TSTP Solution File: SWW470+5 by Vampire-SAT---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SWW470+5 : TPTP v8.1.2. Released v5.3.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n027.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 : 300s
% DateTime : Sun May 5 11:39:05 EDT 2024
% Result : Theorem 17.11s 2.82s
% Output : Refutation 17.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 23
% Syntax : Number of formulae : 116 ( 51 unt; 0 def)
% Number of atoms : 204 ( 76 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 148 ( 60 ~; 63 |; 8 &)
% ( 4 <=>; 13 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 14 ( 2 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 30 ( 30 usr; 12 con; 0-5 aty)
% Number of variables : 213 ( 206 !; 7 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f63529,plain,
$false,
inference(resolution,[],[f63466,f492]) ).
fof(f492,plain,
~ hBOOL(fFalse),
inference(cnf_transformation,[],[f156]) ).
fof(f156,axiom,
~ hBOOL(fFalse),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fFalse_1_1_U) ).
fof(f63466,plain,
hBOOL(fFalse),
inference(forward_demodulation,[],[f63465,f1919]) ).
fof(f1919,plain,
! [X0,X1] : fFalse = hAPP(X0,bool,bot_bot(fun(X0,bool)),X1),
inference(backward_demodulation,[],[f998,f1917]) ).
fof(f1917,plain,
fFalse = bot_bot(bool),
inference(backward_demodulation,[],[f832,f1912]) ).
fof(f1912,plain,
fFalse = ti(bool,bot_bot(bool)),
inference(resolution,[],[f1901,f1234]) ).
fof(f1234,plain,
! [X0] :
( hBOOL(X0)
| fFalse = ti(bool,X0) ),
inference(resolution,[],[f1228,f492]) ).
fof(f1228,plain,
! [X0] :
( hBOOL(fFalse)
| hBOOL(X0)
| fFalse = ti(bool,X0) ),
inference(superposition,[],[f516,f1216]) ).
fof(f1216,plain,
! [X0] :
( fFalse = hAPP(bool,bool,fNot,X0)
| fFalse = ti(bool,X0) ),
inference(resolution,[],[f906,f990]) ).
fof(f990,plain,
hBOOL(fTrue),
inference(superposition,[],[f505,f987]) ).
fof(f987,plain,
! [X0] : fTrue = hAPP(fun(bool,bool),bool,finite_finite_1(bool),X0),
inference(resolution,[],[f949,f494]) ).
fof(f494,plain,
finite_finite(bool),
inference(cnf_transformation,[],[f141]) ).
fof(f141,axiom,
finite_finite(bool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL_Obool___Finite__Set_Ofinite) ).
fof(f949,plain,
! [X0,X1] :
( ~ finite_finite(X0)
| fTrue = hAPP(fun(X0,bool),bool,finite_finite_1(X0),X1) ),
inference(forward_demodulation,[],[f945,f630]) ).
fof(f630,plain,
! [X2,X3,X0,X1] : hAPP(X1,X0,X2,X3) = ti(X0,hAPP(X1,X0,X2,X3)),
inference(cnf_transformation,[],[f248]) ).
fof(f248,plain,
! [X0,X1,X2,X3] : hAPP(X1,X0,X2,X3) = ti(X0,hAPP(X1,X0,X2,X3)),
inference(rectify,[],[f32]) ).
fof(f32,axiom,
! [X1,X2,X3,X4] : hAPP(X2,X1,X3,X4) = ti(X1,hAPP(X2,X1,X3,X4)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_hAPP_res) ).
fof(f945,plain,
! [X0,X1] :
( fTrue = ti(bool,hAPP(fun(X0,bool),bool,finite_finite_1(X0),X1))
| ~ finite_finite(X0) ),
inference(resolution,[],[f939,f520]) ).
fof(f520,plain,
! [X0,X1] :
( hBOOL(hAPP(fun(X0,bool),bool,finite_finite_1(X0),X1))
| ~ finite_finite(X0) ),
inference(cnf_transformation,[],[f297]) ).
fof(f297,plain,
! [X0] :
( ! [X1] : hBOOL(hAPP(fun(X0,bool),bool,finite_finite_1(X0),X1))
| ~ finite_finite(X0) ),
inference(ennf_transformation,[],[f172]) ).
fof(f172,plain,
! [X0] :
( finite_finite(X0)
=> ! [X1] : hBOOL(hAPP(fun(X0,bool),bool,finite_finite_1(X0),X1)) ),
inference(rectify,[],[f121]) ).
fof(f121,axiom,
! [X0] :
( finite_finite(X0)
=> ! [X27] : hBOOL(hAPP(fun(X0,bool),bool,finite_finite_1(X0),X27)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_82_finite) ).
fof(f939,plain,
! [X0] :
( ~ hBOOL(X0)
| fTrue = ti(bool,X0) ),
inference(resolution,[],[f928,f492]) ).
fof(f928,plain,
! [X0] :
( hBOOL(fFalse)
| fTrue = ti(bool,X0)
| ~ hBOOL(X0) ),
inference(resolution,[],[f923,f491]) ).
fof(f491,plain,
! [X0] :
( hBOOL(ti(bool,X0))
| ~ hBOOL(X0) ),
inference(cnf_transformation,[],[f380]) ).
fof(f380,plain,
! [X0] :
( ( hBOOL(ti(bool,X0))
| ~ hBOOL(X0) )
& ( hBOOL(X0)
| ~ hBOOL(ti(bool,X0)) ) ),
inference(nnf_transformation,[],[f166]) ).
fof(f166,plain,
! [X0] :
( hBOOL(ti(bool,X0))
<=> hBOOL(X0) ),
inference(rectify,[],[f33]) ).
fof(f33,axiom,
! [X3] :
( hBOOL(ti(bool,X3))
<=> hBOOL(X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_hBOOL_arg1) ).
fof(f923,plain,
! [X0] :
( ~ hBOOL(ti(bool,X0))
| hBOOL(fFalse)
| fTrue = ti(bool,X0) ),
inference(superposition,[],[f491,f863]) ).
fof(f863,plain,
! [X0] :
( fFalse = ti(bool,ti(bool,X0))
| fTrue = ti(bool,X0) ),
inference(superposition,[],[f522,f517]) ).
fof(f517,plain,
! [X0] :
( fTrue = ti(bool,X0)
| fFalse = ti(bool,X0) ),
inference(cnf_transformation,[],[f170]) ).
fof(f170,plain,
! [X0] :
( fFalse = ti(bool,X0)
| fTrue = ti(bool,X0) ),
inference(rectify,[],[f157]) ).
fof(f157,axiom,
! [X64] :
( fFalse = ti(bool,X64)
| fTrue = ti(bool,X64) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fFalse_1_1_T) ).
fof(f522,plain,
! [X0,X1] : ti(X0,X1) = ti(X0,ti(X0,X1)),
inference(cnf_transformation,[],[f174]) ).
fof(f174,plain,
! [X0,X1] : ti(X0,X1) = ti(X0,ti(X0,X1)),
inference(rectify,[],[f143]) ).
fof(f143,axiom,
! [X62,X63] : ti(X62,X63) = ti(X62,ti(X62,X63)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_ti_idem) ).
fof(f505,plain,
! [X0] : hBOOL(hAPP(fun(X0,bool),bool,finite_finite_1(X0),bot_bot(fun(X0,bool)))),
inference(cnf_transformation,[],[f112]) ).
fof(f112,axiom,
! [X0] : hBOOL(hAPP(fun(X0,bool),bool,finite_finite_1(X0),bot_bot(fun(X0,bool)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_73_finite_OemptyI) ).
fof(f906,plain,
! [X0] :
( ~ hBOOL(fTrue)
| fFalse = hAPP(bool,bool,fNot,X0)
| fFalse = ti(bool,X0) ),
inference(duplicate_literal_removal,[],[f900]) ).
fof(f900,plain,
! [X0] :
( ~ hBOOL(fTrue)
| fFalse = hAPP(bool,bool,fNot,X0)
| ~ hBOOL(fTrue)
| fFalse = ti(bool,X0) ),
inference(resolution,[],[f874,f858]) ).
fof(f858,plain,
! [X0] :
( hBOOL(X0)
| ~ hBOOL(fTrue)
| fFalse = ti(bool,X0) ),
inference(superposition,[],[f490,f517]) ).
fof(f490,plain,
! [X0] :
( ~ hBOOL(ti(bool,X0))
| hBOOL(X0) ),
inference(cnf_transformation,[],[f380]) ).
fof(f874,plain,
! [X0] :
( ~ hBOOL(fTrue)
| ~ hBOOL(X0)
| fFalse = hAPP(bool,bool,fNot,X0) ),
inference(forward_demodulation,[],[f872,f630]) ).
fof(f872,plain,
! [X0] :
( ~ hBOOL(fTrue)
| fFalse = ti(bool,hAPP(bool,bool,fNot,X0))
| ~ hBOOL(X0) ),
inference(resolution,[],[f858,f518]) ).
fof(f518,plain,
! [X0] :
( ~ hBOOL(hAPP(bool,bool,fNot,X0))
| ~ hBOOL(X0) ),
inference(cnf_transformation,[],[f171]) ).
fof(f171,plain,
! [X0] :
( ~ hBOOL(X0)
| ~ hBOOL(hAPP(bool,bool,fNot,X0)) ),
inference(rectify,[],[f144]) ).
fof(f144,axiom,
! [X64] :
( ~ hBOOL(X64)
| ~ hBOOL(hAPP(bool,bool,fNot,X64)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fNot_1_1_U) ).
fof(f516,plain,
! [X0] :
( hBOOL(hAPP(bool,bool,fNot,X0))
| hBOOL(X0) ),
inference(cnf_transformation,[],[f169]) ).
fof(f169,plain,
! [X0] :
( hBOOL(hAPP(bool,bool,fNot,X0))
| hBOOL(X0) ),
inference(rectify,[],[f145]) ).
fof(f145,axiom,
! [X64] :
( hBOOL(hAPP(bool,bool,fNot,X64))
| hBOOL(X64) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fNot_2_1_U) ).
fof(f1901,plain,
~ hBOOL(bot_bot(bool)),
inference(forward_demodulation,[],[f1900,f998]) ).
fof(f1900,plain,
! [X0,X1] : ~ hBOOL(hAPP(X0,bool,bot_bot(fun(X0,bool)),X1)),
inference(trivial_inequality_removal,[],[f1891]) ).
fof(f1891,plain,
! [X0,X1] :
( bot_bot(fun(X0,bool)) != bot_bot(fun(X0,bool))
| ~ hBOOL(hAPP(X0,bool,bot_bot(fun(X0,bool)),X1)) ),
inference(superposition,[],[f732,f1493]) ).
fof(f1493,plain,
! [X0] : bot_bot(fun(X0,bool)) = ti(fun(X0,bool),bot_bot(fun(X0,bool))),
inference(resolution,[],[f833,f493]) ).
fof(f493,plain,
bot(bool),
inference(cnf_transformation,[],[f142]) ).
fof(f142,axiom,
bot(bool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL_Obool___Orderings_Obot) ).
fof(f833,plain,
! [X0,X1] :
( ~ bot(X1)
| bot_bot(fun(X0,X1)) = ti(fun(X0,X1),bot_bot(fun(X0,X1))) ),
inference(resolution,[],[f519,f548]) ).
fof(f548,plain,
! [X0,X1] :
( bot(fun(X0,X1))
| ~ bot(X1) ),
inference(cnf_transformation,[],[f299]) ).
fof(f299,plain,
! [X0,X1] :
( bot(fun(X0,X1))
| ~ bot(X1) ),
inference(ennf_transformation,[],[f199]) ).
fof(f199,plain,
! [X0,X1] :
( bot(X1)
=> bot(fun(X0,X1)) ),
inference(rectify,[],[f140]) ).
fof(f140,axiom,
! [X60,X61] :
( bot(X61)
=> bot(fun(X60,X61)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun___Orderings_Obot) ).
fof(f519,plain,
! [X0] :
( ~ bot(X0)
| bot_bot(X0) = ti(X0,bot_bot(X0)) ),
inference(cnf_transformation,[],[f296]) ).
fof(f296,plain,
! [X0] :
( bot_bot(X0) = ti(X0,bot_bot(X0))
| ~ bot(X0) ),
inference(ennf_transformation,[],[f19]) ).
fof(f19,axiom,
! [X0] :
( bot(X0)
=> bot_bot(X0) = ti(X0,bot_bot(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_Orderings_Obot__class_Obot_res) ).
fof(f732,plain,
! [X3,X0,X1] :
( bot_bot(fun(X0,bool)) != ti(fun(X0,bool),X1)
| ~ hBOOL(hAPP(X0,bool,X1,X3)) ),
inference(forward_demodulation,[],[f564,f526]) ).
fof(f526,plain,
! [X0,X1] : hAPP(fun(X0,bool),fun(X0,bool),collect(X0),X1) = ti(fun(X0,bool),X1),
inference(cnf_transformation,[],[f178]) ).
fof(f178,plain,
! [X0,X1] : hAPP(fun(X0,bool),fun(X0,bool),collect(X0),X1) = ti(fun(X0,bool),X1),
inference(rectify,[],[f116]) ).
fof(f116,axiom,
! [X0,X15] : hAPP(fun(X0,bool),fun(X0,bool),collect(X0),X15) = ti(fun(X0,bool),X15),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_77_Collect__def) ).
fof(f564,plain,
! [X3,X0,X1] :
( ~ hBOOL(hAPP(X0,bool,X1,X3))
| bot_bot(fun(X0,bool)) != hAPP(fun(X0,bool),fun(X0,bool),collect(X0),X1) ),
inference(cnf_transformation,[],[f398]) ).
fof(f398,plain,
! [X0,X1] :
( ( bot_bot(fun(X0,bool)) = hAPP(fun(X0,bool),fun(X0,bool),collect(X0),X1)
| hBOOL(hAPP(X0,bool,X1,sK9(X0,X1))) )
& ( ! [X3] : ~ hBOOL(hAPP(X0,bool,X1,X3))
| bot_bot(fun(X0,bool)) != hAPP(fun(X0,bool),fun(X0,bool),collect(X0),X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK9])],[f396,f397]) ).
fof(f397,plain,
! [X0,X1] :
( ? [X2] : hBOOL(hAPP(X0,bool,X1,X2))
=> hBOOL(hAPP(X0,bool,X1,sK9(X0,X1))) ),
introduced(choice_axiom,[]) ).
fof(f396,plain,
! [X0,X1] :
( ( bot_bot(fun(X0,bool)) = hAPP(fun(X0,bool),fun(X0,bool),collect(X0),X1)
| ? [X2] : hBOOL(hAPP(X0,bool,X1,X2)) )
& ( ! [X3] : ~ hBOOL(hAPP(X0,bool,X1,X3))
| bot_bot(fun(X0,bool)) != hAPP(fun(X0,bool),fun(X0,bool),collect(X0),X1) ) ),
inference(rectify,[],[f395]) ).
fof(f395,plain,
! [X0,X1] :
( ( bot_bot(fun(X0,bool)) = hAPP(fun(X0,bool),fun(X0,bool),collect(X0),X1)
| ? [X2] : hBOOL(hAPP(X0,bool,X1,X2)) )
& ( ! [X2] : ~ hBOOL(hAPP(X0,bool,X1,X2))
| bot_bot(fun(X0,bool)) != hAPP(fun(X0,bool),fun(X0,bool),collect(X0),X1) ) ),
inference(nnf_transformation,[],[f208]) ).
fof(f208,plain,
! [X0,X1] :
( bot_bot(fun(X0,bool)) = hAPP(fun(X0,bool),fun(X0,bool),collect(X0),X1)
<=> ! [X2] : ~ hBOOL(hAPP(X0,bool,X1,X2)) ),
inference(rectify,[],[f57]) ).
fof(f57,axiom,
! [X0,X15] :
( bot_bot(fun(X0,bool)) = hAPP(fun(X0,bool),fun(X0,bool),collect(X0),X15)
<=> ! [X30] : ~ hBOOL(hAPP(X0,bool,X15,X30)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_18_Collect__empty__eq) ).
fof(f832,plain,
bot_bot(bool) = ti(bool,bot_bot(bool)),
inference(resolution,[],[f519,f493]) ).
fof(f998,plain,
! [X0,X1] : hAPP(X0,bool,bot_bot(fun(X0,bool)),X1) = bot_bot(bool),
inference(resolution,[],[f549,f493]) ).
fof(f549,plain,
! [X2,X0,X1] :
( ~ bot(X1)
| bot_bot(X1) = hAPP(X0,X1,bot_bot(fun(X0,X1)),X2) ),
inference(cnf_transformation,[],[f300]) ).
fof(f300,plain,
! [X0,X1] :
( ! [X2] : bot_bot(X1) = hAPP(X0,X1,bot_bot(fun(X0,X1)),X2)
| ~ bot(X1) ),
inference(ennf_transformation,[],[f200]) ).
fof(f200,plain,
! [X0,X1] :
( bot(X1)
=> ! [X2] : bot_bot(X1) = hAPP(X0,X1,bot_bot(fun(X0,X1)),X2) ),
inference(rectify,[],[f82]) ).
fof(f82,axiom,
! [X1,X0] :
( bot(X0)
=> ! [X31] : bot_bot(X0) = hAPP(X1,X0,bot_bot(fun(X1,X0)),X31) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_43_bot__apply) ).
fof(f63465,plain,
hBOOL(hAPP(state,bool,bot_bot(fun(state,bool)),sK37(x_a,g,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)),hAPP(fun(state,bool),fun(x_a,fun(state,bool)),combk(fun(state,bool),x_a),bot_bot(fun(state,bool)))))),
inference(forward_demodulation,[],[f63464,f632]) ).
fof(f632,plain,
! [X2,X3,X0,X1] : hAPP(X0,X1,X2,X3) = hAPP(X0,X1,ti(fun(X0,X1),X2),X3),
inference(cnf_transformation,[],[f250]) ).
fof(f250,plain,
! [X0,X1,X2,X3] : hAPP(X0,X1,X2,X3) = hAPP(X0,X1,ti(fun(X0,X1),X2),X3),
inference(rectify,[],[f30]) ).
fof(f30,axiom,
! [X2,X1,X3,X4] : hAPP(X2,X1,ti(fun(X2,X1),X3),X4) = hAPP(X2,X1,X3,X4),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_hAPP_arg1) ).
fof(f63464,plain,
hBOOL(hAPP(state,bool,ti(fun(state,bool),bot_bot(fun(state,bool))),sK37(x_a,g,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)),hAPP(fun(state,bool),fun(x_a,fun(state,bool)),combk(fun(state,bool),x_a),bot_bot(fun(state,bool)))))),
inference(forward_demodulation,[],[f63424,f633]) ).
fof(f633,plain,
! [X2,X3,X0,X1] : hAPP(X0,X1,hAPP(X1,fun(X0,X1),combk(X1,X0),X2),X3) = ti(X1,X2),
inference(cnf_transformation,[],[f251]) ).
fof(f251,plain,
! [X0,X1,X2,X3] : hAPP(X0,X1,hAPP(X1,fun(X0,X1),combk(X1,X0),X2),X3) = ti(X1,X2),
inference(rectify,[],[f148]) ).
fof(f148,axiom,
! [X0,X2,X64,X65] : hAPP(X0,X2,hAPP(X2,fun(X0,X2),combk(X2,X0),X64),X65) = ti(X2,X64),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBK_1_1_U) ).
fof(f63424,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))),sK36(x_a,g,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)),hAPP(fun(state,bool),fun(x_a,fun(state,bool)),combk(fun(state,bool),x_a),bot_bot(fun(state,bool))))),sK37(x_a,g,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)),hAPP(fun(state,bool),fun(x_a,fun(state,bool)),combk(fun(state,bool),x_a),bot_bot(fun(state,bool)))))),
inference(resolution,[],[f4548,f794]) ).
fof(f794,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),X1),hAPP(hoare_509422987triple(X0),fun(hoare_509422987triple(X0),bool),fequal(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),X2),X3))))
| hBOOL(hAPP(state,bool,hAPP(X0,fun(state,bool),X4,sK36(X0,X1,X2,X3,X4)),sK37(X0,X1,X2,X3,X4))) ),
inference(forward_demodulation,[],[f678,f759]) ).
fof(f759,plain,
! [X0,X1] : hAPP(X0,fun(X0,bool),fequal(X0),X1) = hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),bot_bot(fun(X0,bool))),
inference(backward_demodulation,[],[f726,f630]) ).
fof(f726,plain,
! [X0,X1] : hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),bot_bot(fun(X0,bool))) = ti(fun(X0,bool),hAPP(X0,fun(X0,bool),fequal(X0),X1)),
inference(forward_demodulation,[],[f536,f526]) ).
fof(f536,plain,
! [X0,X1] : hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),bot_bot(fun(X0,bool))) = hAPP(fun(X0,bool),fun(X0,bool),collect(X0),hAPP(X0,fun(X0,bool),fequal(X0),X1)),
inference(cnf_transformation,[],[f187]) ).
fof(f187,plain,
! [X0,X1] : hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),bot_bot(fun(X0,bool))) = hAPP(fun(X0,bool),fun(X0,bool),collect(X0),hAPP(X0,fun(X0,bool),fequal(X0),X1)),
inference(rectify,[],[f51]) ).
fof(f51,axiom,
! [X0,X25] : hAPP(fun(X0,bool),fun(X0,bool),collect(X0),hAPP(X0,fun(X0,bool),fequal(X0),X25)) = hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X25),bot_bot(fun(X0,bool))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_12_singleton__conv2) ).
fof(f678,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),X1),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),X2),X3)),bot_bot(fun(hoare_509422987triple(X0),bool)))))
| hBOOL(hAPP(state,bool,hAPP(X0,fun(state,bool),X4,sK36(X0,X1,X2,X3,X4)),sK37(X0,X1,X2,X3,X4))) ),
inference(cnf_transformation,[],[f459]) ).
fof(f459,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),X1),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),X2),X3)),bot_bot(fun(hoare_509422987triple(X0),bool)))))
| ( ~ hBOOL(hAPP(fun(hoare_509422987triple(X0),bool),bool,hAPP(fun(hoare_509422987triple(X0),bool),fun(fun(hoare_509422987triple(X0),bool),bool),hoare_122391849derivs(X0),X1),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),hAPP(fun(state,bool),fun(X0,fun(state,bool)),combk(fun(state,bool),X0),hAPP(state,fun(state,bool),hAPP(fun(state,fun(state,bool)),fun(state,fun(state,bool)),combc(state,state,bool),fequal(state)),sK37(X0,X1,X2,X3,X4)))),X2),hAPP(fun(state,bool),fun(X0,fun(state,bool)),combk(fun(state,bool),X0),hAPP(X0,fun(state,bool),X3,sK36(X0,X1,X2,X3,X4))))),bot_bot(fun(hoare_509422987triple(X0),bool)))))
& hBOOL(hAPP(state,bool,hAPP(X0,fun(state,bool),X4,sK36(X0,X1,X2,X3,X4)),sK37(X0,X1,X2,X3,X4))) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK36,sK37])],[f361,f458]) ).
fof(f458,plain,
! [X0,X1,X2,X3,X4] :
( ? [X5,X6] :
( ~ hBOOL(hAPP(fun(hoare_509422987triple(X0),bool),bool,hAPP(fun(hoare_509422987triple(X0),bool),fun(fun(hoare_509422987triple(X0),bool),bool),hoare_122391849derivs(X0),X1),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),hAPP(fun(state,bool),fun(X0,fun(state,bool)),combk(fun(state,bool),X0),hAPP(state,fun(state,bool),hAPP(fun(state,fun(state,bool)),fun(state,fun(state,bool)),combc(state,state,bool),fequal(state)),X6))),X2),hAPP(fun(state,bool),fun(X0,fun(state,bool)),combk(fun(state,bool),X0),hAPP(X0,fun(state,bool),X3,X5)))),bot_bot(fun(hoare_509422987triple(X0),bool)))))
& hBOOL(hAPP(state,bool,hAPP(X0,fun(state,bool),X4,X5),X6)) )
=> ( ~ hBOOL(hAPP(fun(hoare_509422987triple(X0),bool),bool,hAPP(fun(hoare_509422987triple(X0),bool),fun(fun(hoare_509422987triple(X0),bool),bool),hoare_122391849derivs(X0),X1),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),hAPP(fun(state,bool),fun(X0,fun(state,bool)),combk(fun(state,bool),X0),hAPP(state,fun(state,bool),hAPP(fun(state,fun(state,bool)),fun(state,fun(state,bool)),combc(state,state,bool),fequal(state)),sK37(X0,X1,X2,X3,X4)))),X2),hAPP(fun(state,bool),fun(X0,fun(state,bool)),combk(fun(state,bool),X0),hAPP(X0,fun(state,bool),X3,sK36(X0,X1,X2,X3,X4))))),bot_bot(fun(hoare_509422987triple(X0),bool)))))
& hBOOL(hAPP(state,bool,hAPP(X0,fun(state,bool),X4,sK36(X0,X1,X2,X3,X4)),sK37(X0,X1,X2,X3,X4))) ) ),
introduced(choice_axiom,[]) ).
fof(f361,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),X1),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),X2),X3)),bot_bot(fun(hoare_509422987triple(X0),bool)))))
| ? [X5,X6] :
( ~ hBOOL(hAPP(fun(hoare_509422987triple(X0),bool),bool,hAPP(fun(hoare_509422987triple(X0),bool),fun(fun(hoare_509422987triple(X0),bool),bool),hoare_122391849derivs(X0),X1),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),hAPP(fun(state,bool),fun(X0,fun(state,bool)),combk(fun(state,bool),X0),hAPP(state,fun(state,bool),hAPP(fun(state,fun(state,bool)),fun(state,fun(state,bool)),combc(state,state,bool),fequal(state)),X6))),X2),hAPP(fun(state,bool),fun(X0,fun(state,bool)),combk(fun(state,bool),X0),hAPP(X0,fun(state,bool),X3,X5)))),bot_bot(fun(hoare_509422987triple(X0),bool)))))
& hBOOL(hAPP(state,bool,hAPP(X0,fun(state,bool),X4,X5),X6)) ) ),
inference(ennf_transformation,[],[f280]) ).
fof(f280,plain,
! [X0,X1,X2,X3,X4] :
( ! [X5,X6] :
( hBOOL(hAPP(state,bool,hAPP(X0,fun(state,bool),X4,X5),X6))
=> hBOOL(hAPP(fun(hoare_509422987triple(X0),bool),bool,hAPP(fun(hoare_509422987triple(X0),bool),fun(fun(hoare_509422987triple(X0),bool),bool),hoare_122391849derivs(X0),X1),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),hAPP(fun(state,bool),fun(X0,fun(state,bool)),combk(fun(state,bool),X0),hAPP(state,fun(state,bool),hAPP(fun(state,fun(state,bool)),fun(state,fun(state,bool)),combc(state,state,bool),fequal(state)),X6))),X2),hAPP(fun(state,bool),fun(X0,fun(state,bool)),combk(fun(state,bool),X0),hAPP(X0,fun(state,bool),X3,X5)))),bot_bot(fun(hoare_509422987triple(X0),bool))))) )
=> hBOOL(hAPP(fun(hoare_509422987triple(X0),bool),bool,hAPP(fun(hoare_509422987triple(X0),bool),fun(fun(hoare_509422987triple(X0),bool),bool),hoare_122391849derivs(X0),X1),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),X2),X3)),bot_bot(fun(hoare_509422987triple(X0),bool))))) ),
inference(rectify,[],[f44]) ).
fof(f44,axiom,
! [X0,X5,X16,X17,X15] :
( ! [X19,X20] :
( hBOOL(hAPP(state,bool,hAPP(X0,fun(state,bool),X15,X19),X20))
=> hBOOL(hAPP(fun(hoare_509422987triple(X0),bool),bool,hAPP(fun(hoare_509422987triple(X0),bool),fun(fun(hoare_509422987triple(X0),bool),bool),hoare_122391849derivs(X0),X5),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),hAPP(fun(state,bool),fun(X0,fun(state,bool)),combk(fun(state,bool),X0),hAPP(state,fun(state,bool),hAPP(fun(state,fun(state,bool)),fun(state,fun(state,bool)),combc(state,state,bool),fequal(state)),X20))),X16),hAPP(fun(state,bool),fun(X0,fun(state,bool)),combk(fun(state,bool),X0),hAPP(X0,fun(state,bool),X17,X19)))),bot_bot(fun(hoare_509422987triple(X0),bool))))) )
=> hBOOL(hAPP(fun(hoare_509422987triple(X0),bool),bool,hAPP(fun(hoare_509422987triple(X0),bool),fun(fun(hoare_509422987triple(X0),bool),bool),hoare_122391849derivs(X0),X5),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),X15),X16),X17)),bot_bot(fun(hoare_509422987triple(X0),bool))))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5_escape) ).
fof(f4548,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(backward_demodulation,[],[f768,f4525]) ).
fof(f4525,plain,
! [X0] : bot_bot(fun(X0,bool)) = hAPP(bool,fun(X0,bool),combk(bool,X0),fFalse),
inference(resolution,[],[f4445,f492]) ).
fof(f4445,plain,
! [X0,X1] :
( hBOOL(X1)
| bot_bot(fun(X0,bool)) = hAPP(bool,fun(X0,bool),combk(bool,X0),X1) ),
inference(resolution,[],[f2729,f490]) ).
fof(f2729,plain,
! [X0,X1] :
( hBOOL(ti(bool,X1))
| bot_bot(fun(X0,bool)) = hAPP(bool,fun(X0,bool),combk(bool,X0),X1) ),
inference(forward_demodulation,[],[f2716,f630]) ).
fof(f2716,plain,
! [X0,X1] :
( hBOOL(ti(bool,X1))
| bot_bot(fun(X0,bool)) = ti(fun(X0,bool),hAPP(bool,fun(X0,bool),combk(bool,X0),X1)) ),
inference(superposition,[],[f731,f633]) ).
fof(f731,plain,
! [X0,X1] :
( hBOOL(hAPP(X0,bool,X1,sK9(X0,X1)))
| bot_bot(fun(X0,bool)) = ti(fun(X0,bool),X1) ),
inference(forward_demodulation,[],[f565,f526]) ).
fof(f565,plain,
! [X0,X1] :
( bot_bot(fun(X0,bool)) = hAPP(fun(X0,bool),fun(X0,bool),collect(X0),X1)
| hBOOL(hAPP(X0,bool,X1,sK9(X0,X1))) ),
inference(cnf_transformation,[],[f398]) ).
fof(f768,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),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)))))),
inference(backward_demodulation,[],[f727,f630]) ).
fof(f727,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),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),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))))))),
inference(backward_demodulation,[],[f482,f726]) ).
fof(f482,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(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(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,[],[f163]) ).
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) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.14 % Problem : SWW470+5 : TPTP v8.1.2. Released v5.3.0.
% 0.03/0.16 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.13/0.37 % Computer : n027.cluster.edu
% 0.13/0.37 % Model : x86_64 x86_64
% 0.13/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.37 % Memory : 8042.1875MB
% 0.13/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.37 % CPULimit : 300
% 0.13/0.37 % WCLimit : 300
% 0.13/0.37 % DateTime : Fri May 3 19:25:53 EDT 2024
% 0.13/0.37 % CPUTime :
% 0.13/0.37 % (24609)Running in auto input_syntax mode. Trying TPTP
% 0.20/0.41 % (24613)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.20/0.41 % (24612)WARNING: value z3 for option sas not known
% 0.20/0.41 % (24610)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.20/0.41 % (24611)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.20/0.41 % (24612)dis+2_11_add=large:afr=on:amm=off:bd=off:bce=on:fsd=off:fde=none:gs=on:gsaa=full_model:gsem=off:irw=on:msp=off:nm=4:nwc=1.3:sas=z3:sims=off:sac=on:sp=reverse_arity_569 on theBenchmark for (569ds/0Mi)
% 0.20/0.42 % (24614)ott+10_10:1_add=off:afr=on:amm=off:anc=all:bd=off:bs=on:fsr=off:irw=on:lma=on:msp=off:nm=4:nwc=4.0:sac=on:sp=reverse_frequency_531 on theBenchmark for (531ds/0Mi)
% 0.20/0.42 % (24615)ott-10_8_av=off:bd=preordered:bs=on:fsd=off:fsr=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=4:nwc=1.7:sp=frequency_522 on theBenchmark for (522ds/0Mi)
% 0.20/0.42 % (24616)ott+1_64_av=off:bd=off:bce=on:fsd=off:fde=unused:gsp=on:irw=on:lcm=predicate:lma=on:nm=2:nwc=1.1:sims=off:urr=on_497 on theBenchmark for (497ds/0Mi)
% 5.49/1.18 TRYING [1]
% 5.49/1.23 TRYING [2]
% 11.25/1.98 TRYING [1]
% 11.25/2.02 TRYING [2]
% 11.70/2.06 TRYING [3]
% 15.90/2.66 TRYING [3]
% 16.59/2.81 % (24615)First to succeed.
% 17.11/2.82 % (24615)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-24609"
% 17.11/2.82 % (24615)Refutation found. Thanks to Tanya!
% 17.11/2.82 % SZS status Theorem for theBenchmark
% 17.11/2.82 % SZS output start Proof for theBenchmark
% See solution above
% 17.11/2.82 % (24615)------------------------------
% 17.11/2.82 % (24615)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 17.11/2.82 % (24615)Termination reason: Refutation
% 17.11/2.82
% 17.11/2.82 % (24615)Memory used [KB]: 23518
% 17.11/2.82 % (24615)Time elapsed: 2.404 s
% 17.11/2.82 % (24615)Instructions burned: 7848 (million)
% 17.11/2.82 % (24609)Success in time 2.415 s
%------------------------------------------------------------------------------