TSTP Solution File: NUM926_2 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : NUM926_2 : 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 : n017.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 : Tue Apr 30 14:39:04 EDT 2024
% Result : Theorem 13.00s 2.24s
% Output : Refutation 13.00s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 77
% Syntax : Number of formulae : 106 ( 16 unt; 67 typ; 0 def)
% Number of atoms : 67 ( 33 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 57 ( 29 ~; 21 |; 1 &)
% ( 2 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 7 ( 3 avg)
% Number of types : 5 ( 4 usr)
% Number of type conns : 78 ( 43 >; 35 *; 0 +; 0 <<)
% Number of predicates : 21 ( 19 usr; 1 prp; 0-3 aty)
% Number of functors : 44 ( 44 usr; 20 con; 0-3 aty)
% Number of variables : 47 ( 31 !; 16 ?; 47 :)
% 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(f202827,plain,
$false,
inference(unit_resulting_resolution,[],[f3051,f3778,f3053,f2322]) ).
tff(f2322,plain,
! [X0: int,X1: int] :
( ord_less_int(X1,X0)
| ord_less_int(X0,X1)
| ( X0 = X1 ) ),
inference(cnf_transformation,[],[f955]) ).
tff(f955,plain,
! [X0: int,X1: int] :
( ord_less_int(X1,X0)
| ( X0 = X1 )
| ord_less_int(X0,X1) ),
inference(rectify,[],[f39]) ).
tff(f39,axiom,
! [X18: int,X19: int] :
( ord_less_int(X19,X18)
| ( X18 = X19 )
| ord_less_int(X18,X19) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_38_zless__linear) ).
tff(f3053,plain,
~ ord_less_int(one_one_int,t),
inference(subsumption_resolution,[],[f3052,f2975]) ).
tff(f2975,plain,
! [X0: int,X1: int] : ( plus_plus_int(power_power_int(X0,number_number_of_nat(bit0(bit1(zero_zero_int)))),power_power_int(X1,number_number_of_nat(bit0(bit1(zero_zero_int))))) != plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(zero_zero_int)))),m),one_one_int) ),
inference(forward_demodulation,[],[f1915,f1925]) ).
tff(f1925,plain,
pls = zero_zero_int,
inference(cnf_transformation,[],[f357]) ).
tff(f357,axiom,
pls = zero_zero_int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_356_Pls__def) ).
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/benchmark/theBenchmark.p',conj_0) ).
tff(f3052,plain,
( ( plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(zero_zero_int)))),m),one_one_int) = plus_plus_int(power_power_int(sK8,number_number_of_nat(bit0(bit1(zero_zero_int)))),power_power_int(sK9,number_number_of_nat(bit0(bit1(zero_zero_int))))) )
| ~ ord_less_int(one_one_int,t) ),
inference(forward_demodulation,[],[f1992,f1925]) ).
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/benchmark/theBenchmark.p',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(f3778,plain,
~ ord_less_int(t,one_one_int),
inference(unit_resulting_resolution,[],[f1931,f3474]) ).
tff(f3474,plain,
! [X0: int,X1: int] :
( ~ ord_less_eq_int(X0,X1)
| ~ ord_less_int(X1,X0) ),
inference(forward_demodulation,[],[f3473,f2005]) ).
tff(f2005,plain,
! [X0: int] : ( number_number_of_int(X0) = X0 ),
inference(cnf_transformation,[],[f710]) ).
tff(f710,plain,
! [X0: int] : ( number_number_of_int(X0) = X0 ),
inference(rectify,[],[f143]) ).
tff(f143,axiom,
! [X20: int] : ( number_number_of_int(X20) = X20 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_142_number__of__is__id) ).
tff(f3473,plain,
! [X0: int,X1: int] :
( ~ ord_less_eq_int(number_number_of_int(X0),X1)
| ~ ord_less_int(X1,X0) ),
inference(forward_demodulation,[],[f3472,f2005]) ).
tff(f3472,plain,
! [X0: int,X1: int] :
( ~ ord_less_int(X1,X0)
| ~ ord_less_eq_int(number_number_of_int(X0),number_number_of_int(X1)) ),
inference(forward_demodulation,[],[f3471,f2005]) ).
tff(f3471,plain,
! [X0: int,X1: int] :
( ~ ord_less_int(number_number_of_int(X1),X0)
| ~ ord_less_eq_int(number_number_of_int(X0),number_number_of_int(X1)) ),
inference(forward_demodulation,[],[f2526,f2005]) ).
tff(f2526,plain,
! [X0: int,X1: int] :
( ~ ord_less_int(number_number_of_int(X1),number_number_of_int(X0))
| ~ ord_less_eq_int(number_number_of_int(X0),number_number_of_int(X1)) ),
inference(cnf_transformation,[],[f1826]) ).
tff(f1826,plain,
! [X0: int,X1: int] :
( ( ord_less_eq_int(number_number_of_int(X0),number_number_of_int(X1))
| ord_less_int(number_number_of_int(X1),number_number_of_int(X0)) )
& ( ~ ord_less_int(number_number_of_int(X1),number_number_of_int(X0))
| ~ ord_less_eq_int(number_number_of_int(X0),number_number_of_int(X1)) ) ),
inference(nnf_transformation,[],[f1077]) ).
tff(f1077,plain,
! [X0: int,X1: int] :
( ord_less_eq_int(number_number_of_int(X0),number_number_of_int(X1))
<=> ~ ord_less_int(number_number_of_int(X1),number_number_of_int(X0)) ),
inference(rectify,[],[f51]) ).
tff(f51,axiom,
! [X27: int,X17: int] :
( ord_less_eq_int(number_number_of_int(X27),number_number_of_int(X17))
<=> ~ ord_less_int(number_number_of_int(X17),number_number_of_int(X27)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_50_le__number__of__eq__not__less) ).
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/benchmark/theBenchmark.p',fact_0_tpos) ).
tff(f3051,plain,
one_one_int != t,
inference(subsumption_resolution,[],[f3050,f2975]) ).
tff(f3050,plain,
( ( plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(zero_zero_int)))),m),one_one_int) = plus_plus_int(power_power_int(sK6,number_number_of_nat(bit0(bit1(zero_zero_int)))),power_power_int(sK7,number_number_of_nat(bit0(bit1(zero_zero_int))))) )
| ( one_one_int != t ) ),
inference(forward_demodulation,[],[f1991,f1925]) ).
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/benchmark/theBenchmark.p',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
% 0.03/0.12 % Problem : NUM926_2 : TPTP v8.1.2. Released v5.3.0.
% 0.13/0.14 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.15/0.35 % Computer : n017.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
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Mon Apr 29 23:32:03 EDT 2024
% 0.15/0.36 % CPUTime :
% 0.15/0.36 % (24955)Running in auto input_syntax mode. Trying TPTP
% 0.15/0.41 % (24974)WARNING: value z3 for option sas not known
% 0.15/0.41 % (24973)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.15/0.41 % (24974)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)
% 0.15/0.41 % (24975)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.15/0.41 % (24972)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.15/0.41 % (24977)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)
% 0.15/0.41 % (24976)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)
% 0.15/0.41 % (24978)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)
% 1.42/0.59 TRYING [1,1,1,1]
% 1.42/0.60 TRYING [1,1,2,1]
% 1.42/0.62 TRYING [1,1,3,1]
% 1.97/0.67 TRYING [1,1,4,1]
% 1.97/0.71 TRYING [1]
% 2.48/0.74 TRYING [2]
% 3.54/0.88 TRYING [1,1,5,1]
% 4.06/0.97 TRYING [3]
% 8.17/1.57 TRYING [1,1,1,1]
% 8.17/1.57 TRYING [1,1,2,1]
% 8.17/1.58 TRYING [1,1,3,1]
% 8.17/1.61 TRYING [1,1,4,1]
% 8.80/1.67 TRYING [1,1,6,1]
% 9.25/1.77 TRYING [1,1,5,1]
% 13.00/2.24 % (24978)First to succeed.
% 13.00/2.24 % (24978)Refutation found. Thanks to Tanya!
% 13.00/2.24 % SZS status Theorem for theBenchmark
% 13.00/2.24 % SZS output start Proof for theBenchmark
% See solution above
% 13.00/2.25 % (24978)------------------------------
% 13.00/2.25 % (24978)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 13.00/2.25 % (24978)Termination reason: Refutation
% 13.00/2.25
% 13.00/2.25 % (24978)Memory used [KB]: 27902
% 13.00/2.25 % (24978)Time elapsed: 1.833 s
% 13.00/2.25 % (24978)Instructions burned: 5642 (million)
% 13.00/2.25 % (24978)------------------------------
% 13.00/2.25 % (24978)------------------------------
% 13.00/2.25 % (24955)Success in time 1.849 s
%------------------------------------------------------------------------------