%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : NUM983_5 : TPTP v9.3.1. Released v6.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n004.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 12:26:20 PM UTC 2026
% Result : Theorem 0.18s 0.48s
% Output : Refutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 5
% Syntax : Number of formulae : 18 ( 16 unt; 0 typ; 0 def)
% Number of atoms : 20 ( 17 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 9 ( 7 ~; 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 : 14 ( 12 usr; 1 prp; 0-3 aty)
% Number of functors : 28 ( 28 usr; 17 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 ).
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(func_def_26,type,
sK5: int ).
tff(func_def_27,type,
sK6: ( int * int ) > nat ).
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(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/sandbox/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/sandbox/benchmark/theBenchmark.p',fact_1_sw) ).
tff(f51,axiom,
plus_plus(nat,one_one(nat),one_one(nat)) = number_number_of(nat,bit0(bit1(pls))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_50_nat__1__add__1) ).
tff(f85,axiom,
! [X0: int] : ( bit0(X0) = plus_plus(int,X0,X0) ),
file('/export/starexec/sandbox/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/sandbox/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(f162,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(f164,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(f227,plain,
number_number_of(nat,bit0(bit1(pls))) = plus_plus(nat,one_one(nat),one_one(nat)),
inference(cnf_transformation,[],[f51]) ).
tff(f267,plain,
! [X0: int] : ( bit0(X0) = plus_plus(int,X0,X0) ),
inference(cnf_transformation,[],[f85]) ).
tff(f298,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(f335,plain,
plus_plus(nat,one_one(nat),one_one(nat)) = number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls))),
inference(definition_unfolding,[],[f227,f267]) ).
tff(f350,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,[],[f298,f267,f267,f267,f267]) ).
tff(f532,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,v,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(superposition,[],[f350,f162]) ).
tff(f533,plain,
plus_plus(int,power_power(int,v,plus_plus(nat,one_one(nat),one_one(nat))),power_power(int,w,plus_plus(nat,one_one(nat),one_one(nat)))) != plus_plus(int,power_power(int,v,plus_plus(nat,one_one(nat),one_one(nat))),power_power(int,minus_minus(int,y,times_times(int,sa,plus_plus(int,one_one(int),semiring_1_of_nat(int,n)))),plus_plus(nat,one_one(nat),one_one(nat)))),
inference(forward_demodulation,[],[f532,f335]) ).
tff(f534,plain,
plus_plus(int,power_power(int,v,plus_plus(nat,one_one(nat),one_one(nat))),power_power(int,w,plus_plus(nat,one_one(nat),one_one(nat)))) != plus_plus(int,power_power(int,v,plus_plus(nat,one_one(nat),one_one(nat))),power_power(int,w,plus_plus(nat,one_one(nat),one_one(nat)))),
inference(forward_demodulation,[],[f533,f164]) ).
tff(f535,plain,
$false,
inference(trivial_inequality_removal,[],[f534]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM983_5 : TPTP v9.3.1. Released v6.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.11/0.39 % Computer : n004.cluster.edu
% 0.11/0.39 % Model : x86_64 x86_64
% 0.11/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.39 % Memory : 8046.5625MB
% 0.11/0.39 % OS : Linux 6.8.0-71-generic
% 0.11/0.39 % CPULimit : 300
% 0.11/0.39 % WCLimit : 300
% 0.11/0.39 % DateTime : Sun Sep 27 21:49:22 UTC 2026
% 0.11/0.39 % CPUTime :
% 0.11/0.39 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.11/0.43 Running first-order model finding
% 0.11/0.43 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.18/0.48 % (3909503)Will run a generic schedule for satisfiability detection.
% 0.18/0.48 % (3909512)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2278854287:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.18/0.48 % (3909509)% WARNING: option uhcvi not known.
% 0.18/0.48 % (3909508)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=3401697081_2999 on theBenchmark for (2999ds/0Mi)
% 0.18/0.48 % (3909512) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3909503-3909512"...
% 0.18/0.48 % (3909509)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3835376347:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.18/0.48 % (3909510)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1582624543:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.18/0.48 % (3909511)dis+10_1_sil=32000:sp=arity:random_seed=4043926257:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.18/0.48 % (3909513)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=225572871:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.18/0.48 % (3909514)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2719792171:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.18/0.48 % (3909512)...printing done.
% 0.18/0.48 % (3909512)Refutation found. Thanks to Tanya!
% 0.18/0.48 % SZS status Theorem for theBenchmark
% 0.18/0.48 % SZS output start Proof for theBenchmark
% See solution above
% 0.18/0.48 % (3909512)------------------------------
% 0.18/0.48 % (3909512)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.18/0.48 % (3909512)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.18/0.48 % (3909512)CaDiCaL version: 2.1.3
% 0.18/0.48 % (3909512)Termination reason: Refutation
% 0.18/0.48 % (3909512)Time elapsed: 0.007 s
% 0.18/0.48 % (3909512)Peak memory usage: 12 MB
% 0.18/0.48 % (3909512)Instructions burned: 22 (million)
% 0.18/0.48 % (3909503)Success in time 0.041 s
% 0.18/0.48 % Vampire exiting
%------------------------------------------------------------------------------