TSTP Solution File: SWW470+6 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SWW470+6 : TPTP v8.1.0. Released v5.3.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n032.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 : Thu Jul 21 01:28:33 EDT 2022
% Result : Theorem 24.65s 24.87s
% Output : Refutation 24.86s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 21
% Syntax : Number of clauses : 58 ( 33 unt; 16 nHn; 58 RR)
% Number of literals : 98 ( 0 equ; 31 neg)
% Maximal clause size : 5 ( 1 avg)
% Maximal term depth : 15 ( 2 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 45 ( 45 usr; 24 con; 0-5 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(23,axiom,
~ hBOOL(fFalse),
file('SWW470+6.p',unknown),
[] ).
cnf(25,axiom,
equal(ti(bool,fFalse),fFalse),
file('SWW470+6.p',unknown),
[] ).
cnf(32,axiom,
( ~ hBOOL(ti(bool,u))
| hBOOL(u) ),
file('SWW470+6.p',unknown),
[] ).
cnf(33,axiom,
( ~ hBOOL(u)
| hBOOL(ti(bool,u)) ),
file('SWW470+6.p',unknown),
[] ).
cnf(47,axiom,
( hBOOL(u)
| hBOOL(hAPP(bool,bool,fNot,u)) ),
file('SWW470+6.p',unknown),
[] ).
cnf(58,axiom,
( ~ hBOOL(u)
| ~ hBOOL(hAPP(bool,bool,fNot,u)) ),
file('SWW470+6.p',unknown),
[] ).
cnf(60,axiom,
( equal(ti(bool,u),fFalse)
| equal(ti(bool,u),fTrue) ),
file('SWW470+6.p',unknown),
[] ).
cnf(85,axiom,
equal(hAPP(u,v,w,ti(u,x)),hAPP(u,v,w,x)),
file('SWW470+6.p',unknown),
[] ).
cnf(86,axiom,
equal(ti(u,hAPP(v,u,w,x)),hAPP(v,u,w,x)),
file('SWW470+6.p',unknown),
[] ).
cnf(104,axiom,
equal(hAPP(u,v,ti(fun(u,v),w),x),hAPP(u,v,w,x)),
file('SWW470+6.p',unknown),
[] ).
cnf(110,axiom,
equal(hAPP(fun(u,bool),fun(u,bool),collect(u),v),ti(fun(u,bool),v)),
file('SWW470+6.p',unknown),
[] ).
cnf(123,axiom,
equal(hAPP(u,v,hAPP(v,fun(u,v),combk(v,u),w),x),ti(v,w)),
file('SWW470+6.p',unknown),
[] ).
cnf(169,axiom,
equal(hAPP(fun(u,bool),fun(u,bool),collect(u),hAPP(bool,fun(u,bool),combk(bool,u),fFalse)),bot_bot(fun(u,bool))),
file('SWW470+6.p',unknown),
[] ).
cnf(197,axiom,
hBOOL(hAPP(fun(hoare_1656922687triple(u),bool),bool,hAPP(fun(hoare_1656922687triple(u),bool),fun(fun(hoare_1656922687triple(u),bool),bool),hoare_279057269derivs(u),v),bot_bot(fun(hoare_1656922687triple(u),bool)))),
file('SWW470+6.p',unknown),
[] ).
cnf(352,axiom,
equal(hAPP(fun(u,bool),fun(u,bool),hAPP(u,fun(fun(u,bool),fun(u,bool)),insert(u),v),bot_bot(fun(u,bool))),hAPP(fun(u,bool),fun(u,bool),collect(u),hAPP(u,fun(u,bool),fequal(u),v))),
file('SWW470+6.p',unknown),
[] ).
cnf(541,axiom,
( ~ hBOOL(hAPP(fun(hoare_1656922687triple(u),bool),bool,hAPP(fun(hoare_1656922687triple(u),bool),fun(fun(hoare_1656922687triple(u),bool),bool),hoare_279057269derivs(u),v),w))
| ~ hBOOL(hAPP(fun(hoare_1656922687triple(u),bool),bool,hAPP(fun(hoare_1656922687triple(u),bool),fun(fun(hoare_1656922687triple(u),bool),bool),hoare_279057269derivs(u),x),v))
| hBOOL(hAPP(fun(hoare_1656922687triple(u),bool),bool,hAPP(fun(hoare_1656922687triple(u),bool),fun(fun(hoare_1656922687triple(u),bool),bool),hoare_279057269derivs(u),x),w)) ),
file('SWW470+6.p',unknown),
[] ).
cnf(550,axiom,
( ~ hBOOL(hAPP(fun(u,bool),bool,v,hAPP(fun(u,bool),fun(u,bool),hAPP(u,fun(fun(u,bool),fun(u,bool)),insert(u),skf173(v,u)),bot_bot(fun(u,bool)))))
| ~ hBOOL(hAPP(fun(u,bool),bool,finite_finite_1(u),w))
| hBOOL(hAPP(fun(u,bool),bool,v,skf174(v,u)))
| hBOOL(hAPP(fun(u,bool),bool,v,w))
| equal(ti(fun(u,bool),w),bot_bot(fun(u,bool))) ),
file('SWW470+6.p',unknown),
[] ).
cnf(712,axiom,
( hBOOL(hAPP(state,bool,hAPP(u,fun(state,bool),v,skf133(v,u,w,x,y)),skf132(v,u,w,x,y)))
| hBOOL(hAPP(fun(hoare_1656922687triple(u),bool),bool,hAPP(fun(hoare_1656922687triple(u),bool),fun(fun(hoare_1656922687triple(u),bool),bool),hoare_279057269derivs(u),z),hAPP(fun(hoare_1656922687triple(u),bool),fun(hoare_1656922687triple(u),bool),hAPP(hoare_1656922687triple(u),fun(fun(hoare_1656922687triple(u),bool),fun(hoare_1656922687triple(u),bool)),insert(hoare_1656922687triple(u)),hAPP(fun(u,fun(state,bool)),hoare_1656922687triple(u),hAPP(com,fun(fun(u,fun(state,bool)),hoare_1656922687triple(u)),hAPP(fun(u,fun(state,bool)),fun(com,fun(fun(u,fun(state,bool)),hoare_1656922687triple(u))),hoare_246368825triple(u),v),x1),x2)),bot_bot(fun(hoare_1656922687triple(u),bool))))) ),
file('SWW470+6.p',unknown),
[] ).
cnf(713,axiom,
( hBOOL(hAPP(state,bool,hAPP(u,fun(state,bool),v,skf109(v,u,w,x,y)),skf108(v,u,w,x,y)))
| hBOOL(hAPP(fun(hoare_1656922687triple(u),bool),bool,hAPP(fun(hoare_1656922687triple(u),bool),fun(fun(hoare_1656922687triple(u),bool),bool),hoare_279057269derivs(u),z),hAPP(fun(hoare_1656922687triple(u),bool),fun(hoare_1656922687triple(u),bool),hAPP(hoare_1656922687triple(u),fun(fun(hoare_1656922687triple(u),bool),fun(hoare_1656922687triple(u),bool)),insert(hoare_1656922687triple(u)),hAPP(fun(u,fun(state,bool)),hoare_1656922687triple(u),hAPP(com,fun(fun(u,fun(state,bool)),hoare_1656922687triple(u)),hAPP(fun(u,fun(state,bool)),fun(com,fun(fun(u,fun(state,bool)),hoare_1656922687triple(u))),hoare_246368825triple(u),v),x1),x2)),bot_bot(fun(hoare_1656922687triple(u),bool))))) ),
file('SWW470+6.p',unknown),
[] ).
cnf(819,axiom,
hBOOL(hAPP(fun(hoare_1656922687triple(u),bool),bool,hAPP(fun(hoare_1656922687triple(u),bool),fun(fun(hoare_1656922687triple(u),bool),bool),hoare_279057269derivs(u),v),hAPP(fun(hoare_1656922687triple(u),bool),fun(hoare_1656922687triple(u),bool),hAPP(hoare_1656922687triple(u),fun(fun(hoare_1656922687triple(u),bool),fun(hoare_1656922687triple(u),bool)),insert(hoare_1656922687triple(u)),hAPP(fun(u,fun(state,bool)),hoare_1656922687triple(u),hAPP(com,fun(fun(u,fun(state,bool)),hoare_1656922687triple(u)),hAPP(fun(u,fun(state,bool)),fun(com,fun(fun(u,fun(state,bool)),hoare_1656922687triple(u))),hoare_246368825triple(u),hAPP(fun(state,state),fun(u,fun(state,bool)),hAPP(fun(u,fun(fun(state,state),fun(state,bool))),fun(fun(state,state),fun(u,fun(state,bool))),combc(u,fun(state,state),fun(state,bool)),hAPP(fun(u,fun(state,bool)),fun(u,fun(fun(state,state),fun(state,bool))),hAPP(fun(fun(state,bool),fun(fun(state,state),fun(state,bool))),fun(fun(u,fun(state,bool)),fun(u,fun(fun(state,state),fun(state,bool)))),combb(fun(state,bool),fun(fun(state,state),fun(state,bool)),u),combb(state,bool,state)),w)),hAPP(fun(state,nat),fun(state,state),hAPP(fun(state,fun(nat,state)),fun(fun(state,nat),fun(state,state)),combs(state,nat,state),hAPP(vname,fun(state,fun(nat,state)),hAPP(fun(state,fun(vname,fun(nat,state))),fun(vname,fun(state,fun(nat,state))),combc(state,vname,fun(nat,state)),update),x)),y))),hAPP(fun(state,nat),com,hAPP(vname,fun(fun(state,nat),com),ass,x),y)),w)),bot_bot(fun(hoare_1656922687triple(u),bool))))),
file('SWW470+6.p',unknown),
[] ).
cnf(821,axiom,
~ hBOOL(hAPP(fun(hoare_1656922687triple(x_a),bool),bool,hAPP(fun(hoare_1656922687triple(x_a),bool),fun(fun(hoare_1656922687triple(x_a),bool),bool),hoare_279057269derivs(x_a),g),hAPP(fun(hoare_1656922687triple(x_a),bool),fun(hoare_1656922687triple(x_a),bool),hAPP(hoare_1656922687triple(x_a),fun(fun(hoare_1656922687triple(x_a),bool),fun(hoare_1656922687triple(x_a),bool)),insert(hoare_1656922687triple(x_a)),hAPP(fun(x_a,fun(state,bool)),hoare_1656922687triple(x_a),hAPP(com,fun(fun(x_a,fun(state,bool)),hoare_1656922687triple(x_a)),hAPP(fun(x_a,fun(state,bool)),fun(com,fun(fun(x_a,fun(state,bool)),hoare_1656922687triple(x_a))),hoare_246368825triple(x_a),hAPP(fun(state,bool),fun(x_a,fun(state,bool)),combk(fun(state,bool),x_a),hAPP(bool,fun(state,bool),combk(bool,state),fFalse))),c),hAPP(fun(state,bool),fun(x_a,fun(state,bool)),hAPP(fun(x_a,fun(fun(state,bool),fun(state,bool))),fun(fun(state,bool),fun(x_a,fun(state,bool))),combc(x_a,fun(state,bool),fun(state,bool)),hAPP(fun(x_a,fun(state,fun(bool,bool))),fun(x_a,fun(fun(state,bool),fun(state,bool))),hAPP(fun(fun(state,fun(bool,bool)),fun(fun(state,bool),fun(state,bool))),fun(fun(x_a,fun(state,fun(bool,bool))),fun(x_a,fun(fun(state,bool),fun(state,bool)))),combb(fun(state,fun(bool,bool)),fun(fun(state,bool),fun(state,bool)),x_a),combs(state,bool,bool)),hAPP(fun(x_a,fun(state,bool)),fun(x_a,fun(state,fun(bool,bool))),hAPP(fun(fun(state,bool),fun(state,fun(bool,bool))),fun(fun(x_a,fun(state,bool)),fun(x_a,fun(state,fun(bool,bool)))),combb(fun(state,bool),fun(state,fun(bool,bool)),x_a),hAPP(fun(bool,fun(bool,bool)),fun(fun(state,bool),fun(state,fun(bool,bool))),combb(bool,fun(bool,bool),state),fconj)),p))),hAPP(fun(state,bool),fun(state,bool),hAPP(fun(bool,bool),fun(fun(state,bool),fun(state,bool)),combb(bool,bool,state),fNot),b)))),bot_bot(fun(hoare_1656922687triple(x_a),bool))))),
file('SWW470+6.p',unknown),
[] ).
cnf(824,plain,
equal(hAPP(bool,fun(u,bool),combk(bool,u),fFalse),bot_bot(fun(u,bool))),
inference(rew,[status(thm),theory(equality)],[86,169,110]),
[iquote('0:Rew:86.0,169.0,110.0,169.0')] ).
cnf(830,plain,
equal(hAPP(fun(u,bool),fun(u,bool),hAPP(u,fun(fun(u,bool),fun(u,bool)),insert(u),v),bot_bot(fun(u,bool))),hAPP(u,fun(u,bool),fequal(u),v)),
inference(rew,[status(thm),theory(equality)],[86,352,110]),
[iquote('0:Rew:86.0,352.0,110.0,352.0')] ).
cnf(847,plain,
( ~ hBOOL(hAPP(fun(u,bool),bool,v,hAPP(u,fun(u,bool),fequal(u),skf173(v,u))))
| ~ hBOOL(hAPP(fun(u,bool),bool,finite_finite_1(u),w))
| hBOOL(hAPP(fun(u,bool),bool,v,w))
| hBOOL(hAPP(fun(u,bool),bool,v,skf174(v,u)))
| equal(ti(fun(u,bool),w),bot_bot(fun(u,bool))) ),
inference(rew,[status(thm),theory(equality)],[830,550]),
[iquote('0:Rew:830.0,550.0')] ).
cnf(889,plain,
( hBOOL(hAPP(state,bool,hAPP(u,fun(state,bool),v,skf133(v,u,w,x,y)),skf132(v,u,w,x,y)))
| hBOOL(hAPP(fun(hoare_1656922687triple(u),bool),bool,hAPP(fun(hoare_1656922687triple(u),bool),fun(fun(hoare_1656922687triple(u),bool),bool),hoare_279057269derivs(u),z),hAPP(hoare_1656922687triple(u),fun(hoare_1656922687triple(u),bool),fequal(hoare_1656922687triple(u)),hAPP(fun(u,fun(state,bool)),hoare_1656922687triple(u),hAPP(com,fun(fun(u,fun(state,bool)),hoare_1656922687triple(u)),hAPP(fun(u,fun(state,bool)),fun(com,fun(fun(u,fun(state,bool)),hoare_1656922687triple(u))),hoare_246368825triple(u),v),x1),x2)))) ),
inference(rew,[status(thm),theory(equality)],[830,712]),
[iquote('0:Rew:830.0,712.1')] ).
cnf(890,plain,
( hBOOL(hAPP(state,bool,hAPP(u,fun(state,bool),v,skf109(v,u,w,x,y)),skf108(v,u,w,x,y)))
| hBOOL(hAPP(fun(hoare_1656922687triple(u),bool),bool,hAPP(fun(hoare_1656922687triple(u),bool),fun(fun(hoare_1656922687triple(u),bool),bool),hoare_279057269derivs(u),z),hAPP(hoare_1656922687triple(u),fun(hoare_1656922687triple(u),bool),fequal(hoare_1656922687triple(u)),hAPP(fun(u,fun(state,bool)),hoare_1656922687triple(u),hAPP(com,fun(fun(u,fun(state,bool)),hoare_1656922687triple(u)),hAPP(fun(u,fun(state,bool)),fun(com,fun(fun(u,fun(state,bool)),hoare_1656922687triple(u))),hoare_246368825triple(u),v),x1),x2)))) ),
inference(rew,[status(thm),theory(equality)],[830,713]),
[iquote('0:Rew:830.0,713.1')] ).
cnf(957,plain,
hBOOL(hAPP(fun(hoare_1656922687triple(u),bool),bool,hAPP(fun(hoare_1656922687triple(u),bool),fun(fun(hoare_1656922687triple(u),bool),bool),hoare_279057269derivs(u),v),hAPP(hoare_1656922687triple(u),fun(hoare_1656922687triple(u),bool),fequal(hoare_1656922687triple(u)),hAPP(fun(u,fun(state,bool)),hoare_1656922687triple(u),hAPP(com,fun(fun(u,fun(state,bool)),hoare_1656922687triple(u)),hAPP(fun(u,fun(state,bool)),fun(com,fun(fun(u,fun(state,bool)),hoare_1656922687triple(u))),hoare_246368825triple(u),hAPP(fun(state,state),fun(u,fun(state,bool)),hAPP(fun(u,fun(fun(state,state),fun(state,bool))),fun(fun(state,state),fun(u,fun(state,bool))),combc(u,fun(state,state),fun(state,bool)),hAPP(fun(u,fun(state,bool)),fun(u,fun(fun(state,state),fun(state,bool))),hAPP(fun(fun(state,bool),fun(fun(state,state),fun(state,bool))),fun(fun(u,fun(state,bool)),fun(u,fun(fun(state,state),fun(state,bool)))),combb(fun(state,bool),fun(fun(state,state),fun(state,bool)),u),combb(state,bool,state)),w)),hAPP(fun(state,nat),fun(state,state),hAPP(fun(state,fun(nat,state)),fun(fun(state,nat),fun(state,state)),combs(state,nat,state),hAPP(vname,fun(state,fun(nat,state)),hAPP(fun(state,fun(vname,fun(nat,state))),fun(vname,fun(state,fun(nat,state))),combc(state,vname,fun(nat,state)),update),x)),y))),hAPP(fun(state,nat),com,hAPP(vname,fun(fun(state,nat),com),ass,x),y)),w)))),
inference(rew,[status(thm),theory(equality)],[830,819]),
[iquote('0:Rew:830.0,819.0')] ).
cnf(959,plain,
~ hBOOL(hAPP(fun(hoare_1656922687triple(x_a),bool),bool,hAPP(fun(hoare_1656922687triple(x_a),bool),fun(fun(hoare_1656922687triple(x_a),bool),bool),hoare_279057269derivs(x_a),g),hAPP(hoare_1656922687triple(x_a),fun(hoare_1656922687triple(x_a),bool),fequal(hoare_1656922687triple(x_a)),hAPP(fun(x_a,fun(state,bool)),hoare_1656922687triple(x_a),hAPP(com,fun(fun(x_a,fun(state,bool)),hoare_1656922687triple(x_a)),hAPP(fun(x_a,fun(state,bool)),fun(com,fun(fun(x_a,fun(state,bool)),hoare_1656922687triple(x_a))),hoare_246368825triple(x_a),hAPP(fun(state,bool),fun(x_a,fun(state,bool)),combk(fun(state,bool),x_a),bot_bot(fun(state,bool)))),c),hAPP(fun(state,bool),fun(x_a,fun(state,bool)),hAPP(fun(x_a,fun(fun(state,bool),fun(state,bool))),fun(fun(state,bool),fun(x_a,fun(state,bool))),combc(x_a,fun(state,bool),fun(state,bool)),hAPP(fun(x_a,fun(state,fun(bool,bool))),fun(x_a,fun(fun(state,bool),fun(state,bool))),hAPP(fun(fun(state,fun(bool,bool)),fun(fun(state,bool),fun(state,bool))),fun(fun(x_a,fun(state,fun(bool,bool))),fun(x_a,fun(fun(state,bool),fun(state,bool)))),combb(fun(state,fun(bool,bool)),fun(fun(state,bool),fun(state,bool)),x_a),combs(state,bool,bool)),hAPP(fun(x_a,fun(state,bool)),fun(x_a,fun(state,fun(bool,bool))),hAPP(fun(fun(state,bool),fun(state,fun(bool,bool))),fun(fun(x_a,fun(state,bool)),fun(x_a,fun(state,fun(bool,bool)))),combb(fun(state,bool),fun(state,fun(bool,bool)),x_a),hAPP(fun(bool,fun(bool,bool)),fun(fun(state,bool),fun(state,fun(bool,bool))),combb(bool,fun(bool,bool),state),fconj)),p))),hAPP(fun(state,bool),fun(state,bool),hAPP(fun(bool,bool),fun(fun(state,bool),fun(state,bool)),combb(bool,bool,state),fNot),b)))))),
inference(rew,[status(thm),theory(equality)],[830,821,824]),
[iquote('0:Rew:830.0,821.0,824.0,821.0')] ).
cnf(972,plain,
( ~ hBOOL(hAPP(fun(hoare_1656922687triple(x_a),bool),bool,hAPP(fun(hoare_1656922687triple(x_a),bool),fun(fun(hoare_1656922687triple(x_a),bool),bool),hoare_279057269derivs(x_a),g),hAPP(hoare_1656922687triple(x_a),fun(hoare_1656922687triple(x_a),bool),fequal(hoare_1656922687triple(x_a)),skf173(hAPP(fun(hoare_1656922687triple(x_a),bool),fun(fun(hoare_1656922687triple(x_a),bool),bool),hoare_279057269derivs(x_a),g),hoare_1656922687triple(x_a)))))
| ~ hBOOL(hAPP(fun(hoare_1656922687triple(x_a),bool),bool,finite_finite_1(hoare_1656922687triple(x_a)),hAPP(hoare_1656922687triple(x_a),fun(hoare_1656922687triple(x_a),bool),fequal(hoare_1656922687triple(x_a)),hAPP(fun(x_a,fun(state,bool)),hoare_1656922687triple(x_a),hAPP(com,fun(fun(x_a,fun(state,bool)),hoare_1656922687triple(x_a)),hAPP(fun(x_a,fun(state,bool)),fun(com,fun(fun(x_a,fun(state,bool)),hoare_1656922687triple(x_a))),hoare_246368825triple(x_a),hAPP(fun(state,bool),fun(x_a,fun(state,bool)),combk(fun(state,bool),x_a),bot_bot(fun(state,bool)))),c),hAPP(fun(state,bool),fun(x_a,fun(state,bool)),hAPP(fun(x_a,fun(fun(state,bool),fun(state,bool))),fun(fun(state,bool),fun(x_a,fun(state,bool))),combc(x_a,fun(state,bool),fun(state,bool)),hAPP(fun(x_a,fun(state,fun(bool,bool))),fun(x_a,fun(fun(state,bool),fun(state,bool))),hAPP(fun(fun(state,fun(bool,bool)),fun(fun(state,bool),fun(state,bool))),fun(fun(x_a,fun(state,fun(bool,bool))),fun(x_a,fun(fun(state,bool),fun(state,bool)))),combb(fun(state,fun(bool,bool)),fun(fun(state,bool),fun(state,bool)),x_a),combs(state,bool,bool)),hAPP(fun(x_a,fun(state,bool)),fun(x_a,fun(state,fun(bool,bool))),hAPP(fun(fun(state,bool),fun(state,fun(bool,bool))),fun(fun(x_a,fun(state,bool)),fun(x_a,fun(state,fun(bool,bool)))),combb(fun(state,bool),fun(state,fun(bool,bool)),x_a),hAPP(fun(bool,fun(bool,bool)),fun(fun(state,bool),fun(state,fun(bool,bool))),combb(bool,fun(bool,bool),state),fconj)),p))),hAPP(fun(state,bool),fun(state,bool),hAPP(fun(bool,bool),fun(fun(state,bool),fun(state,bool)),combb(bool,bool,state),fNot),b))))))
| hBOOL(hAPP(fun(hoare_1656922687triple(x_a),bool),bool,hAPP(fun(hoare_1656922687triple(x_a),bool),fun(fun(hoare_1656922687triple(x_a),bool),bool),hoare_279057269derivs(x_a),g),skf174(hAPP(fun(hoare_1656922687triple(x_a),bool),fun(fun(hoare_1656922687triple(x_a),bool),bool),hoare_279057269derivs(x_a),g),hoare_1656922687triple(x_a))))
| equal(ti(fun(hoare_1656922687triple(x_a),bool),hAPP(hoare_1656922687triple(x_a),fun(hoare_1656922687triple(x_a),bool),fequal(hoare_1656922687triple(x_a)),hAPP(fun(x_a,fun(state,bool)),hoare_1656922687triple(x_a),hAPP(com,fun(fun(x_a,fun(state,bool)),hoare_1656922687triple(x_a)),hAPP(fun(x_a,fun(state,bool)),fun(com,fun(fun(x_a,fun(state,bool)),hoare_1656922687triple(x_a))),hoare_246368825triple(x_a),hAPP(fun(state,bool),fun(x_a,fun(state,bool)),combk(fun(state,bool),x_a),bot_bot(fun(state,bool)))),c),hAPP(fun(state,bool),fun(x_a,fun(state,bool)),hAPP(fun(x_a,fun(fun(state,bool),fun(state,bool))),fun(fun(state,bool),fun(x_a,fun(state,bool))),combc(x_a,fun(state,bool),fun(state,bool)),hAPP(fun(x_a,fun(state,fun(bool,bool))),fun(x_a,fun(fun(state,bool),fun(state,bool))),hAPP(fun(fun(state,fun(bool,bool)),fun(fun(state,bool),fun(state,bool))),fun(fun(x_a,fun(state,fun(bool,bool))),fun(x_a,fun(fun(state,bool),fun(state,bool)))),combb(fun(state,fun(bool,bool)),fun(fun(state,bool),fun(state,bool)),x_a),combs(state,bool,bool)),hAPP(fun(x_a,fun(state,bool)),fun(x_a,fun(state,fun(bool,bool))),hAPP(fun(fun(state,bool),fun(state,fun(bool,bool))),fun(fun(x_a,fun(state,bool)),fun(x_a,fun(state,fun(bool,bool)))),combb(fun(state,bool),fun(state,fun(bool,bool)),x_a),hAPP(fun(bool,fun(bool,bool)),fun(fun(state,bool),fun(state,fun(bool,bool))),combb(bool,fun(bool,bool),state),fconj)),p))),hAPP(fun(state,bool),fun(state,bool),hAPP(fun(bool,bool),fun(fun(state,bool),fun(state,bool)),combb(bool,bool,state),fNot),b))))),bot_bot(fun(hoare_1656922687triple(x_a),bool))) ),
inference(res,[status(thm),theory(equality)],[847,959]),
[iquote('0:Res:847.3,959.0')] ).
cnf(979,plain,
( ~ hBOOL(hAPP(fun(hoare_1656922687triple(x_a),bool),bool,hAPP(fun(hoare_1656922687triple(x_a),bool),fun(fun(hoare_1656922687triple(x_a),bool),bool),hoare_279057269derivs(x_a),u),hAPP(hoare_1656922687triple(x_a),fun(hoare_1656922687triple(x_a),bool),fequal(hoare_1656922687triple(x_a)),hAPP(fun(x_a,fun(state,bool)),hoare_1656922687triple(x_a),hAPP(com,fun(fun(x_a,fun(state,bool)),hoare_1656922687triple(x_a)),hAPP(fun(x_a,fun(state,bool)),fun(com,fun(fun(x_a,fun(state,bool)),hoare_1656922687triple(x_a))),hoare_246368825triple(x_a),hAPP(fun(state,bool),fun(x_a,fun(state,bool)),combk(fun(state,bool),x_a),bot_bot(fun(state,bool)))),c),hAPP(fun(state,bool),fun(x_a,fun(state,bool)),hAPP(fun(x_a,fun(fun(state,bool),fun(state,bool))),fun(fun(state,bool),fun(x_a,fun(state,bool))),combc(x_a,fun(state,bool),fun(state,bool)),hAPP(fun(x_a,fun(state,fun(bool,bool))),fun(x_a,fun(fun(state,bool),fun(state,bool))),hAPP(fun(fun(state,fun(bool,bool)),fun(fun(state,bool),fun(state,bool))),fun(fun(x_a,fun(state,fun(bool,bool))),fun(x_a,fun(fun(state,bool),fun(state,bool)))),combb(fun(state,fun(bool,bool)),fun(fun(state,bool),fun(state,bool)),x_a),combs(state,bool,bool)),hAPP(fun(x_a,fun(state,bool)),fun(x_a,fun(state,fun(bool,bool))),hAPP(fun(fun(state,bool),fun(state,fun(bool,bool))),fun(fun(x_a,fun(state,bool)),fun(x_a,fun(state,fun(bool,bool)))),combb(fun(state,bool),fun(state,fun(bool,bool)),x_a),hAPP(fun(bool,fun(bool,bool)),fun(fun(state,bool),fun(state,fun(bool,bool))),combb(bool,fun(bool,bool),state),fconj)),p))),hAPP(fun(state,bool),fun(state,bool),hAPP(fun(bool,bool),fun(fun(state,bool),fun(state,bool)),combb(bool,bool,state),fNot),b))))))
| ~ hBOOL(hAPP(fun(hoare_1656922687triple(x_a),bool),bool,hAPP(fun(hoare_1656922687triple(x_a),bool),fun(fun(hoare_1656922687triple(x_a),bool),bool),hoare_279057269derivs(x_a),g),u)) ),
inference(res,[status(thm),theory(equality)],[541,959]),
[iquote('0:Res:541.2,959.0')] ).
cnf(986,plain,
hBOOL(hAPP(state,bool,hAPP(x_a,fun(state,bool),hAPP(fun(state,bool),fun(x_a,fun(state,bool)),combk(fun(state,bool),x_a),bot_bot(fun(state,bool))),skf109(hAPP(fun(state,bool),fun(x_a,fun(state,bool)),combk(fun(state,bool),x_a),bot_bot(fun(state,bool))),x_a,u,v,w)),skf108(hAPP(fun(state,bool),fun(x_a,fun(state,bool)),combk(fun(state,bool),x_a),bot_bot(fun(state,bool))),x_a,u,v,w))),
inference(res,[status(thm),theory(equality)],[890,959]),
[iquote('0:Res:890.1,959.0')] ).
cnf(987,plain,
hBOOL(hAPP(state,bool,hAPP(x_a,fun(state,bool),hAPP(fun(state,bool),fun(x_a,fun(state,bool)),combk(fun(state,bool),x_a),bot_bot(fun(state,bool))),skf133(hAPP(fun(state,bool),fun(x_a,fun(state,bool)),combk(fun(state,bool),x_a),bot_bot(fun(state,bool))),x_a,u,v,w)),skf132(hAPP(fun(state,bool),fun(x_a,fun(state,bool)),combk(fun(state,bool),x_a),bot_bot(fun(state,bool))),x_a,u,v,w))),
inference(res,[status(thm),theory(equality)],[889,959]),
[iquote('0:Res:889.1,959.0')] ).
cnf(1014,plain,
hBOOL(hAPP(state,bool,bot_bot(fun(state,bool)),skf132(hAPP(fun(state,bool),fun(x_a,fun(state,bool)),combk(fun(state,bool),x_a),bot_bot(fun(state,bool))),x_a,u,v,w))),
inference(rew,[status(thm),theory(equality)],[104,987,123]),
[iquote('0:Rew:104.0,987.0,123.0,987.0')] ).
cnf(1015,plain,
hBOOL(hAPP(state,bool,bot_bot(fun(state,bool)),skf108(hAPP(fun(state,bool),fun(x_a,fun(state,bool)),combk(fun(state,bool),x_a),bot_bot(fun(state,bool))),x_a,u,v,w))),
inference(rew,[status(thm),theory(equality)],[104,986,123]),
[iquote('0:Rew:104.0,986.0,123.0,986.0')] ).
cnf(1023,plain,
( ~ hBOOL(hAPP(fun(hoare_1656922687triple(x_a),bool),bool,finite_finite_1(hoare_1656922687triple(x_a)),hAPP(hoare_1656922687triple(x_a),fun(hoare_1656922687triple(x_a),bool),fequal(hoare_1656922687triple(x_a)),hAPP(fun(x_a,fun(state,bool)),hoare_1656922687triple(x_a),hAPP(com,fun(fun(x_a,fun(state,bool)),hoare_1656922687triple(x_a)),hAPP(fun(x_a,fun(state,bool)),fun(com,fun(fun(x_a,fun(state,bool)),hoare_1656922687triple(x_a))),hoare_246368825triple(x_a),hAPP(fun(state,bool),fun(x_a,fun(state,bool)),combk(fun(state,bool),x_a),bot_bot(fun(state,bool)))),c),hAPP(fun(state,bool),fun(x_a,fun(state,bool)),hAPP(fun(x_a,fun(fun(state,bool),fun(state,bool))),fun(fun(state,bool),fun(x_a,fun(state,bool))),combc(x_a,fun(state,bool),fun(state,bool)),hAPP(fun(x_a,fun(state,fun(bool,bool))),fun(x_a,fun(fun(state,bool),fun(state,bool))),hAPP(fun(fun(state,fun(bool,bool)),fun(fun(state,bool),fun(state,bool))),fun(fun(x_a,fun(state,fun(bool,bool))),fun(x_a,fun(fun(state,bool),fun(state,bool)))),combb(fun(state,fun(bool,bool)),fun(fun(state,bool),fun(state,bool)),x_a),combs(state,bool,bool)),hAPP(fun(x_a,fun(state,bool)),fun(x_a,fun(state,fun(bool,bool))),hAPP(fun(fun(state,bool),fun(state,fun(bool,bool))),fun(fun(x_a,fun(state,bool)),fun(x_a,fun(state,fun(bool,bool)))),combb(fun(state,bool),fun(state,fun(bool,bool)),x_a),hAPP(fun(bool,fun(bool,bool)),fun(fun(state,bool),fun(state,fun(bool,bool))),combb(bool,fun(bool,bool),state),fconj)),p))),hAPP(fun(state,bool),fun(state,bool),hAPP(fun(bool,bool),fun(fun(state,bool),fun(state,bool)),combb(bool,bool,state),fNot),b))))))
| ~ hBOOL(hAPP(fun(hoare_1656922687triple(x_a),bool),bool,hAPP(fun(hoare_1656922687triple(x_a),bool),fun(fun(hoare_1656922687triple(x_a),bool),bool),hoare_279057269derivs(x_a),g),hAPP(hoare_1656922687triple(x_a),fun(hoare_1656922687triple(x_a),bool),fequal(hoare_1656922687triple(x_a)),skf173(hAPP(fun(hoare_1656922687triple(x_a),bool),fun(fun(hoare_1656922687triple(x_a),bool),bool),hoare_279057269derivs(x_a),g),hoare_1656922687triple(x_a)))))
| hBOOL(hAPP(fun(hoare_1656922687triple(x_a),bool),bool,hAPP(fun(hoare_1656922687triple(x_a),bool),fun(fun(hoare_1656922687triple(x_a),bool),bool),hoare_279057269derivs(x_a),g),skf174(hAPP(fun(hoare_1656922687triple(x_a),bool),fun(fun(hoare_1656922687triple(x_a),bool),bool),hoare_279057269derivs(x_a),g),hoare_1656922687triple(x_a))))
| equal(hAPP(hoare_1656922687triple(x_a),fun(hoare_1656922687triple(x_a),bool),fequal(hoare_1656922687triple(x_a)),hAPP(fun(x_a,fun(state,bool)),hoare_1656922687triple(x_a),hAPP(com,fun(fun(x_a,fun(state,bool)),hoare_1656922687triple(x_a)),hAPP(fun(x_a,fun(state,bool)),fun(com,fun(fun(x_a,fun(state,bool)),hoare_1656922687triple(x_a))),hoare_246368825triple(x_a),hAPP(fun(state,bool),fun(x_a,fun(state,bool)),combk(fun(state,bool),x_a),bot_bot(fun(state,bool)))),c),hAPP(fun(state,bool),fun(x_a,fun(state,bool)),hAPP(fun(x_a,fun(fun(state,bool),fun(state,bool))),fun(fun(state,bool),fun(x_a,fun(state,bool))),combc(x_a,fun(state,bool),fun(state,bool)),hAPP(fun(x_a,fun(state,fun(bool,bool))),fun(x_a,fun(fun(state,bool),fun(state,bool))),hAPP(fun(fun(state,fun(bool,bool)),fun(fun(state,bool),fun(state,bool))),fun(fun(x_a,fun(state,fun(bool,bool))),fun(x_a,fun(fun(state,bool),fun(state,bool)))),combb(fun(state,fun(bool,bool)),fun(fun(state,bool),fun(state,bool)),x_a),combs(state,bool,bool)),hAPP(fun(x_a,fun(state,bool)),fun(x_a,fun(state,fun(bool,bool))),hAPP(fun(fun(state,bool),fun(state,fun(bool,bool))),fun(fun(x_a,fun(state,bool)),fun(x_a,fun(state,fun(bool,bool)))),combb(fun(state,bool),fun(state,fun(bool,bool)),x_a),hAPP(fun(bool,fun(bool,bool)),fun(fun(state,bool),fun(state,fun(bool,bool))),combb(bool,fun(bool,bool),state),fconj)),p))),hAPP(fun(state,bool),fun(state,bool),hAPP(fun(bool,bool),fun(fun(state,bool),fun(state,bool)),combb(bool,bool,state),fNot),b)))),bot_bot(fun(hoare_1656922687triple(x_a),bool))) ),
inference(rew,[status(thm),theory(equality)],[86,972]),
[iquote('0:Rew:86.0,972.3')] ).
cnf(1029,plain,
equal(hAPP(hoare_1656922687triple(x_a),fun(hoare_1656922687triple(x_a),bool),fequal(hoare_1656922687triple(x_a)),hAPP(fun(x_a,fun(state,bool)),hoare_1656922687triple(x_a),hAPP(com,fun(fun(x_a,fun(state,bool)),hoare_1656922687triple(x_a)),hAPP(fun(x_a,fun(state,bool)),fun(com,fun(fun(x_a,fun(state,bool)),hoare_1656922687triple(x_a))),hoare_246368825triple(x_a),hAPP(fun(state,bool),fun(x_a,fun(state,bool)),combk(fun(state,bool),x_a),bot_bot(fun(state,bool)))),c),hAPP(fun(state,bool),fun(x_a,fun(state,bool)),hAPP(fun(x_a,fun(fun(state,bool),fun(state,bool))),fun(fun(state,bool),fun(x_a,fun(state,bool))),combc(x_a,fun(state,bool),fun(state,bool)),hAPP(fun(x_a,fun(state,fun(bool,bool))),fun(x_a,fun(fun(state,bool),fun(state,bool))),hAPP(fun(fun(state,fun(bool,bool)),fun(fun(state,bool),fun(state,bool))),fun(fun(x_a,fun(state,fun(bool,bool))),fun(x_a,fun(fun(state,bool),fun(state,bool)))),combb(fun(state,fun(bool,bool)),fun(fun(state,bool),fun(state,bool)),x_a),combs(state,bool,bool)),hAPP(fun(x_a,fun(state,bool)),fun(x_a,fun(state,fun(bool,bool))),hAPP(fun(fun(state,bool),fun(state,fun(bool,bool))),fun(fun(x_a,fun(state,bool)),fun(x_a,fun(state,fun(bool,bool)))),combb(fun(state,bool),fun(state,fun(bool,bool)),x_a),hAPP(fun(bool,fun(bool,bool)),fun(fun(state,bool),fun(state,fun(bool,bool))),combb(bool,fun(bool,bool),state),fconj)),p))),hAPP(fun(state,bool),fun(state,bool),hAPP(fun(bool,bool),fun(fun(state,bool),fun(state,bool)),combb(bool,bool,state),fNot),b)))),bot_bot(fun(hoare_1656922687triple(x_a),bool))),
inference(spt,[spt(split,[position(s1)])],[1023]),
[iquote('1:Spt:1023.3')] ).
cnf(1037,plain,
( ~ hBOOL(hAPP(fun(hoare_1656922687triple(x_a),bool),bool,hAPP(fun(hoare_1656922687triple(x_a),bool),fun(fun(hoare_1656922687triple(x_a),bool),bool),hoare_279057269derivs(x_a),u),bot_bot(fun(hoare_1656922687triple(x_a),bool))))
| ~ hBOOL(hAPP(fun(hoare_1656922687triple(x_a),bool),bool,hAPP(fun(hoare_1656922687triple(x_a),bool),fun(fun(hoare_1656922687triple(x_a),bool),bool),hoare_279057269derivs(x_a),g),u)) ),
inference(rew,[status(thm),theory(equality)],[1029,979]),
[iquote('1:Rew:1029.0,979.0')] ).
cnf(1042,plain,
~ hBOOL(hAPP(fun(hoare_1656922687triple(x_a),bool),bool,hAPP(fun(hoare_1656922687triple(x_a),bool),fun(fun(hoare_1656922687triple(x_a),bool),bool),hoare_279057269derivs(x_a),g),u)),
inference(mrr,[status(thm)],[1037,197]),
[iquote('1:MRR:1037.0,197.0')] ).
cnf(1043,plain,
$false,
inference(unc,[status(thm)],[1042,957]),
[iquote('1:UnC:1042.0,957.0')] ).
cnf(1050,plain,
~ equal(hAPP(hoare_1656922687triple(x_a),fun(hoare_1656922687triple(x_a),bool),fequal(hoare_1656922687triple(x_a)),hAPP(fun(x_a,fun(state,bool)),hoare_1656922687triple(x_a),hAPP(com,fun(fun(x_a,fun(state,bool)),hoare_1656922687triple(x_a)),hAPP(fun(x_a,fun(state,bool)),fun(com,fun(fun(x_a,fun(state,bool)),hoare_1656922687triple(x_a))),hoare_246368825triple(x_a),hAPP(fun(state,bool),fun(x_a,fun(state,bool)),combk(fun(state,bool),x_a),bot_bot(fun(state,bool)))),c),hAPP(fun(state,bool),fun(x_a,fun(state,bool)),hAPP(fun(x_a,fun(fun(state,bool),fun(state,bool))),fun(fun(state,bool),fun(x_a,fun(state,bool))),combc(x_a,fun(state,bool),fun(state,bool)),hAPP(fun(x_a,fun(state,fun(bool,bool))),fun(x_a,fun(fun(state,bool),fun(state,bool))),hAPP(fun(fun(state,fun(bool,bool)),fun(fun(state,bool),fun(state,bool))),fun(fun(x_a,fun(state,fun(bool,bool))),fun(x_a,fun(fun(state,bool),fun(state,bool)))),combb(fun(state,fun(bool,bool)),fun(fun(state,bool),fun(state,bool)),x_a),combs(state,bool,bool)),hAPP(fun(x_a,fun(state,bool)),fun(x_a,fun(state,fun(bool,bool))),hAPP(fun(fun(state,bool),fun(state,fun(bool,bool))),fun(fun(x_a,fun(state,bool)),fun(x_a,fun(state,fun(bool,bool)))),combb(fun(state,bool),fun(state,fun(bool,bool)),x_a),hAPP(fun(bool,fun(bool,bool)),fun(fun(state,bool),fun(state,fun(bool,bool))),combb(bool,fun(bool,bool),state),fconj)),p))),hAPP(fun(state,bool),fun(state,bool),hAPP(fun(bool,bool),fun(fun(state,bool),fun(state,bool)),combb(bool,bool,state),fNot),b)))),bot_bot(fun(hoare_1656922687triple(x_a),bool))),
inference(spt,[spt(split,[position(sa)])],[1043,1029]),
[iquote('1:Spt:1043.0,1023.3,1029.0')] ).
cnf(1051,plain,
( ~ hBOOL(hAPP(fun(hoare_1656922687triple(x_a),bool),bool,finite_finite_1(hoare_1656922687triple(x_a)),hAPP(hoare_1656922687triple(x_a),fun(hoare_1656922687triple(x_a),bool),fequal(hoare_1656922687triple(x_a)),hAPP(fun(x_a,fun(state,bool)),hoare_1656922687triple(x_a),hAPP(com,fun(fun(x_a,fun(state,bool)),hoare_1656922687triple(x_a)),hAPP(fun(x_a,fun(state,bool)),fun(com,fun(fun(x_a,fun(state,bool)),hoare_1656922687triple(x_a))),hoare_246368825triple(x_a),hAPP(fun(state,bool),fun(x_a,fun(state,bool)),combk(fun(state,bool),x_a),bot_bot(fun(state,bool)))),c),hAPP(fun(state,bool),fun(x_a,fun(state,bool)),hAPP(fun(x_a,fun(fun(state,bool),fun(state,bool))),fun(fun(state,bool),fun(x_a,fun(state,bool))),combc(x_a,fun(state,bool),fun(state,bool)),hAPP(fun(x_a,fun(state,fun(bool,bool))),fun(x_a,fun(fun(state,bool),fun(state,bool))),hAPP(fun(fun(state,fun(bool,bool)),fun(fun(state,bool),fun(state,bool))),fun(fun(x_a,fun(state,fun(bool,bool))),fun(x_a,fun(fun(state,bool),fun(state,bool)))),combb(fun(state,fun(bool,bool)),fun(fun(state,bool),fun(state,bool)),x_a),combs(state,bool,bool)),hAPP(fun(x_a,fun(state,bool)),fun(x_a,fun(state,fun(bool,bool))),hAPP(fun(fun(state,bool),fun(state,fun(bool,bool))),fun(fun(x_a,fun(state,bool)),fun(x_a,fun(state,fun(bool,bool)))),combb(fun(state,bool),fun(state,fun(bool,bool)),x_a),hAPP(fun(bool,fun(bool,bool)),fun(fun(state,bool),fun(state,fun(bool,bool))),combb(bool,fun(bool,bool),state),fconj)),p))),hAPP(fun(state,bool),fun(state,bool),hAPP(fun(bool,bool),fun(fun(state,bool),fun(state,bool)),combb(bool,bool,state),fNot),b))))))
| ~ hBOOL(hAPP(fun(hoare_1656922687triple(x_a),bool),bool,hAPP(fun(hoare_1656922687triple(x_a),bool),fun(fun(hoare_1656922687triple(x_a),bool),bool),hoare_279057269derivs(x_a),g),hAPP(hoare_1656922687triple(x_a),fun(hoare_1656922687triple(x_a),bool),fequal(hoare_1656922687triple(x_a)),skf173(hAPP(fun(hoare_1656922687triple(x_a),bool),fun(fun(hoare_1656922687triple(x_a),bool),bool),hoare_279057269derivs(x_a),g),hoare_1656922687triple(x_a)))))
| hBOOL(hAPP(fun(hoare_1656922687triple(x_a),bool),bool,hAPP(fun(hoare_1656922687triple(x_a),bool),fun(fun(hoare_1656922687triple(x_a),bool),bool),hoare_279057269derivs(x_a),g),skf174(hAPP(fun(hoare_1656922687triple(x_a),bool),fun(fun(hoare_1656922687triple(x_a),bool),bool),hoare_279057269derivs(x_a),g),hoare_1656922687triple(x_a)))) ),
inference(spt,[spt(split,[position(s2)])],[1023]),
[iquote('1:Spt:1043.0,1023.0,1023.1,1023.2')] ).
cnf(1105,plain,
( ~ hBOOL(u)
| equal(ti(bool,u),fFalse)
| hBOOL(fTrue) ),
inference(spr,[status(thm),theory(equality)],[60,33]),
[iquote('0:SpR:60.1,33.1')] ).
cnf(1110,plain,
( ~ hBOOL(fTrue)
| equal(ti(bool,u),fFalse)
| hBOOL(u) ),
inference(spl,[status(thm),theory(equality)],[60,32]),
[iquote('0:SpL:60.1,32.0')] ).
cnf(1133,plain,
( ~ hBOOL(u)
| equal(ti(bool,u),fFalse) ),
inference(spt,[spt(split,[position(s2s1)])],[1105]),
[iquote('2:Spt:1105.0,1105.1')] ).
cnf(1135,plain,
( ~ hBOOL(u)
| hBOOL(fFalse) ),
inference(rew,[status(thm),theory(equality)],[1133,33]),
[iquote('2:Rew:1133.1,33.1')] ).
cnf(1136,plain,
~ hBOOL(u),
inference(mrr,[status(thm)],[1135,23]),
[iquote('2:MRR:1135.1,23.0')] ).
cnf(1137,plain,
$false,
inference(unc,[status(thm)],[1136,1014]),
[iquote('2:UnC:1136.0,1014.0')] ).
cnf(1138,plain,
hBOOL(fTrue),
inference(spt,[spt(split,[position(s2s2)])],[1105]),
[iquote('2:Spt:1137.0,1105.2')] ).
cnf(1139,plain,
( equal(ti(bool,u),fFalse)
| hBOOL(u) ),
inference(mrr,[status(thm)],[1110,1138]),
[iquote('2:MRR:1110.0,1138.0')] ).
cnf(1226,plain,
( hBOOL(u)
| equal(hAPP(bool,v,w,fFalse),hAPP(bool,v,w,u)) ),
inference(spr,[status(thm),theory(equality)],[1139,85]),
[iquote('2:SpR:1139.0,85.0')] ).
cnf(1289,plain,
( hBOOL(u)
| hBOOL(u)
| hBOOL(hAPP(bool,bool,fNot,fFalse)) ),
inference(spr,[status(thm),theory(equality)],[1226,47]),
[iquote('2:SpR:1226.1,47.1')] ).
cnf(1297,plain,
( hBOOL(u)
| hBOOL(hAPP(bool,bool,fNot,fFalse)) ),
inference(obv,[status(thm),theory(equality)],[1289]),
[iquote('2:Obv:1289.0')] ).
cnf(1298,plain,
hBOOL(hAPP(bool,bool,fNot,fFalse)),
inference(con,[status(thm)],[1297]),
[iquote('2:Con:1297.0')] ).
cnf(1306,plain,
~ hBOOL(fFalse),
inference(res,[status(thm),theory(equality)],[1298,58]),
[iquote('2:Res:1298.0,58.1')] ).
cnf(10539,plain,
equal(hAPP(u,bool,bot_bot(fun(u,bool)),v),ti(bool,fFalse)),
inference(spr,[status(thm),theory(equality)],[824,123]),
[iquote('0:SpR:824.0,123.0')] ).
cnf(10542,plain,
equal(hAPP(u,bool,bot_bot(fun(u,bool)),v),fFalse),
inference(rew,[status(thm),theory(equality)],[25,10539]),
[iquote('0:Rew:25.0,10539.0')] ).
cnf(10546,plain,
hBOOL(fFalse),
inference(rew,[status(thm),theory(equality)],[10542,1015]),
[iquote('0:Rew:10542.0,1015.0')] ).
cnf(10548,plain,
$false,
inference(mrr,[status(thm)],[10546,1306]),
[iquote('2:MRR:10546.0,1306.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : SWW470+6 : TPTP v8.1.0. Released v5.3.0.
% 0.04/0.12 % Command : run_spass %d %s
% 0.11/0.33 % Computer : n032.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 600
% 0.11/0.33 % DateTime : Sun Jun 5 02:51:33 EDT 2022
% 0.11/0.33 % CPUTime :
% 24.65/24.87
% 24.65/24.87 SPASS V 3.9
% 24.65/24.87 SPASS beiseite: Proof found.
% 24.65/24.87 % SZS status Theorem
% 24.65/24.87 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 24.65/24.87 SPASS derived 7172 clauses, backtracked 2141 clauses, performed 9 splits and kept 3862 clauses.
% 24.65/24.87 SPASS allocated 148509 KBytes.
% 24.65/24.87 SPASS spent 0:0:24.53 on the problem.
% 24.65/24.87 0:00:00.06 for the input.
% 24.65/24.87 0:0:13.69 for the FLOTTER CNF translation.
% 24.65/24.87 0:00:00.08 for inferences.
% 24.65/24.87 0:00:00.16 for the backtracking.
% 24.65/24.87 0:00:09.61 for the reduction.
% 24.65/24.87
% 24.65/24.87
% 24.65/24.87 Here is a proof with depth 4, length 58 :
% 24.65/24.87 % SZS output start Refutation
% See solution above
% 24.86/25.15 Formulae used in the proof : help_fFalse_1_1_U tsy_c_fFalse_res tsy_c_hBOOL_arg1 help_fNot_2_1_U help_fNot_1_1_U help_fFalse_1_1_T tsy_c_hAPP_arg2 tsy_c_hAPP_res tsy_c_hAPP_arg1 fact_77_Collect__def help_COMBK_1_1_U fact_23_empty__def fact_0_empty fact_12_singleton__conv2 fact_2_cut fact_155_finite__ne__induct fact_138_finite_OemptyI fact_51_conseq fact_5_escape fact_58_Ass conj_0
% 24.86/25.15
%------------------------------------------------------------------------------