TSTP Solution File: NUM925_1 by SnakeForV-SAT---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SnakeForV-SAT---1.0
% Problem : NUM925_1 : TPTP v8.1.0. Released v5.3.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_sat --cores 0 -t %d %s
% Computer : n011.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 : Wed Aug 31 18:07:18 EDT 2022
% Result : Theorem 0.19s 0.54s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 45
% Syntax : Number of formulae : 87 ( 40 unt; 28 typ; 0 def)
% Number of atoms : 84 ( 68 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 54 ( 29 ~; 15 |; 2 &)
% ( 8 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of FOOLs : 1 ( 1 fml; 0 var)
% Number of types : 3 ( 2 usr)
% Number of type conns : 18 ( 12 >; 6 *; 0 +; 0 <<)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 24 ( 24 usr; 14 con; 0-2 aty)
% Number of variables : 32 ( 32 !; 0 ?; 32 :)
% Comments :
%------------------------------------------------------------------------------
tff(type_def_5,type,
int: $tType ).
tff(type_def_6,type,
nat: $tType ).
tff(func_def_0,type,
one_one_int: int ).
tff(func_def_1,type,
one_one_nat: nat ).
tff(func_def_2,type,
plus_plus_int: ( int * int ) > int ).
tff(func_def_3,type,
plus_plus_nat: ( nat * nat ) > nat ).
tff(func_def_4,type,
zero_zero_int: int ).
tff(func_def_5,type,
zero_zero_nat: nat ).
tff(func_def_6,type,
bit0: int > int ).
tff(func_def_7,type,
bit1: int > int ).
tff(func_def_8,type,
pls: int ).
tff(func_def_9,type,
number_number_of_int: int > int ).
tff(func_def_10,type,
number_number_of_nat: int > nat ).
tff(func_def_11,type,
semiri1621563631at_int: nat > int ).
tff(func_def_12,type,
semiri984289939at_nat: nat > nat ).
tff(func_def_13,type,
power_power_int: ( int * nat ) > int ).
tff(func_def_14,type,
power_power_nat: ( nat * nat ) > nat ).
tff(func_def_15,type,
n: nat ).
tff(func_def_16,type,
t: int ).
tff(func_def_17,type,
sF0: int ).
tff(func_def_18,type,
sF1: int ).
tff(func_def_19,type,
sF2: int ).
tff(func_def_20,type,
sF3: int ).
tff(func_def_21,type,
sF4: int ).
tff(func_def_22,type,
sF5: nat ).
tff(func_def_23,type,
sF6: int ).
tff(pred_def_1,type,
ord_less_int: ( int * int ) > $o ).
tff(pred_def_2,type,
ord_less_nat: ( nat * nat ) > $o ).
tff(f1123,plain,
$false,
inference(resolution,[],[f1118,f462]) ).
tff(f462,plain,
~ ord_less_int(pls,pls),
inference(forward_demodulation,[],[f461,f448]) ).
tff(f448,plain,
pls = plus_plus_int(pls,pls),
inference(equality_resolution,[],[f430]) ).
tff(f430,plain,
! [X0: int] :
( ( pls = plus_plus_int(X0,X0) )
| ( pls != X0 ) ),
inference(definition_unfolding,[],[f329,f306]) ).
tff(f306,plain,
! [X0: int] : ( plus_plus_int(X0,X0) = bit0(X0) ),
inference(cnf_transformation,[],[f173]) ).
tff(f173,plain,
! [X0: int] : ( plus_plus_int(X0,X0) = bit0(X0) ),
inference(rectify,[],[f84]) ).
tff(f84,axiom,
! [X18: int] : ( bit0(X18) = plus_plus_int(X18,X18) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_83_Bit0__def) ).
tff(f329,plain,
! [X0: int] :
( ( pls = bit0(X0) )
| ( pls != X0 ) ),
inference(cnf_transformation,[],[f114]) ).
tff(f114,plain,
! [X0: int] :
( ( pls = X0 )
<=> ( pls = bit0(X0) ) ),
inference(rectify,[],[f76]) ).
tff(f76,axiom,
! [X8: int] :
( ( pls = bit0(X8) )
<=> ( pls = X8 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_75_rel__simps_I44_J) ).
tff(f461,plain,
~ ord_less_int(pls,plus_plus_int(pls,pls)),
inference(forward_demodulation,[],[f460,f459]) ).
tff(f459,plain,
pls = power_power_int(pls,plus_plus_nat(one_one_nat,one_one_nat)),
inference(forward_demodulation,[],[f444,f427]) ).
tff(f427,plain,
plus_plus_nat(one_one_nat,one_one_nat) = 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,[],[f325,f306,f312]) ).
tff(f312,plain,
! [X0: int] : ( bit1(X0) = plus_plus_int(plus_plus_int(one_one_int,X0),X0) ),
inference(cnf_transformation,[],[f159]) ).
tff(f159,plain,
! [X0: int] : ( bit1(X0) = plus_plus_int(plus_plus_int(one_one_int,X0),X0) ),
inference(rectify,[],[f100]) ).
tff(f100,axiom,
! [X18: int] : ( bit1(X18) = plus_plus_int(plus_plus_int(one_one_int,X18),X18) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_99_Bit1__def) ).
tff(f325,plain,
number_number_of_nat(bit0(bit1(pls))) = plus_plus_nat(one_one_nat,one_one_nat),
inference(cnf_transformation,[],[f13]) ).
tff(f13,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_12_semiring__one__add__one__is__two) ).
tff(f444,plain,
pls = power_power_int(pls,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(equality_resolution,[],[f389]) ).
tff(f389,plain,
! [X0: int] :
( ( pls = power_power_int(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)))) )
| ( pls != X0 ) ),
inference(definition_unfolding,[],[f273,f265,f306,f312,f265]) ).
tff(f265,plain,
zero_zero_int = pls,
inference(cnf_transformation,[],[f79]) ).
tff(f79,axiom,
zero_zero_int = pls,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_78_Pls__def) ).
tff(f273,plain,
! [X0: int] :
( ( zero_zero_int = power_power_int(X0,number_number_of_nat(bit0(bit1(pls)))) )
| ( zero_zero_int != X0 ) ),
inference(cnf_transformation,[],[f142]) ).
tff(f142,plain,
! [X0: int] :
( ( zero_zero_int = X0 )
<=> ( zero_zero_int = power_power_int(X0,number_number_of_nat(bit0(bit1(pls)))) ) ),
inference(rectify,[],[f8]) ).
tff(f8,axiom,
! [X2: int] :
( ( zero_zero_int = power_power_int(X2,number_number_of_nat(bit0(bit1(pls)))) )
<=> ( zero_zero_int = X2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7_zero__eq__power2) ).
tff(f460,plain,
~ ord_less_int(pls,plus_plus_int(power_power_int(pls,plus_plus_nat(one_one_nat,one_one_nat)),power_power_int(pls,plus_plus_nat(one_one_nat,one_one_nat)))),
inference(forward_demodulation,[],[f441,f427]) ).
tff(f441,plain,
~ ord_less_int(pls,plus_plus_int(power_power_int(pls,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_int(pls,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(equality_resolution,[],[f440]) ).
tff(f440,plain,
! [X1: int] :
( ( pls != X1 )
| ~ ord_less_int(pls,plus_plus_int(power_power_int(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_int(pls,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(equality_resolution,[],[f379]) ).
tff(f379,plain,
! [X0: int,X1: int] :
( ( pls != X0 )
| ( pls != X1 )
| ~ ord_less_int(pls,plus_plus_int(power_power_int(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_int(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,[],[f255,f265,f265,f265,f306,f312,f306,f312]) ).
tff(f255,plain,
! [X0: int,X1: int] :
( ( zero_zero_int != X0 )
| ( zero_zero_int != X1 )
| ~ ord_less_int(zero_zero_int,plus_plus_int(power_power_int(X1,number_number_of_nat(bit0(bit1(pls)))),power_power_int(X0,number_number_of_nat(bit0(bit1(pls)))))) ),
inference(cnf_transformation,[],[f126]) ).
tff(f126,plain,
! [X1: int,X0: int] :
( ord_less_int(zero_zero_int,plus_plus_int(power_power_int(X1,number_number_of_nat(bit0(bit1(pls)))),power_power_int(X0,number_number_of_nat(bit0(bit1(pls))))))
<=> ( ( zero_zero_int != X1 )
| ( zero_zero_int != X0 ) ) ),
inference(rectify,[],[f106]) ).
tff(f106,axiom,
! [X1: int,X0: int] :
( ( ( zero_zero_int != X1 )
| ( zero_zero_int != X0 ) )
<=> ord_less_int(zero_zero_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)))))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_105_sum__power2__gt__zero__iff) ).
tff(f1118,plain,
ord_less_int(pls,pls),
inference(superposition,[],[f515,f1116]) ).
tff(f1116,plain,
pls = sF1,
inference(trivial_inequality_removal,[],[f1115]) ).
tff(f1115,plain,
( ( pls != pls )
| ( pls = sF1 ) ),
inference(superposition,[],[f1111,f469]) ).
tff(f469,plain,
pls = power_power_int(sF1,sF5),
inference(forward_demodulation,[],[f456,f457]) ).
tff(f457,plain,
pls = sF6,
inference(definition_folding,[],[f339,f456,f455,f454,f453,f452,f453,f452,f451,f450]) ).
tff(f450,plain,
semiri1621563631at_int(n) = sF0,
introduced(function_definition,[]) ).
tff(f451,plain,
sF1 = plus_plus_int(one_one_int,sF0),
introduced(function_definition,[]) ).
tff(f452,plain,
sF2 = plus_plus_int(one_one_int,pls),
introduced(function_definition,[]) ).
tff(f453,plain,
sF3 = plus_plus_int(sF2,pls),
introduced(function_definition,[]) ).
tff(f454,plain,
plus_plus_int(sF3,sF3) = sF4,
introduced(function_definition,[]) ).
tff(f455,plain,
sF5 = number_number_of_nat(sF4),
introduced(function_definition,[]) ).
tff(f339,plain,
pls = power_power_int(plus_plus_int(one_one_int,semiri1621563631at_int(n)),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,[],[f193,f265,f306,f312]) ).
tff(f193,plain,
zero_zero_int = power_power_int(plus_plus_int(one_one_int,semiri1621563631at_int(n)),number_number_of_nat(bit0(bit1(pls)))),
inference(cnf_transformation,[],[f177]) ).
tff(f177,plain,
zero_zero_int = power_power_int(plus_plus_int(one_one_int,semiri1621563631at_int(n)),number_number_of_nat(bit0(bit1(pls)))),
inference(flattening,[],[f108]) ).
tff(f108,negated_conjecture,
( ~ zero_zero_int )
!= power_power_int(plus_plus_int(one_one_int,semiri1621563631at_int(n)),number_number_of_nat(bit0(bit1(pls)))),
inference(negated_conjecture,[],[f107]) ).
tff(f107,conjecture,
zero_zero_int != power_power_int(plus_plus_int(one_one_int,semiri1621563631at_int(n)),number_number_of_nat(bit0(bit1(pls)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
tff(f456,plain,
sF6 = power_power_int(sF1,sF5),
introduced(function_definition,[]) ).
tff(f1111,plain,
! [X3: int] :
( ( pls != power_power_int(X3,sF5) )
| ( pls = X3 ) ),
inference(superposition,[],[f388,f455]) ).
tff(f388,plain,
! [X0: int,X1: int] :
( ( pls != power_power_int(X0,number_number_of_nat(X1)) )
| ( pls = X0 ) ),
inference(definition_unfolding,[],[f269,f265,f265]) ).
tff(f269,plain,
! [X0: int,X1: int] :
( ( zero_zero_int = X0 )
| ( zero_zero_int != power_power_int(X0,number_number_of_nat(X1)) ) ),
inference(cnf_transformation,[],[f120]) ).
tff(f120,plain,
! [X0: int,X1: int] :
( ( zero_zero_int = power_power_int(X0,number_number_of_nat(X1)) )
<=> ( ( zero_zero_nat != number_number_of_nat(X1) )
& ( zero_zero_int = X0 ) ) ),
inference(rectify,[],[f93]) ).
tff(f93,axiom,
! [X2: int,X22: int] :
( ( ( zero_zero_int = X2 )
& ( zero_zero_nat != number_number_of_nat(X22) ) )
<=> ( zero_zero_int = power_power_int(X2,number_number_of_nat(X22)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_92_power__eq__0__iff__number__of) ).
tff(f515,plain,
ord_less_int(pls,sF1),
inference(forward_demodulation,[],[f514,f451]) ).
tff(f514,plain,
ord_less_int(pls,plus_plus_int(one_one_int,sF0)),
inference(superposition,[],[f404,f450]) ).
tff(f404,plain,
ord_less_int(pls,plus_plus_int(one_one_int,semiri1621563631at_int(n))),
inference(definition_unfolding,[],[f292,f265]) ).
tff(f292,plain,
ord_less_int(zero_zero_int,plus_plus_int(one_one_int,semiri1621563631at_int(n))),
inference(cnf_transformation,[],[f1]) ).
tff(f1,axiom,
ord_less_int(zero_zero_int,plus_plus_int(one_one_int,semiri1621563631at_int(n))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0_n1pos) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : NUM925_1 : TPTP v8.1.0. Released v5.3.0.
% 0.07/0.13 % Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_sat --cores 0 -t %d %s
% 0.13/0.35 % Computer : n011.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Tue Aug 30 09:19:25 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.19/0.50 % (10831)ott+10_1:32_bd=off:fsr=off:newcnf=on:tgt=full:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.19/0.52 % (10839)ott+10_1:32_bd=off:fsr=off:newcnf=on:tgt=full:i=100:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/100Mi)
% 0.19/0.53 % (10851)ott+11_1:1_drc=off:nwc=5.0:slsq=on:slsqc=1:spb=goal_then_units:to=lpo:i=467:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/467Mi)
% 0.19/0.53 % (10831)First to succeed.
% 0.19/0.53 % (10833)dis+34_1:32_abs=on:add=off:bsr=on:gsp=on:sp=weighted_frequency:i=48:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/48Mi)
% 0.19/0.54 % (10831)Refutation found. Thanks to Tanya!
% 0.19/0.54 % SZS status Theorem for theBenchmark
% 0.19/0.54 % SZS output start Proof for theBenchmark
% See solution above
% 0.19/0.54 % (10831)------------------------------
% 0.19/0.54 % (10831)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.54 % (10831)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.54 % (10831)Termination reason: Refutation
% 0.19/0.54
% 0.19/0.54 % (10831)Memory used [KB]: 5884
% 0.19/0.54 % (10831)Time elapsed: 0.105 s
% 0.19/0.54 % (10831)Instructions burned: 26 (million)
% 0.19/0.54 % (10831)------------------------------
% 0.19/0.54 % (10831)------------------------------
% 0.19/0.54 % (10827)Success in time 0.181 s
%------------------------------------------------------------------------------