%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWW470+5 : TPTP v9.3.1. Released v5.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n007.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 01:30:25 PM UTC 2026
% Result : Theorem 4.93s 1.53s
% Output : Refutation 6.20s
% 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(f23,axiom,
ti(bool,fFalse) = fFalse,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_fFalse_res) ).
fof(f30,axiom,
! [X0,X1,X2,X3] : hAPP(X0,X1,ti(fun(X0,X1),X2),X3) = hAPP(X0,X1,X2,X3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_hAPP_arg1) ).
fof(f94,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/sandbox/benchmark/theBenchmark.p',fact_55_the__eq__trivial) ).
fof(f101,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_509422987triple(X0),bool),bool,hAPP(fun(hoare_509422987triple(X0),bool),fun(fun(hoare_509422987triple(X0),bool),bool),hoare_122391849derivs(X0),X2),hAPP(fun(hoare_509422987triple(X0),bool),fun(hoare_509422987triple(X0),bool),hAPP(hoare_509422987triple(X0),fun(fun(hoare_509422987triple(X0),bool),fun(hoare_509422987triple(X0),bool)),insert(hoare_509422987triple(X0)),hAPP(fun(X0,fun(state,bool)),hoare_509422987triple(X0),hAPP(com,fun(fun(X0,fun(state,bool)),hoare_509422987triple(X0)),hAPP(fun(X0,fun(state,bool)),fun(com,fun(fun(X0,fun(state,bool)),hoare_509422987triple(X0))),hoare_1008221573triple(X0),X7),X3),X8)),bot_bot(fun(hoare_509422987triple(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_509422987triple(X0),bool),bool,hAPP(fun(hoare_509422987triple(X0),bool),fun(fun(hoare_509422987triple(X0),bool),bool),hoare_122391849derivs(X0),X2),hAPP(fun(hoare_509422987triple(X0),bool),fun(hoare_509422987triple(X0),bool),hAPP(hoare_509422987triple(X0),fun(fun(hoare_509422987triple(X0),bool),fun(hoare_509422987triple(X0),bool)),insert(hoare_509422987triple(X0)),hAPP(fun(X0,fun(state,bool)),hoare_509422987triple(X0),hAPP(com,fun(fun(X0,fun(state,bool)),hoare_509422987triple(X0)),hAPP(fun(X0,fun(state,bool)),fun(com,fun(fun(X0,fun(state,bool)),hoare_509422987triple(X0))),hoare_1008221573triple(X0),X4),X3),X1)),bot_bot(fun(hoare_509422987triple(X0),bool))))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_62_conseq) ).
fof(f148,axiom,
! [X0,X1,X2,X3] : hAPP(X0,X1,hAPP(X1,fun(X0,X1),combk(X1,X0),X2),X3) = ti(X1,X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBK_1_1_U) ).
fof(f156,axiom,
~ hBOOL(fFalse),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fFalse_1_1_U) ).
fof(f163,conjecture,
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('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
fof(f164,negated_conjecture,
~ 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))))),
inference(negated_conjecture,[status(cth)],[f163]) ).
fof(f165,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(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))))),
inference(flattening,[],[f164]) ).
fof(f172,plain,
! [X0,X1,X2,X3,X4] :
( hBOOL(hAPP(fun(hoare_509422987triple(X0),bool),bool,hAPP(fun(hoare_509422987triple(X0),bool),fun(fun(hoare_509422987triple(X0),bool),bool),hoare_122391849derivs(X0),X2),hAPP(fun(hoare_509422987triple(X0),bool),fun(hoare_509422987triple(X0),bool),hAPP(hoare_509422987triple(X0),fun(fun(hoare_509422987triple(X0),bool),fun(hoare_509422987triple(X0),bool)),insert(hoare_509422987triple(X0)),hAPP(fun(X0,fun(state,bool)),hoare_509422987triple(X0),hAPP(com,fun(fun(X0,fun(state,bool)),hoare_509422987triple(X0)),hAPP(fun(X0,fun(state,bool)),fun(com,fun(fun(X0,fun(state,bool)),hoare_509422987triple(X0))),hoare_1008221573triple(X0),X4),X3),X1)),bot_bot(fun(hoare_509422987triple(X0),bool)))))
| ? [X5,X6] :
( ! [X7,X8] :
( ~ hBOOL(hAPP(fun(hoare_509422987triple(X0),bool),bool,hAPP(fun(hoare_509422987triple(X0),bool),fun(fun(hoare_509422987triple(X0),bool),bool),hoare_122391849derivs(X0),X2),hAPP(fun(hoare_509422987triple(X0),bool),fun(hoare_509422987triple(X0),bool),hAPP(hoare_509422987triple(X0),fun(fun(hoare_509422987triple(X0),bool),fun(hoare_509422987triple(X0),bool)),insert(hoare_509422987triple(X0)),hAPP(fun(X0,fun(state,bool)),hoare_509422987triple(X0),hAPP(com,fun(fun(X0,fun(state,bool)),hoare_509422987triple(X0)),hAPP(fun(X0,fun(state,bool)),fun(com,fun(fun(X0,fun(state,bool)),hoare_509422987triple(X0))),hoare_1008221573triple(X0),X7),X3),X8)),bot_bot(fun(hoare_509422987triple(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,[],[f101]) ).
fof(f190,plain,
! [X0,X1,X2,X3,X4] :
( hBOOL(hAPP(fun(hoare_509422987triple(X0),bool),bool,hAPP(fun(hoare_509422987triple(X0),bool),fun(fun(hoare_509422987triple(X0),bool),bool),hoare_122391849derivs(X0),X2),hAPP(fun(hoare_509422987triple(X0),bool),fun(hoare_509422987triple(X0),bool),hAPP(hoare_509422987triple(X0),fun(fun(hoare_509422987triple(X0),bool),fun(hoare_509422987triple(X0),bool)),insert(hoare_509422987triple(X0)),hAPP(fun(X0,fun(state,bool)),hoare_509422987triple(X0),hAPP(com,fun(fun(X0,fun(state,bool)),hoare_509422987triple(X0)),hAPP(fun(X0,fun(state,bool)),fun(com,fun(fun(X0,fun(state,bool)),hoare_509422987triple(X0))),hoare_1008221573triple(X0),X4),X3),X1)),bot_bot(fun(hoare_509422987triple(X0),bool)))))
| ( ! [X7,X8] :
( ~ hBOOL(hAPP(fun(hoare_509422987triple(X0),bool),bool,hAPP(fun(hoare_509422987triple(X0),bool),fun(fun(hoare_509422987triple(X0),bool),bool),hoare_122391849derivs(X0),X2),hAPP(fun(hoare_509422987triple(X0),bool),fun(hoare_509422987triple(X0),bool),hAPP(hoare_509422987triple(X0),fun(fun(hoare_509422987triple(X0),bool),fun(hoare_509422987triple(X0),bool)),insert(hoare_509422987triple(X0)),hAPP(fun(X0,fun(state,bool)),hoare_509422987triple(X0),hAPP(com,fun(fun(X0,fun(state,bool)),hoare_509422987triple(X0)),hAPP(fun(X0,fun(state,bool)),fun(com,fun(fun(X0,fun(state,bool)),hoare_509422987triple(X0))),hoare_1008221573triple(X0),X7),X3),X8)),bot_bot(fun(hoare_509422987triple(X0),bool)))))
| ( ~ hBOOL(hAPP(state,bool,hAPP(X0,fun(state,bool),X1,sK1(X0,X1,X2,X3,X4)),sK3(X0,X1,X2,X3,X4,X7,X8)))
& ! [X10] :
( hBOOL(hAPP(state,bool,hAPP(X0,fun(state,bool),X8,X10),sK3(X0,X1,X2,X3,X4,X7,X8)))
| ~ hBOOL(hAPP(state,bool,hAPP(X0,fun(state,bool),X7,X10),sK2(X0,X1,X2,X3,X4))) ) ) )
& hBOOL(hAPP(state,bool,hAPP(X0,fun(state,bool),X4,sK1(X0,X1,X2,X3,X4)),sK2(X0,X1,X2,X3,X4))) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2,sK3]),skolemize(X5,sK1(X0,X1,X2,X3,X4)),skolemize(X6,sK2(X0,X1,X2,X3,X4)),skolemize(X9,sK3(X0,X1,X2,X3,X4,X7,X8))],[f172]) ).
fof(f206,plain,
fFalse = ti(bool,fFalse),
inference(cnf_transformation,[],[f23]) ).
fof(f215,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(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))))),
inference(cnf_transformation,[],[f165]) ).
fof(f220,plain,
! [X2,X3,X0,X1] : hAPP(X0,X1,ti(fun(X0,X1),X2),X3) = hAPP(X0,X1,X2,X3),
inference(cnf_transformation,[],[f30]) ).
fof(f222,plain,
~ hBOOL(fFalse),
inference(cnf_transformation,[],[f156]) ).
fof(f240,plain,
! [X2,X3,X0,X1,X4] :
( hBOOL(hAPP(fun(hoare_509422987triple(X0),bool),bool,hAPP(fun(hoare_509422987triple(X0),bool),fun(fun(hoare_509422987triple(X0),bool),bool),hoare_122391849derivs(X0),X2),hAPP(fun(hoare_509422987triple(X0),bool),fun(hoare_509422987triple(X0),bool),hAPP(hoare_509422987triple(X0),fun(fun(hoare_509422987triple(X0),bool),fun(hoare_509422987triple(X0),bool)),insert(hoare_509422987triple(X0)),hAPP(fun(X0,fun(state,bool)),hoare_509422987triple(X0),hAPP(com,fun(fun(X0,fun(state,bool)),hoare_509422987triple(X0)),hAPP(fun(X0,fun(state,bool)),fun(com,fun(fun(X0,fun(state,bool)),hoare_509422987triple(X0))),hoare_1008221573triple(X0),X4),X3),X1)),bot_bot(fun(hoare_509422987triple(X0),bool)))))
| hBOOL(hAPP(state,bool,hAPP(X0,fun(state,bool),X4,sK1(X0,X1,X2,X3,X4)),sK2(X0,X1,X2,X3,X4))) ),
inference(cnf_transformation,[],[f190]) ).
fof(f284,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,[],[f94]) ).
fof(f287,plain,
! [X2,X3,X0,X1] : hAPP(X0,X1,hAPP(X1,fun(X0,X1),combk(X1,X0),X2),X3) = ti(X1,X2),
inference(cnf_transformation,[],[f148]) ).
fof(f306,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,[],[f206,f284]) ).
fof(f319,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,[],[f220,f284]) ).
fof(f331,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,[],[f287,f284]) ).
fof(f595,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,[],[f319,f331]) ).
fof(f1436,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)),sK1(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)))),sK2(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,[],[f240,f215]) ).
fof(f1453,plain,
hBOOL(hAPP(state,bool,hAPP(bool,fun(state,bool),combk(bool,state),fFalse),sK2(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,[],[f1436,f595]) ).
fof(f1454,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,[],[f1453,f331]) ).
fof(f1455,plain,
hBOOL(fFalse),
inference(forward_demodulation,[],[f1454,f306]) ).
fof(f1456,plain,
$false,
inference(forward_subsumption_resolution,[],[f1455,f222]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWW470+5 : TPTP v9.3.1. Released v5.3.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.20 % Computer : n007.cluster.edu
% 0.10/0.20 % Model : x86_64 x86_64
% 0.10/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.20 % Memory : 8046.5625MB
% 0.10/0.20 % OS : Linux 6.8.0-71-generic
% 0.10/0.20 % CPULimit : 300
% 0.10/0.20 % WCLimit : 300
% 0.10/0.20 % DateTime : Mon Sep 28 14:00:40 UTC 2026
% 0.10/0.20 % CPUTime :
% 0.10/0.20 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.25 Running first-order theorem proving
% 0.10/0.25 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 4.93/1.53 % (2400526)Detected formulas, will run a generic FOF schedule.
% 4.93/1.53 % (2400531)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=2773811829:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 4.93/1.53 % (2400536)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1192314206:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 4.93/1.53 % (2400533)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=2785031777:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 4.93/1.53 % (2400535)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=390733841:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 4.93/1.53 % (2400534)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1824086509:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 4.93/1.53 % (2400532)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=4145374380:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 4.93/1.53 % (2400537)dis-21_1_sil=8000:lcm=predicate:random_seed=4125485278: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)
% 4.93/1.53 % (2400534)Instruction limit reached!
% 4.93/1.53 % (2400534)------------------------------
% 4.93/1.53 % (2400534)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.93/1.53 % (2400534)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.93/1.53 % (2400534)CaDiCaL version: 2.1.3
% 4.93/1.53 % (2400534)Termination reason: Instruction limit
% 4.93/1.53 % (2400534)Termination phase: Saturation
% 4.93/1.53 % (2400534)Time elapsed: 0.043 s
% 4.93/1.53 % (2400534)Peak memory usage: 88 MB
% 4.93/1.53 % (2400534)Instructions burned: 112 (million)
% 4.93/1.53 % (2400537)Instruction limit reached!
% 4.93/1.53 % (2400537)------------------------------
% 4.93/1.53 % (2400537)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.93/1.53 % (2400537)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.93/1.53 % (2400537)CaDiCaL version: 2.1.3
% 4.93/1.53 % (2400537)Termination reason: Instruction limit
% 4.93/1.53 % (2400537)Termination phase: Saturation
% 4.93/1.53 % (2400537)Time elapsed: 0.061 s
% 4.93/1.53 % (2400537)Peak memory usage: 89 MB
% 4.93/1.53 % (2400537)Instructions burned: 129 (million)
% 4.93/1.53 % (2400535)Instruction limit reached!
% 4.93/1.53 % (2400535)------------------------------
% 4.93/1.53 % (2400535)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.93/1.53 % (2400535)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.93/1.53 % (2400535)CaDiCaL version: 2.1.3
% 4.93/1.53 % (2400535)Termination reason: Instruction limit
% 4.93/1.53 % (2400535)Termination phase: Saturation
% 4.93/1.53 % (2400535)Time elapsed: 0.066 s
% 4.93/1.53 % (2400535)Peak memory usage: 88 MB
% 4.93/1.53 % (2400535)Instructions burned: 119 (million)
% 4.93/1.53 % (2400536)Instruction limit reached!
% 4.93/1.53 % (2400536)------------------------------
% 4.93/1.53 % (2400536)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.93/1.53 % (2400536)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.93/1.53 % (2400536)CaDiCaL version: 2.1.3
% 4.93/1.53 % (2400536)Termination reason: Instruction limit
% 4.93/1.53 % (2400536)Termination phase: Saturation
% 4.93/1.53 % (2400536)Time elapsed: 0.109 s
% 4.93/1.53 % (2400536)Peak memory usage: 89 MB
% 4.93/1.53 % (2400536)Instructions burned: 139 (million)
% 4.93/1.53 % (2400545)lrs+10_1_sil=8000:sp=occurrence:random_seed=2286968550:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 4.93/1.53 % (2400546)lrs+10_1_sil=32000:urr=on:br=off:random_seed=26934016:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 4.93/1.53 % (2400547)lrs+1011_1_sil=32000:sp=occurrence:random_seed=1202548228:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 4.93/1.53 % (2400548)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=3917143618:s2a=on:i=248:s2at=1.23:gtg=position_2996 on theBenchmark for (2996ds/248Mi)
% 4.93/1.53 % (2400546)Instruction limit reached!
% 4.93/1.53 % (2400546)------------------------------
% 4.93/1.53 % (2400546)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.93/1.53 % (2400546)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.93/1.53 % (2400546)CaDiCaL version: 2.1.3
% 4.93/1.53 % (2400546)Termination reason: Instruction limit
% 4.93/1.53 % (2400546)Termination phase: Saturation
% 4.93/1.53 % (2400546)Time elapsed: 0.083 s
% 4.93/1.53 % (2400546)Peak memory usage: 90 MB
% 4.93/1.53 % (2400546)Instructions burned: 159 (million)
% 4.93/1.53 % (2400547)First to succeed.
% 4.93/1.53 % (2400547)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2400526"
% 4.93/1.53 % (2400545)Instruction limit reached!
% 4.93/1.53 % (2400545)------------------------------
% 4.93/1.53 % (2400545)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.93/1.53 % (2400545)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.93/1.53 % (2400545)CaDiCaL version: 2.1.3
% 4.93/1.53 % (2400545)Termination reason: Instruction limit
% 4.93/1.53 % (2400545)Termination phase: Saturation
% 4.93/1.53 % (2400545)Time elapsed: 0.168 s
% 4.93/1.53 % (2400545)Peak memory usage: 91 MB
% 4.93/1.53 % (2400545)Instructions burned: 287 (million)
% 4.93/1.53 % (2400548)Instruction limit reached!
% 4.93/1.53 % (2400548)------------------------------
% 4.93/1.53 % (2400548)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.93/1.53 % (2400548)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.93/1.53 % (2400548)CaDiCaL version: 2.1.3
% 4.93/1.53 % (2400548)Termination reason: Instruction limit
% 4.93/1.53 % (2400548)Termination phase: Saturation
% 4.93/1.53 % (2400548)Time elapsed: 0.135 s
% 4.93/1.53 % (2400548)Peak memory usage: 91 MB
% 4.93/1.53 % (2400548)Instructions burned: 250 (million)
% 4.93/1.53 % (2400553)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=868433199:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2995 on theBenchmark for (2995ds/294Mi)
% 4.93/1.53 % (2400531)Also succeeded, but the first one will report.
% 4.93/1.53 % (2400554)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=2859529823:i=2350_2994 on theBenchmark for (2994ds/2350Mi)
% 4.93/1.53 % (2400553)Instruction limit reached!
% 4.93/1.53 % (2400553)------------------------------
% 4.93/1.53 % (2400553)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.93/1.53 % (2400553)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.93/1.53 % (2400553)CaDiCaL version: 2.1.3
% 4.93/1.53 % (2400553)Termination reason: Instruction limit
% 4.93/1.53 % (2400553)Termination phase: Saturation
% 4.93/1.53 % (2400553)Time elapsed: 0.109 s
% 4.93/1.53 % (2400553)Peak memory usage: 89 MB
% 4.93/1.53 % (2400553)Instructions burned: 295 (million)
% 4.93/1.53 % (2400555)dis-1011_32:1_sfv=off:sil=16000:sos=all:erd=off:acc=on:fd=off:flr=on:random_seed=3096398439:cts=off:i=113:fsr=off:ss=included:sgt=4_2994 on theBenchmark for (2994ds/113Mi)
% 4.93/1.53 % (2400547)Refutation found. Thanks to Tanya!
% 4.93/1.53 % SZS status Theorem for theBenchmark
% 4.93/1.53 % SZS output start Proof for theBenchmark
% See solution above
% 6.20/1.72 % (2400547)------------------------------
% 6.20/1.72 % (2400547)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.20/1.72 % (2400547)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.20/1.72 % (2400547)CaDiCaL version: 2.1.3
% 6.20/1.72 % (2400547)Termination reason: Refutation
% 6.20/1.72 % (2400547)Time elapsed: 0.110 s
% 6.20/1.72 % (2400547)Peak memory usage: 91 MB
% 6.20/1.72 % (2400547)Instructions burned: 181 (million)
% 6.20/1.72 % (2400547)------------------------------
% 6.20/1.72 % (2400547)------------------------------
% 6.20/1.72 % (2400526)Success in time 0.789 s
% 6.20/1.73 % Vampire exiting
%------------------------------------------------------------------------------