TSTP Solution File: SWW470+5 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SWW470+5 : TPTP v8.1.0. Released v5.3.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n021.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 1.70s 1.91s
% Output : Refutation 1.70s
% 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 : 14 ( 2 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 42 ( 42 usr; 21 con; 0-5 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(3,axiom,
~ hBOOL(fFalse),
file('SWW470+5.p',unknown),
[] ).
cnf(5,axiom,
equal(ti(bool,fFalse),fFalse),
file('SWW470+5.p',unknown),
[] ).
cnf(10,axiom,
( ~ hBOOL(ti(bool,u))
| hBOOL(u) ),
file('SWW470+5.p',unknown),
[] ).
cnf(11,axiom,
( ~ hBOOL(u)
| hBOOL(ti(bool,u)) ),
file('SWW470+5.p',unknown),
[] ).
cnf(15,axiom,
( hBOOL(u)
| hBOOL(hAPP(bool,bool,fNot,u)) ),
file('SWW470+5.p',unknown),
[] ).
cnf(24,axiom,
( ~ hBOOL(u)
| ~ hBOOL(hAPP(bool,bool,fNot,u)) ),
file('SWW470+5.p',unknown),
[] ).
cnf(25,axiom,
( equal(ti(bool,u),fFalse)
| equal(ti(bool,u),fTrue) ),
file('SWW470+5.p',unknown),
[] ).
cnf(38,axiom,
equal(hAPP(u,v,w,ti(u,x)),hAPP(u,v,w,x)),
file('SWW470+5.p',unknown),
[] ).
cnf(39,axiom,
equal(ti(u,hAPP(v,u,w,x)),hAPP(v,u,w,x)),
file('SWW470+5.p',unknown),
[] ).
cnf(49,axiom,
equal(hAPP(u,v,ti(fun(u,v),w),x),hAPP(u,v,w,x)),
file('SWW470+5.p',unknown),
[] ).
cnf(55,axiom,
equal(hAPP(fun(u,bool),fun(u,bool),collect(u),v),ti(fun(u,bool),v)),
file('SWW470+5.p',unknown),
[] ).
cnf(59,axiom,
equal(hAPP(u,v,hAPP(v,fun(u,v),combk(v,u),w),x),ti(v,w)),
file('SWW470+5.p',unknown),
[] ).
cnf(78,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+5.p',unknown),
[] ).
cnf(90,axiom,
hBOOL(hAPP(fun(hoare_509422987triple(u),bool),bool,hAPP(fun(hoare_509422987triple(u),bool),fun(fun(hoare_509422987triple(u),bool),bool),hoare_122391849derivs(u),v),bot_bot(fun(hoare_509422987triple(u),bool)))),
file('SWW470+5.p',unknown),
[] ).
cnf(129,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+5.p',unknown),
[] ).
cnf(170,axiom,
( ~ hBOOL(hAPP(fun(hoare_509422987triple(u),bool),bool,hAPP(fun(hoare_509422987triple(u),bool),fun(fun(hoare_509422987triple(u),bool),bool),hoare_122391849derivs(u),v),w))
| ~ hBOOL(hAPP(fun(hoare_509422987triple(u),bool),bool,hAPP(fun(hoare_509422987triple(u),bool),fun(fun(hoare_509422987triple(u),bool),bool),hoare_122391849derivs(u),x),v))
| hBOOL(hAPP(fun(hoare_509422987triple(u),bool),bool,hAPP(fun(hoare_509422987triple(u),bool),fun(fun(hoare_509422987triple(u),bool),bool),hoare_122391849derivs(u),x),w)) ),
file('SWW470+5.p',unknown),
[] ).
cnf(172,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),skf99(v,u)),bot_bot(fun(u,bool)))))
| ~ hBOOL(hAPP(fun(u,bool),bool,finite_finite_1(u),w))
| hBOOL(hAPP(fun(u,bool),bool,finite_finite_1(u),skf100(v,u)))
| hBOOL(hAPP(fun(u,bool),bool,v,w))
| equal(ti(fun(u,bool),w),bot_bot(fun(u,bool))) ),
file('SWW470+5.p',unknown),
[] ).
cnf(186,axiom,
hBOOL(hAPP(fun(hoare_509422987triple(u),bool),bool,hAPP(fun(hoare_509422987triple(u),bool),fun(fun(hoare_509422987triple(u),bool),bool),hoare_122391849derivs(u),v),hAPP(fun(hoare_509422987triple(u),bool),fun(hoare_509422987triple(u),bool),hAPP(hoare_509422987triple(u),fun(fun(hoare_509422987triple(u),bool),fun(hoare_509422987triple(u),bool)),insert(hoare_509422987triple(u)),hAPP(fun(u,fun(state,bool)),hoare_509422987triple(u),hAPP(com,fun(fun(u,fun(state,bool)),hoare_509422987triple(u)),hAPP(fun(u,fun(state,bool)),fun(com,fun(fun(u,fun(state,bool)),hoare_509422987triple(u))),hoare_1008221573triple(u),w),skip),w)),bot_bot(fun(hoare_509422987triple(u),bool))))),
file('SWW470+5.p',unknown),
[] ).
cnf(208,axiom,
( hBOOL(hAPP(state,bool,hAPP(u,fun(state,bool),v,skf77(v,u,w,x,y)),skf76(v,u,w,x,y)))
| hBOOL(hAPP(fun(hoare_509422987triple(u),bool),bool,hAPP(fun(hoare_509422987triple(u),bool),fun(fun(hoare_509422987triple(u),bool),bool),hoare_122391849derivs(u),z),hAPP(fun(hoare_509422987triple(u),bool),fun(hoare_509422987triple(u),bool),hAPP(hoare_509422987triple(u),fun(fun(hoare_509422987triple(u),bool),fun(hoare_509422987triple(u),bool)),insert(hoare_509422987triple(u)),hAPP(fun(u,fun(state,bool)),hoare_509422987triple(u),hAPP(com,fun(fun(u,fun(state,bool)),hoare_509422987triple(u)),hAPP(fun(u,fun(state,bool)),fun(com,fun(fun(u,fun(state,bool)),hoare_509422987triple(u))),hoare_1008221573triple(u),v),x1),x2)),bot_bot(fun(hoare_509422987triple(u),bool))))) ),
file('SWW470+5.p',unknown),
[] ).
cnf(209,axiom,
( hBOOL(hAPP(state,bool,hAPP(u,fun(state,bool),v,skf49(v,u,w,x,y)),skf48(v,u,w,x,y)))
| hBOOL(hAPP(fun(hoare_509422987triple(u),bool),bool,hAPP(fun(hoare_509422987triple(u),bool),fun(fun(hoare_509422987triple(u),bool),bool),hoare_122391849derivs(u),z),hAPP(fun(hoare_509422987triple(u),bool),fun(hoare_509422987triple(u),bool),hAPP(hoare_509422987triple(u),fun(fun(hoare_509422987triple(u),bool),fun(hoare_509422987triple(u),bool)),insert(hoare_509422987triple(u)),hAPP(fun(u,fun(state,bool)),hoare_509422987triple(u),hAPP(com,fun(fun(u,fun(state,bool)),hoare_509422987triple(u)),hAPP(fun(u,fun(state,bool)),fun(com,fun(fun(u,fun(state,bool)),hoare_509422987triple(u))),hoare_1008221573triple(u),v),x1),x2)),bot_bot(fun(hoare_509422987triple(u),bool))))) ),
file('SWW470+5.p',unknown),
[] ).
cnf(234,axiom,
~ hBOOL(hAPP(fun(hoare_509422987triple(x_a),bool),bool,hAPP(fun(hoare_509422987triple(x_a),bool),fun(fun(hoare_509422987triple(x_a),bool),bool),hoare_122391849derivs(x_a),g),hAPP(fun(hoare_509422987triple(x_a),bool),fun(hoare_509422987triple(x_a),bool),hAPP(hoare_509422987triple(x_a),fun(fun(hoare_509422987triple(x_a),bool),fun(hoare_509422987triple(x_a),bool)),insert(hoare_509422987triple(x_a)),hAPP(fun(x_a,fun(state,bool)),hoare_509422987triple(x_a),hAPP(com,fun(fun(x_a,fun(state,bool)),hoare_509422987triple(x_a)),hAPP(fun(x_a,fun(state,bool)),fun(com,fun(fun(x_a,fun(state,bool)),hoare_509422987triple(x_a))),hoare_1008221573triple(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_509422987triple(x_a),bool))))),
file('SWW470+5.p',unknown),
[] ).
cnf(236,plain,
equal(hAPP(bool,fun(u,bool),combk(bool,u),fFalse),bot_bot(fun(u,bool))),
inference(rew,[status(thm),theory(equality)],[39,78,55]),
[iquote('0:Rew:39.0,78.0,55.0,78.0')] ).
cnf(241,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)],[39,129,55]),
[iquote('0:Rew:39.0,129.0,55.0,129.0')] ).
cnf(254,plain,
( ~ hBOOL(hAPP(fun(u,bool),bool,v,hAPP(u,fun(u,bool),fequal(u),skf99(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,finite_finite_1(u),skf100(v,u)))
| equal(ti(fun(u,bool),w),bot_bot(fun(u,bool))) ),
inference(rew,[status(thm),theory(equality)],[241,172]),
[iquote('0:Rew:241.0,172.0')] ).
cnf(257,plain,
hBOOL(hAPP(fun(hoare_509422987triple(u),bool),bool,hAPP(fun(hoare_509422987triple(u),bool),fun(fun(hoare_509422987triple(u),bool),bool),hoare_122391849derivs(u),v),hAPP(hoare_509422987triple(u),fun(hoare_509422987triple(u),bool),fequal(hoare_509422987triple(u)),hAPP(fun(u,fun(state,bool)),hoare_509422987triple(u),hAPP(com,fun(fun(u,fun(state,bool)),hoare_509422987triple(u)),hAPP(fun(u,fun(state,bool)),fun(com,fun(fun(u,fun(state,bool)),hoare_509422987triple(u))),hoare_1008221573triple(u),w),skip),w)))),
inference(rew,[status(thm),theory(equality)],[241,186]),
[iquote('0:Rew:241.0,186.0')] ).
cnf(271,plain,
( hBOOL(hAPP(state,bool,hAPP(u,fun(state,bool),v,skf77(v,u,w,x,y)),skf76(v,u,w,x,y)))
| hBOOL(hAPP(fun(hoare_509422987triple(u),bool),bool,hAPP(fun(hoare_509422987triple(u),bool),fun(fun(hoare_509422987triple(u),bool),bool),hoare_122391849derivs(u),z),hAPP(hoare_509422987triple(u),fun(hoare_509422987triple(u),bool),fequal(hoare_509422987triple(u)),hAPP(fun(u,fun(state,bool)),hoare_509422987triple(u),hAPP(com,fun(fun(u,fun(state,bool)),hoare_509422987triple(u)),hAPP(fun(u,fun(state,bool)),fun(com,fun(fun(u,fun(state,bool)),hoare_509422987triple(u))),hoare_1008221573triple(u),v),x1),x2)))) ),
inference(rew,[status(thm),theory(equality)],[241,208]),
[iquote('0:Rew:241.0,208.1')] ).
cnf(272,plain,
( hBOOL(hAPP(state,bool,hAPP(u,fun(state,bool),v,skf49(v,u,w,x,y)),skf48(v,u,w,x,y)))
| hBOOL(hAPP(fun(hoare_509422987triple(u),bool),bool,hAPP(fun(hoare_509422987triple(u),bool),fun(fun(hoare_509422987triple(u),bool),bool),hoare_122391849derivs(u),z),hAPP(hoare_509422987triple(u),fun(hoare_509422987triple(u),bool),fequal(hoare_509422987triple(u)),hAPP(fun(u,fun(state,bool)),hoare_509422987triple(u),hAPP(com,fun(fun(u,fun(state,bool)),hoare_509422987triple(u)),hAPP(fun(u,fun(state,bool)),fun(com,fun(fun(u,fun(state,bool)),hoare_509422987triple(u))),hoare_1008221573triple(u),v),x1),x2)))) ),
inference(rew,[status(thm),theory(equality)],[241,209]),
[iquote('0:Rew:241.0,209.1')] ).
cnf(294,plain,
~ hBOOL(hAPP(fun(hoare_509422987triple(x_a),bool),bool,hAPP(fun(hoare_509422987triple(x_a),bool),fun(fun(hoare_509422987triple(x_a),bool),bool),hoare_122391849derivs(x_a),g),hAPP(hoare_509422987triple(x_a),fun(hoare_509422987triple(x_a),bool),fequal(hoare_509422987triple(x_a)),hAPP(fun(x_a,fun(state,bool)),hoare_509422987triple(x_a),hAPP(com,fun(fun(x_a,fun(state,bool)),hoare_509422987triple(x_a)),hAPP(fun(x_a,fun(state,bool)),fun(com,fun(fun(x_a,fun(state,bool)),hoare_509422987triple(x_a))),hoare_1008221573triple(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)],[241,234,236]),
[iquote('0:Rew:241.0,234.0,236.0,234.0')] ).
cnf(304,plain,
( ~ hBOOL(hAPP(fun(hoare_509422987triple(x_a),bool),bool,hAPP(fun(hoare_509422987triple(x_a),bool),fun(fun(hoare_509422987triple(x_a),bool),bool),hoare_122391849derivs(x_a),g),hAPP(hoare_509422987triple(x_a),fun(hoare_509422987triple(x_a),bool),fequal(hoare_509422987triple(x_a)),skf99(hAPP(fun(hoare_509422987triple(x_a),bool),fun(fun(hoare_509422987triple(x_a),bool),bool),hoare_122391849derivs(x_a),g),hoare_509422987triple(x_a)))))
| ~ hBOOL(hAPP(fun(hoare_509422987triple(x_a),bool),bool,finite_finite_1(hoare_509422987triple(x_a)),hAPP(hoare_509422987triple(x_a),fun(hoare_509422987triple(x_a),bool),fequal(hoare_509422987triple(x_a)),hAPP(fun(x_a,fun(state,bool)),hoare_509422987triple(x_a),hAPP(com,fun(fun(x_a,fun(state,bool)),hoare_509422987triple(x_a)),hAPP(fun(x_a,fun(state,bool)),fun(com,fun(fun(x_a,fun(state,bool)),hoare_509422987triple(x_a))),hoare_1008221573triple(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_509422987triple(x_a),bool),bool,finite_finite_1(hoare_509422987triple(x_a)),skf100(hAPP(fun(hoare_509422987triple(x_a),bool),fun(fun(hoare_509422987triple(x_a),bool),bool),hoare_122391849derivs(x_a),g),hoare_509422987triple(x_a))))
| equal(ti(fun(hoare_509422987triple(x_a),bool),hAPP(hoare_509422987triple(x_a),fun(hoare_509422987triple(x_a),bool),fequal(hoare_509422987triple(x_a)),hAPP(fun(x_a,fun(state,bool)),hoare_509422987triple(x_a),hAPP(com,fun(fun(x_a,fun(state,bool)),hoare_509422987triple(x_a)),hAPP(fun(x_a,fun(state,bool)),fun(com,fun(fun(x_a,fun(state,bool)),hoare_509422987triple(x_a))),hoare_1008221573triple(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_509422987triple(x_a),bool))) ),
inference(res,[status(thm),theory(equality)],[254,294]),
[iquote('0:Res:254.3,294.0')] ).
cnf(309,plain,
( ~ hBOOL(hAPP(fun(hoare_509422987triple(x_a),bool),bool,hAPP(fun(hoare_509422987triple(x_a),bool),fun(fun(hoare_509422987triple(x_a),bool),bool),hoare_122391849derivs(x_a),u),hAPP(hoare_509422987triple(x_a),fun(hoare_509422987triple(x_a),bool),fequal(hoare_509422987triple(x_a)),hAPP(fun(x_a,fun(state,bool)),hoare_509422987triple(x_a),hAPP(com,fun(fun(x_a,fun(state,bool)),hoare_509422987triple(x_a)),hAPP(fun(x_a,fun(state,bool)),fun(com,fun(fun(x_a,fun(state,bool)),hoare_509422987triple(x_a))),hoare_1008221573triple(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_509422987triple(x_a),bool),bool,hAPP(fun(hoare_509422987triple(x_a),bool),fun(fun(hoare_509422987triple(x_a),bool),bool),hoare_122391849derivs(x_a),g),u)) ),
inference(res,[status(thm),theory(equality)],[170,294]),
[iquote('0:Res:170.2,294.0')] ).
cnf(312,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))),skf49(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)),skf48(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)],[272,294]),
[iquote('0:Res:272.1,294.0')] ).
cnf(313,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))),skf77(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)),skf76(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)],[271,294]),
[iquote('0:Res:271.1,294.0')] ).
cnf(329,plain,
hBOOL(hAPP(state,bool,bot_bot(fun(state,bool)),skf76(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)],[49,313,59]),
[iquote('0:Rew:49.0,313.0,59.0,313.0')] ).
cnf(330,plain,
hBOOL(hAPP(state,bool,bot_bot(fun(state,bool)),skf48(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)],[49,312,59]),
[iquote('0:Rew:49.0,312.0,59.0,312.0')] ).
cnf(337,plain,
( ~ hBOOL(hAPP(fun(hoare_509422987triple(x_a),bool),bool,finite_finite_1(hoare_509422987triple(x_a)),hAPP(hoare_509422987triple(x_a),fun(hoare_509422987triple(x_a),bool),fequal(hoare_509422987triple(x_a)),hAPP(fun(x_a,fun(state,bool)),hoare_509422987triple(x_a),hAPP(com,fun(fun(x_a,fun(state,bool)),hoare_509422987triple(x_a)),hAPP(fun(x_a,fun(state,bool)),fun(com,fun(fun(x_a,fun(state,bool)),hoare_509422987triple(x_a))),hoare_1008221573triple(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_509422987triple(x_a),bool),bool,hAPP(fun(hoare_509422987triple(x_a),bool),fun(fun(hoare_509422987triple(x_a),bool),bool),hoare_122391849derivs(x_a),g),hAPP(hoare_509422987triple(x_a),fun(hoare_509422987triple(x_a),bool),fequal(hoare_509422987triple(x_a)),skf99(hAPP(fun(hoare_509422987triple(x_a),bool),fun(fun(hoare_509422987triple(x_a),bool),bool),hoare_122391849derivs(x_a),g),hoare_509422987triple(x_a)))))
| hBOOL(hAPP(fun(hoare_509422987triple(x_a),bool),bool,finite_finite_1(hoare_509422987triple(x_a)),skf100(hAPP(fun(hoare_509422987triple(x_a),bool),fun(fun(hoare_509422987triple(x_a),bool),bool),hoare_122391849derivs(x_a),g),hoare_509422987triple(x_a))))
| equal(hAPP(hoare_509422987triple(x_a),fun(hoare_509422987triple(x_a),bool),fequal(hoare_509422987triple(x_a)),hAPP(fun(x_a,fun(state,bool)),hoare_509422987triple(x_a),hAPP(com,fun(fun(x_a,fun(state,bool)),hoare_509422987triple(x_a)),hAPP(fun(x_a,fun(state,bool)),fun(com,fun(fun(x_a,fun(state,bool)),hoare_509422987triple(x_a))),hoare_1008221573triple(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_509422987triple(x_a),bool))) ),
inference(rew,[status(thm),theory(equality)],[39,304]),
[iquote('0:Rew:39.0,304.3')] ).
cnf(344,plain,
equal(hAPP(hoare_509422987triple(x_a),fun(hoare_509422987triple(x_a),bool),fequal(hoare_509422987triple(x_a)),hAPP(fun(x_a,fun(state,bool)),hoare_509422987triple(x_a),hAPP(com,fun(fun(x_a,fun(state,bool)),hoare_509422987triple(x_a)),hAPP(fun(x_a,fun(state,bool)),fun(com,fun(fun(x_a,fun(state,bool)),hoare_509422987triple(x_a))),hoare_1008221573triple(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_509422987triple(x_a),bool))),
inference(spt,[spt(split,[position(s1)])],[337]),
[iquote('1:Spt:337.3')] ).
cnf(349,plain,
( ~ hBOOL(hAPP(fun(hoare_509422987triple(x_a),bool),bool,hAPP(fun(hoare_509422987triple(x_a),bool),fun(fun(hoare_509422987triple(x_a),bool),bool),hoare_122391849derivs(x_a),u),bot_bot(fun(hoare_509422987triple(x_a),bool))))
| ~ hBOOL(hAPP(fun(hoare_509422987triple(x_a),bool),bool,hAPP(fun(hoare_509422987triple(x_a),bool),fun(fun(hoare_509422987triple(x_a),bool),bool),hoare_122391849derivs(x_a),g),u)) ),
inference(rew,[status(thm),theory(equality)],[344,309]),
[iquote('1:Rew:344.0,309.0')] ).
cnf(352,plain,
~ hBOOL(hAPP(fun(hoare_509422987triple(x_a),bool),bool,hAPP(fun(hoare_509422987triple(x_a),bool),fun(fun(hoare_509422987triple(x_a),bool),bool),hoare_122391849derivs(x_a),g),u)),
inference(mrr,[status(thm)],[349,90]),
[iquote('1:MRR:349.0,90.0')] ).
cnf(353,plain,
$false,
inference(unc,[status(thm)],[352,257]),
[iquote('1:UnC:352.0,257.0')] ).
cnf(358,plain,
~ equal(hAPP(hoare_509422987triple(x_a),fun(hoare_509422987triple(x_a),bool),fequal(hoare_509422987triple(x_a)),hAPP(fun(x_a,fun(state,bool)),hoare_509422987triple(x_a),hAPP(com,fun(fun(x_a,fun(state,bool)),hoare_509422987triple(x_a)),hAPP(fun(x_a,fun(state,bool)),fun(com,fun(fun(x_a,fun(state,bool)),hoare_509422987triple(x_a))),hoare_1008221573triple(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_509422987triple(x_a),bool))),
inference(spt,[spt(split,[position(sa)])],[353,344]),
[iquote('1:Spt:353.0,337.3,344.0')] ).
cnf(359,plain,
( ~ hBOOL(hAPP(fun(hoare_509422987triple(x_a),bool),bool,finite_finite_1(hoare_509422987triple(x_a)),hAPP(hoare_509422987triple(x_a),fun(hoare_509422987triple(x_a),bool),fequal(hoare_509422987triple(x_a)),hAPP(fun(x_a,fun(state,bool)),hoare_509422987triple(x_a),hAPP(com,fun(fun(x_a,fun(state,bool)),hoare_509422987triple(x_a)),hAPP(fun(x_a,fun(state,bool)),fun(com,fun(fun(x_a,fun(state,bool)),hoare_509422987triple(x_a))),hoare_1008221573triple(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_509422987triple(x_a),bool),bool,hAPP(fun(hoare_509422987triple(x_a),bool),fun(fun(hoare_509422987triple(x_a),bool),bool),hoare_122391849derivs(x_a),g),hAPP(hoare_509422987triple(x_a),fun(hoare_509422987triple(x_a),bool),fequal(hoare_509422987triple(x_a)),skf99(hAPP(fun(hoare_509422987triple(x_a),bool),fun(fun(hoare_509422987triple(x_a),bool),bool),hoare_122391849derivs(x_a),g),hoare_509422987triple(x_a)))))
| hBOOL(hAPP(fun(hoare_509422987triple(x_a),bool),bool,finite_finite_1(hoare_509422987triple(x_a)),skf100(hAPP(fun(hoare_509422987triple(x_a),bool),fun(fun(hoare_509422987triple(x_a),bool),bool),hoare_122391849derivs(x_a),g),hoare_509422987triple(x_a)))) ),
inference(spt,[spt(split,[position(s2)])],[337]),
[iquote('1:Spt:353.0,337.0,337.1,337.2')] ).
cnf(403,plain,
( ~ hBOOL(u)
| equal(ti(bool,u),fFalse)
| hBOOL(fTrue) ),
inference(spr,[status(thm),theory(equality)],[25,11]),
[iquote('0:SpR:25.1,11.1')] ).
cnf(408,plain,
( ~ hBOOL(fTrue)
| equal(ti(bool,u),fFalse)
| hBOOL(u) ),
inference(spl,[status(thm),theory(equality)],[25,10]),
[iquote('0:SpL:25.1,10.0')] ).
cnf(431,plain,
( ~ hBOOL(u)
| equal(ti(bool,u),fFalse) ),
inference(spt,[spt(split,[position(s2s1)])],[403]),
[iquote('2:Spt:403.0,403.1')] ).
cnf(433,plain,
( ~ hBOOL(u)
| hBOOL(fFalse) ),
inference(rew,[status(thm),theory(equality)],[431,11]),
[iquote('2:Rew:431.1,11.1')] ).
cnf(434,plain,
~ hBOOL(u),
inference(mrr,[status(thm)],[433,3]),
[iquote('2:MRR:433.1,3.0')] ).
cnf(435,plain,
$false,
inference(unc,[status(thm)],[434,329]),
[iquote('2:UnC:434.0,329.0')] ).
cnf(436,plain,
hBOOL(fTrue),
inference(spt,[spt(split,[position(s2s2)])],[403]),
[iquote('2:Spt:435.0,403.2')] ).
cnf(437,plain,
( equal(ti(bool,u),fFalse)
| hBOOL(u) ),
inference(mrr,[status(thm)],[408,436]),
[iquote('2:MRR:408.0,436.0')] ).
cnf(497,plain,
( hBOOL(u)
| equal(hAPP(bool,v,w,fFalse),hAPP(bool,v,w,u)) ),
inference(spr,[status(thm),theory(equality)],[437,38]),
[iquote('2:SpR:437.0,38.0')] ).
cnf(529,plain,
( hBOOL(u)
| hBOOL(u)
| hBOOL(hAPP(bool,bool,fNot,fFalse)) ),
inference(spr,[status(thm),theory(equality)],[497,15]),
[iquote('2:SpR:497.1,15.1')] ).
cnf(535,plain,
( hBOOL(u)
| hBOOL(hAPP(bool,bool,fNot,fFalse)) ),
inference(obv,[status(thm),theory(equality)],[529]),
[iquote('2:Obv:529.0')] ).
cnf(536,plain,
hBOOL(hAPP(bool,bool,fNot,fFalse)),
inference(con,[status(thm)],[535]),
[iquote('2:Con:535.0')] ).
cnf(551,plain,
~ hBOOL(fFalse),
inference(res,[status(thm),theory(equality)],[536,24]),
[iquote('2:Res:536.0,24.1')] ).
cnf(1557,plain,
equal(hAPP(u,bool,bot_bot(fun(u,bool)),v),ti(bool,fFalse)),
inference(spr,[status(thm),theory(equality)],[236,59]),
[iquote('0:SpR:236.0,59.0')] ).
cnf(1566,plain,
equal(hAPP(u,bool,bot_bot(fun(u,bool)),v),fFalse),
inference(rew,[status(thm),theory(equality)],[5,1557]),
[iquote('0:Rew:5.0,1557.0')] ).
cnf(1570,plain,
hBOOL(fFalse),
inference(rew,[status(thm),theory(equality)],[1566,330]),
[iquote('0:Rew:1566.0,330.0')] ).
cnf(1572,plain,
$false,
inference(mrr,[status(thm)],[1570,551]),
[iquote('2:MRR:1570.0,551.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.14 % Problem : SWW470+5 : TPTP v8.1.0. Released v5.3.0.
% 0.08/0.15 % Command : run_spass %d %s
% 0.15/0.36 % Computer : n021.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 600
% 0.15/0.36 % DateTime : Sat Jun 4 14:05:18 EDT 2022
% 0.15/0.37 % CPUTime :
% 1.70/1.91
% 1.70/1.91 SPASS V 3.9
% 1.70/1.91 SPASS beiseite: Proof found.
% 1.70/1.91 % SZS status Theorem
% 1.70/1.91 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 1.70/1.91 SPASS derived 977 clauses, backtracked 14 clauses, performed 2 splits and kept 374 clauses.
% 1.70/1.91 SPASS allocated 108328 KBytes.
% 1.70/1.91 SPASS spent 0:00:01.53 on the problem.
% 1.70/1.91 0:00:00.04 for the input.
% 1.70/1.91 0:00:01.05 for the FLOTTER CNF translation.
% 1.70/1.91 0:00:00.01 for inferences.
% 1.70/1.91 0:00:00.01 for the backtracking.
% 1.70/1.91 0:00:00.23 for the reduction.
% 1.70/1.91
% 1.70/1.91
% 1.70/1.91 Here is a proof with depth 4, length 58 :
% 1.70/1.91 % SZS output start Refutation
% See solution above
% 1.70/1.93 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_97_finite__ne__induct fact_33_insertI1 fact_21_ex__in__conv fact_45_hoare__derivs_OSkip fact_62_conseq fact_5_escape conj_0
% 1.70/1.93
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