24]),
[iquote('0:Res:22.2,24.0')] ).
cnf(99,plain,
( ~ product(u,v,w)
| equal(w,compose(u,v)) ),
inference(mrr,[status(thm)],[96,8]),
[iquote('0:MRR:96.0,8.1')] ).
cnf(100,plain,
( ~ identity_map(u)
| ~ product(u,v,w)
| equal(w,v) ),
inference(mrr,[status(thm)],[97,8]),
[iquote('0:MRR:97.1,8.1')] ).
cnf(113,plain,
( ~ identity_map(domain__dfg(u))
| ~ defined(domain__dfg(u),v)
| defined(u,v) ),
inference(res,[status(thm),theory(equality)],[18,15]),
[iquote('0:Res:18.0,15.1')] ).
cnf(127,plain,
( ~ defined(domain__dfg(u),v)
| defined(u,v) ),
inference(ssi,[status(thm)],[113,16]),
[iquote('0:SSi:113.0,16.0')] ).
cnf(145,plain,
( ~ defined(c,u)
| ~ product(h,v,u)
| defined(d,v) ),
inference(res,[status(thm),theory(equality)],[4,13]),
[iquote('0:Res:4.0,13.1')] ).
cnf(146,plain,
( ~ defined(a,u)
| ~ product(b,v,u)
| defined(c,v) ),
inference(res,[status(thm),theory(equality)],[3,13]),
[iquote('0:Res:3.0,13.1')] ).
cnf(149,plain,
( ~ defined(u,v)
| ~ defined(u,w)
| ~ product(v,x,w)
| defined(compose(u,v),x) ),
inference(res,[status(thm),theory(equality)],[7,13]),
[iquote('0:Res:7.1,13.1')] ).
cnf(152,plain,
( ~ defined(u,v)
| ~ product(w,x,v)
| defined(compose(u,w),x) ),
inference(mrr,[status(thm)],[149,12]),
[iquote('0:MRR:149.0,12.2')] ).
cnf(168,plain,
( ~ defined(u,v)
| ~ product(w,codomain(v),u)
| defined(w,v) ),
inference(res,[status(thm),theory(equality)],[21,10]),
[iquote('0:Res:21.0,10.1')] ).
cnf(170,plain,
( ~ defined(u,v)
| ~ defined(w,v)
| ~ product(x,u,w)
| defined(x,compose(u,v)) ),
inference(res,[status(thm),theory(equality)],[7,10]),
[iquote('0:Res:7.1,10.1')] ).
cnf(173,plain,
( ~ defined(u,v)
| ~ product(w,x,u)
| defined(w,compose(x,v)) ),
inference(mrr,[status(thm)],[170,9]),
[iquote('0:MRR:170.0,9.2')] ).
cnf(180,plain,
( ~ product(a,u,v)
| ~ product(b,w,u)
| product(c,w,v) ),
inference(res,[status(thm),theory(equality)],[3,14]),
[iquote('0:Res:3.0,14.0')] ).
cnf(182,plain,
( ~ product(u,v,w)
| ~ product(domain__dfg(u),x,v)
| product(u,x,w) ),
inference(res,[status(thm),theory(equality)],[20,14]),
[iquote('0:Res:20.0,14.0')] ).
cnf(191,plain,
( ~ identity_map(codomain(u))
| ~ defined(v,u)
| ~ defined(codomain(u),w)
| defined(v,w) ),
inference(res,[status(thm),theory(equality)],[56,15]),
[iquote('0:Res:56.1,15.1')] ).
cnf(196,plain,
( ~ defined(u,v)
| ~ defined(codomain(v),w)
| defined(u,w) ),
inference(ssi,[status(thm)],[191,17]),
[iquote('0:SSi:191.0,17.0')] ).
cnf(218,plain,
defined(u,domain__dfg(domain__dfg(u))),
inference(res,[status(thm),theory(equality)],[18,127]),
[iquote('0:Res:18.0,127.0')] ).
cnf(242,plain,
( ~ identity_map(u)
| ~ defined(b,u)
| equal(u,domain__dfg(b)) ),
inference(res,[status(thm),theory(equality)],[23,75]),
[iquote('0:Res:23.2,75.0')] ).
cnf(249,plain,
( ~ identity_map(u)
| ~ defined(a,u)
| equal(u,domain__dfg(a)) ),
inference(res,[status(thm),theory(equality)],[23,87]),
[iquote('0:Res:23.2,87.0')] ).
cnf(267,plain,
( ~ defined(codomain(u),u)
| equal(compose(codomain(u),u),u) ),
inference(res,[status(thm),theory(equality)],[7,94]),
[iquote('0:Res:7.1,94.0')] ).
cnf(270,plain,
equal(compose(codomain(u),u),u),
inference(mrr,[status(thm)],[267,19]),
[iquote('0:MRR:267.0,19.0')] ).
cnf(310,plain,
( ~ identity_map(u)
| ~ defined(u,v)
| equal(compose(u,v),v) ),
inference(res,[status(thm),theory(equality)],[22,99]),
[iquote('0:Res:22.2,99.0')] ).
cnf(387,plain,
( ~ identity_map(u)
| ~ identity_map(v)
| ~ defined(v,u)
| equal(v,u) ),
inference(res,[status(thm),theory(equality)],[23,100]),
[iquote('0:Res:23.2,100.1')] ).
cnf(448,plain,
( ~ defined(c,h)
| defined(d,domain__dfg(h)) ),
inference(res,[status(thm),theory(equality)],[20,145]),
[iquote('0:Res:20.0,145.1')] ).
cnf(453,plain,
defined(d,domain__dfg(h)),
inference(mrr,[status(thm)],[448,32]),
[iquote('0:MRR:448.0,32.0')] ).
cnf(458,plain,
( ~ identity_map(domain__dfg(h))
| ~ defined(domain__dfg(h),u)
| defined(d,u) ),
inference(res,[status(thm),theory(equality)],[453,15]),
[iquote('0:Res:453.0,15.1')] ).
cnf(461,plain,
( ~ defined(domain__dfg(h),u)
| defined(d,u) ),
inference(ssi,[status(thm)],[458,16]),
[iquote('0:SSi:458.0,16.0')] ).
cnf(483,plain,
( ~ defined(a,b)
| defined(c,domain__dfg(b)) ),
inference(res,[status(thm),theory(equality)],[20,146]),
[iquote('0:Res:20.0,146.1')] ).
cnf(488,plain,
defined(c,domain__dfg(b)),
inference(mrr,[status(thm)],[483,33]),
[iquote('0:MRR:483.0,33.0')] ).
cnf(493,plain,
( ~ identity_map(domain__dfg(b))
| ~ defined(domain__dfg(b),u)
| defined(c,u) ),
inference(res,[status(thm),theory(equality)],[488,15]),
[iquote('0:Res:488.0,15.1')] ).
cnf(496,plain,
( ~ defined(domain__dfg(b),u)
| defined(c,u) ),
inference(ssi,[status(thm)],[493,16]),
[iquote('0:SSi:493.0,16.0')] ).
cnf(601,plain,
( ~ defined(u,v)
| defined(codomain(compose(u,v)),u) ),
inference(res,[status(thm),theory(equality)],[19,58]),
[iquote('0:Res:19.0,58.1')] ).
cnf(604,plain,
( ~ defined(u,compose(v,w))
| ~ defined(v,w)
| defined(domain__dfg(u),v) ),
inference(res,[status(thm),theory(equality)],[68,58]),
[iquote('0:Res:68.1,58.1')] ).
cnf(626,plain,
( ~ defined(h,u)
| defined(d,u) ),
inference(res,[status(thm),theory(equality)],[68,461]),
[iquote('0:Res:68.1,461.0')] ).
cnf(701,plain,
( ~ defined(b,u)
| defined(c,u) ),
inference(res,[status(thm),theory(equality)],[68,496]),
[iquote('0:Res:68.1,496.0')] ).
cnf(706,plain,
( ~ defined(codomain(u),u)
| defined(codomain(codomain(u)),u) ),
inference(res,[status(thm),theory(equality)],[21,168]),
[iquote('0:Res:21.0,168.1')] ).
cnf(711,plain,
defined(codomain(codomain(u)),u),
inference(mrr,[status(thm)],[706,19]),
[iquote('0:MRR:706.0,19.0')] ).
cnf(865,plain,
( ~ defined(a,u)
| ~ product(b,v,u)
| product(c,v,compose(a,u)) ),
inference(res,[status(thm),theory(equality)],[7,180]),
[iquote('0:Res:7.1,180.0')] ).
cnf(1346,plain,
( ~ defined(u,v)
| defined(compose(u,v),domain__dfg(v)) ),
inference(res,[status(thm),theory(equality)],[20,152]),
[iquote('0:Res:20.0,152.1')] ).
cnf(1397,plain,
( ~ defined(d,u)
| defined(c,compose(h,u)) ),
inference(res,[status(thm),theory(equality)],[4,173]),
[iquote('0:Res:4.0,173.1')] ).
cnf(1398,plain,
( ~ defined(c,u)
| defined(a,compose(b,u)) ),
inference(res,[status(thm),theory(equality)],[3,173]),
[iquote('0:Res:3.0,173.1')] ).
cnf(1400,plain,
( ~ defined(u,v)
| defined(u,compose(domain__dfg(u),v)) ),
inference(res,[status(thm),theory(equality)],[20,173]),
[iquote('0:Res:20.0,173.1')] ).
cnf(1401,plain,
( ~ defined(u,v)
| ~ defined(compose(u,v),w)
| defined(u,compose(v,w)) ),
inference(res,[status(thm),theory(equality)],[7,173]),
[iquote('0:Res:7.1,173.1')] ).
cnf(1685,plain,
( ~ defined(domain__dfg(u),v)
| ~ product(u,compose(domain__dfg(u),v),w)
| product(u,v,w) ),
inference(res,[status(thm),theory(equality)],[7,182]),
[iquote('0:Res:7.1,182.1')] ).
cnf(3835,plain,
( ~ defined(domain__dfg(u),v)
| defined(u,compose(domain__dfg(domain__dfg(u)),v)) ),
inference(res,[status(thm),theory(equality)],[1400,127]),
[iquote('0:Res:1400.1,127.0')] ).
cnf(3884,plain,
( ~ identity_map(codomain(u))
| ~ defined(b,u)
| equal(codomain(u),domain__dfg(b)) ),
inference(res,[status(thm),theory(equality)],[56,242]),
[iquote('0:Res:56.1,242.1')] ).
cnf(3899,plain,
( ~ identity_map(domain__dfg(c))
| equal(domain__dfg(c),domain__dfg(b)) ),
inference(res,[status(thm),theory(equality)],[80,242]),
[iquote('0:Res:80.0,242.1')] ).
cnf(3921,plain,
equal(domain__dfg(c),domain__dfg(b)),
inference(ssi,[status(thm)],[3899,16]),
[iquote('0:SSi:3899.0,16.0')] ).
cnf(4104,plain,
( ~ defined(b,u)
| equal(codomain(u),domain__dfg(b)) ),
inference(ssi,[status(thm)],[3884,17]),
[iquote('0:SSi:3884.0,17.0')] ).
cnf(4399,plain,
( ~ identity_map(codomain(u))
| ~ defined(a,u)
| equal(codomain(u),domain__dfg(a)) ),
inference(res,[status(thm),theory(equality)],[56,249]),
[iquote('0:Res:56.1,249.1')] ).
cnf(4433,plain,
( ~ defined(a,u)
| equal(codomain(u),domain__dfg(a)) ),
inference(ssi,[status(thm)],[4399,17]),
[iquote('0:SSi:4399.0,17.0')] ).
cnf(4831,plain,
( ~ defined(u,codomain(v))
| defined(u,v) ),
inference(res,[status(thm),theory(equality)],[711,196]),
[iquote('0:Res:711.0,196.1')] ).
cnf(4906,plain,
( ~ identity_map(u)
| ~ defined(u,v)
| ~ defined(u,v)
| defined(codomain(v),u) ),
inference(spr,[status(thm),theory(equality)],[310,601]),
[iquote('0:SpR:310.2,601.1')] ).
cnf(4934,plain,
( ~ identity_map(u)
| ~ defined(u,v)
| defined(codomain(v),u) ),
inference(obv,[status(thm),theory(equality)],[4906]),
[iquote('0:Obv:4906.1')] ).
cnf(6121,plain,
( ~ identity_map(codomain(u))
| ~ identity_map(v)
| ~ defined(v,u)
| equal(v,codomain(u)) ),
inference(res,[status(thm),theory(equality)],[56,387]),
[iquote('0:Res:56.1,387.2')] ).
cnf(6279,plain,
( ~ identity_map(u)
| ~ identity_map(domain__dfg(v))
| ~ defined(v,u)
| equal(domain__dfg(v),u) ),
inference(res,[status(thm),theory(equality)],[68,387]),
[iquote('0:Res:68.1,387.2')] ).
cnf(6737,plain,
( ~ identity_map(u)
| ~ defined(u,v)
| equal(u,codomain(v)) ),
inference(ssi,[status(thm)],[6121,17]),
[iquote('0:SSi:6121.0,17.0')] ).
cnf(6809,plain,
( ~ identity_map(u)
| ~ defined(v,u)
| equal(domain__dfg(v),u) ),
inference(ssi,[status(thm)],[6279,16]),
[iquote('0:SSi:6279.1,16.0')] ).
cnf(7457,plain,
( ~ defined(d,u)
| ~ defined(h,u)
| defined(domain__dfg(c),h) ),
inference(res,[status(thm),theory(equality)],[1397,604]),
[iquote('0:Res:1397.1,604.0')] ).
cnf(7458,plain,
( ~ defined(c,u)
| ~ defined(b,u)
| defined(domain__dfg(a),b) ),
inference(res,[status(thm),theory(equality)],[1398,604]),
[iquote('0:Res:1398.1,604.0')] ).
cnf(7468,plain,
( ~ defined(d,u)
| ~ defined(h,u)
| defined(domain__dfg(b),h) ),
inference(rew,[status(thm),theory(equality)],[3921,7457]),
[iquote('0:Rew:3921.0,7457.2')] ).
cnf(7469,plain,
( ~ defined(h,u)
| defined(domain__dfg(b),h) ),
inference(mrr,[status(thm)],[7468,626]),
[iquote('0:MRR:7468.0,626.1')] ).
cnf(7470,plain,
( ~ defined(b,u)
| defined(domain__dfg(a),b) ),
inference(mrr,[status(thm)],[7458,701]),
[iquote('0:MRR:7458.0,701.1')] ).
cnf(7856,plain,
( ~ defined(a,u)
| ~ product(b,g,u)
| equal(compose(a,u),d) ),
inference(res,[status(thm),theory(equality)],[865,91]),
[iquote('0:Res:865.2,91.0')] ).
cnf(7877,plain,
( ~ defined(a,u)
| ~ product(b,h,u)
| equal(compose(a,u),d) ),
inference(res,[status(thm),theory(equality)],[865,92]),
[iquote('0:Res:865.2,92.0')] ).
cnf(7896,plain,
defined(domain__dfg(b),h),
inference(res,[status(thm),theory(equality)],[18,7469]),
[iquote('0:Res:18.0,7469.0')] ).
cnf(8017,plain,
defined(domain__dfg(a),b),
inference(res,[status(thm),theory(equality)],[18,7470]),
[iquote('0:Res:18.0,7470.0')] ).
cnf(12005,plain,
( ~ defined(u,compose(domain__dfg(u),v))
| ~ defined(domain__dfg(u),v)
| product(u,v,compose(u,compose(domain__dfg(u),v))) ),
inference(res,[status(thm),theory(equality)],[7,1685]),
[iquote('0:Res:7.1,1685.1')] ).
cnf(15339,plain,
equal(codomain(g),domain__dfg(b)),
inference(res,[status(thm),theory(equality)],[81,4104]),
[iquote('0:Res:81.0,4104.0')] ).
cnf(15340,plain,
equal(codomain(h),domain__dfg(b)),
inference(res,[status(thm),theory(equality)],[82,4104]),
[iquote('0:Res:82.0,4104.0')] ).
cnf(15944,plain,
( ~ defined(u,domain__dfg(b))
| defined(u,g) ),
inference(spl,[status(thm),theory(equality)],[15339,4831]),
[iquote('0:SpL:15339.0,4831.0')] ).
cnf(15970,plain,
equal(compose(domain__dfg(b),h),h),
inference(spr,[status(thm),theory(equality)],[15340,270]),
[iquote('0:SpR:15340.0,270.0')] ).
cnf(15993,plain,
( ~ defined(u,domain__dfg(b))
| defined(u,h) ),
inference(spl,[status(thm),theory(equality)],[15340,4831]),
[iquote('0:SpL:15340.0,4831.0')] ).
cnf(16383,plain,
equal(codomain(b),domain__dfg(a)),
inference(res,[status(thm),theory(equality)],[33,4433]),
[iquote('0:Res:33.0,4433.0')] ).
cnf(16594,plain,
( ~ defined(u,domain__dfg(a))
| defined(u,b) ),
inference(spl,[status(thm),theory(equality)],[16383,4831]),
[iquote('0:SpL:16383.0,4831.0')] ).
cnf(17244,plain,
( ~ defined(u,b)
| defined(compose(u,b),g) ),
inference(res,[status(thm),theory(equality)],[1346,15944]),
[iquote('0:Res:1346.1,15944.0')] ).
cnf(21029,plain,
( ~ defined(u,b)
| defined(compose(u,b),h) ),
inference(res,[status(thm),theory(equality)],[1346,15993]),
[iquote('0:Res:1346.1,15993.0')] ).
cnf(27498,plain,
( ~ identity_map(domain__dfg(a))
| ~ defined(domain__dfg(a),u)
| defined(codomain(u),b) ),
inference(res,[status(thm),theory(equality)],[4934,16594]),
[iquote('0:Res:4934.2,16594.0')] ).
cnf(27522,plain,
( ~ defined(domain__dfg(a),u)
| defined(codomain(u),b) ),
inference(ssi,[status(thm)],[27498,16]),
[iquote('0:SSi:27498.0,16.0')] ).
cnf(29914,plain,
( ~ identity_map(domain__dfg(domain__dfg(u)))
| equal(domain__dfg(domain__dfg(u)),domain__dfg(u)) ),
inference(res,[status(thm),theory(equality)],[218,6809]),
[iquote('0:Res:218.0,6809.1')] ).
cnf(30081,plain,
equal(domain__dfg(domain__dfg(u)),domain__dfg(u)),
inference(ssi,[status(thm)],[29914,16]),
[iquote('0:SSi:29914.0,16.0,16.0')] ).
cnf(30190,plain,
( ~ defined(domain__dfg(u),v)
| defined(u,compose(domain__dfg(u),v)) ),
inference(rew,[status(thm),theory(equality)],[30081,3835]),
[iquote('0:Rew:30081.0,3835.1')] ).
cnf(30312,plain,
( ~ defined(domain__dfg(u),v)
| product(u,v,compose(u,compose(domain__dfg(u),v))) ),
inference(mrr,[status(thm)],[12005,30190]),
[iquote('0:MRR:12005.0,30190.1')] ).
cnf(31124,plain,
( ~ defined(u,b)
| ~ defined(u,b)
| defined(u,compose(b,g)) ),
inference(res,[status(thm),theory(equality)],[17244,1401]),
[iquote('0:Res:17244.1,1401.1')] ).
cnf(31131,plain,
( ~ defined(u,b)
| defined(u,compose(b,g)) ),
inference(obv,[status(thm),theory(equality)],[31124]),
[iquote('0:Obv:31124.0')] ).
cnf(31377,plain,
( ~ defined(u,b)
| ~ defined(u,b)
| defined(u,compose(b,h)) ),
inference(res,[status(thm),theory(equality)],[21029,1401]),
[iquote('0:Res:21029.1,1401.1')] ).
cnf(31384,plain,
( ~ defined(u,b)
| defined(u,compose(b,h)) ),
inference(obv,[status(thm),theory(equality)],[31377]),
[iquote('0:Obv:31377.0')] ).
cnf(31648,plain,
( ~ identity_map(codomain(u))
| ~ defined(domain__dfg(a),u)
| equal(codomain(u),codomain(b)) ),
inference(res,[status(thm),theory(equality)],[27522,6737]),
[iquote('0:Res:27522.1,6737.1')] ).
cnf(31656,plain,
( ~ identity_map(codomain(u))
| ~ defined(domain__dfg(a),u)
| equal(codomain(u),domain__dfg(a)) ),
inference(rew,[status(thm),theory(equality)],[16383,31648]),
[iquote('0:Rew:16383.0,31648.2')] ).
cnf(31657,plain,
( ~ defined(domain__dfg(a),u)
| equal(codomain(u),domain__dfg(a)) ),
inference(ssi,[status(thm)],[31656,17]),
[iquote('0:SSi:31656.0,17.0')] ).
cnf(41867,plain,
( ~ defined(b,g)
| ~ defined(a,compose(b,g))
| equal(compose(a,compose(b,g)),d) ),
inference(res,[status(thm),theory(equality)],[7,7856]),
[iquote('0:Res:7.1,7856.1')] ).
cnf(41874,plain,
( ~ defined(a,compose(b,g))
| equal(compose(a,compose(b,g)),d) ),
inference(mrr,[status(thm)],[41867,81]),
[iquote('0:MRR:41867.0,81.0')] ).
cnf(41961,plain,
( ~ defined(b,h)
| ~ defined(a,compose(b,h))
| equal(compose(a,compose(b,h)),d) ),
inference(res,[status(thm),theory(equality)],[7,7877]),
[iquote('0:Res:7.1,7877.1')] ).
cnf(41968,plain,
( ~ defined(a,compose(b,h))
| equal(compose(a,compose(b,h)),d) ),
inference(mrr,[status(thm)],[41961,82]),
[iquote('0:MRR:41961.0,82.0')] ).
cnf(42633,plain,
( ~ defined(domain__dfg(a),b)
| equal(codomain(compose(b,g)),domain__dfg(a)) ),
inference(res,[status(thm),theory(equality)],[31131,31657]),
[iquote('0:Res:31131.1,31657.0')] ).
cnf(42634,plain,
( ~ defined(domain__dfg(a),b)
| equal(codomain(compose(b,h)),domain__dfg(a)) ),
inference(res,[status(thm),theory(equality)],[31384,31657]),
[iquote('0:Res:31384.1,31657.0')] ).
cnf(42709,plain,
equal(codomain(compose(b,g)),domain__dfg(a)),
inference(mrr,[status(thm)],[42633,8017]),
[iquote('0:MRR:42633.0,8017.0')] ).
cnf(42725,plain,
equal(codomain(compose(b,h)),domain__dfg(a)),
inference(mrr,[status(thm)],[42634,8017]),
[iquote('0:MRR:42634.0,8017.0')] ).
cnf(42742,plain,
defined(domain__dfg(a),compose(b,g)),
inference(spr,[status(thm),theory(equality)],[42709,19]),
[iquote('0:SpR:42709.0,19.0')] ).
cnf(42867,plain,
defined(a,compose(b,g)),
inference(res,[status(thm),theory(equality)],[42742,127]),
[iquote('0:Res:42742.0,127.0')] ).
cnf(42874,plain,
equal(compose(a,compose(b,g)),d),
inference(mrr,[status(thm)],[41874,42867]),
[iquote('0:MRR:41874.0,42867.0')] ).
cnf(42910,plain,
defined(domain__dfg(a),compose(b,h)),
inference(spr,[status(thm),theory(equality)],[42725,19]),
[iquote('0:SpR:42725.0,19.0')] ).
cnf(43035,plain,
defined(a,compose(b,h)),
inference(res,[status(thm),theory(equality)],[42910,127]),
[iquote('0:Res:42910.0,127.0')] ).
cnf(43042,plain,
equal(compose(a,compose(b,h)),d),
inference(mrr,[status(thm)],[41968,43035]),
[iquote('0:MRR:41968.0,43035.0')] ).
cnf(43104,plain,
( ~ defined(a,compose(b,g))
| ~ product(a,u,d)
| equal(u,compose(b,g)) ),
inference(spl,[status(thm),theory(equality)],[42874,88]),
[iquote('0:SpL:42874.0,88.1')] ).
cnf(43117,plain,
( ~ product(a,u,d)
| equal(u,compose(b,g)) ),
inference(mrr,[status(thm)],[43104,42867]),
[iquote('0:MRR:43104.0,42867.0')] ).
cnf(43258,plain,
( ~ defined(a,compose(b,h))
| product(a,compose(b,h),d) ),
inference(spr,[status(thm),theory(equality)],[43042,7]),
[iquote('0:SpR:43042.0,7.1')] ).
cnf(43287,plain,
product(a,compose(b,h),d),
inference(mrr,[status(thm)],[43258,43035]),
[iquote('0:MRR:43258.0,43035.0')] ).
cnf(51181,plain,
( ~ defined(domain__dfg(b),h)
| product(b,h,compose(b,h)) ),
inference(spr,[status(thm),theory(equality)],[15970,30312]),
[iquote('0:SpR:15970.0,30312.1')] ).
cnf(51301,plain,
product(b,h,compose(b,h)),
inference(mrr,[status(thm)],[51181,7896]),
[iquote('0:MRR:51181.0,7896.0')] ).
cnf(64477,plain,
equal(compose(b,g),compose(b,h)),
inference(res,[status(thm),theory(equality)],[43287,43117]),
[iquote('0:Res:43287.0,43117.0')] ).
cnf(64480,plain,
~ product(b,h,compose(b,h)),
inference(rew,[status(thm),theory(equality)],[64477,83]),
[iquote('0:Rew:64477.0,83.0')] ).
cnf(64913,plain,
$false,
inference(mrr,[status(thm)],[64480,51301]),
[iquote('0:MRR:64480.0,51301.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : CAT002-1 : TPTP v8.1.0. Released v1.0.0.
% 0.03/0.13 % Command : run_spass %d %s
% 0.13/0.34 % Computer : n026.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Sun May 29 16:02:39 EDT 2022
% 0.13/0.35 % CPUTime :
% 30.49/30.72
% 30.49/30.72 SPASS V 3.9
% 30.49/30.72 SPASS beiseite: Proof found.
% 30.49/30.72 % SZS status Theorem
% 30.49/30.72 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 30.49/30.72 SPASS derived 47571 clauses, backtracked 0 clauses, performed 0 splits and kept 13541 clauses.
% 30.49/30.72 SPASS allocated 112080 KBytes.
% 30.49/30.72 SPASS spent 0:0:30.31 on the problem.
% 30.49/30.72 0:00:00.04 for the input.
% 30.49/30.72 0:00:00.00 for the FLOTTER CNF translation.
% 30.49/30.72 0:00:00.47 for inferences.
% 30.49/30.72 0:00:00.00 for the backtracking.
% 30.49/30.72 0:0:29.50 for the reduction.
% 30.49/30.72
% 30.49/30.72
% 30.49/30.72 Here is a proof with depth 10, length 156 :
% 30.49/30.72 % SZS output start Refutation
% See solution above
% 32.03/32.20 Formulae used in the proof : cancellation_for_product1 cancellation_for_product2 ab_equals_c ch_equals_d cg_equals_d prove_h_equals_g closure_of_composition associative_property1 associative_property2 category_theory_axiom1 category_theory_axiom3 category_theory_axiom4 category_theory_axiom5 category_theory_axiom6 domain_is_an_identity_map codomain_is_an_identity_map mapping_from_x_to_its_domain mapping_from_codomain_of_x_to_x product_on_domain product_on_codomain identity1 identity2 composition_is_well_defined
% 32.03/32.20
%------------------------------------------------------------------------------