%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM983_5 : TPTP v9.3.1. Released v6.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n008.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 12:17:44 PM UTC 2026
% Result : Theorem 2.55s 1.26s
% Output : Refutation 2.55s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 5
% Syntax : Number of formulae : 16 ( 14 unt; 0 typ; 1 def)
% Number of atoms : 18 ( 11 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 7 ( 5 ~; 0 |; 2 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 2 ( 2 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of FOOLs : 1 ( 1 fml; 0 var)
% Number of types : 4 ( 3 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 21 ( 19 usr; 1 prp; 0-3 aty)
% Number of functors : 26 ( 26 usr; 15 con; 0-3 aty)
% Number of variables : 2 ( 2 !; 0 ?; 2 :)
% Comments :
%------------------------------------------------------------------------------
tff(type_def_5,type,
bool: $tType ).
tff(type_def_6,type,
int: $tType ).
tff(type_def_7,type,
nat: $tType ).
tff(func_def_0,type,
abs_abs:
!>[X0: $tType] : ( X0 > X0 ) ).
tff(func_def_1,type,
minus_minus:
!>[X0: $tType] : ( ( X0 * X0 ) > X0 ) ).
tff(func_def_2,type,
one_one:
!>[X0: $tType] : X0 ).
tff(func_def_3,type,
plus_plus:
!>[X0: $tType] : ( ( X0 * X0 ) > X0 ) ).
tff(func_def_4,type,
times_times:
!>[X0: $tType] : ( ( X0 * X0 ) > X0 ) ).
tff(func_def_5,type,
bit0: int > int ).
tff(func_def_6,type,
bit1: int > int ).
tff(func_def_7,type,
pls: int ).
tff(func_def_8,type,
number_number_of:
!>[X0: $tType] : ( int > X0 ) ).
tff(func_def_9,type,
semiring_1_of_nat:
!>[X0: $tType] : ( nat > X0 ) ).
tff(func_def_10,type,
power_power:
!>[X0: $tType] : ( ( X0 * nat ) > X0 ) ).
tff(func_def_11,type,
fFalse: bool ).
tff(func_def_12,type,
fTrue: bool ).
tff(func_def_13,type,
m: int ).
tff(func_def_14,type,
n: nat ).
tff(func_def_15,type,
r: int ).
tff(func_def_16,type,
sa: int ).
tff(func_def_17,type,
v: int ).
tff(func_def_18,type,
w: int ).
tff(func_def_19,type,
x: int ).
tff(func_def_20,type,
y: int ).
tff(func_def_21,type,
sK0: ( int * int ) > nat ).
tff(func_def_22,type,
sK1: int ).
tff(func_def_23,type,
sK2: int ).
tff(func_def_24,type,
sK3: int ).
tff(func_def_25,type,
sK4: int ).
tff(pred_def_1,type,
number:
!>[X0: $tType] : $o ).
tff(pred_def_2,type,
ring:
!>[X0: $tType] : $o ).
tff(pred_def_3,type,
semiring:
!>[X0: $tType] : $o ).
tff(pred_def_4,type,
number_ring:
!>[X0: $tType] : $o ).
tff(pred_def_5,type,
ring_char_0:
!>[X0: $tType] : $o ).
tff(pred_def_6,type,
semiring_1:
!>[X0: $tType] : $o ).
tff(pred_def_7,type,
monoid_mult:
!>[X0: $tType] : $o ).
tff(pred_def_8,type,
number_semiring:
!>[X0: $tType] : $o ).
tff(pred_def_9,type,
linordered_idom:
!>[X0: $tType] : $o ).
tff(pred_def_10,type,
zprime: int > $o ).
tff(pred_def_11,type,
ord_less_eq:
!>[X0: $tType] : ( ( X0 * X0 ) > $o ) ).
tff(pred_def_12,type,
pp: bool > $o ).
tff(pred_def_13,type,
sP5: int > $o ).
tff(pred_def_14,type,
sP6: int > $o ).
tff(pred_def_15,type,
sP7: int > $o ).
tff(pred_def_16,type,
sP8: int > $o ).
tff(pred_def_17,type,
sP9: int > $o ).
tff(pred_def_18,type,
sP10: int > $o ).
tff(pred_def_19,type,
sP11: int > $o ).
tff(f1,axiom,
( ( v = minus_minus(int,x,times_times(int,r,plus_plus(int,one_one(int),semiring_1_of_nat(int,n)))) )
& ord_less_eq(int,times_times(int,number_number_of(int,bit0(bit1(pls))),abs_abs(int,v)),plus_plus(int,one_one(int),semiring_1_of_nat(int,n))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0_rv) ).
tff(f2,axiom,
( ( w = minus_minus(int,y,times_times(int,sa,plus_plus(int,one_one(int),semiring_1_of_nat(int,n)))) )
& ord_less_eq(int,times_times(int,number_number_of(int,bit0(bit1(pls))),abs_abs(int,w)),plus_plus(int,one_one(int),semiring_1_of_nat(int,n))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1_sw) ).
tff(f85,axiom,
! [X0: int] : ( bit0(X0) = plus_plus(int,X0,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_84_Bit0__def) ).
tff(f115,conjecture,
plus_plus(int,power_power(int,v,number_number_of(nat,bit0(bit1(pls)))),power_power(int,w,number_number_of(nat,bit0(bit1(pls))))) = plus_plus(int,power_power(int,minus_minus(int,x,times_times(int,r,plus_plus(int,one_one(int),semiring_1_of_nat(int,n)))),number_number_of(nat,bit0(bit1(pls)))),power_power(int,minus_minus(int,y,times_times(int,sa,plus_plus(int,one_one(int),semiring_1_of_nat(int,n)))),number_number_of(nat,bit0(bit1(pls))))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
tff(f116,negated_conjecture,
( ( ~ plus_plus(int,power_power(int,v,number_number_of(nat,bit0(bit1(pls)))),power_power(int,w,number_number_of(nat,bit0(bit1(pls))))) ) = plus_plus(int,power_power(int,minus_minus(int,x,times_times(int,r,plus_plus(int,one_one(int),semiring_1_of_nat(int,n)))),number_number_of(nat,bit0(bit1(pls)))),power_power(int,minus_minus(int,y,times_times(int,sa,plus_plus(int,one_one(int),semiring_1_of_nat(int,n)))),number_number_of(nat,bit0(bit1(pls))))) ),
inference(negated_conjecture,[status(cth)],[f115]) ).
tff(f117,plain,
plus_plus(int,power_power(int,v,number_number_of(nat,bit0(bit1(pls)))),power_power(int,w,number_number_of(nat,bit0(bit1(pls))))) != plus_plus(int,power_power(int,minus_minus(int,x,times_times(int,r,plus_plus(int,one_one(int),semiring_1_of_nat(int,n)))),number_number_of(nat,bit0(bit1(pls)))),power_power(int,minus_minus(int,y,times_times(int,sa,plus_plus(int,one_one(int),semiring_1_of_nat(int,n)))),number_number_of(nat,bit0(bit1(pls))))),
inference(flattening,[],[f116]) ).
tff(f131,plain,
plus_plus(int,power_power(int,v,number_number_of(nat,bit0(bit1(pls)))),power_power(int,w,number_number_of(nat,bit0(bit1(pls))))) != plus_plus(int,power_power(int,minus_minus(int,x,times_times(int,r,plus_plus(int,one_one(int),semiring_1_of_nat(int,n)))),number_number_of(nat,bit0(bit1(pls)))),power_power(int,minus_minus(int,y,times_times(int,sa,plus_plus(int,one_one(int),semiring_1_of_nat(int,n)))),number_number_of(nat,bit0(bit1(pls))))),
inference(cnf_transformation,[],[f117]) ).
tff(f144,plain,
! [X0: int] : ( bit0(X0) = plus_plus(int,X0,X0) ),
inference(cnf_transformation,[],[f85]) ).
tff(f187,plain,
v = minus_minus(int,x,times_times(int,r,plus_plus(int,one_one(int),semiring_1_of_nat(int,n)))),
inference(cnf_transformation,[],[f1]) ).
tff(f189,plain,
w = minus_minus(int,y,times_times(int,sa,plus_plus(int,one_one(int),semiring_1_of_nat(int,n)))),
inference(cnf_transformation,[],[f2]) ).
tff(f194,plain,
plus_plus(int,power_power(int,v,number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls)))),power_power(int,w,number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls))))) != plus_plus(int,power_power(int,minus_minus(int,x,times_times(int,r,plus_plus(int,one_one(int),semiring_1_of_nat(int,n)))),number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls)))),power_power(int,minus_minus(int,y,times_times(int,sa,plus_plus(int,one_one(int),semiring_1_of_nat(int,n)))),number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls))))),
inference(definition_unfolding,[],[f131,f144,f144,f144,f144]) ).
tff(f222,definition,
~ sP5(plus_plus(int,power_power(int,v,number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls)))),power_power(int,w,number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls)))))),
introduced(definition,[new_symbols(definition,[sP5])],[inequality_splitting_name_introduction]) ).
tff(f223,plain,
sP5(plus_plus(int,power_power(int,minus_minus(int,x,times_times(int,r,plus_plus(int,one_one(int),semiring_1_of_nat(int,n)))),number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls)))),power_power(int,minus_minus(int,y,times_times(int,sa,plus_plus(int,one_one(int),semiring_1_of_nat(int,n)))),number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls)))))),
inference(inequality_splitting,[],[f194,f222]) ).
tff(f240,plain,
sP5(plus_plus(int,power_power(int,minus_minus(int,x,times_times(int,r,plus_plus(int,one_one(int),semiring_1_of_nat(int,n)))),number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls)))),power_power(int,w,number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls)))))),
inference(forward_demodulation,[],[f223,f189]) ).
tff(f241,plain,
sP5(plus_plus(int,power_power(int,v,number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls)))),power_power(int,w,number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls)))))),
inference(forward_demodulation,[],[f240,f187]) ).
tff(f242,plain,
$false,
inference(forward_subsumption_resolution,[],[f241,f222]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM983_5 : TPTP v9.3.1. Released v6.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.39 % Computer : n008.cluster.edu
% 0.10/0.39 % Model : x86_64 x86_64
% 0.10/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.39 % Memory : 8046.5625MB
% 0.10/0.39 % OS : Linux 6.8.0-71-generic
% 0.10/0.39 % CPULimit : 300
% 0.10/0.39 % WCLimit : 300
% 0.10/0.39 % DateTime : Sun Sep 27 21:50:09 UTC 2026
% 0.10/0.39 % CPUTime :
% 0.10/0.39 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.43 Running first-order theorem proving
% 0.10/0.43 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 2.55/1.26 % (1635061)Detected formulas, will run a generic FOF schedule.
% 2.55/1.26 % (1635069)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=348459881:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.55/1.26 % (1635069)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 2.55/1.26 % (1635069)First to succeed.
% 2.55/1.26 % (1635069)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-1635061"
% 2.55/1.26 % (1635066)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=full:npcc=on:drc=off:sp=weighted_frequency:spb=goal:fd=preordered:foolp=on:random_seed=3102095875:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.55/1.26 % (1635072)dis-21_1_sil=8000:lcm=predicate:random_seed=3861221751:st=5:avsq=on:i=129:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/129Mi)
% 2.55/1.26 % (1635068)lrs+1010_1_anc=all:sfv=off:to=kbo:ncem=casc2026/models/loop7.pt:sil=128000:npcc=on:prc=on:sos=all:bsr=unit_only:sac=on:random_seed=1749549694:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.55/1.26 % (1635071)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2173081964:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.55/1.26 % (1635067)lrs+11_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:lma=off:spb=units:urr=ec_only:bce=on:s2agt=64:updr=off:random_seed=1790951171:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.55/1.26 % (1635070)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2484007146:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.55/1.26 % (1635068)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 2.55/1.26 % (1635072)Refutation not found, incomplete strategy
% 2.55/1.26 % (1635072)------------------------------
% 2.55/1.26 % (1635072)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.55/1.26 % (1635072)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.55/1.26 % (1635072)CaDiCaL version: 2.1.3
% 2.55/1.26 % (1635072)Termination reason: Refutation not found, incomplete strategy
% 2.55/1.26 % (1635072)Time elapsed: 0.009 s
% 2.55/1.26 % (1635072)Peak memory usage: 88 MB
% 2.55/1.26 % (1635072)Instructions burned: 14 (million)
% 2.55/1.26 % (1635070)Also succeeded, but the first one will report.
% 2.55/1.26 % (1635071)Also succeeded, but the first one will report.
% 2.55/1.26 % (1635069)Refutation found. Thanks to Tanya!
% 2.55/1.26 % SZS status Theorem for theBenchmark
% 2.55/1.26 % SZS output start Proof for theBenchmark
% See solution above
% 2.55/1.26 % (1635069)------------------------------
% 2.55/1.26 % (1635069)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.55/1.26 % (1635069)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.55/1.26 % (1635069)CaDiCaL version: 2.1.3
% 2.55/1.26 % (1635069)Termination reason: Refutation
% 2.55/1.26 % (1635069)Time elapsed: 0.003 s
% 2.55/1.26 % (1635069)Peak memory usage: 88 MB
% 2.55/1.26 % (1635069)Instructions burned: 6 (million)
% 2.55/1.26 % (1635069)------------------------------
% 2.55/1.26 % (1635069)------------------------------
% 2.55/1.26 % (1635061)Success in time 0.295 s
% 2.55/1.26 % Vampire exiting
%------------------------------------------------------------------------------