TSTP Solution File: NUN018_5 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : NUN018_5 : TPTP v8.1.2. Released v6.0.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n016.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 08:44:54 EDT 2024
% Result : ContradictoryAxioms 0.14s 0.34s
% Output : Refutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 47
% Syntax : Number of formulae : 80 ( 26 unt; 37 typ; 0 def)
% Number of atoms : 66 ( 42 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 46 ( 23 ~; 17 |; 0 &)
% ( 0 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of types : 4 ( 3 usr)
% Number of type conns : 17 ( 10 >; 7 *; 0 +; 0 <<)
% Number of predicates : 21 ( 19 usr; 1 prp; 0-3 aty)
% Number of functors : 15 ( 15 usr; 7 con; 0-4 aty)
% Number of variables : 41 ( 18 !; 0 ?; 41 :)
% ( 23 !>; 0 ?*; 0 @-; 0 @+)
% Comments :
%------------------------------------------------------------------------------
tff(type_def_5,type,
bool: $tType ).
tff(type_def_6,type,
int: $tType ).
tff(type_def_7,type,
nat: $tType ).
tff(type_def_8,type,
fun: ( $tType * $tType ) > $tType ).
tff(func_def_0,type,
plus_plus:
!>[X0: $tType] : ( ( X0 * X0 ) > X0 ) ).
tff(func_def_1,type,
zero_zero:
!>[X0: $tType] : X0 ).
tff(func_def_2,type,
bit0: int > int ).
tff(func_def_3,type,
bit1: int > int ).
tff(func_def_4,type,
pls: int ).
tff(func_def_5,type,
number_number_of:
!>[X0: $tType] : ( int > X0 ) ).
tff(func_def_6,type,
power_power:
!>[X0: $tType] : ( ( X0 * nat ) > X0 ) ).
tff(func_def_7,type,
aa:
!>[X0: $tType,X1: $tType] : ( ( fun(X0,X1) * X0 ) > X1 ) ).
tff(func_def_8,type,
fFalse: bool ).
tff(func_def_9,type,
fTrue: bool ).
tff(func_def_10,type,
n: nat ).
tff(func_def_11,type,
tn: nat ).
tff(func_def_12,type,
v: int ).
tff(func_def_13,type,
w: int ).
tff(pred_def_1,type,
number:
!>[X0: $tType] : $o ).
tff(pred_def_2,type,
zero:
!>[X0: $tType] : $o ).
tff(pred_def_3,type,
power:
!>[X0: $tType] : $o ).
tff(pred_def_4,type,
number_ring:
!>[X0: $tType] : $o ).
tff(pred_def_5,type,
ring_char_0:
!>[X0: $tType] : $o ).
tff(pred_def_6,type,
mult_zero:
!>[X0: $tType] : $o ).
tff(pred_def_7,type,
semiring_1:
!>[X0: $tType] : $o ).
tff(pred_def_8,type,
zero_neq_one:
!>[X0: $tType] : $o ).
tff(pred_def_9,type,
number_semiring:
!>[X0: $tType] : $o ).
tff(pred_def_10,type,
linordered_idom:
!>[X0: $tType] : $o ).
tff(pred_def_11,type,
no_zero_divisors:
!>[X0: $tType] : $o ).
tff(pred_def_12,type,
linordered_semidom:
!>[X0: $tType] : $o ).
tff(pred_def_13,type,
cancel_semigroup_add:
!>[X0: $tType] : $o ).
tff(pred_def_14,type,
ring_11004092258visors:
!>[X0: $tType] : $o ).
tff(pred_def_15,type,
linord219039673up_add:
!>[X0: $tType] : $o ).
tff(pred_def_16,type,
ordere236663937imp_le:
!>[X0: $tType] : $o ).
tff(pred_def_17,type,
ord_less:
!>[X0: $tType] : ( ( X0 * X0 ) > $o ) ).
tff(pred_def_18,type,
pp: bool > $o ).
tff(pred_def_19,type,
sP0: ( nat * nat * fun(nat,fun(nat,bool)) ) > $o ).
tff(f1013,plain,
$false,
inference(trivial_inequality_removal,[],[f1012]) ).
tff(f1012,plain,
pls != pls,
inference(superposition,[],[f540,f1010]) ).
tff(f1010,plain,
w = pls,
inference(resolution,[],[f1009,f326]) ).
tff(f326,plain,
ring_11004092258visors(int),
inference(cnf_transformation,[],[f100]) ).
tff(f100,axiom,
ring_11004092258visors(int),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Oring__1__no__zero__divisors) ).
tff(f1009,plain,
( ~ ring_11004092258visors(int)
| ( w = pls ) ),
inference(forward_demodulation,[],[f1008,f354]) ).
tff(f354,plain,
zero_zero(int) = pls,
inference(cnf_transformation,[],[f38]) ).
tff(f38,axiom,
zero_zero(int) = pls,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_37_Pls__def) ).
tff(f1008,plain,
( ( w = zero_zero(int) )
| ~ ring_11004092258visors(int) ),
inference(trivial_inequality_removal,[],[f1007]) ).
tff(f1007,plain,
( ( pls != pls )
| ( w = zero_zero(int) )
| ~ ring_11004092258visors(int) ),
inference(forward_demodulation,[],[f1006,f354]) ).
tff(f1006,plain,
( ( zero_zero(int) != pls )
| ( w = zero_zero(int) )
| ~ ring_11004092258visors(int) ),
inference(superposition,[],[f378,f800]) ).
tff(f800,plain,
pls = power_power(int,w,number_number_of(nat,bit0(bit1(pls)))),
inference(superposition,[],[f783,f373]) ).
tff(f373,plain,
! [X0: int] : ( plus_plus(int,pls,X0) = X0 ),
inference(cnf_transformation,[],[f139]) ).
tff(f139,plain,
! [X0: int] : ( plus_plus(int,pls,X0) = X0 ),
inference(rectify,[],[f74]) ).
tff(f74,axiom,
! [X8: int] : ( plus_plus(int,pls,X8) = X8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_73_add__Pls) ).
tff(f783,plain,
pls = plus_plus(int,pls,power_power(int,w,number_number_of(nat,bit0(bit1(pls))))),
inference(backward_demodulation,[],[f570,f782]) ).
tff(f782,plain,
pls = power_power(int,pls,number_number_of(nat,bit0(bit1(pls)))),
inference(forward_demodulation,[],[f780,f354]) ).
tff(f780,plain,
zero_zero(int) = power_power(int,zero_zero(int),number_number_of(nat,bit0(bit1(pls)))),
inference(resolution,[],[f408,f333]) ).
tff(f333,plain,
semiring_1(int),
inference(cnf_transformation,[],[f107]) ).
tff(f107,axiom,
semiring_1(int),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Osemiring__1) ).
tff(f408,plain,
! [X0: $tType] :
( ~ semiring_1(X0)
| ( zero_zero(X0) = power_power(X0,zero_zero(X0),number_number_of(nat,bit0(bit1(pls)))) ) ),
inference(cnf_transformation,[],[f234]) ).
tff(f234,plain,
! [X0: $tType] :
( ( zero_zero(X0) = power_power(X0,zero_zero(X0),number_number_of(nat,bit0(bit1(pls)))) )
| ~ semiring_1(X0) ),
inference(ennf_transformation,[],[f3]) ).
tff(f3,axiom,
! [X0: $tType] :
( semiring_1(X0)
=> ( zero_zero(X0) = power_power(X0,zero_zero(X0),number_number_of(nat,bit0(bit1(pls)))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2_zero__power2) ).
tff(f570,plain,
pls = plus_plus(int,power_power(int,pls,number_number_of(nat,bit0(bit1(pls)))),power_power(int,w,number_number_of(nat,bit0(bit1(pls))))),
inference(backward_demodulation,[],[f544,f569]) ).
tff(f569,plain,
pls = v,
inference(resolution,[],[f547,f352]) ).
tff(f352,plain,
~ ord_less(int,pls,pls),
inference(cnf_transformation,[],[f28]) ).
tff(f28,axiom,
~ ord_less(int,pls,pls),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_27_rel__simps_I2_J) ).
tff(f547,plain,
( ord_less(int,pls,pls)
| ( pls = v ) ),
inference(forward_demodulation,[],[f546,f354]) ).
tff(f546,plain,
( ord_less(int,pls,pls)
| ( zero_zero(int) = v ) ),
inference(forward_demodulation,[],[f545,f354]) ).
tff(f545,plain,
( ord_less(int,zero_zero(int),pls)
| ( zero_zero(int) = v ) ),
inference(forward_demodulation,[],[f363,f544]) ).
tff(f363,plain,
( ord_less(int,zero_zero(int),plus_plus(int,power_power(int,v,number_number_of(nat,bit0(bit1(pls)))),power_power(int,w,number_number_of(nat,bit0(bit1(pls))))))
| ( zero_zero(int) = v ) ),
inference(cnf_transformation,[],[f212]) ).
tff(f212,plain,
( ord_less(int,zero_zero(int),plus_plus(int,power_power(int,v,number_number_of(nat,bit0(bit1(pls)))),power_power(int,w,number_number_of(nat,bit0(bit1(pls))))))
| ( zero_zero(int) = v ) ),
inference(ennf_transformation,[],[f63]) ).
tff(f63,axiom,
( ( zero_zero(int) != v )
=> ord_less(int,zero_zero(int),plus_plus(int,power_power(int,v,number_number_of(nat,bit0(bit1(pls)))),power_power(int,w,number_number_of(nat,bit0(bit1(pls)))))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_62_calculation_I2_J) ).
tff(f544,plain,
pls = plus_plus(int,power_power(int,v,number_number_of(nat,bit0(bit1(pls)))),power_power(int,w,number_number_of(nat,bit0(bit1(pls))))),
inference(forward_demodulation,[],[f362,f354]) ).
tff(f362,plain,
zero_zero(int) = plus_plus(int,power_power(int,v,number_number_of(nat,bit0(bit1(pls)))),power_power(int,w,number_number_of(nat,bit0(bit1(pls))))),
inference(cnf_transformation,[],[f51]) ).
tff(f51,axiom,
zero_zero(int) = plus_plus(int,power_power(int,v,number_number_of(nat,bit0(bit1(pls)))),power_power(int,w,number_number_of(nat,bit0(bit1(pls))))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_50_calculation_I1_J) ).
tff(f378,plain,
! [X0: $tType,X2: X0,X1: nat] :
( ( zero_zero(X0) != power_power(X0,X2,X1) )
| ( zero_zero(X0) = X2 )
| ~ ring_11004092258visors(X0) ),
inference(cnf_transformation,[],[f214]) ).
tff(f214,plain,
! [X0: $tType] :
( ! [X1: nat,X2: X0] :
( ( zero_zero(X0) != power_power(X0,X2,X1) )
| ( zero_zero(X0) = X2 ) )
| ~ ring_11004092258visors(X0) ),
inference(ennf_transformation,[],[f143]) ).
tff(f143,plain,
! [X0: $tType] :
( ring_11004092258visors(X0)
=> ! [X1: nat,X2: X0] :
( ( zero_zero(X0) != X2 )
=> ( zero_zero(X0) != power_power(X0,X2,X1) ) ) ),
inference(rectify,[],[f86]) ).
tff(f86,axiom,
! [X0: $tType] :
( ring_11004092258visors(X0)
=> ! [X17: nat,X15: X0] :
( ( zero_zero(X0) != X15 )
=> ( zero_zero(X0) != power_power(X0,X15,X17) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_85_field__power__not__zero) ).
tff(f540,plain,
w != pls,
inference(backward_demodulation,[],[f351,f354]) ).
tff(f351,plain,
w != zero_zero(int),
inference(cnf_transformation,[],[f1]) ).
tff(f1,axiom,
w != zero_zero(int),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0__096w_A_126_061_A0_096) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.09 % Problem : NUN018_5 : TPTP v8.1.2. Released v6.0.0.
% 0.07/0.10 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.09/0.30 % Computer : n016.cluster.edu
% 0.09/0.30 % Model : x86_64 x86_64
% 0.09/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.30 % Memory : 8042.1875MB
% 0.09/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.30 % CPULimit : 300
% 0.09/0.30 % WCLimit : 300
% 0.09/0.30 % DateTime : Fri May 3 18:52:22 EDT 2024
% 0.09/0.30 % CPUTime :
% 0.09/0.30 % (9320)Running in auto input_syntax mode. Trying TPTP
% 0.14/0.32 % (9323)WARNING: value z3 for option sas not known
% 0.14/0.32 % (9324)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.14/0.32 % (9322)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.14/0.32 % (9327)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)
% 0.14/0.32 % (9323)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)
% 0.14/0.32 % (9321)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.14/0.32 % (9326)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)
% 0.14/0.32 % (9325)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)
% 0.14/0.32 % (9327)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.14/0.32 % Exception at run slice level
% 0.14/0.32 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.14/0.32 % Exception at run slice level
% 0.14/0.32 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.14/0.32 % Exception at run slice level
% 0.14/0.32 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.14/0.34 % (9326)First to succeed.
% 0.14/0.34 % (9329)ott+1_9_av=off:bd=off:bs=on:gsp=on:lcm=predicate:nm=4:sp=weighted_frequency:urr=on_382 on theBenchmark for (382ds/0Mi)
% 0.14/0.34 % (9330)lrs-11_2:5_fsd=off:fde=none:nm=4:nwc=5.0:sims=off:sp=reverse_weighted_frequency:stl=62_367 on theBenchmark for (367ds/0Mi)
% 0.14/0.34 % (9326)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-9320"
% 0.14/0.34 % (9328)fmb+10_1_fmbas=expand:fmbsr=1.1:gsp=on:nm=4_411 on theBenchmark for (411ds/0Mi)
% 0.14/0.34 % (9326)Refutation found. Thanks to Tanya!
% 0.14/0.34 % SZS status ContradictoryAxioms for theBenchmark
% 0.14/0.34 % SZS output start Proof for theBenchmark
% See solution above
% 0.14/0.34 % (9326)------------------------------
% 0.14/0.34 % (9326)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.14/0.34 % (9326)Termination reason: Refutation
% 0.14/0.34
% 0.14/0.34 % (9326)Memory used [KB]: 1127
% 0.14/0.34 % (9326)Time elapsed: 0.021 s
% 0.14/0.34 % (9326)Instructions burned: 38 (million)
% 0.14/0.34 % (9320)Success in time 0.039 s
%------------------------------------------------------------------------------