%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWW470+6 : TPTP v9.3.1. Released v5.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n005.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 01:30:26 PM UTC 2026
% Result : Theorem 5.53s 1.59s
% Output : Refutation 6.48s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 7
% Syntax : Number of formulae : 27 ( 23 unt; 0 def)
% Number of atoms : 43 ( 12 equ)
% Maximal formula atoms : 6 ( 1 avg)
% Number of connectives : 27 ( 11 ~; 7 |; 5 &)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 4 avg)
% Maximal term depth : 14 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 28 ( 28 usr; 11 con; 0-7 aty)
% Number of variables : 69 ( 64 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f53,axiom,
ti(bool,fFalse) = fFalse,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_fFalse_res) ).
fof(f60,axiom,
! [X0,X1,X2,X3] : hAPP(X0,X1,ti(fun(X0,X1),X2),X3) = hAPP(X0,X1,X2,X3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_hAPP_arg1) ).
fof(f120,axiom,
! [X0,X1,X2,X3,X4] :
( ! [X5,X6] :
( hBOOL(hAPP(state,bool,hAPP(X0,fun(state,bool),X4,X5),X6))
=> ? [X7,X8] :
( hBOOL(hAPP(fun(hoare_1656922687triple(X0),bool),bool,hAPP(fun(hoare_1656922687triple(X0),bool),fun(fun(hoare_1656922687triple(X0),bool),bool),hoare_279057269derivs(X0),X2),hAPP(fun(hoare_1656922687triple(X0),bool),fun(hoare_1656922687triple(X0),bool),hAPP(hoare_1656922687triple(X0),fun(fun(hoare_1656922687triple(X0),bool),fun(hoare_1656922687triple(X0),bool)),insert(hoare_1656922687triple(X0)),hAPP(fun(X0,fun(state,bool)),hoare_1656922687triple(X0),hAPP(com,fun(fun(X0,fun(state,bool)),hoare_1656922687triple(X0)),hAPP(fun(X0,fun(state,bool)),fun(com,fun(fun(X0,fun(state,bool)),hoare_1656922687triple(X0))),hoare_246368825triple(X0),X7),X3),X8)),bot_bot(fun(hoare_1656922687triple(X0),bool)))))
& ! [X9] :
( ! [X10] :
( hBOOL(hAPP(state,bool,hAPP(X0,fun(state,bool),X7,X10),X6))
=> hBOOL(hAPP(state,bool,hAPP(X0,fun(state,bool),X8,X10),X9)) )
=> hBOOL(hAPP(state,bool,hAPP(X0,fun(state,bool),X1,X5),X9)) ) ) )
=> hBOOL(hAPP(fun(hoare_1656922687triple(X0),bool),bool,hAPP(fun(hoare_1656922687triple(X0),bool),fun(fun(hoare_1656922687triple(X0),bool),bool),hoare_279057269derivs(X0),X2),hAPP(fun(hoare_1656922687triple(X0),bool),fun(hoare_1656922687triple(X0),bool),hAPP(hoare_1656922687triple(X0),fun(fun(hoare_1656922687triple(X0),bool),fun(hoare_1656922687triple(X0),bool)),insert(hoare_1656922687triple(X0)),hAPP(fun(X0,fun(state,bool)),hoare_1656922687triple(X0),hAPP(com,fun(fun(X0,fun(state,bool)),hoare_1656922687triple(X0)),hAPP(fun(X0,fun(state,bool)),fun(com,fun(fun(X0,fun(state,bool)),hoare_1656922687triple(X0))),hoare_246368825triple(X0),X4),X3),X1)),bot_bot(fun(hoare_1656922687triple(X0),bool))))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_51_conseq) ).
fof(f151,axiom,
! [X0,X1] : hAPP(fun(X0,bool),X0,the(X0),hAPP(X0,fun(X0,bool),hAPP(fun(X0,fun(X0,bool)),fun(X0,fun(X0,bool)),combc(X0,X0,bool),fequal(X0)),X1)) = ti(X0,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_82_the__eq__trivial) ).
fof(f608,axiom,
! [X0,X1,X2,X3] : hAPP(X0,X1,hAPP(X1,fun(X0,X1),combk(X1,X0),X2),X3) = ti(X1,X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBK_1_1_U) ).
fof(f616,axiom,
~ hBOOL(fFalse),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fFalse_1_1_U) ).
fof(f623,conjecture,
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('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
fof(f624,negated_conjecture,
~ 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))))),
inference(negated_conjecture,[status(cth)],[f623]) ).
fof(f625,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(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))))),
inference(flattening,[],[f624]) ).
fof(f639,plain,
! [X0,X1,X2,X3,X4] :
( hBOOL(hAPP(fun(hoare_1656922687triple(X0),bool),bool,hAPP(fun(hoare_1656922687triple(X0),bool),fun(fun(hoare_1656922687triple(X0),bool),bool),hoare_279057269derivs(X0),X2),hAPP(fun(hoare_1656922687triple(X0),bool),fun(hoare_1656922687triple(X0),bool),hAPP(hoare_1656922687triple(X0),fun(fun(hoare_1656922687triple(X0),bool),fun(hoare_1656922687triple(X0),bool)),insert(hoare_1656922687triple(X0)),hAPP(fun(X0,fun(state,bool)),hoare_1656922687triple(X0),hAPP(com,fun(fun(X0,fun(state,bool)),hoare_1656922687triple(X0)),hAPP(fun(X0,fun(state,bool)),fun(com,fun(fun(X0,fun(state,bool)),hoare_1656922687triple(X0))),hoare_246368825triple(X0),X4),X3),X1)),bot_bot(fun(hoare_1656922687triple(X0),bool)))))
| ? [X5,X6] :
( ! [X7,X8] :
( ~ hBOOL(hAPP(fun(hoare_1656922687triple(X0),bool),bool,hAPP(fun(hoare_1656922687triple(X0),bool),fun(fun(hoare_1656922687triple(X0),bool),bool),hoare_279057269derivs(X0),X2),hAPP(fun(hoare_1656922687triple(X0),bool),fun(hoare_1656922687triple(X0),bool),hAPP(hoare_1656922687triple(X0),fun(fun(hoare_1656922687triple(X0),bool),fun(hoare_1656922687triple(X0),bool)),insert(hoare_1656922687triple(X0)),hAPP(fun(X0,fun(state,bool)),hoare_1656922687triple(X0),hAPP(com,fun(fun(X0,fun(state,bool)),hoare_1656922687triple(X0)),hAPP(fun(X0,fun(state,bool)),fun(com,fun(fun(X0,fun(state,bool)),hoare_1656922687triple(X0))),hoare_246368825triple(X0),X7),X3),X8)),bot_bot(fun(hoare_1656922687triple(X0),bool)))))
| ? [X9] :
( ~ hBOOL(hAPP(state,bool,hAPP(X0,fun(state,bool),X1,X5),X9))
& ! [X10] :
( hBOOL(hAPP(state,bool,hAPP(X0,fun(state,bool),X8,X10),X9))
| ~ hBOOL(hAPP(state,bool,hAPP(X0,fun(state,bool),X7,X10),X6)) ) ) )
& hBOOL(hAPP(state,bool,hAPP(X0,fun(state,bool),X4,X5),X6)) ) ),
inference(ennf_transformation,[],[f120]) ).
fof(f668,plain,
! [X0,X1,X2,X3,X4] :
( hBOOL(hAPP(fun(hoare_1656922687triple(X0),bool),bool,hAPP(fun(hoare_1656922687triple(X0),bool),fun(fun(hoare_1656922687triple(X0),bool),bool),hoare_279057269derivs(X0),X2),hAPP(fun(hoare_1656922687triple(X0),bool),fun(hoare_1656922687triple(X0),bool),hAPP(hoare_1656922687triple(X0),fun(fun(hoare_1656922687triple(X0),bool),fun(hoare_1656922687triple(X0),bool)),insert(hoare_1656922687triple(X0)),hAPP(fun(X0,fun(state,bool)),hoare_1656922687triple(X0),hAPP(com,fun(fun(X0,fun(state,bool)),hoare_1656922687triple(X0)),hAPP(fun(X0,fun(state,bool)),fun(com,fun(fun(X0,fun(state,bool)),hoare_1656922687triple(X0))),hoare_246368825triple(X0),X4),X3),X1)),bot_bot(fun(hoare_1656922687triple(X0),bool)))))
| ( ! [X7,X8] :
( ~ hBOOL(hAPP(fun(hoare_1656922687triple(X0),bool),bool,hAPP(fun(hoare_1656922687triple(X0),bool),fun(fun(hoare_1656922687triple(X0),bool),bool),hoare_279057269derivs(X0),X2),hAPP(fun(hoare_1656922687triple(X0),bool),fun(hoare_1656922687triple(X0),bool),hAPP(hoare_1656922687triple(X0),fun(fun(hoare_1656922687triple(X0),bool),fun(hoare_1656922687triple(X0),bool)),insert(hoare_1656922687triple(X0)),hAPP(fun(X0,fun(state,bool)),hoare_1656922687triple(X0),hAPP(com,fun(fun(X0,fun(state,bool)),hoare_1656922687triple(X0)),hAPP(fun(X0,fun(state,bool)),fun(com,fun(fun(X0,fun(state,bool)),hoare_1656922687triple(X0))),hoare_246368825triple(X0),X7),X3),X8)),bot_bot(fun(hoare_1656922687triple(X0),bool)))))
| ( ~ hBOOL(hAPP(state,bool,hAPP(X0,fun(state,bool),X1,sK5(X0,X1,X2,X3,X4)),sK7(X0,X1,X2,X3,X4,X7,X8)))
& ! [X10] :
( hBOOL(hAPP(state,bool,hAPP(X0,fun(state,bool),X8,X10),sK7(X0,X1,X2,X3,X4,X7,X8)))
| ~ hBOOL(hAPP(state,bool,hAPP(X0,fun(state,bool),X7,X10),sK6(X0,X1,X2,X3,X4))) ) ) )
& hBOOL(hAPP(state,bool,hAPP(X0,fun(state,bool),X4,sK5(X0,X1,X2,X3,X4)),sK6(X0,X1,X2,X3,X4))) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5,sK6,sK7]),skolemize(X5,sK5(X0,X1,X2,X3,X4)),skolemize(X6,sK6(X0,X1,X2,X3,X4)),skolemize(X9,sK7(X0,X1,X2,X3,X4,X7,X8))],[f639]) ).
fof(f686,plain,
fFalse = ti(bool,fFalse),
inference(cnf_transformation,[],[f53]) ).
fof(f695,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(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))))),
inference(cnf_transformation,[],[f625]) ).
fof(f700,plain,
! [X2,X3,X0,X1] : hAPP(X0,X1,ti(fun(X0,X1),X2),X3) = hAPP(X0,X1,X2,X3),
inference(cnf_transformation,[],[f60]) ).
fof(f702,plain,
~ hBOOL(fFalse),
inference(cnf_transformation,[],[f616]) ).
fof(f734,plain,
! [X2,X3,X0,X1,X4] :
( hBOOL(hAPP(fun(hoare_1656922687triple(X0),bool),bool,hAPP(fun(hoare_1656922687triple(X0),bool),fun(fun(hoare_1656922687triple(X0),bool),bool),hoare_279057269derivs(X0),X2),hAPP(fun(hoare_1656922687triple(X0),bool),fun(hoare_1656922687triple(X0),bool),hAPP(hoare_1656922687triple(X0),fun(fun(hoare_1656922687triple(X0),bool),fun(hoare_1656922687triple(X0),bool)),insert(hoare_1656922687triple(X0)),hAPP(fun(X0,fun(state,bool)),hoare_1656922687triple(X0),hAPP(com,fun(fun(X0,fun(state,bool)),hoare_1656922687triple(X0)),hAPP(fun(X0,fun(state,bool)),fun(com,fun(fun(X0,fun(state,bool)),hoare_1656922687triple(X0))),hoare_246368825triple(X0),X4),X3),X1)),bot_bot(fun(hoare_1656922687triple(X0),bool)))))
| hBOOL(hAPP(state,bool,hAPP(X0,fun(state,bool),X4,sK5(X0,X1,X2,X3,X4)),sK6(X0,X1,X2,X3,X4))) ),
inference(cnf_transformation,[],[f668]) ).
fof(f792,plain,
! [X0,X1] : ti(X0,X1) = hAPP(fun(X0,bool),X0,the(X0),hAPP(X0,fun(X0,bool),hAPP(fun(X0,fun(X0,bool)),fun(X0,fun(X0,bool)),combc(X0,X0,bool),fequal(X0)),X1)),
inference(cnf_transformation,[],[f151]) ).
fof(f795,plain,
! [X2,X3,X0,X1] : ti(X1,X2) = hAPP(X0,X1,hAPP(X1,fun(X0,X1),combk(X1,X0),X2),X3),
inference(cnf_transformation,[],[f608]) ).
fof(f817,plain,
fFalse = hAPP(fun(bool,bool),bool,the(bool),hAPP(bool,fun(bool,bool),hAPP(fun(bool,fun(bool,bool)),fun(bool,fun(bool,bool)),combc(bool,bool,bool),fequal(bool)),fFalse)),
inference(definition_unfolding,[],[f686,f792]) ).
fof(f830,plain,
! [X2,X3,X0,X1] : hAPP(X0,X1,X2,X3) = hAPP(X0,X1,hAPP(fun(fun(X0,X1),bool),fun(X0,X1),the(fun(X0,X1)),hAPP(fun(X0,X1),fun(fun(X0,X1),bool),hAPP(fun(fun(X0,X1),fun(fun(X0,X1),bool)),fun(fun(X0,X1),fun(fun(X0,X1),bool)),combc(fun(X0,X1),fun(X0,X1),bool),fequal(fun(X0,X1))),X2)),X3),
inference(definition_unfolding,[],[f700,f792]) ).
fof(f843,plain,
! [X2,X3,X0,X1] : hAPP(X0,X1,hAPP(X1,fun(X0,X1),combk(X1,X0),X2),X3) = hAPP(fun(X1,bool),X1,the(X1),hAPP(X1,fun(X1,bool),hAPP(fun(X1,fun(X1,bool)),fun(X1,fun(X1,bool)),combc(X1,X1,bool),fequal(X1)),X2)),
inference(definition_unfolding,[],[f795,f792]) ).
fof(f1274,plain,
! [X2,X3,X0,X1,X4,X5] : hAPP(X1,X2,X3,X5) = hAPP(X1,X2,hAPP(X0,fun(X1,X2),hAPP(fun(X1,X2),fun(X0,fun(X1,X2)),combk(fun(X1,X2),X0),X3),X4),X5),
inference(superposition,[],[f830,f843]) ).
fof(f3040,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),hAPP(bool,fun(state,bool),combk(bool,state),fFalse)),sK5(x_a,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)),g,c,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)))),sK6(x_a,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)),g,c,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))))),
inference(resolution,[],[f734,f695]) ).
fof(f3061,plain,
hBOOL(hAPP(state,bool,hAPP(bool,fun(state,bool),combk(bool,state),fFalse),sK6(x_a,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)),g,c,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))))),
inference(forward_demodulation,[],[f3040,f1274]) ).
fof(f3062,plain,
hBOOL(hAPP(fun(bool,bool),bool,the(bool),hAPP(bool,fun(bool,bool),hAPP(fun(bool,fun(bool,bool)),fun(bool,fun(bool,bool)),combc(bool,bool,bool),fequal(bool)),fFalse))),
inference(forward_demodulation,[],[f3061,f843]) ).
fof(f3063,plain,
hBOOL(fFalse),
inference(forward_demodulation,[],[f3062,f817]) ).
fof(f3064,plain,
$false,
inference(forward_subsumption_resolution,[],[f3063,f702]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWW470+6 : TPTP v9.3.1. Released v5.3.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.19 % Computer : n005.cluster.edu
% 0.07/0.19 % Model : x86_64 x86_64
% 0.07/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.19 % Memory : 8046.5625MB
% 0.07/0.19 % OS : Linux 6.8.0-71-generic
% 0.07/0.19 % CPULimit : 300
% 0.07/0.19 % WCLimit : 300
% 0.07/0.19 % DateTime : Mon Sep 28 14:02:31 UTC 2026
% 0.07/0.19 % CPUTime :
% 0.07/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.22 Running first-order theorem proving
% 0.07/0.22 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 5.53/1.59 % (797034)Detected formulas, will run a generic FOF schedule.
% 5.53/1.59 % (797039)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=full:npcc=on:drc=off:sp=weighted_frequency:spb=goal:fd=preordered:foolp=on:random_seed=932171475:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 5.53/1.59 % (797044)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3564520901:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 5.53/1.59 % (797041)lrs+1010_1_anc=all:sfv=off:to=kbo:ncem=casc2026/models/loop7.pt:sil=128000:npcc=on:prc=on:sos=all:bsr=unit_only:sac=on:random_seed=3999393073:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 5.53/1.59 % (797042)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3977271195:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 5.53/1.59 % (797045)dis-21_1_sil=8000:lcm=predicate:random_seed=1147923936:st=5:avsq=on:i=129:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/129Mi)
% 5.53/1.59 % (797040)lrs+11_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:lma=off:spb=units:urr=ec_only:bce=on:s2agt=64:updr=off:random_seed=1687091657:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 5.53/1.59 % (797043)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=985126479:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 5.53/1.59 % (797042)Instruction limit reached!
% 5.53/1.59 % (797042)------------------------------
% 5.53/1.59 % (797042)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.53/1.59 % (797042)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.53/1.59 % (797042)CaDiCaL version: 2.1.3
% 5.53/1.59 % (797042)Termination reason: Instruction limit
% 5.53/1.59 % (797042)Termination phase: Saturation
% 5.53/1.59 % (797042)Time elapsed: 0.044 s
% 5.53/1.59 % (797042)Peak memory usage: 89 MB
% 5.53/1.59 % (797042)Instructions burned: 111 (million)
% 5.53/1.59 % (797045)Instruction limit reached!
% 5.53/1.59 % (797045)------------------------------
% 5.53/1.59 % (797045)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.53/1.59 % (797045)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.53/1.59 % (797045)CaDiCaL version: 2.1.3
% 5.53/1.59 % (797045)Termination reason: Instruction limit
% 5.53/1.59 % (797045)Termination phase: Property scanning
% 5.53/1.59 % (797045)Time elapsed: 0.049 s
% 5.53/1.59 % (797045)Peak memory usage: 87 MB
% 5.53/1.59 % (797045)Instructions burned: 131 (million)
% 5.53/1.59 % (797044)Instruction limit reached!
% 5.53/1.59 % (797044)------------------------------
% 5.53/1.59 % (797044)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.53/1.59 % (797044)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.53/1.59 % (797044)CaDiCaL version: 2.1.3
% 5.53/1.59 % (797044)Termination reason: Instruction limit
% 5.53/1.59 % (797044)Termination phase: Property scanning
% 5.53/1.59 % (797044)Time elapsed: 0.054 s
% 5.53/1.59 % (797044)Peak memory usage: 87 MB
% 5.53/1.59 % (797044)Instructions burned: 142 (million)
% 5.53/1.59 % (797043)Instruction limit reached!
% 5.53/1.59 % (797043)------------------------------
% 5.53/1.59 % (797043)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.53/1.59 % (797043)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.53/1.59 % (797043)CaDiCaL version: 2.1.3
% 5.53/1.59 % (797043)Termination reason: Instruction limit
% 5.53/1.59 % (797043)Termination phase: Saturation
% 5.53/1.59 % (797043)Time elapsed: 0.058 s
% 5.53/1.59 % (797043)Peak memory usage: 89 MB
% 5.53/1.59 % (797043)Instructions burned: 120 (million)
% 5.53/1.59 % (797053)lrs+10_1_sil=8000:sp=occurrence:random_seed=1199710881:i=285:sd=3:ss=axioms:sgt=8_2996 on theBenchmark for (2996ds/285Mi)
% 5.53/1.59 % (797054)lrs+10_1_sil=32000:urr=on:br=off:random_seed=2479023461:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2996 on theBenchmark for (2996ds/157Mi)
% 5.53/1.59 % (797055)lrs+1011_1_sil=32000:sp=occurrence:random_seed=1972097123:i=325:sd=1:ss=axioms:sgt=32_2996 on theBenchmark for (2996ds/325Mi)
% 5.53/1.59 % (797056)dis+10_5:1_slsqr=1,4:sil=8000:fde=unused:erd=off:urr=full:fd=off:s2agt=8:br=off:slsq=on:random_seed=1439304518:s2a=on:i=248:s2at=1.23:gtg=position_2996 on theBenchmark for (2996ds/248Mi)
% 5.53/1.59 % (797054)Instruction limit reached!
% 5.53/1.59 % (797054)------------------------------
% 5.53/1.59 % (797054)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.53/1.59 % (797054)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.53/1.59 % (797054)CaDiCaL version: 2.1.3
% 5.53/1.59 % (797054)Termination reason: Instruction limit
% 5.53/1.59 % (797054)Termination phase: Saturation
% 5.53/1.59 % (797054)Time elapsed: 0.077 s
% 5.53/1.59 % (797054)Peak memory usage: 90 MB
% 5.53/1.59 % (797054)Instructions burned: 157 (million)
% 5.53/1.59 % (797056)Instruction limit reached!
% 5.53/1.59 % (797056)------------------------------
% 5.53/1.59 % (797056)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.53/1.59 % (797056)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.53/1.59 % (797056)CaDiCaL version: 2.1.3
% 5.53/1.59 % (797056)Termination reason: Instruction limit
% 5.53/1.59 % (797056)Termination phase: Saturation
% 5.53/1.59 % (797056)Time elapsed: 0.117 s
% 5.53/1.59 % (797056)Peak memory usage: 90 MB
% 5.53/1.59 % (797056)Instructions burned: 249 (million)
% 5.53/1.59 % (797053)Instruction limit reached!
% 5.53/1.59 % (797053)------------------------------
% 5.53/1.59 % (797053)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.53/1.59 % (797053)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.53/1.59 % (797053)CaDiCaL version: 2.1.3
% 5.53/1.59 % (797053)Termination reason: Instruction limit
% 5.53/1.59 % (797053)Termination phase: Saturation
% 5.53/1.59 % (797053)Time elapsed: 0.155 s
% 5.53/1.59 % (797053)Peak memory usage: 91 MB
% 5.53/1.59 % (797053)Instructions burned: 285 (million)
% 5.53/1.59 % (797055)First to succeed.
% 5.53/1.59 % (797055)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-797034"
% 5.53/1.59 % (797061)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=938281315:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2994 on theBenchmark for (2994ds/294Mi)
% 5.53/1.59 % (797062)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=303070080:i=2350_2994 on theBenchmark for (2994ds/2350Mi)
% 5.53/1.59 % (797063)dis-1011_32:1_sfv=off:sil=16000:sos=all:erd=off:acc=on:fd=off:flr=on:random_seed=2100290770:cts=off:i=113:fsr=off:ss=included:sgt=4_2994 on theBenchmark for (2994ds/113Mi)
% 5.53/1.59 % (797063)Instruction limit reached!
% 5.53/1.59 % (797063)------------------------------
% 5.53/1.59 % (797063)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.53/1.59 % (797063)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.53/1.59 % (797063)CaDiCaL version: 2.1.3
% 5.53/1.59 % (797063)Termination reason: Instruction limit
% 5.53/1.59 % (797063)Termination phase: Property scanning
% 5.53/1.59 % (797063)Time elapsed: 0.045 s
% 5.53/1.59 % (797063)Peak memory usage: 87 MB
% 5.53/1.59 % (797063)Instructions burned: 115 (million)
% 5.53/1.59 % (797061)Instruction limit reached!
% 5.53/1.59 % (797061)------------------------------
% 5.53/1.59 % (797061)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.53/1.59 % (797061)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.53/1.59 % (797061)CaDiCaL version: 2.1.3
% 5.53/1.59 % (797061)Termination reason: Instruction limit
% 5.53/1.59 % (797061)Termination phase: Saturation
% 5.53/1.59 % (797061)Time elapsed: 0.119 s
% 5.53/1.59 % (797061)Peak memory usage: 91 MB
% 5.53/1.59 % (797061)Instructions burned: 296 (million)
% 5.53/1.59 % (797055)Refutation found. Thanks to Tanya!
% 5.53/1.59 % SZS status Theorem for theBenchmark
% 5.53/1.59 % SZS output start Proof for theBenchmark
% See solution above
% 6.48/1.69 % (797055)------------------------------
% 6.48/1.69 % (797055)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.48/1.69 % (797055)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.48/1.69 % (797055)CaDiCaL version: 2.1.3
% 6.48/1.69 % (797055)Termination reason: Refutation
% 6.48/1.69 % (797055)Time elapsed: 0.199 s
% 6.48/1.69 % (797055)Peak memory usage: 92 MB
% 6.48/1.69 % (797055)Instructions burned: 327 (million)
% 6.48/1.69 % (797055)------------------------------
% 6.48/1.69 % (797055)------------------------------
% 6.48/1.69 % (797034)Success in time 0.929 s
% 6.48/1.69 % Vampire exiting
%------------------------------------------------------------------------------