%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : CAT004-2 : 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 00:07:28 EDT 2022
% Result : Unsatisfiable 213.40s 213.68s
% Output : Refutation 228.29s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 13
% Syntax : Number of clauses : 80 ( 22 unt; 0 nHn; 80 RR)
% Number of literals : 216 ( 0 equ; 143 neg)
% Maximal clause size : 6 ( 2 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 8 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
( ~ equal(domain__dfg(u),codomain(a))
| ~ equal(domain__dfg(v),codomain(a))
| ~ equal(compose(a,u),w)
| ~ equal(compose(a,v),w)
| equal(v,u) ),
file('CAT004-2.p',unknown),
[] ).
cnf(2,axiom,
( ~ equal(domain__dfg(u),codomain(b))
| ~ equal(domain__dfg(v),codomain(b))
| ~ equal(compose(b,u),w)
| ~ equal(compose(b,v),w)
| equal(v,u) ),
file('CAT004-2.p',unknown),
[] ).
cnf(3,axiom,
equal(domain__dfg(b),codomain(a)),
file('CAT004-2.p',unknown),
[] ).
cnf(4,axiom,
equal(codomain(compose(a,b)),domain__dfg(h)),
file('CAT004-2.p',unknown),
[] ).
cnf(5,axiom,
equal(codomain(compose(a,b)),domain__dfg(g)),
file('CAT004-2.p',unknown),
[] ).
cnf(6,axiom,
equal(compose(compose(a,b),g),compose(compose(a,b),h)),
file('CAT004-2.p',unknown),
[] ).
cnf(7,axiom,
~ equal(g,h),
file('CAT004-2.p',unknown),
[] ).
cnf(8,axiom,
equal(codomain(domain__dfg(u)),domain__dfg(u)),
file('CAT004-2.p',unknown),
[] ).
cnf(9,axiom,
equal(domain__dfg(codomain(u)),codomain(u)),
file('CAT004-2.p',unknown),
[] ).
cnf(10,axiom,
equal(compose(domain__dfg(u),u),u),
file('CAT004-2.p',unknown),
[] ).
cnf(12,axiom,
( ~ equal(codomain(u),domain__dfg(v))
| equal(domain__dfg(compose(u,v)),domain__dfg(u)) ),
file('CAT004-2.p',unknown),
[] ).
cnf(13,axiom,
( ~ equal(codomain(u),domain__dfg(v))
| equal(codomain(compose(u,v)),codomain(v)) ),
file('CAT004-2.p',unknown),
[] ).
cnf(14,axiom,
( ~ equal(codomain(u),domain__dfg(v))
| ~ equal(codomain(w),domain__dfg(u))
| equal(compose(compose(w,u),v),compose(w,compose(u,v))) ),
file('CAT004-2.p',unknown),
[] ).
cnf(15,plain,
equal(domain__dfg(g),domain__dfg(h)),
inference(rew,[status(thm),theory(equality)],[5,4]),
[iquote('0:Rew:5.0,4.0')] ).
cnf(16,plain,
equal(codomain(compose(a,b)),domain__dfg(h)),
inference(rew,[status(thm),theory(equality)],[15,5]),
[iquote('0:Rew:15.0,5.0')] ).
cnf(19,plain,
( ~ equal(domain__dfg(h),codomain(b))
| ~ equal(compose(b,h),u)
| ~ equal(domain__dfg(g),codomain(b))
| ~ equal(compose(b,g),u) ),
inference(res,[status(thm),theory(equality)],[2,7]),
[iquote('0:Res:2.4,7.0')] ).
cnf(23,plain,
( ~ equal(domain__dfg(h),codomain(b))
| ~ equal(compose(b,h),u)
| ~ equal(domain__dfg(h),codomain(b))
| ~ equal(compose(b,g),u) ),
inference(rew,[status(thm),theory(equality)],[15,19]),
[iquote('0:Rew:15.0,19.2')] ).
cnf(24,plain,
( ~ equal(domain__dfg(h),codomain(b))
| ~ equal(compose(b,g),u)
| ~ equal(compose(b,h),u) ),
inference(obv,[status(thm),theory(equality)],[23]),
[iquote('0:Obv:23.0')] ).
cnf(32,plain,
equal(codomain(codomain(u)),codomain(u)),
inference(spr,[status(thm),theory(equality)],[9,8]),
[iquote('0:SpR:9.0,8.0')] ).
cnf(44,plain,
equal(compose(codomain(a),b),b),
inference(spr,[status(thm),theory(equality)],[3,10]),
[iquote('0:SpR:3.0,10.0')] ).
cnf(79,plain,
( ~ equal(domain__dfg(b),codomain(a))
| equal(domain__dfg(h),codomain(b)) ),
inference(spr,[status(thm),theory(equality)],[13,16]),
[iquote('0:SpR:13.1,16.0')] ).
cnf(89,plain,
( ~ equal(codomain(a),codomain(a))
| equal(domain__dfg(h),codomain(b)) ),
inference(rew,[status(thm),theory(equality)],[3,79]),
[iquote('0:Rew:3.0,79.0')] ).
cnf(90,plain,
equal(domain__dfg(h),codomain(b)),
inference(obv,[status(thm),theory(equality)],[89]),
[iquote('0:Obv:89.0')] ).
cnf(91,plain,
equal(domain__dfg(g),codomain(b)),
inference(rew,[status(thm),theory(equality)],[90,15]),
[iquote('0:Rew:90.0,15.0')] ).
cnf(95,plain,
( ~ equal(codomain(b),codomain(b))
| ~ equal(compose(b,g),u)
| ~ equal(compose(b,h),u) ),
inference(rew,[status(thm),theory(equality)],[90,24]),
[iquote('0:Rew:90.0,24.0')] ).
cnf(100,plain,
( ~ equal(compose(b,g),u)
| ~ equal(compose(b,h),u) ),
inference(obv,[status(thm),theory(equality)],[95]),
[iquote('0:Obv:95.0')] ).
cnf(103,plain,
equal(compose(codomain(b),h),h),
inference(spr,[status(thm),theory(equality)],[90,10]),
[iquote('0:SpR:90.0,10.0')] ).
cnf(177,plain,
( ~ equal(domain__dfg(g),codomain(b))
| ~ equal(domain__dfg(b),codomain(a))
| equal(compose(compose(a,b),h),compose(a,compose(b,g))) ),
inference(spr,[status(thm),theory(equality)],[14,6]),
[iquote('0:SpR:14.2,6.0')] ).
cnf(179,plain,
( ~ equal(codomain(u),domain__dfg(v))
| ~ equal(codomain(w),domain__dfg(u))
| ~ equal(codomain(compose(w,u)),domain__dfg(v))
| equal(codomain(compose(w,compose(u,v))),codomain(v)) ),
inference(spr,[status(thm),theory(equality)],[14,13]),
[iquote('0:SpR:14.2,13.1')] ).
cnf(180,plain,
( ~ equal(codomain(u),domain__dfg(v))
| ~ equal(codomain(w),domain__dfg(u))
| ~ equal(codomain(compose(w,u)),domain__dfg(v))
| equal(domain__dfg(compose(w,compose(u,v))),domain__dfg(compose(w,u))) ),
inference(spr,[status(thm),theory(equality)],[14,12]),
[iquote('0:SpR:14.2,12.1')] ).
cnf(182,plain,
( ~ equal(codomain(u),domain__dfg(v))
| ~ equal(codomain(w),domain__dfg(u))
| ~ equal(codomain(v),domain__dfg(x))
| ~ equal(codomain(compose(w,u)),domain__dfg(v))
| equal(compose(compose(w,compose(u,v)),x),compose(compose(w,u),compose(v,x))) ),
inference(spr,[status(thm),theory(equality)],[14]),
[iquote('0:SpR:14.2,14.2')] ).
cnf(185,plain,
( ~ equal(domain__dfg(u),codomain(b))
| ~ equal(codomain(codomain(a)),domain__dfg(b))
| equal(compose(codomain(a),compose(b,u)),compose(b,u)) ),
inference(spr,[status(thm),theory(equality)],[44,14]),
[iquote('0:SpR:44.0,14.2')] ).
cnf(199,plain,
( ~ equal(domain__dfg(u),codomain(b))
| ~ equal(codomain(a),codomain(a))
| equal(compose(codomain(a),compose(b,u)),compose(b,u)) ),
inference(rew,[status(thm),theory(equality)],[32,185,3]),
[iquote('0:Rew:32.0,185.1,3.0,185.1')] ).
cnf(200,plain,
( ~ equal(domain__dfg(u),codomain(b))
| equal(compose(codomain(a),compose(b,u)),compose(b,u)) ),
inference(obv,[status(thm),theory(equality)],[199]),
[iquote('0:Obv:199.1')] ).
cnf(202,plain,
( ~ equal(codomain(b),codomain(b))
| ~ equal(codomain(a),codomain(a))
| equal(compose(compose(a,b),h),compose(a,compose(b,g))) ),
inference(rew,[status(thm),theory(equality)],[3,177,91]),
[iquote('0:Rew:3.0,177.1,91.0,177.0')] ).
cnf(203,plain,
equal(compose(compose(a,b),h),compose(a,compose(b,g))),
inference(obv,[status(thm),theory(equality)],[202]),
[iquote('0:Obv:202.1')] ).
cnf(223,plain,
( ~ equal(codomain(u),domain__dfg(v))
| ~ equal(codomain(w),domain__dfg(u))
| ~ equal(codomain(u),domain__dfg(v))
| equal(codomain(compose(w,compose(u,v))),codomain(v)) ),
inference(rew,[status(thm),theory(equality)],[13,179]),
[iquote('0:Rew:13.1,179.2')] ).
cnf(224,plain,
( ~ equal(codomain(u),domain__dfg(v))
| ~ equal(codomain(v),domain__dfg(w))
| equal(codomain(compose(u,compose(v,w))),codomain(w)) ),
inference(obv,[status(thm),theory(equality)],[223]),
[iquote('0:Obv:223.0')] ).
cnf(227,plain,
( ~ equal(codomain(u),domain__dfg(v))
| ~ equal(codomain(w),domain__dfg(u))
| ~ equal(codomain(u),domain__dfg(v))
| equal(domain__dfg(compose(w,compose(u,v))),domain__dfg(w)) ),
inference(rew,[status(thm),theory(equality)],[12,180,13]),
[iquote('0:Rew:12.1,180.3,13.1,180.2')] ).
cnf(228,plain,
( ~ equal(codomain(u),domain__dfg(v))
| ~ equal(codomain(v),domain__dfg(w))
| equal(domain__dfg(compose(u,compose(v,w))),domain__dfg(u)) ),
inference(obv,[status(thm),theory(equality)],[227]),
[iquote('0:Obv:227.0')] ).
cnf(229,plain,
( ~ equal(codomain(u),domain__dfg(v))
| ~ equal(codomain(w),domain__dfg(u))
| ~ equal(codomain(v),domain__dfg(x))
| ~ equal(codomain(u),domain__dfg(v))
| equal(compose(compose(w,compose(u,v)),x),compose(compose(w,u),compose(v,x))) ),
inference(rew,[status(thm),theory(equality)],[13,182]),
[iquote('0:Rew:13.1,182.3')] ).
cnf(230,plain,
( ~ equal(codomain(u),domain__dfg(v))
| ~ equal(codomain(w),domain__dfg(x))
| ~ equal(codomain(v),domain__dfg(w))
| equal(compose(compose(u,compose(v,w)),x),compose(compose(u,v),compose(w,x))) ),
inference(obv,[status(thm),theory(equality)],[229]),
[iquote('0:Obv:229.0')] ).
cnf(246,plain,
( ~ equal(domain__dfg(h),codomain(b))
| ~ equal(domain__dfg(b),codomain(a))
| equal(compose(a,compose(b,g)),compose(a,compose(b,h))) ),
inference(spr,[status(thm),theory(equality)],[203,14]),
[iquote('0:SpR:203.0,14.2')] ).
cnf(248,plain,
( ~ equal(codomain(b),codomain(b))
| ~ equal(codomain(a),codomain(a))
| equal(compose(a,compose(b,g)),compose(a,compose(b,h))) ),
inference(rew,[status(thm),theory(equality)],[3,246,90]),
[iquote('0:Rew:3.0,246.1,90.0,246.0')] ).
cnf(249,plain,
equal(compose(a,compose(b,g)),compose(a,compose(b,h))),
inference(obv,[status(thm),theory(equality)],[248]),
[iquote('0:Obv:248.1')] ).
cnf(288,plain,
~ equal(compose(b,g),compose(b,h)),
inference(eqr,[status(thm),theory(equality)],[100]),
[iquote('0:EqR:100.0')] ).
cnf(334,plain,
( ~ equal(codomain(u),domain__dfg(v))
| ~ equal(domain__dfg(u),codomain(a))
| ~ equal(domain__dfg(w),codomain(a))
| ~ equal(compose(a,compose(u,v)),x)
| ~ equal(compose(a,w),x)
| equal(w,compose(u,v)) ),
inference(spl,[status(thm),theory(equality)],[12,1]),
[iquote('0:SpL:12.1,1.0')] ).
cnf(1128,plain,
( ~ equal(codomain(u),domain__dfg(codomain(a)))
| ~ equal(codomain(codomain(a)),domain__dfg(b))
| equal(codomain(compose(u,b)),codomain(b)) ),
inference(spr,[status(thm),theory(equality)],[44,224]),
[iquote('0:SpR:44.0,224.2')] ).
cnf(1184,plain,
( ~ equal(codomain(u),codomain(a))
| ~ equal(codomain(a),codomain(a))
| equal(codomain(compose(u,b)),codomain(b)) ),
inference(rew,[status(thm),theory(equality)],[32,1128,3,9]),
[iquote('0:Rew:32.0,1128.1,3.0,1128.1,9.0,1128.0')] ).
cnf(1185,plain,
( ~ equal(codomain(u),codomain(a))
| equal(codomain(compose(u,b)),codomain(b)) ),
inference(obv,[status(thm),theory(equality)],[1184]),
[iquote('0:Obv:1184.1')] ).
cnf(1366,plain,
( ~ equal(codomain(u),domain__dfg(codomain(a)))
| ~ equal(codomain(codomain(a)),domain__dfg(b))
| equal(domain__dfg(compose(u,b)),domain__dfg(u)) ),
inference(spr,[status(thm),theory(equality)],[44,228]),
[iquote('0:SpR:44.0,228.2')] ).
cnf(1383,plain,
( ~ equal(codomain(u),domain__dfg(codomain(b)))
| ~ equal(codomain(codomain(b)),domain__dfg(h))
| equal(domain__dfg(compose(u,h)),domain__dfg(u)) ),
inference(spr,[status(thm),theory(equality)],[103,228]),
[iquote('0:SpR:103.0,228.2')] ).
cnf(1418,plain,
( ~ equal(codomain(u),codomain(b))
| ~ equal(codomain(b),codomain(b))
| equal(domain__dfg(compose(u,h)),domain__dfg(u)) ),
inference(rew,[status(thm),theory(equality)],[32,1383,90,9]),
[iquote('0:Rew:32.0,1383.1,90.0,1383.1,9.0,1383.0')] ).
cnf(1419,plain,
( ~ equal(codomain(u),codomain(b))
| equal(domain__dfg(compose(u,h)),domain__dfg(u)) ),
inference(obv,[status(thm),theory(equality)],[1418]),
[iquote('0:Obv:1418.1')] ).
cnf(1424,plain,
( ~ equal(codomain(u),codomain(a))
| ~ equal(codomain(a),codomain(a))
| equal(domain__dfg(compose(u,b)),domain__dfg(u)) ),
inference(rew,[status(thm),theory(equality)],[32,1366,3,9]),
[iquote('0:Rew:32.0,1366.1,3.0,1366.1,9.0,1366.0')] ).
cnf(1425,plain,
( ~ equal(codomain(u),codomain(a))
| equal(domain__dfg(compose(u,b)),domain__dfg(u)) ),
inference(obv,[status(thm),theory(equality)],[1424]),
[iquote('0:Obv:1424.1')] ).
cnf(1522,plain,
( ~ equal(codomain(u),codomain(b))
| equal(compose(domain__dfg(u),compose(u,h)),compose(u,h)) ),
inference(spr,[status(thm),theory(equality)],[1419,10]),
[iquote('0:SpR:1419.1,10.0')] ).
cnf(2151,plain,
( ~ equal(codomain(b),codomain(b))
| equal(compose(codomain(a),compose(b,h)),compose(b,h)) ),
inference(spr,[status(thm),theory(equality)],[3,1522]),
[iquote('0:SpR:3.0,1522.1')] ).
cnf(2171,plain,
equal(compose(codomain(a),compose(b,h)),compose(b,h)),
inference(obv,[status(thm),theory(equality)],[2151]),
[iquote('0:Obv:2151.0')] ).
cnf(2233,plain,
( ~ equal(codomain(u),domain__dfg(v))
| ~ equal(codomain(w),domain__dfg(x))
| ~ equal(codomain(v),domain__dfg(w))
| ~ equal(codomain(compose(v,w)),domain__dfg(x))
| ~ equal(codomain(u),domain__dfg(compose(v,w)))
| equal(compose(compose(u,v),compose(w,x)),compose(u,compose(compose(v,w),x))) ),
inference(spr,[status(thm),theory(equality)],[230,14]),
[iquote('0:SpR:230.3,14.2')] ).
cnf(2510,plain,
( ~ equal(codomain(u),domain__dfg(v))
| ~ equal(codomain(w),domain__dfg(x))
| ~ equal(codomain(v),domain__dfg(w))
| ~ equal(codomain(w),domain__dfg(x))
| ~ equal(codomain(u),domain__dfg(v))
| equal(compose(compose(u,v),compose(w,x)),compose(u,compose(v,compose(w,x)))) ),
inference(rew,[status(thm),theory(equality)],[14,2233,12,13]),
[iquote('0:Rew:14.2,2233.5,12.1,2233.4,13.1,2233.3')] ).
cnf(2511,plain,
( ~ equal(codomain(u),domain__dfg(v))
| ~ equal(codomain(v),domain__dfg(w))
| ~ equal(codomain(x),domain__dfg(u))
| equal(compose(compose(x,u),compose(v,w)),compose(x,compose(u,compose(v,w)))) ),
inference(obv,[status(thm),theory(equality)],[2510]),
[iquote('0:Obv:2510.1')] ).
cnf(2512,plain,
( ~ equal(codomain(u),domain__dfg(v))
| ~ equal(codomain(w),domain__dfg(x))
| ~ equal(codomain(v),domain__dfg(w))
| equal(compose(compose(u,compose(v,w)),x),compose(u,compose(v,compose(w,x)))) ),
inference(rew,[status(thm),theory(equality)],[2511,230]),
[iquote('0:Rew:2511.3,230.3')] ).
cnf(2718,plain,
( ~ equal(codomain(u),domain__dfg(codomain(a)))
| ~ equal(domain__dfg(v),codomain(b))
| ~ equal(codomain(codomain(a)),domain__dfg(b))
| equal(compose(u,compose(codomain(a),compose(b,v))),compose(compose(u,b),v)) ),
inference(spr,[status(thm),theory(equality)],[44,2512]),
[iquote('0:SpR:44.0,2512.3')] ).
cnf(2813,plain,
( ~ equal(codomain(u),codomain(a))
| ~ equal(domain__dfg(v),codomain(b))
| ~ equal(codomain(a),codomain(a))
| equal(compose(compose(u,b),v),compose(u,compose(b,v))) ),
inference(rew,[status(thm),theory(equality)],[200,2718,32,3,9]),
[iquote('0:Rew:200.1,2718.3,32.0,2718.2,3.0,2718.2,9.0,2718.0')] ).
cnf(2814,plain,
( ~ equal(codomain(u),codomain(a))
| ~ equal(domain__dfg(v),codomain(b))
| equal(compose(compose(u,b),v),compose(u,compose(b,v))) ),
inference(obv,[status(thm),theory(equality)],[2813]),
[iquote('0:Obv:2813.2')] ).
cnf(3761,plain,
( ~ equal(codomain(u),domain__dfg(v))
| ~ equal(domain__dfg(u),codomain(a))
| ~ equal(domain__dfg(w),codomain(a))
| ~ equal(compose(a,w),compose(a,compose(u,v)))
| equal(w,compose(u,v)) ),
inference(eqr,[status(thm),theory(equality)],[334]),
[iquote('0:EqR:334.3')] ).
cnf(7754,plain,
( ~ equal(codomain(u),codomain(a))
| ~ equal(domain__dfg(h),codomain(b))
| ~ equal(codomain(compose(u,b)),codomain(b))
| equal(domain__dfg(compose(u,compose(b,h))),domain__dfg(compose(u,b))) ),
inference(spr,[status(thm),theory(equality)],[2814,1419]),
[iquote('0:SpR:2814.2,1419.1')] ).
cnf(7790,plain,
( ~ equal(codomain(u),codomain(a))
| ~ equal(codomain(b),codomain(b))
| ~ equal(codomain(b),codomain(b))
| equal(domain__dfg(compose(u,compose(b,h))),domain__dfg(u)) ),
inference(rew,[status(thm),theory(equality)],[1425,7754,1185,90]),
[iquote('0:Rew:1425.1,7754.3,1185.1,7754.2,90.0,7754.1')] ).
cnf(7791,plain,
( ~ equal(codomain(u),codomain(a))
| equal(domain__dfg(compose(u,compose(b,h))),domain__dfg(u)) ),
inference(obv,[status(thm),theory(equality)],[7790]),
[iquote('0:Obv:7790.2')] ).
cnf(7912,plain,
( ~ equal(codomain(codomain(a)),codomain(a))
| equal(domain__dfg(compose(b,h)),domain__dfg(codomain(a))) ),
inference(spr,[status(thm),theory(equality)],[2171,7791]),
[iquote('0:SpR:2171.0,7791.1')] ).
cnf(7924,plain,
( ~ equal(codomain(a),codomain(a))
| equal(domain__dfg(compose(b,h)),codomain(a)) ),
inference(rew,[status(thm),theory(equality)],[9,7912,32]),
[iquote('0:Rew:9.0,7912.1,32.0,7912.0')] ).
cnf(7925,plain,
equal(domain__dfg(compose(b,h)),codomain(a)),
inference(obv,[status(thm),theory(equality)],[7924]),
[iquote('0:Obv:7924.0')] ).
cnf(28465,plain,
( ~ equal(domain__dfg(g),codomain(b))
| ~ equal(domain__dfg(b),codomain(a))
| ~ equal(domain__dfg(u),codomain(a))
| ~ equal(compose(a,u),compose(a,compose(b,h)))
| equal(u,compose(b,g)) ),
inference(spl,[status(thm),theory(equality)],[249,3761]),
[iquote('0:SpL:249.0,3761.3')] ).
cnf(28472,plain,
( ~ equal(codomain(b),codomain(b))
| ~ equal(codomain(a),codomain(a))
| ~ equal(domain__dfg(u),codomain(a))
| ~ equal(compose(a,u),compose(a,compose(b,h)))
| equal(u,compose(b,g)) ),
inference(rew,[status(thm),theory(equality)],[3,28465,91]),
[iquote('0:Rew:3.0,28465.1,91.0,28465.0')] ).
cnf(28473,plain,
( ~ equal(domain__dfg(u),codomain(a))
| ~ equal(compose(a,u),compose(a,compose(b,h)))
| equal(u,compose(b,g)) ),
inference(obv,[status(thm),theory(equality)],[28472]),
[iquote('0:Obv:28472.1')] ).
cnf(76400,plain,
( ~ equal(domain__dfg(compose(b,h)),codomain(a))
| equal(compose(b,g),compose(b,h)) ),
inference(eqr,[status(thm),theory(equality)],[28473]),
[iquote('0:EqR:28473.1')] ).
cnf(76411,plain,
( ~ equal(codomain(a),codomain(a))
| equal(compose(b,g),compose(b,h)) ),
inference(rew,[status(thm),theory(equality)],[7925,76400]),
[iquote('0:Rew:7925.0,76400.0')] ).
cnf(76412,plain,
equal(compose(b,g),compose(b,h)),
inference(obv,[status(thm),theory(equality)],[76411]),
[iquote('0:Obv:76411.0')] ).
cnf(76413,plain,
$false,
inference(mrr,[status(thm)],[76412,288]),
[iquote('0:MRR:76412.0,288.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : CAT004-2 : TPTP v8.1.0. Released v1.0.0.
% 0.10/0.12 % 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
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Sun May 29 15:40:54 EDT 2022
% 0.12/0.33 % CPUTime :
% 213.40/213.68
% 213.40/213.68 SPASS V 3.9
% 213.40/213.68 SPASS beiseite: Proof found.
% 213.40/213.68 % SZS status Theorem
% 213.40/213.68 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 213.40/213.68 SPASS derived 33519 clauses, backtracked 0 clauses, performed 0 splits and kept 10312 clauses.
% 213.40/213.68 SPASS allocated 152329 KBytes.
% 213.40/213.68 SPASS spent 0:3:33.26 on the problem.
% 213.40/213.68 0:00:00.03 for the input.
% 213.40/213.68 0:00:00.00 for the FLOTTER CNF translation.
% 213.40/213.68 0:00:00.95 for inferences.
% 213.40/213.68 0:00:00.00 for the backtracking.
% 213.40/213.68 0:3:32.17 for the reduction.
% 213.40/213.68
% 213.40/213.68
% 213.40/213.68 Here is a proof with depth 6, length 80 :
% 213.40/213.68 % SZS output start Refutation
% See solution above
% 228.29/228.56 Formulae used in the proof : epimorphism1 epimorphism2 codomain_of_a_equals_domain_of_b codomain_of_ab_equals_domain_of_h codomain_of_ab_equals_domain_of_g ab_h_equals_ab_g prove_h_equals_g codomain_of_domain_is_domain domain_of_codomain_is_codomain domain_composition codomain_domain1 codomain_domain2 star_property
% 228.29/228.56
%------------------------------------------------------------------------------