%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : NUM994_5 : TPTP v9.3.1. Released v6.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n011.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 12:26:21 PM UTC 2026
% Result : Theorem 0.21s 0.54s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 11
% Syntax : Number of formulae : 49 ( 21 unt; 0 typ; 2 def)
% Number of atoms : 77 ( 12 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 52 ( 24 ~; 21 |; 2 &)
% ( 3 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of types : 4 ( 3 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 24 ( 22 usr; 3 prp; 0-3 aty)
% Number of functors : 11 ( 11 usr; 5 con; 0-3 aty)
% Number of variables : 25 ( 0 sgn 25 !; 0 ?; 25 :)
% 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,
times_times:
!>[X0: $tType] : ( ( X0 * X0 ) > X0 ) ).
tff(func_def_2,type,
zero_zero:
!>[X0: $tType] : X0 ).
tff(func_def_3,type,
bit0: int > int ).
tff(func_def_4,type,
bit1: int > int ).
tff(func_def_5,type,
pls: int ).
tff(func_def_6,type,
number_number_of:
!>[X0: $tType] : ( int > X0 ) ).
tff(func_def_7,type,
fFalse: bool ).
tff(func_def_8,type,
fTrue: bool ).
tff(func_def_9,type,
v: int ).
tff(func_def_10,type,
w: int ).
tff(pred_def_1,type,
number:
!>[X0: $tType] : $o ).
tff(pred_def_2,type,
zero:
!>[X0: $tType] : $o ).
tff(pred_def_3,type,
number_ring:
!>[X0: $tType] : $o ).
tff(pred_def_4,type,
ring_char_0:
!>[X0: $tType] : $o ).
tff(pred_def_5,type,
mult_zero:
!>[X0: $tType] : $o ).
tff(pred_def_6,type,
ordered_ring:
!>[X0: $tType] : $o ).
tff(pred_def_7,type,
number_semiring:
!>[X0: $tType] : $o ).
tff(pred_def_8,type,
linordered_idom:
!>[X0: $tType] : $o ).
tff(pred_def_9,type,
linordered_ring:
!>[X0: $tType] : $o ).
tff(pred_def_10,type,
no_zero_divisors:
!>[X0: $tType] : $o ).
tff(pred_def_11,type,
ordered_ring_abs:
!>[X0: $tType] : $o ).
tff(pred_def_12,type,
ordered_semiring:
!>[X0: $tType] : $o ).
tff(pred_def_13,type,
ab_semigroup_mult:
!>[X0: $tType] : $o ).
tff(pred_def_14,type,
ordere1490568538miring:
!>[X0: $tType] : $o ).
tff(pred_def_15,type,
ring_n68954251visors:
!>[X0: $tType] : $o ).
tff(pred_def_16,type,
linord581940658strict:
!>[X0: $tType] : $o ).
tff(pred_def_17,type,
ordere453448008miring:
!>[X0: $tType] : $o ).
tff(pred_def_18,type,
ordere142940540dd_abs:
!>[X0: $tType] : $o ).
tff(pred_def_19,type,
ord_less_eq:
!>[X0: $tType] : ( ( X0 * X0 ) > $o ) ).
tff(pred_def_20,type,
pp: bool > $o ).
tff(f3,axiom,
! [X0: int] :
( ord_less_eq(int,pls,bit0(X0))
<=> ord_less_eq(int,pls,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2_rel__simps_I21_J) ).
tff(f30,axiom,
! [X0: int,X1: int] : ( times_times(int,bit0(X1),X0) = bit0(times_times(int,X1,X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_29_mult__Bit0) ).
tff(f34,axiom,
! [X0: int] : ( number_number_of(int,X0) = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_33_number__of__is__id) ).
tff(f37,axiom,
pls = zero_zero(int),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_36_Pls__def) ).
tff(f45,axiom,
! [X0: $tType] :
( ordere142940540dd_abs(X0)
=> ! [X1: X0] : ord_less_eq(X0,zero_zero(X0),abs_abs(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_44_abs__ge__zero) ).
tff(f50,axiom,
! [X0: $tType] :
( number_ring(X0)
=> ! [X1: X0] : ( times_times(X0,number_number_of(X0,bit1(pls)),X1) = X1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_49_mult__numeral__1) ).
tff(f98,axiom,
ordere142940540dd_abs(int),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Oordered__ab__group__add__abs) ).
tff(f113,axiom,
number_ring(int),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Int_Onumber__ring) ).
tff(f127,conjecture,
( ord_less_eq(int,zero_zero(int),times_times(int,number_number_of(int,bit0(bit1(pls))),abs_abs(int,v)))
& ord_less_eq(int,zero_zero(int),times_times(int,number_number_of(int,bit0(bit1(pls))),abs_abs(int,w))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
tff(f128,negated_conjecture,
~ ( ord_less_eq(int,zero_zero(int),times_times(int,number_number_of(int,bit0(bit1(pls))),abs_abs(int,v)))
& ord_less_eq(int,zero_zero(int),times_times(int,number_number_of(int,bit0(bit1(pls))),abs_abs(int,w))) ),
inference(negated_conjecture,[status(cth)],[f127]) ).
tff(f151,plain,
! [X0: $tType] :
( ! [X1: X0] : ord_less_eq(X0,zero_zero(X0),abs_abs(X0,X1))
| ~ ordere142940540dd_abs(X0) ),
inference(ennf_transformation,[],[f45]) ).
tff(f155,plain,
! [X0: $tType] :
( ! [X1: X0] : ( times_times(X0,number_number_of(X0,bit1(pls)),X1) = X1 )
| ~ number_ring(X0) ),
inference(ennf_transformation,[],[f50]) ).
tff(f205,plain,
( ~ ord_less_eq(int,zero_zero(int),times_times(int,number_number_of(int,bit0(bit1(pls))),abs_abs(int,v)))
| ~ ord_less_eq(int,zero_zero(int),times_times(int,number_number_of(int,bit0(bit1(pls))),abs_abs(int,w))) ),
inference(ennf_transformation,[],[f128]) ).
tff(f210,plain,
! [X0: int] :
( ord_less_eq(int,pls,bit0(X0))
| ~ ord_less_eq(int,pls,X0) ),
inference(cnf_transformation,[],[f3]) ).
tff(f251,plain,
! [X0: int,X1: int] : ( times_times(int,bit0(X1),X0) = bit0(times_times(int,X1,X0)) ),
inference(cnf_transformation,[],[f30]) ).
tff(f253,plain,
! [X0: int] : ( number_number_of(int,X0) = X0 ),
inference(cnf_transformation,[],[f34]) ).
tff(f256,plain,
pls = zero_zero(int),
inference(cnf_transformation,[],[f37]) ).
tff(f267,plain,
! [X0: $tType,X1: X0] :
( ~ ordere142940540dd_abs(X0)
| ord_less_eq(X0,zero_zero(X0),abs_abs(X0,X1)) ),
inference(cnf_transformation,[],[f151]) ).
tff(f273,plain,
! [X0: $tType,X1: X0] :
( ~ number_ring(X0)
| ( times_times(X0,number_number_of(X0,bit1(pls)),X1) = X1 ) ),
inference(cnf_transformation,[],[f155]) ).
tff(f348,plain,
ordere142940540dd_abs(int),
inference(cnf_transformation,[],[f98]) ).
tff(f363,plain,
number_ring(int),
inference(cnf_transformation,[],[f113]) ).
tff(f377,plain,
( ~ ord_less_eq(int,zero_zero(int),times_times(int,number_number_of(int,bit0(bit1(pls))),abs_abs(int,w)))
| ~ ord_less_eq(int,zero_zero(int),times_times(int,number_number_of(int,bit0(bit1(pls))),abs_abs(int,v))) ),
inference(cnf_transformation,[],[f205]) ).
tff(f395,definition,
( spl0_1
<=> ord_less_eq(int,zero_zero(int),times_times(int,number_number_of(int,bit0(bit1(pls))),abs_abs(int,v))) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
tff(f397,plain,
( ~ ord_less_eq(int,zero_zero(int),times_times(int,number_number_of(int,bit0(bit1(pls))),abs_abs(int,v)))
| spl0_1 ),
inference(avatar_component_clause,[],[f395]) ).
tff(f399,definition,
( spl0_2
<=> ord_less_eq(int,zero_zero(int),times_times(int,number_number_of(int,bit0(bit1(pls))),abs_abs(int,w))) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
tff(f401,plain,
( ~ ord_less_eq(int,zero_zero(int),times_times(int,number_number_of(int,bit0(bit1(pls))),abs_abs(int,w)))
| spl0_2 ),
inference(avatar_component_clause,[],[f399]) ).
tff(f402,plain,
( ~ spl0_1
| ~ spl0_2 ),
inference(avatar_split_clause,[],[f377,f399,f395]) ).
tff(f407,plain,
( ~ ord_less_eq(int,zero_zero(int),times_times(int,bit0(bit1(pls)),abs_abs(int,v)))
| spl0_1 ),
inference(forward_demodulation,[],[f397,f253]) ).
tff(f408,plain,
( ~ ord_less_eq(int,pls,times_times(int,bit0(bit1(pls)),abs_abs(int,v)))
| spl0_1 ),
inference(forward_demodulation,[],[f407,f256]) ).
tff(f437,plain,
! [X0: int] : ord_less_eq(int,zero_zero(int),abs_abs(int,X0)),
inference(resolution,[],[f267,f348]) ).
tff(f438,plain,
! [X0: int] : ord_less_eq(int,pls,abs_abs(int,X0)),
inference(forward_demodulation,[],[f437,f256]) ).
tff(f505,plain,
! [X0: int] : ( times_times(int,number_number_of(int,bit1(pls)),X0) = X0 ),
inference(resolution,[],[f273,f363]) ).
tff(f506,plain,
! [X0: int] : ( times_times(int,bit1(pls),X0) = X0 ),
inference(forward_demodulation,[],[f505,f253]) ).
tff(f508,plain,
! [X0: int] : ( bit0(X0) = times_times(int,bit0(bit1(pls)),X0) ),
inference(superposition,[],[f251,f506]) ).
tff(f532,plain,
( ~ ord_less_eq(int,pls,bit0(abs_abs(int,v)))
| spl0_1 ),
inference(superposition,[],[f408,f508]) ).
tff(f548,plain,
( ~ ord_less_eq(int,pls,abs_abs(int,v))
| spl0_1 ),
inference(resolution,[],[f532,f210]) ).
tff(f549,plain,
( $false
| spl0_1 ),
inference(forward_subsumption_resolution,[],[f548,f438]) ).
tff(f550,plain,
spl0_1,
inference(avatar_contradiction_clause,[],[f549]) ).
tff(f552,plain,
( ~ ord_less_eq(int,zero_zero(int),times_times(int,bit0(bit1(pls)),abs_abs(int,w)))
| spl0_2 ),
inference(forward_demodulation,[],[f401,f253]) ).
tff(f554,plain,
( ~ ord_less_eq(int,zero_zero(int),bit0(abs_abs(int,w)))
| spl0_2 ),
inference(forward_demodulation,[],[f552,f508]) ).
tff(f556,plain,
( ~ ord_less_eq(int,pls,bit0(abs_abs(int,w)))
| spl0_2 ),
inference(forward_demodulation,[],[f554,f256]) ).
tff(f558,plain,
( ~ ord_less_eq(int,pls,abs_abs(int,w))
| spl0_2 ),
inference(resolution,[],[f556,f210]) ).
tff(f559,plain,
( $false
| spl0_2 ),
inference(forward_subsumption_resolution,[],[f558,f438]) ).
tff(f560,plain,
spl0_2,
inference(avatar_contradiction_clause,[],[f559]) ).
cnf(s1,plain,
( ~ spl0_1
| ~ spl0_2 ),
inference(sat_conversion,[],[f402]) ).
cnf(s2,plain,
spl0_1,
inference(sat_conversion,[],[f550]) ).
cnf(s3,plain,
spl0_2,
inference(sat_conversion,[],[f560]) ).
cnf(s4,plain,
$false,
inference(rat,[],[s1,s3,s2]) ).
tff(f561,plain,
$false,
inference(avatar_sat_refutation,[],[s4]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : NUM994_5 : TPTP v9.3.1. Released v6.0.0.
% 0.00/0.07 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.15/0.42 % Computer : n011.cluster.edu
% 0.15/0.42 % Model : x86_64 x86_64
% 0.15/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.42 % Memory : 8046.5625MB
% 0.15/0.42 % OS : Linux 6.8.0-71-generic
% 0.15/0.43 % CPULimit : 300
% 0.15/0.43 % WCLimit : 300
% 0.15/0.43 % DateTime : Sun Sep 27 21:49:45 UTC 2026
% 0.15/0.43 % CPUTime :
% 0.15/0.43 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.21/0.48 Running first-order model finding
% 0.21/0.48 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.21/0.54 % (2790805)Will run a generic schedule for satisfiability detection.
% 0.21/0.54 % (2790815)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1886149448:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.21/0.54 % (2790814)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2742985782:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.21/0.54 % (2790811)% WARNING: option uhcvi not known.
% 0.21/0.54 % (2790816)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=3380298439:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.21/0.54 % (2790810)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=3977503549_2999 on theBenchmark for (2999ds/0Mi)
% 0.21/0.54 % (2790812)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2076182097:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.21/0.54 % (2790811)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2641931564:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.21/0.54 % (2790813)dis+10_1_sil=32000:sp=arity:random_seed=1394715447:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.21/0.54 % Exception at run slice level
% 0.21/0.54 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.21/0.54 % (2790814) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2790805-2790814"...
% 0.21/0.54 % (2790814)...printing done.
% 0.21/0.54 % (2790814)Refutation found. Thanks to Tanya!
% 0.21/0.54 % SZS status Theorem for theBenchmark
% 0.21/0.54 % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.54 % (2790814)------------------------------
% 0.21/0.54 % (2790814)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.54 % (2790814)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.54 % (2790814)CaDiCaL version: 2.1.3
% 0.21/0.54 % (2790814)Termination reason: Refutation
% 0.21/0.54 % (2790814)Time elapsed: 0.015 s
% 0.21/0.54 % (2790814)Peak memory usage: 13 MB
% 0.21/0.54 % (2790814)Instructions burned: 19 (million)
% 0.21/0.54 % (2790805)Success in time 0.053 s
% 0.21/0.54 % Vampire exiting
%------------------------------------------------------------------------------