TSTP Solution File: NUM925+6 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : NUM925+6 : 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 : n005.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 08:43:29 EDT 2024
% Result : Theorem 1.29s 0.58s
% Output : Refutation 1.29s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 12
% Syntax : Number of formulae : 53 ( 39 unt; 0 def)
% Number of atoms : 83 ( 52 equ)
% Maximal formula atoms : 6 ( 1 avg)
% Number of connectives : 59 ( 29 ~; 18 |; 6 &)
% ( 2 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 19 ( 19 usr; 8 con; 0-4 aty)
% Number of variables : 45 ( 45 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f4505,plain,
$false,
inference(resolution,[],[f4493,f2816]) ).
fof(f2816,plain,
! [X1] : ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X1),X1)),
inference(equality_resolution,[],[f2617]) ).
fof(f2617,plain,
! [X0,X1] :
( X0 != X1
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X0),X1)) ),
inference(cnf_transformation,[],[f1819]) ).
fof(f1819,plain,
! [X0,X1] :
( ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X0),X1))
| X0 = X1
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X0),X1)) )
& ( ( X0 != X1
& hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X0),X1)) )
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X0),X1)) ) ),
inference(flattening,[],[f1818]) ).
fof(f1818,plain,
! [X0,X1] :
( ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X0),X1))
| X0 = X1
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X0),X1)) )
& ( ( X0 != X1
& hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X0),X1)) )
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X0),X1)) ) ),
inference(nnf_transformation,[],[f1052]) ).
fof(f1052,plain,
! [X0,X1] :
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X0),X1))
<=> ( X0 != X1
& hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X0),X1)) ) ),
inference(rectify,[],[f300]) ).
fof(f300,axiom,
! [X28,X23] :
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X28),X23))
<=> ( X23 != X28
& hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X28),X23)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_254_zless__le) ).
fof(f4493,plain,
hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),pls)),
inference(backward_demodulation,[],[f3500,f4491]) ).
fof(f4491,plain,
pls = hAPP(int,int,succ,hAPP(nat,int,semiring_1_of_nat(int),n)),
inference(resolution,[],[f4489,f1895]) ).
fof(f1895,plain,
ring_11004092258visors(int),
inference(cnf_transformation,[],[f554]) ).
fof(f554,axiom,
ring_11004092258visors(int),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Oring__1__no__zero__divisors) ).
fof(f4489,plain,
( ~ ring_11004092258visors(int)
| pls = hAPP(int,int,succ,hAPP(nat,int,semiring_1_of_nat(int),n)) ),
inference(forward_demodulation,[],[f4488,f2000]) ).
fof(f2000,plain,
pls = zero_zero(int),
inference(cnf_transformation,[],[f119]) ).
fof(f119,axiom,
pls = zero_zero(int),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_73_Pls__def) ).
fof(f4488,plain,
( zero_zero(int) = hAPP(int,int,succ,hAPP(nat,int,semiring_1_of_nat(int),n))
| ~ ring_11004092258visors(int) ),
inference(forward_demodulation,[],[f4487,f2692]) ).
fof(f2692,plain,
! [X2,X0,X1] : hAPP(X0,X0,X1,X2) = ti(X0,hAPP(X0,X0,X1,X2)),
inference(cnf_transformation,[],[f1085]) ).
fof(f1085,plain,
! [X0,X1,X2] : hAPP(X0,X0,X1,X2) = ti(X0,hAPP(X0,X0,X1,X2)),
inference(rectify,[],[f40]) ).
fof(f40,axiom,
! [X0,X1,X3] : hAPP(X0,X0,X1,X3) = ti(X0,hAPP(X0,X0,X1,X3)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_hAPP_4_res) ).
fof(f4487,plain,
( zero_zero(int) = ti(int,hAPP(int,int,succ,hAPP(nat,int,semiring_1_of_nat(int),n)))
| ~ ring_11004092258visors(int) ),
inference(trivial_inequality_removal,[],[f4486]) ).
fof(f4486,plain,
( pls != pls
| zero_zero(int) = ti(int,hAPP(int,int,succ,hAPP(nat,int,semiring_1_of_nat(int),n)))
| ~ ring_11004092258visors(int) ),
inference(forward_demodulation,[],[f4466,f2000]) ).
fof(f4466,plain,
( pls != zero_zero(int)
| zero_zero(int) = ti(int,hAPP(int,int,succ,hAPP(nat,int,semiring_1_of_nat(int),n)))
| ~ ring_11004092258visors(int) ),
inference(superposition,[],[f2087,f3499]) ).
fof(f3499,plain,
pls = hAPP(nat,int,power_power(int,hAPP(int,int,succ,hAPP(nat,int,semiring_1_of_nat(int),n))),number_number_of(nat,hAPP(int,int,bit0,one_one(int)))),
inference(backward_demodulation,[],[f3042,f3478]) ).
fof(f3478,plain,
! [X0] : hAPP(int,int,succ,X0) = hAPP(int,int,plus_plus(int,one_one(int)),X0),
inference(superposition,[],[f2486,f2061]) ).
fof(f2061,plain,
! [X0] : hAPP(int,int,succ,X0) = hAPP(int,int,plus_plus(int,X0),one_one(int)),
inference(cnf_transformation,[],[f681]) ).
fof(f681,plain,
! [X0] : hAPP(int,int,succ,X0) = hAPP(int,int,plus_plus(int,X0),one_one(int)),
inference(rectify,[],[f366]) ).
fof(f366,axiom,
! [X19] : hAPP(int,int,succ,X19) = hAPP(int,int,plus_plus(int,X19),one_one(int)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_320_succ__def) ).
fof(f2486,plain,
! [X0,X1] : hAPP(int,int,plus_plus(int,X0),X1) = hAPP(int,int,plus_plus(int,X1),X0),
inference(cnf_transformation,[],[f968]) ).
fof(f968,plain,
! [X0,X1] : hAPP(int,int,plus_plus(int,X0),X1) = hAPP(int,int,plus_plus(int,X1),X0),
inference(rectify,[],[f93]) ).
fof(f93,axiom,
! [X15,X7] : hAPP(int,int,plus_plus(int,X15),X7) = hAPP(int,int,plus_plus(int,X7),X15),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_47_zadd__commute) ).
fof(f3042,plain,
pls = hAPP(nat,int,power_power(int,hAPP(int,int,plus_plus(int,one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),n))),number_number_of(nat,hAPP(int,int,bit0,one_one(int)))),
inference(backward_demodulation,[],[f2836,f3018]) ).
fof(f3018,plain,
hAPP(nat,nat,plus_plus(nat,one_one(nat)),one_one(nat)) = number_number_of(nat,hAPP(int,int,bit0,one_one(int))),
inference(backward_demodulation,[],[f2033,f3013]) ).
fof(f3013,plain,
one_one(int) = hAPP(int,int,bit1,pls),
inference(superposition,[],[f2016,f2041]) ).
fof(f2041,plain,
! [X0] : number_number_of(int,X0) = X0,
inference(cnf_transformation,[],[f663]) ).
fof(f663,plain,
! [X0] : number_number_of(int,X0) = X0,
inference(rectify,[],[f165]) ).
fof(f165,axiom,
! [X19] : number_number_of(int,X19) = X19,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_119_number__of__is__id) ).
fof(f2016,plain,
one_one(int) = number_number_of(int,hAPP(int,int,bit1,pls)),
inference(cnf_transformation,[],[f83]) ).
fof(f83,axiom,
one_one(int) = number_number_of(int,hAPP(int,int,bit1,pls)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_37_one__is__num__one) ).
fof(f2033,plain,
number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))) = hAPP(nat,nat,plus_plus(nat,one_one(nat)),one_one(nat)),
inference(cnf_transformation,[],[f75]) ).
fof(f75,axiom,
number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))) = hAPP(nat,nat,plus_plus(nat,one_one(nat)),one_one(nat)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_29_nat__1__add__1) ).
fof(f2836,plain,
pls = hAPP(nat,int,power_power(int,hAPP(int,int,plus_plus(int,one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),n))),hAPP(nat,nat,plus_plus(nat,one_one(nat)),one_one(nat))),
inference(backward_demodulation,[],[f2825,f2033]) ).
fof(f2825,plain,
pls = hAPP(nat,int,power_power(int,hAPP(int,int,plus_plus(int,one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),n))),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),
inference(backward_demodulation,[],[f1884,f2000]) ).
fof(f1884,plain,
zero_zero(int) = hAPP(nat,int,power_power(int,hAPP(int,int,plus_plus(int,one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),n))),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),
inference(cnf_transformation,[],[f662]) ).
fof(f662,plain,
zero_zero(int) = hAPP(nat,int,power_power(int,hAPP(int,int,plus_plus(int,one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),n))),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),
inference(flattening,[],[f661]) ).
fof(f661,negated_conjecture,
~ ( zero_zero(int) != hAPP(nat,int,power_power(int,hAPP(int,int,plus_plus(int,one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),n))),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) ),
inference(negated_conjecture,[],[f660]) ).
fof(f660,conjecture,
zero_zero(int) != hAPP(nat,int,power_power(int,hAPP(int,int,plus_plus(int,one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),n))),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
fof(f2087,plain,
! [X2,X0,X1] :
( zero_zero(X0) != hAPP(nat,X0,power_power(X0,X2),X1)
| zero_zero(X0) = ti(X0,X2)
| ~ ring_11004092258visors(X0) ),
inference(cnf_transformation,[],[f1147]) ).
fof(f1147,plain,
! [X0] :
( ! [X1,X2] :
( zero_zero(X0) != hAPP(nat,X0,power_power(X0,X2),X1)
| zero_zero(X0) = ti(X0,X2) )
| ~ ring_11004092258visors(X0) ),
inference(ennf_transformation,[],[f701]) ).
fof(f701,plain,
! [X0] :
( ring_11004092258visors(X0)
=> ! [X1,X2] :
( zero_zero(X0) != ti(X0,X2)
=> zero_zero(X0) != hAPP(nat,X0,power_power(X0,X2),X1) ) ),
inference(rectify,[],[f210]) ).
fof(f210,axiom,
! [X0] :
( ring_11004092258visors(X0)
=> ! [X14,X30] :
( zero_zero(X0) != ti(X0,X30)
=> zero_zero(X0) != hAPP(nat,X0,power_power(X0,X30),X14) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_164_field__power__not__zero) ).
fof(f3500,plain,
hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),hAPP(int,int,succ,hAPP(nat,int,semiring_1_of_nat(int),n)))),
inference(backward_demodulation,[],[f2840,f3478]) ).
fof(f2840,plain,
hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),hAPP(int,int,plus_plus(int,one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),n)))),
inference(forward_demodulation,[],[f2038,f2000]) ).
fof(f2038,plain,
hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(int,int,plus_plus(int,one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),n)))),
inference(cnf_transformation,[],[f46]) ).
fof(f46,axiom,
hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(int,int,plus_plus(int,one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),n)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0_n1pos) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : NUM925+6 : TPTP v8.1.2. Released v5.3.0.
% 0.03/0.14 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.15/0.35 % Computer : n005.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 300
% 0.15/0.35 % DateTime : Fri May 3 15:10:53 EDT 2024
% 0.15/0.35 % CPUTime :
% 0.15/0.36 % (20485)Running in auto input_syntax mode. Trying TPTP
% 0.21/0.43 % (20489)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.21/0.43 % (20488)WARNING: value z3 for option sas not known
% 0.21/0.43 % (20487)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.21/0.43 % (20486)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.21/0.43 % (20488)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)
% 0.21/0.43 % (20490)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)
% 0.21/0.43 % (20491)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)
% 0.21/0.43 % (20492)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)
% 1.29/0.58 % (20491)First to succeed.
% 1.29/0.58 % (20490)Also succeeded, but the first one will report.
% 1.29/0.58 % (20491)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-20485"
% 1.29/0.58 % (20491)Refutation found. Thanks to Tanya!
% 1.29/0.58 % SZS status Theorem for theBenchmark
% 1.29/0.58 % SZS output start Proof for theBenchmark
% See solution above
% 1.29/0.58 % (20491)------------------------------
% 1.29/0.58 % (20491)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 1.29/0.58 % (20491)Termination reason: Refutation
% 1.29/0.58
% 1.29/0.58 % (20491)Memory used [KB]: 3561
% 1.29/0.58 % (20491)Time elapsed: 0.148 s
% 1.29/0.58 % (20491)Instructions burned: 301 (million)
% 1.29/0.58 % (20485)Success in time 0.207 s
%------------------------------------------------------------------------------