TSTP Solution File: NUM926_2 by Vampire---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : NUM926_2 : TPTP v8.1.2. Released v5.3.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -t %d %s
% Computer : n014.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 : Thu Aug 31 12:16:54 EDT 2023
% Result : Theorem 0.28s 0.59s
% Output : Refutation 0.28s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 78
% Syntax : Number of formulae : 103 ( 12 unt; 70 typ; 0 def)
% Number of atoms : 66 ( 28 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 60 ( 27 ~; 20 |; 6 &)
% ( 3 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 7 ( 3 avg)
% Number of types : 5 ( 4 usr)
% Number of type conns : 84 ( 46 >; 38 *; 0 +; 0 <<)
% Number of predicates : 24 ( 22 usr; 1 prp; 0-3 aty)
% Number of functors : 44 ( 44 usr; 20 con; 0-3 aty)
% Number of variables : 40 (; 24 !; 16 ?; 40 :)
% Comments :
%------------------------------------------------------------------------------
tff(type_def_5,type,
int: $tType ).
tff(type_def_6,type,
nat: $tType ).
tff(type_def_7,type,
real: $tType ).
tff(type_def_8,type,
product_prod_int_int: $tType ).
tff(func_def_0,type,
minus_minus_int: ( int * int ) > int ).
tff(func_def_1,type,
minus_minus_nat: ( nat * nat ) > nat ).
tff(func_def_2,type,
minus_minus_real: ( real * real ) > real ).
tff(func_def_3,type,
one_one_int: int ).
tff(func_def_4,type,
one_one_nat: nat ).
tff(func_def_5,type,
one_one_real: real ).
tff(func_def_6,type,
plus_plus_int: ( int * int ) > int ).
tff(func_def_7,type,
plus_plus_nat: ( nat * nat ) > nat ).
tff(func_def_8,type,
plus_plus_real: ( real * real ) > real ).
tff(func_def_9,type,
times_times_int: ( int * int ) > int ).
tff(func_def_10,type,
times_times_nat: ( nat * nat ) > nat ).
tff(func_def_11,type,
times_times_real: ( real * real ) > real ).
tff(func_def_12,type,
zero_zero_int: int ).
tff(func_def_13,type,
zero_zero_nat: nat ).
tff(func_def_14,type,
zero_zero_real: real ).
tff(func_def_15,type,
bit0: int > int ).
tff(func_def_16,type,
bit1: int > int ).
tff(func_def_17,type,
min: int ).
tff(func_def_18,type,
pls: int ).
tff(func_def_19,type,
number_number_of_int: int > int ).
tff(func_def_20,type,
number_number_of_nat: int > nat ).
tff(func_def_21,type,
number267125858f_real: int > real ).
tff(func_def_22,type,
power_power_int: ( int * nat ) > int ).
tff(func_def_23,type,
power_power_nat: ( nat * nat ) > nat ).
tff(func_def_24,type,
power_power_real: ( real * nat ) > real ).
tff(func_def_25,type,
product_Pair_int_int: ( int * int ) > product_prod_int_int ).
tff(func_def_26,type,
legendre: ( int * int ) > int ).
tff(func_def_27,type,
twoSqu2107342101sum2sq: product_prod_int_int > int ).
tff(func_def_28,type,
m: int ).
tff(func_def_29,type,
s1: int ).
tff(func_def_30,type,
s: int ).
tff(func_def_31,type,
t: int ).
tff(func_def_32,type,
sK6: int ).
tff(func_def_33,type,
sK7: int ).
tff(func_def_34,type,
sK8: int ).
tff(func_def_35,type,
sK9: int ).
tff(func_def_36,type,
sK10: int ).
tff(func_def_37,type,
sK11: int ).
tff(func_def_38,type,
sK12: int ).
tff(func_def_39,type,
sK13: int > int ).
tff(func_def_40,type,
sK14: ( real * nat ) > real ).
tff(func_def_41,type,
sK15: ( int * int ) > int ).
tff(func_def_42,type,
sK16: ( int * int * int ) > int ).
tff(func_def_43,type,
sK17: int ).
tff(pred_def_1,type,
zcong: ( int * int * int ) > $o ).
tff(pred_def_2,type,
zprime: int > $o ).
tff(pred_def_3,type,
ord_less_int: ( int * int ) > $o ).
tff(pred_def_4,type,
ord_less_nat: ( nat * nat ) > $o ).
tff(pred_def_5,type,
ord_less_real: ( real * real ) > $o ).
tff(pred_def_6,type,
ord_less_eq_int: ( int * int ) > $o ).
tff(pred_def_7,type,
ord_less_eq_nat: ( nat * nat ) > $o ).
tff(pred_def_8,type,
ord_less_eq_real: ( real * real ) > $o ).
tff(pred_def_9,type,
quadRes: ( int * int ) > $o ).
tff(pred_def_10,type,
dvd_dvd_int: ( int * int ) > $o ).
tff(pred_def_11,type,
dvd_dvd_nat: ( nat * nat ) > $o ).
tff(pred_def_12,type,
dvd_dvd_real: ( real * real ) > $o ).
tff(pred_def_13,type,
twoSqu512355103sum2sq: int > $o ).
tff(pred_def_14,type,
sP0: int > $o ).
tff(pred_def_15,type,
sP1: ( int * int ) > $o ).
tff(pred_def_16,type,
sP2: ( int * int ) > $o ).
tff(pred_def_17,type,
sP3: ( int * int ) > $o ).
tff(pred_def_18,type,
sP4: ( int * int ) > $o ).
tff(pred_def_19,type,
sP5: ( int * int ) > $o ).
tff(pred_def_20,type,
sQ18_eqProxy: ( int * int ) > $o ).
tff(pred_def_21,type,
sQ19_eqProxy: ( real * real ) > $o ).
tff(pred_def_22,type,
sQ20_eqProxy: ( nat * nat ) > $o ).
tff(f3680,plain,
$false,
inference(subsumption_resolution,[],[f3553,f3521]) ).
tff(f3521,plain,
~ ord_less_int(one_one_int,t),
inference(resolution,[],[f3518,f3024]) ).
tff(f3024,plain,
( sQ18_eqProxy(plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int),plus_plus_int(power_power_int(sK8,number_number_of_nat(bit0(bit1(pls)))),power_power_int(sK9,number_number_of_nat(bit0(bit1(pls))))))
| ~ ord_less_int(one_one_int,t) ),
inference(equality_proxy_replacement,[],[f1992,f2975]) ).
tff(f2975,plain,
! [X0: int,X1: int] :
( sQ18_eqProxy(X0,X1)
<=> ( X0 = X1 ) ),
introduced(equality_proxy_definition,[new_symbols(naming,[sQ18_eqProxy])]) ).
tff(f1992,plain,
( ( plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int) = plus_plus_int(power_power_int(sK8,number_number_of_nat(bit0(bit1(pls)))),power_power_int(sK9,number_number_of_nat(bit0(bit1(pls))))) )
| ~ ord_less_int(one_one_int,t) ),
inference(cnf_transformation,[],[f1681]) ).
tff(f1681,plain,
( ( plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int) = plus_plus_int(power_power_int(sK8,number_number_of_nat(bit0(bit1(pls)))),power_power_int(sK9,number_number_of_nat(bit0(bit1(pls))))) )
| ~ ord_less_int(one_one_int,t) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK8,sK9])],[f1324,f1680]) ).
tff(f1680,plain,
( ? [X0: int,X1: int] : ( plus_plus_int(power_power_int(X0,number_number_of_nat(bit0(bit1(pls)))),power_power_int(X1,number_number_of_nat(bit0(bit1(pls))))) = plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int) )
=> ( plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int) = plus_plus_int(power_power_int(sK8,number_number_of_nat(bit0(bit1(pls)))),power_power_int(sK9,number_number_of_nat(bit0(bit1(pls))))) ) ),
introduced(choice_axiom,[]) ).
tff(f1324,plain,
( ? [X0: int,X1: int] : ( plus_plus_int(power_power_int(X0,number_number_of_nat(bit0(bit1(pls)))),power_power_int(X1,number_number_of_nat(bit0(bit1(pls))))) = plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int) )
| ~ ord_less_int(one_one_int,t) ),
inference(ennf_transformation,[],[f3]) ).
tff(f3,axiom,
( ord_less_int(one_one_int,t)
=> ? [X0: int,X1: int] : ( plus_plus_int(power_power_int(X0,number_number_of_nat(bit0(bit1(pls)))),power_power_int(X1,number_number_of_nat(bit0(bit1(pls))))) = plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int) ) ),
file('/export/starexec/sandbox2/tmp/tmp.mLEr8YmdMP/Vampire---4.8_23682',fact_2__0961_A_060_At_A_061_061_062_AEX_Ax_Ay_O_Ax_A_094_A2_A_L_Ay_A_094_A2_A_06) ).
tff(f3518,plain,
! [X8: int,X9: int] : ~ sQ18_eqProxy(plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int),plus_plus_int(power_power_int(X8,number_number_of_nat(bit0(bit1(pls)))),power_power_int(X9,number_number_of_nat(bit0(bit1(pls)))))),
inference(resolution,[],[f2976,f3509]) ).
tff(f3509,plain,
! [X0: int,X1: int] :
( sQ18_eqProxy(X1,X0)
| ~ sQ18_eqProxy(X0,X1) ),
inference(equality_proxy_axiom,[],[f2975]) ).
tff(f2976,plain,
! [X0: int,X1: int] : ~ sQ18_eqProxy(plus_plus_int(power_power_int(X0,number_number_of_nat(bit0(bit1(pls)))),power_power_int(X1,number_number_of_nat(bit0(bit1(pls))))),plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int)),
inference(equality_proxy_replacement,[],[f1915,f2975]) ).
tff(f1915,plain,
! [X0: int,X1: int] : ( plus_plus_int(power_power_int(X0,number_number_of_nat(bit0(bit1(pls)))),power_power_int(X1,number_number_of_nat(bit0(bit1(pls))))) != plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int) ),
inference(cnf_transformation,[],[f1322]) ).
tff(f1322,plain,
! [X0: int,X1: int] : ( plus_plus_int(power_power_int(X0,number_number_of_nat(bit0(bit1(pls)))),power_power_int(X1,number_number_of_nat(bit0(bit1(pls))))) != plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int) ),
inference(ennf_transformation,[],[f700]) ).
tff(f700,negated_conjecture,
~ ? [X0: int,X1: int] : ( plus_plus_int(power_power_int(X0,number_number_of_nat(bit0(bit1(pls)))),power_power_int(X1,number_number_of_nat(bit0(bit1(pls))))) = plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int) ),
inference(negated_conjecture,[],[f699]) ).
tff(f699,conjecture,
? [X0: int,X1: int] : ( plus_plus_int(power_power_int(X0,number_number_of_nat(bit0(bit1(pls)))),power_power_int(X1,number_number_of_nat(bit0(bit1(pls))))) = plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int) ),
file('/export/starexec/sandbox2/tmp/tmp.mLEr8YmdMP/Vampire---4.8_23682',conj_0) ).
tff(f3553,plain,
ord_less_int(one_one_int,t),
inference(subsumption_resolution,[],[f3547,f1931]) ).
tff(f1931,plain,
ord_less_eq_int(one_one_int,t),
inference(cnf_transformation,[],[f1]) ).
tff(f1,axiom,
ord_less_eq_int(one_one_int,t),
file('/export/starexec/sandbox2/tmp/tmp.mLEr8YmdMP/Vampire---4.8_23682',fact_0_tpos) ).
tff(f3547,plain,
( ord_less_int(one_one_int,t)
| ~ ord_less_eq_int(one_one_int,t) ),
inference(resolution,[],[f3520,f3274]) ).
tff(f3274,plain,
! [X0: int,X1: int] :
( sQ18_eqProxy(X0,X1)
| ord_less_int(X0,X1)
| ~ ord_less_eq_int(X0,X1) ),
inference(equality_proxy_replacement,[],[f2418,f2975]) ).
tff(f2418,plain,
! [X0: int,X1: int] :
( ord_less_int(X0,X1)
| ( X0 = X1 )
| ~ ord_less_eq_int(X0,X1) ),
inference(cnf_transformation,[],[f1763]) ).
tff(f1763,plain,
! [X0: int,X1: int] :
( ( ord_less_int(X0,X1)
| ( X0 = X1 )
| ~ ord_less_eq_int(X0,X1) )
& ( ( ( X0 != X1 )
& ord_less_eq_int(X0,X1) )
| ~ ord_less_int(X0,X1) ) ),
inference(flattening,[],[f1762]) ).
tff(f1762,plain,
! [X0: int,X1: int] :
( ( ord_less_int(X0,X1)
| ( X0 = X1 )
| ~ ord_less_eq_int(X0,X1) )
& ( ( ( X0 != X1 )
& ord_less_eq_int(X0,X1) )
| ~ ord_less_int(X0,X1) ) ),
inference(nnf_transformation,[],[f1033]) ).
tff(f1033,plain,
! [X0: int,X1: int] :
( ord_less_int(X0,X1)
<=> ( ( X0 != X1 )
& ord_less_eq_int(X0,X1) ) ),
inference(rectify,[],[f38]) ).
tff(f38,axiom,
! [X16: int,X17: int] :
( ord_less_int(X16,X17)
<=> ( ( X16 != X17 )
& ord_less_eq_int(X16,X17) ) ),
file('/export/starexec/sandbox2/tmp/tmp.mLEr8YmdMP/Vampire---4.8_23682',fact_37_zless__le) ).
tff(f3520,plain,
~ sQ18_eqProxy(one_one_int,t),
inference(resolution,[],[f3518,f3023]) ).
tff(f3023,plain,
( sQ18_eqProxy(plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int),plus_plus_int(power_power_int(sK6,number_number_of_nat(bit0(bit1(pls)))),power_power_int(sK7,number_number_of_nat(bit0(bit1(pls))))))
| ~ sQ18_eqProxy(one_one_int,t) ),
inference(equality_proxy_replacement,[],[f1991,f2975,f2975]) ).
tff(f1991,plain,
( ( plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int) = plus_plus_int(power_power_int(sK6,number_number_of_nat(bit0(bit1(pls)))),power_power_int(sK7,number_number_of_nat(bit0(bit1(pls))))) )
| ( one_one_int != t ) ),
inference(cnf_transformation,[],[f1679]) ).
tff(f1679,plain,
( ( plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int) = plus_plus_int(power_power_int(sK6,number_number_of_nat(bit0(bit1(pls)))),power_power_int(sK7,number_number_of_nat(bit0(bit1(pls))))) )
| ( one_one_int != t ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK6,sK7])],[f1323,f1678]) ).
tff(f1678,plain,
( ? [X0: int,X1: int] : ( plus_plus_int(power_power_int(X0,number_number_of_nat(bit0(bit1(pls)))),power_power_int(X1,number_number_of_nat(bit0(bit1(pls))))) = plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int) )
=> ( plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int) = plus_plus_int(power_power_int(sK6,number_number_of_nat(bit0(bit1(pls)))),power_power_int(sK7,number_number_of_nat(bit0(bit1(pls))))) ) ),
introduced(choice_axiom,[]) ).
tff(f1323,plain,
( ? [X0: int,X1: int] : ( plus_plus_int(power_power_int(X0,number_number_of_nat(bit0(bit1(pls)))),power_power_int(X1,number_number_of_nat(bit0(bit1(pls))))) = plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int) )
| ( one_one_int != t ) ),
inference(ennf_transformation,[],[f2]) ).
tff(f2,axiom,
( ( one_one_int = t )
=> ? [X0: int,X1: int] : ( plus_plus_int(power_power_int(X0,number_number_of_nat(bit0(bit1(pls)))),power_power_int(X1,number_number_of_nat(bit0(bit1(pls))))) = plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int) ) ),
file('/export/starexec/sandbox2/tmp/tmp.mLEr8YmdMP/Vampire---4.8_23682',fact_1__096t_A_061_A1_A_061_061_062_AEX_Ax_Ay_O_Ax_A_094_A2_A_L_Ay_A_094_A2_A_06) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.19 % Problem : NUM926_2 : TPTP v8.1.2. Released v5.3.0.
% 0.21/0.21 % Command : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -t %d %s
% 0.21/0.42 % Computer : n014.cluster.edu
% 0.21/0.42 % Model : x86_64 x86_64
% 0.21/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.21/0.42 % Memory : 8042.1875MB
% 0.21/0.42 % OS : Linux 3.10.0-693.el7.x86_64
% 0.21/0.42 % CPULimit : 300
% 0.21/0.42 % WCLimit : 300
% 0.21/0.42 % DateTime : Fri Aug 25 16:31:18 EDT 2023
% 0.21/0.42 % CPUTime :
% 0.21/0.42 This is a TF0_THM_EQU_NAR problem
% 0.21/0.43 Running vampire_casc2023 --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/tmp/tmp.mLEr8YmdMP/Vampire---4.8_23682
% 0.21/0.43 % (23805)Running in auto input_syntax mode. Trying TPTP
% 0.28/0.52 % (23806)lrs-1010_2_av=off:bce=on:cond=on:er=filter:fde=unused:lcm=predicate:nm=2:nwc=3.0:sims=off:sp=frequency:urr=on:stl=188_1064 on Vampire---4 for (1064ds/0Mi)
% 0.28/0.52 % (23809)dis-1010_4:3_afr=on:amm=off:bsr=on:bce=on:drc=off:fsd=off:fde=unused:gs=on:gsaa=from_current:irw=on:nwc=1.3:nicw=on:sas=z3:tgt=full:urr=ec_only_619 on Vampire---4 for (619ds/0Mi)
% 0.28/0.52 % (23810)lrs+1002_9_av=off:bs=on:bsr=on:bce=on:cond=on:drc=off:er=filter:flr=on:fsd=off:fsr=off:fde=unused:lcm=predicate:nm=2:nwc=1.3:sims=off:stl=62_466 on Vampire---4 for (466ds/0Mi)
% 0.28/0.52 % (23808)lrs+1010_4_aac=none:add=off:afr=on:amm=off:anc=all_dependent:bd=off:cond=on:drc=off:flr=on:fde=none:gs=on:lma=on:nm=16:nwc=1.1:sims=off:sos=all:sac=on:sp=occurrence:stl=188_669 on Vampire---4 for (669ds/0Mi)
% 0.28/0.52 % (23811)ott+10_8_br=off:cond=on:fsr=off:gsp=on:nm=16:nwc=3.0:sims=off:sp=reverse_frequency:urr=on_432 on Vampire---4 for (432ds/0Mi)
% 0.28/0.52 % (23807)dis+1010_4:1_anc=none:bd=off:drc=off:flr=on:fsr=off:nm=4:nwc=1.1:nicw=on:sas=z3_957 on Vampire---4 for (957ds/0Mi)
% 0.28/0.56 % (23812)dis+1011_3:2_av=off:ep=RST:fsd=off:fde=none:gsp=on:nm=2:nwc=2.0:sos=on:sp=reverse_frequency_405 on Vampire---4 for (405ds/0Mi)
% 0.28/0.59 % (23812)First to succeed.
% 0.28/0.59 % (23812)Refutation found. Thanks to Tanya!
% 0.28/0.59 % SZS status Theorem for Vampire---4
% 0.28/0.59 % SZS output start Proof for Vampire---4
% See solution above
% 0.28/0.59 % (23812)------------------------------
% 0.28/0.59 % (23812)Version: Vampire 4.7 (commit 05ef610bd on 2023-06-21 19:03:17 +0100)
% 0.28/0.59 % (23812)Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% 0.28/0.59 % (23812)Termination reason: Refutation
% 0.28/0.59
% 0.28/0.59 % (23812)Memory used [KB]: 3454
% 0.28/0.59 % (23812)Time elapsed: 0.034 s
% 0.28/0.59 % (23812)------------------------------
% 0.28/0.59 % (23812)------------------------------
% 0.28/0.59 % (23805)Success in time 0.162 s
% 0.28/0.59 23807 Aborted by signal SIGHUP on /export/starexec/sandbox2/tmp/tmp.mLEr8YmdMP/Vampire---4.8_23682
% 0.28/0.59 % (23807)------------------------------
% 0.28/0.59 % (23807)Version: Vampire 4.7 (commit 05ef610bd on 2023-06-21 19:03:17 +0100)
% 0.28/0.59 % (23807)Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% 0.28/0.59 % (23807)Termination reason: Refutation not found, SMT solver inside AVATAR returned Unknown
% 0.28/0.59
% 0.28/0.59 % (23807)Memory used [KB]: 3198
% 0.28/0.59 % (23807)Time elapsed: 0.077 s
% 0.28/0.59 % (23807)------------------------------
% 0.28/0.59 % (23807)------------------------------
% 0.28/0.59 % Vampire---4.8 exiting
%------------------------------------------------------------------------------