TSTP Solution File: SWW497_5 by Vampire---4.9
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire---4.9
% Problem : SWW497_5 : TPTP v8.2.0. Released v6.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire %s %d THM
% Computer : n025.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 : Mon Jun 24 18:33:16 EDT 2024
% Result : Theorem 0.20s 0.49s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 17
% Syntax : Number of formulae : 56 ( 49 unt; 0 typ; 0 def)
% Number of atoms : 65 ( 64 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 20 ( 11 ~; 6 |; 1 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of FOOLs : 1 ( 1 fml; 0 var)
% Number of types : 6 ( 5 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 26 ( 24 usr; 1 prp; 0-2 aty)
% Number of functors : 33 ( 33 usr; 17 con; 0-4 aty)
% Number of variables : 34 ( 34 !; 0 ?; 34 :)
% Comments :
%------------------------------------------------------------------------------
tff(type_def_5,type,
complex: $tType ).
tff(type_def_6,type,
bool: $tType ).
tff(type_def_7,type,
int: $tType ).
tff(type_def_8,type,
nat: $tType ).
tff(type_def_9,type,
real: $tType ).
tff(type_def_10,type,
fun: ( $tType * $tType ) > $tType ).
tff(func_def_0,type,
complex1: ( real * real ) > complex ).
tff(func_def_1,type,
complex_case:
!>[X0: $tType] : ( ( fun(real,fun(real,X0)) * complex ) > X0 ) ).
tff(func_def_2,type,
complex_rec:
!>[X0: $tType] : ( ( fun(real,fun(real,X0)) * complex ) > X0 ) ).
tff(func_def_3,type,
fundam1563812824_csqrt: complex > complex ).
tff(func_def_4,type,
one_one:
!>[X0: $tType] : X0 ).
tff(func_def_5,type,
plus_plus:
!>[X0: $tType] : ( ( X0 * X0 ) > X0 ) ).
tff(func_def_6,type,
times_times:
!>[X0: $tType] : ( ( X0 * X0 ) > X0 ) ).
tff(func_def_7,type,
zero_zero:
!>[X0: $tType] : X0 ).
tff(func_def_8,type,
bit0: int > int ).
tff(func_def_9,type,
bit1: int > int ).
tff(func_def_10,type,
pls: int ).
tff(func_def_11,type,
number_number_of:
!>[X0: $tType] : ( int > X0 ) ).
tff(func_def_12,type,
sqrt: real > real ).
tff(func_def_13,type,
power_power:
!>[X0: $tType] : ( ( X0 * nat ) > X0 ) ).
tff(func_def_14,type,
norm_norm:
!>[X0: $tType] : ( X0 > real ) ).
tff(func_def_15,type,
aa:
!>[X0: $tType,X1: $tType] : ( ( fun(X0,X1) * X0 ) > X1 ) ).
tff(func_def_16,type,
fFalse: bool ).
tff(func_def_17,type,
fTrue: bool ).
tff(func_def_18,type,
x: real ).
tff(func_def_19,type,
y: real ).
tff(func_def_20,type,
z: complex ).
tff(func_def_21,type,
sK0: real ).
tff(func_def_22,type,
sK1: real ).
tff(func_def_23,type,
sF2: real ).
tff(func_def_24,type,
sF3: int ).
tff(func_def_25,type,
sF4: int ).
tff(func_def_26,type,
sF5: int ).
tff(func_def_27,type,
sF6: int ).
tff(func_def_28,type,
sF7: nat ).
tff(func_def_29,type,
sF8: real ).
tff(func_def_30,type,
sF9: real ).
tff(func_def_31,type,
sF10: real ).
tff(pred_def_1,type,
one:
!>[X0: $tType] : $o ).
tff(pred_def_2,type,
number:
!>[X0: $tType] : $o ).
tff(pred_def_3,type,
zero:
!>[X0: $tType] : $o ).
tff(pred_def_4,type,
power:
!>[X0: $tType] : $o ).
tff(pred_def_5,type,
semiring:
!>[X0: $tType] : $o ).
tff(pred_def_6,type,
number_ring:
!>[X0: $tType] : $o ).
tff(pred_def_7,type,
ring_char_0:
!>[X0: $tType] : $o ).
tff(pred_def_8,type,
mult_zero:
!>[X0: $tType] : $o ).
tff(pred_def_9,type,
semiring_1:
!>[X0: $tType] : $o ).
tff(pred_def_10,type,
monoid_mult:
!>[X0: $tType] : $o ).
tff(pred_def_11,type,
zero_neq_one:
!>[X0: $tType] : $o ).
tff(pred_def_12,type,
number_semiring:
!>[X0: $tType] : $o ).
tff(pred_def_13,type,
no_zero_divisors:
!>[X0: $tType] : $o ).
tff(pred_def_14,type,
ab_semigroup_add:
!>[X0: $tType] : $o ).
tff(pred_def_15,type,
comm_monoid_mult:
!>[X0: $tType] : $o ).
tff(pred_def_16,type,
cancel_semigroup_add:
!>[X0: $tType] : $o ).
tff(pred_def_17,type,
linord581940658strict:
!>[X0: $tType] : $o ).
tff(pred_def_18,type,
real_normed_vector:
!>[X0: $tType] : $o ).
tff(pred_def_19,type,
ring_11004092258visors:
!>[X0: $tType] : $o ).
tff(pred_def_20,type,
cancel146912293up_add:
!>[X0: $tType] : $o ).
tff(pred_def_21,type,
linord219039673up_add:
!>[X0: $tType] : $o ).
tff(pred_def_22,type,
real_n2089651433ebra_1:
!>[X0: $tType] : $o ).
tff(pred_def_23,type,
real_n1866405975lgebra:
!>[X0: $tType] : $o ).
tff(pred_def_24,type,
pp: bool > $o ).
tff(f2103,plain,
$false,
inference(subsumption_resolution,[],[f2099,f627]) ).
tff(f627,plain,
sF2 != sF10,
inference(definition_folding,[],[f550,f626,f625,f623,f622,f621,f620,f619,f621,f620,f619,f624,f623,f622,f621,f620,f619,f621,f620,f619,f618]) ).
tff(f618,plain,
one_one(real) = sF2,
introduced(function_definition,[new_symbols(definition,[sF2])]) ).
tff(f624,plain,
power_power(real,x,sF7) = sF8,
introduced(function_definition,[new_symbols(definition,[sF8])]) ).
tff(f619,plain,
one_one(int) = sF3,
introduced(function_definition,[new_symbols(definition,[sF3])]) ).
tff(f620,plain,
plus_plus(int,sF3,pls) = sF4,
introduced(function_definition,[new_symbols(definition,[sF4])]) ).
tff(f621,plain,
plus_plus(int,sF4,pls) = sF5,
introduced(function_definition,[new_symbols(definition,[sF5])]) ).
tff(f622,plain,
plus_plus(int,sF5,sF5) = sF6,
introduced(function_definition,[new_symbols(definition,[sF6])]) ).
tff(f623,plain,
number_number_of(nat,sF6) = sF7,
introduced(function_definition,[new_symbols(definition,[sF7])]) ).
tff(f625,plain,
power_power(real,y,sF7) = sF9,
introduced(function_definition,[new_symbols(definition,[sF9])]) ).
tff(f626,plain,
plus_plus(real,sF8,sF9) = sF10,
introduced(function_definition,[new_symbols(definition,[sF10])]) ).
tff(f550,plain,
one_one(real) != plus_plus(real,power_power(real,x,number_number_of(nat,plus_plus(int,plus_plus(int,plus_plus(int,one_one(int),pls),pls),plus_plus(int,plus_plus(int,one_one(int),pls),pls)))),power_power(real,y,number_number_of(nat,plus_plus(int,plus_plus(int,plus_plus(int,one_one(int),pls),pls),plus_plus(int,plus_plus(int,one_one(int),pls),pls))))),
inference(definition_unfolding,[],[f348,f441,f442,f441,f442]) ).
tff(f442,plain,
! [X0: int] : ( bit1(X0) = plus_plus(int,plus_plus(int,one_one(int),X0),X0) ),
inference(cnf_transformation,[],[f188]) ).
tff(f188,plain,
! [X0: int] : ( bit1(X0) = plus_plus(int,plus_plus(int,one_one(int),X0),X0) ),
inference(rectify,[],[f27]) ).
tff(f27,axiom,
! [X8: int] : ( bit1(X8) = plus_plus(int,plus_plus(int,one_one(int),X8),X8) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
tff(f441,plain,
! [X0: int] : ( bit0(X0) = plus_plus(int,X0,X0) ),
inference(cnf_transformation,[],[f187]) ).
tff(f187,plain,
! [X0: int] : ( bit0(X0) = plus_plus(int,X0,X0) ),
inference(rectify,[],[f31]) ).
tff(f31,axiom,
! [X8: int] : ( bit0(X8) = plus_plus(int,X8,X8) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
tff(f348,plain,
one_one(real) != plus_plus(real,power_power(real,x,number_number_of(nat,bit0(bit1(pls)))),power_power(real,y,number_number_of(nat,bit0(bit1(pls))))),
inference(cnf_transformation,[],[f180]) ).
tff(f180,plain,
one_one(real) != plus_plus(real,power_power(real,x,number_number_of(nat,bit0(bit1(pls)))),power_power(real,y,number_number_of(nat,bit0(bit1(pls))))),
inference(flattening,[],[f179]) ).
tff(f179,negated_conjecture,
( ~ one_one(real) = plus_plus(real,power_power(real,x,number_number_of(nat,bit0(bit1(pls)))),power_power(real,y,number_number_of(nat,bit0(bit1(pls))))) ),
inference(negated_conjecture,[],[f178]) ).
tff(f178,conjecture,
one_one(real) = plus_plus(real,power_power(real,x,number_number_of(nat,bit0(bit1(pls)))),power_power(real,y,number_number_of(nat,bit0(bit1(pls))))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
tff(f2099,plain,
sF2 = sF10,
inference(trivial_inequality_removal,[],[f2096]) ).
tff(f2096,plain,
( ( sF2 != sF2 )
| ( sF2 = sF10 ) ),
inference(superposition,[],[f673,f1931]) ).
tff(f1931,plain,
sF2 = sqrt(sF10),
inference(forward_demodulation,[],[f1930,f629]) ).
tff(f629,plain,
norm_norm(complex,z) = sF2,
inference(forward_demodulation,[],[f430,f618]) ).
tff(f430,plain,
norm_norm(complex,z) = one_one(real),
inference(cnf_transformation,[],[f1]) ).
tff(f1,axiom,
norm_norm(complex,z) = one_one(real),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
tff(f1930,plain,
norm_norm(complex,z) = sqrt(sF10),
inference(forward_demodulation,[],[f1929,f427]) ).
tff(f427,plain,
z = complex1(x,y),
inference(cnf_transformation,[],[f2]) ).
tff(f2,axiom,
z = complex1(x,y),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
tff(f1929,plain,
norm_norm(complex,complex1(x,y)) = sqrt(sF10),
inference(forward_demodulation,[],[f1911,f626]) ).
tff(f1911,plain,
norm_norm(complex,complex1(x,y)) = sqrt(plus_plus(real,sF8,sF9)),
inference(superposition,[],[f1254,f625]) ).
tff(f1254,plain,
! [X0: real] : ( norm_norm(complex,complex1(x,X0)) = sqrt(plus_plus(real,sF8,power_power(real,X0,sF7))) ),
inference(superposition,[],[f1253,f624]) ).
tff(f1253,plain,
! [X0: real,X1: real] : ( norm_norm(complex,complex1(X1,X0)) = sqrt(plus_plus(real,power_power(real,X1,sF7),power_power(real,X0,sF7))) ),
inference(forward_demodulation,[],[f1252,f623]) ).
tff(f1252,plain,
! [X0: real,X1: real] : ( norm_norm(complex,complex1(X1,X0)) = sqrt(plus_plus(real,power_power(real,X1,number_number_of(nat,sF6)),power_power(real,X0,number_number_of(nat,sF6)))) ),
inference(forward_demodulation,[],[f1251,f634]) ).
tff(f634,plain,
sF6 = plus_plus(int,sF3,sF3),
inference(forward_demodulation,[],[f622,f633]) ).
tff(f633,plain,
sF3 = sF5,
inference(forward_demodulation,[],[f632,f631]) ).
tff(f631,plain,
sF3 = sF4,
inference(forward_demodulation,[],[f620,f439]) ).
tff(f439,plain,
! [X0: int] : ( plus_plus(int,X0,pls) = X0 ),
inference(cnf_transformation,[],[f185]) ).
tff(f185,plain,
! [X0: int] : ( plus_plus(int,X0,pls) = X0 ),
inference(rectify,[],[f29]) ).
tff(f29,axiom,
! [X8: int] : ( plus_plus(int,X8,pls) = X8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
tff(f632,plain,
sF4 = sF5,
inference(forward_demodulation,[],[f621,f439]) ).
tff(f1251,plain,
! [X0: real,X1: real] : ( norm_norm(complex,complex1(X1,X0)) = sqrt(plus_plus(real,power_power(real,X1,number_number_of(nat,plus_plus(int,sF3,sF3))),power_power(real,X0,number_number_of(nat,plus_plus(int,sF3,sF3))))) ),
inference(forward_demodulation,[],[f1250,f619]) ).
tff(f1250,plain,
! [X0: real,X1: real] : ( norm_norm(complex,complex1(X1,X0)) = sqrt(plus_plus(real,power_power(real,X1,number_number_of(nat,plus_plus(int,one_one(int),one_one(int)))),power_power(real,X0,number_number_of(nat,plus_plus(int,one_one(int),one_one(int)))))) ),
inference(forward_demodulation,[],[f1249,f439]) ).
tff(f1249,plain,
! [X0: real,X1: real] : ( norm_norm(complex,complex1(X1,X0)) = sqrt(plus_plus(real,power_power(real,X1,number_number_of(nat,plus_plus(int,plus_plus(int,one_one(int),pls),plus_plus(int,one_one(int),pls)))),power_power(real,X0,number_number_of(nat,plus_plus(int,plus_plus(int,one_one(int),pls),plus_plus(int,one_one(int),pls)))))) ),
inference(forward_demodulation,[],[f581,f439]) ).
tff(f581,plain,
! [X0: real,X1: real] : ( norm_norm(complex,complex1(X1,X0)) = sqrt(plus_plus(real,power_power(real,X1,number_number_of(nat,plus_plus(int,plus_plus(int,plus_plus(int,one_one(int),pls),pls),plus_plus(int,plus_plus(int,one_one(int),pls),pls)))),power_power(real,X0,number_number_of(nat,plus_plus(int,plus_plus(int,plus_plus(int,one_one(int),pls),pls),plus_plus(int,plus_plus(int,one_one(int),pls),pls)))))) ),
inference(definition_unfolding,[],[f523,f441,f442,f441,f442]) ).
tff(f523,plain,
! [X0: real,X1: real] : ( norm_norm(complex,complex1(X1,X0)) = sqrt(plus_plus(real,power_power(real,X1,number_number_of(nat,bit0(bit1(pls)))),power_power(real,X0,number_number_of(nat,bit0(bit1(pls)))))) ),
inference(cnf_transformation,[],[f242]) ).
tff(f242,plain,
! [X0: real,X1: real] : ( norm_norm(complex,complex1(X1,X0)) = sqrt(plus_plus(real,power_power(real,X1,number_number_of(nat,bit0(bit1(pls)))),power_power(real,X0,number_number_of(nat,bit0(bit1(pls)))))) ),
inference(rectify,[],[f56]) ).
tff(f56,axiom,
! [X28: real,X20: real] : ( norm_norm(complex,complex1(X20,X28)) = sqrt(plus_plus(real,power_power(real,X20,number_number_of(nat,bit0(bit1(pls)))),power_power(real,X28,number_number_of(nat,bit0(bit1(pls)))))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
tff(f673,plain,
! [X0: real] :
( ( sqrt(X0) != sF2 )
| ( sF2 = X0 ) ),
inference(forward_demodulation,[],[f672,f618]) ).
tff(f672,plain,
! [X0: real] :
( ( sF2 = X0 )
| ( one_one(real) != sqrt(X0) ) ),
inference(forward_demodulation,[],[f510,f618]) ).
tff(f510,plain,
! [X0: real] :
( ( one_one(real) = X0 )
| ( one_one(real) != sqrt(X0) ) ),
inference(cnf_transformation,[],[f335]) ).
tff(f335,plain,
! [X0: real] :
( ( ( one_one(real) = sqrt(X0) )
| ( one_one(real) != X0 ) )
& ( ( one_one(real) = X0 )
| ( one_one(real) != sqrt(X0) ) ) ),
inference(nnf_transformation,[],[f231]) ).
tff(f231,plain,
! [X0: real] :
( ( one_one(real) = sqrt(X0) )
<=> ( one_one(real) = X0 ) ),
inference(rectify,[],[f64]) ).
tff(f64,axiom,
! [X10: real] :
( ( one_one(real) = sqrt(X10) )
<=> ( one_one(real) = X10 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SWW497_5 : TPTP v8.2.0. Released v6.0.0.
% 0.11/0.12 % Command : run_vampire %s %d THM
% 0.12/0.33 % Computer : n025.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Wed Jun 19 07:55:24 EDT 2024
% 0.12/0.33 % CPUTime :
% 0.12/0.35 This is a TF1_THM_EQU_NAR problem
% 0.12/0.35 Running first-order theorem proving
% 0.12/0.35 Running /export/starexec/sandbox/solver/bin/vampire --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.20/0.42 % (7181)Running in auto input_syntax mode. Trying TPTP
% 0.20/0.42 % (7193)lrs+10_1:3_drc=off:sil=256000:sp=unary_first:lwlo=on:i=216875:kws=precedence:ins=3:rawr=on:nwc=10.0_0 on theBenchmark for (2999ds/216875Mi)
% 0.20/0.42 % (7181)Running in auto input_syntax mode. Trying TPTP
% 0.20/0.42 % (7192)lrs+1010_2201:262144_anc=all:drc=encompass:sil=256000:sims=off:sp=frequency:spb=goal_then_units:rp=on:lwlo=on:st=3.0:i=179501:bs=unit_only:nm=6:ins=2:fsd=on:ss=axioms:sgt=16:afr=on:tgt=ground:awrs=decay:awrsf=200:acc=on:ccuc=first_0 on theBenchmark for (2999ds/179501Mi)
% 0.20/0.42 % (7181)Running in auto input_syntax mode. Trying TPTP
% 0.20/0.42 % (7190)lrs+1011_1:12_anc=none:drc=off:sil=64000:sims=off:sp=unary_first:spb=goal_then_units:lsd=20:rnwc=on:nwc=2.0:i=53554:add=off:awrs=converge:bd=off:uhcvi=on:tgt=ground:afp=300:afq=1.63_0 on theBenchmark for (2999ds/53554Mi)
% 0.20/0.42 % (7181)Running in auto input_syntax mode. Trying TPTP
% 0.20/0.42 % (7191)dis+11_1:1_nwc=5.0:s2a=on:i=66616:s2at=3.0:sil=128000:bd=off_0 on theBenchmark for (2999ds/66616Mi)
% 0.20/0.42 % (7181)Running in auto input_syntax mode. Trying TPTP
% 0.20/0.42 % (7197)dis+1010_159245:1048576_to=lpo:sil=2000:etr=on:sp=unary_frequency:spb=goal:rnwc=on:nwc=10.9066:st=2:i=124:sd=1:nm=3:av=off:ss=axioms:rawr=on:drc=encompass:foolp=on:sgt=5:cond=fast:er=filter:erape=on:erml=2:s2a=on_0 on theBenchmark for (2999ds/124Mi)
% 0.20/0.43 % (7181)Running in auto input_syntax mode. Trying TPTP
% 0.20/0.43 % (7196)dis+1010_1:1_sil=2000:nwc=3.0:s2a=on:i=132:ins=5:fsr=off:ss=axioms:sd=2:fd=off_0 on theBenchmark for (2999ds/132Mi)
% 0.20/0.43 % (7181)Running in auto input_syntax mode. Trying TPTP
% 0.20/0.43 % (7194)dis+1011_3:1_sil=256000:tgt=ground:sac=on:i=109:sd=1:ss=included_0 on theBenchmark for (2999ds/109Mi)
% 0.20/0.48 % (7197)Instruction limit reached!
% 0.20/0.48 % (7197)------------------------------
% 0.20/0.48 % (7197)Version: Vampire 4.9 (commit 18c118a85 on 2024-06-08 21:14:20 +0100)
% 0.20/0.48 % (7197)Linked with Z3 4.12.3.0 79bbbf76d0c123481c8ca05cd3a98939270074d3 z3-4.8.4-7980-g79bbbf76d
% 0.20/0.48 % (7197)Termination reason: Time limit
% 0.20/0.48 % (7197)Termination phase: Saturation
% 0.20/0.48
% 0.20/0.48 % (7197)Memory used [KB]: 1721
% 0.20/0.48 % (7197)Time elapsed: 0.055 s
% 0.20/0.48 % (7197)Instructions burned: 127 (million)
% 0.20/0.48 % (7194)First to succeed.
% 0.20/0.49 % (7194)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-7181"
% 0.20/0.49 % (7181)Running in auto input_syntax mode. Trying TPTP
% 0.20/0.49 % (7194)Refutation found. Thanks to Tanya!
% 0.20/0.49 % SZS status Theorem for theBenchmark
% 0.20/0.49 % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.49 % (7194)------------------------------
% 0.20/0.49 % (7194)Version: Vampire 4.9 (commit 18c118a85 on 2024-06-08 21:14:20 +0100)
% 0.20/0.49 % (7194)Linked with Z3 4.12.3.0 79bbbf76d0c123481c8ca05cd3a98939270074d3 z3-4.8.4-7980-g79bbbf76d
% 0.20/0.49 % (7194)Termination reason: Refutation
% 0.20/0.49
% 0.20/0.49 % (7194)Memory used [KB]: 2111
% 0.20/0.49 % (7194)Time elapsed: 0.056 s
% 0.20/0.49 % (7194)Instructions burned: 108 (million)
% 0.20/0.49 % (7194)------------------------------
% 0.20/0.49 % (7194)------------------------------
% 0.20/0.49 % (7181)Success in time 0.134 s
%------------------------------------------------------------------------------