TSTP Solution File: NUM924_2 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : NUM924_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 : n029.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 14:38:31 EDT 2024
% Result : Theorem 1.74s 0.68s
% Output : Refutation 1.74s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 65
% Syntax : Number of formulae : 94 ( 38 unt; 56 typ; 0 def)
% Number of atoms : 38 ( 21 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 7 ( 7 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 3 ( 2 avg)
% Maximal term depth : 8 ( 3 avg)
% Number of types : 4 ( 3 usr)
% Number of type conns : 67 ( 37 >; 30 *; 0 +; 0 <<)
% Number of predicates : 17 ( 15 usr; 1 prp; 0-3 aty)
% Number of functors : 38 ( 38 usr; 16 con; 0-3 aty)
% Number of variables : 13 ( 13 !; 0 ?; 13 :)
% Comments :
%------------------------------------------------------------------------------
tff(type_def_5,type,
int: $tType ).
tff(type_def_6,type,
nat: $tType ).
tff(type_def_7,type,
real: $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,
legendre: ( int * int ) > int ).
tff(func_def_26,type,
m: int ).
tff(func_def_27,type,
s1: int ).
tff(func_def_28,type,
s: int ).
tff(func_def_29,type,
t: int ).
tff(func_def_30,type,
sK2: int ).
tff(func_def_31,type,
sK3: int ).
tff(func_def_32,type,
sK4: int ).
tff(func_def_33,type,
sK5: int > int ).
tff(func_def_34,type,
sK6: ( real * nat ) > real ).
tff(func_def_35,type,
sK7: ( int * int ) > int ).
tff(func_def_36,type,
sK8: ( int * int * int ) > int ).
tff(func_def_37,type,
sK9: 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(f14140,plain,
$false,
inference(resolution,[],[f3706,f3703]) ).
tff(f3703,plain,
~ ord_less_int(plus_plus_int(one_one_int,power_power_int(s,number_number_of_nat(bit0(one_one_int)))),pls),
inference(forward_demodulation,[],[f3639,f2194]) ).
tff(f2194,plain,
! [X0: int,X1: int] : ( plus_plus_int(X0,X1) = plus_plus_int(X1,X0) ),
inference(cnf_transformation,[],[f890]) ).
tff(f890,plain,
! [X0: int,X1: int] : ( plus_plus_int(X0,X1) = plus_plus_int(X1,X0) ),
inference(rectify,[],[f133]) ).
tff(f133,axiom,
! [X11: int,X9: int] : ( plus_plus_int(X9,X11) = plus_plus_int(X11,X9) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_132_zadd__commute) ).
tff(f3639,plain,
~ ord_less_int(plus_plus_int(power_power_int(s,number_number_of_nat(bit0(one_one_int))),one_one_int),pls),
inference(backward_demodulation,[],[f2930,f3585]) ).
tff(f3585,plain,
plus_plus_nat(one_one_nat,one_one_nat) = number_number_of_nat(bit0(one_one_int)),
inference(backward_demodulation,[],[f1914,f3579]) ).
tff(f3579,plain,
one_one_int = bit1(pls),
inference(superposition,[],[f1896,f1946]) ).
tff(f1946,plain,
! [X0: int] : ( number_number_of_int(X0) = X0 ),
inference(cnf_transformation,[],[f711]) ).
tff(f711,plain,
! [X0: int] : ( number_number_of_int(X0) = X0 ),
inference(rectify,[],[f35]) ).
tff(f35,axiom,
! [X10: int] : ( number_number_of_int(X10) = X10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_34_number__of__is__id) ).
tff(f1896,plain,
one_one_int = number_number_of_int(bit1(pls)),
inference(cnf_transformation,[],[f252]) ).
tff(f252,axiom,
one_one_int = number_number_of_int(bit1(pls)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_251_numeral__1__eq__1) ).
tff(f1914,plain,
number_number_of_nat(bit0(bit1(pls))) = plus_plus_nat(one_one_nat,one_one_nat),
inference(cnf_transformation,[],[f261]) ).
tff(f261,axiom,
number_number_of_nat(bit0(bit1(pls))) = plus_plus_nat(one_one_nat,one_one_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_260_semiring__one__add__one__is__two) ).
tff(f2930,plain,
~ ord_less_int(plus_plus_int(power_power_int(s,plus_plus_nat(one_one_nat,one_one_nat)),one_one_int),pls),
inference(backward_demodulation,[],[f2904,f1914]) ).
tff(f2904,plain,
~ ord_less_int(plus_plus_int(power_power_int(s,number_number_of_nat(bit0(bit1(pls)))),one_one_int),pls),
inference(forward_demodulation,[],[f1855,f1866]) ).
tff(f1866,plain,
zero_zero_int = pls,
inference(cnf_transformation,[],[f171]) ).
tff(f171,axiom,
zero_zero_int = pls,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_170_Pls__def) ).
tff(f1855,plain,
~ ord_less_int(plus_plus_int(power_power_int(s,number_number_of_nat(bit0(bit1(pls)))),one_one_int),zero_zero_int),
inference(cnf_transformation,[],[f701]) ).
tff(f701,plain,
~ ord_less_int(plus_plus_int(power_power_int(s,number_number_of_nat(bit0(bit1(pls)))),one_one_int),zero_zero_int),
inference(flattening,[],[f700]) ).
tff(f700,negated_conjecture,
~ ord_less_int(plus_plus_int(power_power_int(s,number_number_of_nat(bit0(bit1(pls)))),one_one_int),zero_zero_int),
inference(negated_conjecture,[],[f699]) ).
tff(f699,conjecture,
ord_less_int(plus_plus_int(power_power_int(s,number_number_of_nat(bit0(bit1(pls)))),one_one_int),zero_zero_int),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
tff(f3706,plain,
ord_less_int(plus_plus_int(one_one_int,power_power_int(s,number_number_of_nat(bit0(one_one_int)))),pls),
inference(forward_demodulation,[],[f3644,f2194]) ).
tff(f3644,plain,
ord_less_int(plus_plus_int(power_power_int(s,number_number_of_nat(bit0(one_one_int))),one_one_int),pls),
inference(backward_demodulation,[],[f2977,f3585]) ).
tff(f2977,plain,
ord_less_int(plus_plus_int(power_power_int(s,plus_plus_nat(one_one_nat,one_one_nat)),one_one_int),pls),
inference(backward_demodulation,[],[f2965,f2976]) ).
tff(f2976,plain,
! [X0: int] : ( pls = times_times_int(X0,pls) ),
inference(forward_demodulation,[],[f1961,f1866]) ).
tff(f1961,plain,
! [X0: int] : ( zero_zero_int = times_times_int(X0,zero_zero_int) ),
inference(cnf_transformation,[],[f726]) ).
tff(f726,plain,
! [X0: int] : ( zero_zero_int = times_times_int(X0,zero_zero_int) ),
inference(rectify,[],[f363]) ).
tff(f363,axiom,
! [X153: int] : ( zero_zero_int = times_times_int(X153,zero_zero_int) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_362_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J) ).
tff(f2965,plain,
ord_less_int(plus_plus_int(power_power_int(s,plus_plus_nat(one_one_nat,one_one_nat)),one_one_int),times_times_int(plus_plus_int(times_times_int(bit0(bit0(bit1(pls))),m),one_one_int),pls)),
inference(backward_demodulation,[],[f2943,f1946]) ).
tff(f2943,plain,
ord_less_int(plus_plus_int(power_power_int(s,plus_plus_nat(one_one_nat,one_one_nat)),one_one_int),times_times_int(plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int),pls)),
inference(forward_demodulation,[],[f2942,f2939]) ).
tff(f2939,plain,
times_times_int(plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int),t) = plus_plus_int(power_power_int(s,plus_plus_nat(one_one_nat,one_one_nat)),one_one_int),
inference(forward_demodulation,[],[f1927,f1914]) ).
tff(f1927,plain,
times_times_int(plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int),t) = plus_plus_int(power_power_int(s,number_number_of_nat(bit0(bit1(pls)))),one_one_int),
inference(cnf_transformation,[],[f4]) ).
tff(f4,axiom,
times_times_int(plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int),t) = plus_plus_int(power_power_int(s,number_number_of_nat(bit0(bit1(pls)))),one_one_int),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3_t) ).
tff(f2942,plain,
ord_less_int(times_times_int(plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int),t),times_times_int(plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int),pls)),
inference(forward_demodulation,[],[f1929,f1866]) ).
tff(f1929,plain,
ord_less_int(times_times_int(plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int),t),times_times_int(plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int),zero_zero_int)),
inference(cnf_transformation,[],[f3]) ).
tff(f3,axiom,
ord_less_int(times_times_int(plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int),t),times_times_int(plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int),zero_zero_int)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2__096_I4_A_K_Am_A_L_A1_J_A_K_At_A_060_A_I4_A_K_Am_A_L_A1_J_A_K_A0_096) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.14 % Problem : NUM924_2 : TPTP v8.1.2. Released v5.3.0.
% 0.08/0.16 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.14/0.37 % Computer : n029.cluster.edu
% 0.14/0.37 % Model : x86_64 x86_64
% 0.14/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.37 % Memory : 8042.1875MB
% 0.14/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.37 % CPULimit : 300
% 0.14/0.37 % WCLimit : 300
% 0.14/0.38 % DateTime : Mon Apr 29 23:56:35 EDT 2024
% 0.14/0.38 % CPUTime :
% 0.14/0.38 % (24480)Running in auto input_syntax mode. Trying TPTP
% 0.21/0.42 % (24483)WARNING: value z3 for option sas not known
% 0.21/0.43 % (24483)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 % (24484)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.21/0.43 % (24482)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 % (24486)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 % (24487)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)
% 0.21/0.43 % (24485)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 % (24481)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 1.46/0.62 TRYING [1,1,1]
% 1.46/0.64 TRYING [1,1,2]
% 1.74/0.67 TRYING [1,1,3]
% 1.74/0.68 % (24486)First to succeed.
% 1.74/0.68 % (24486)Refutation found. Thanks to Tanya!
% 1.74/0.68 % SZS status Theorem for theBenchmark
% 1.74/0.68 % SZS output start Proof for theBenchmark
% See solution above
% 1.74/0.68 % (24486)------------------------------
% 1.74/0.68 % (24486)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 1.74/0.68 % (24486)Termination reason: Refutation
% 1.74/0.68
% 1.74/0.68 % (24486)Memory used [KB]: 4983
% 1.74/0.68 % (24486)Time elapsed: 0.252 s
% 1.74/0.68 % (24486)Instructions burned: 472 (million)
% 1.74/0.68 % (24486)------------------------------
% 1.74/0.68 % (24486)------------------------------
% 1.74/0.68 % (24480)Success in time 0.296 s
%------------------------------------------------------------------------------