%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM948_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 : n010.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 12:17:40 PM UTC 2026
% Result : Theorem 2.05s 1.76s
% Output : Refutation 5.90s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 13
% Syntax : Number of formulae : 82 ( 44 unt; 0 typ; 2 def)
% Number of atoms : 188 ( 25 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 208 ( 102 ~; 78 |; 21 &)
% ( 2 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 18 ( 16 usr; 4 prp; 0-3 aty)
% Number of functors : 13 ( 13 usr; 6 con; 0-3 aty)
% Number of variables : 53 ( 0 sgn 49 !; 4 ?; 53 :)
% Comments :
%------------------------------------------------------------------------------
tff(type_def_5,type,
bool: $tType ).
tff(type_def_6,type,
int: $tType ).
tff(func_def_0,type,
one_one:
!>[X0: $tType] : X0 ).
tff(func_def_1,type,
plus_plus:
!>[X0: $tType] : ( ( X0 * X0 ) > X0 ) ).
tff(func_def_2,type,
times_times:
!>[X0: $tType] : ( ( X0 * X0 ) > X0 ) ).
tff(func_def_3,type,
zero_zero:
!>[X0: $tType] : X0 ).
tff(func_def_4,type,
bit0: int > int ).
tff(func_def_5,type,
bit1: int > int ).
tff(func_def_6,type,
pls: int ).
tff(func_def_7,type,
number_number_of:
!>[X0: $tType] : ( int > X0 ) ).
tff(func_def_8,type,
fFalse: bool ).
tff(func_def_9,type,
fTrue: bool ).
tff(func_def_10,type,
m: int ).
tff(func_def_11,type,
s1: int ).
tff(func_def_12,type,
sK0: int ).
tff(pred_def_1,type,
number:
!>[X0: $tType] : $o ).
tff(pred_def_2,type,
semiring:
!>[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,
linorder:
!>[X0: $tType] : $o ).
tff(pred_def_6,type,
number_semiring:
!>[X0: $tType] : $o ).
tff(pred_def_7,type,
linordered_idom:
!>[X0: $tType] : $o ).
tff(pred_def_8,type,
linord219039673up_add:
!>[X0: $tType] : $o ).
tff(pred_def_9,type,
zcong: ( int * int * int ) > $o ).
tff(pred_def_10,type,
zprime: int > $o ).
tff(pred_def_11,type,
ord_less:
!>[X0: $tType] : ( ( X0 * X0 ) > $o ) ).
tff(pred_def_12,type,
ord_less_eq:
!>[X0: $tType] : ( ( X0 * X0 ) > $o ) ).
tff(pred_def_13,type,
pp: bool > $o ).
tff(f1,axiom,
? [X1: int] :
( ord_less_eq(int,zero_zero(int),X1)
& ord_less(int,X1,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)))
& zcong(s1,X1,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)))
& ! [X2: int] :
( ( ord_less_eq(int,zero_zero(int),X2)
& ord_less(int,X2,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)))
& zcong(s1,X2,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int))) )
=> ( X2 = X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0__096EX_B_As_O_A0_A_060_061_As_A_G_As_A_060_A4_A_K_Am_A_L_A1_A_G_A_091s1_A_061_As_093_A_Imod_A4_A_K_Am_A_L_A1_J_096) ).
tff(f34,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_33_mult__Bit0) ).
tff(f54,axiom,
! [X0: int,X1: int] : ( plus_plus(int,bit0(X1),bit1(X0)) = bit1(plus_plus(int,X1,X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_53_add__Bit0__Bit1) ).
tff(f55,axiom,
! [X0: $tType] :
( number_ring(X0)
=> ( number_number_of(X0,bit1(pls)) = one_one(X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_54_numeral__1__eq__1) ).
tff(f62,axiom,
! [X0: int] : ( number_number_of(int,X0) = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_61_number__of__is__id) ).
tff(f63,axiom,
pls = zero_zero(int),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_62_Pls__def) ).
tff(f69,axiom,
! [X0: int] : ( plus_plus(int,X0,pls) = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_68_add__Pls__right) ).
tff(f97,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_96_mult__numeral__1) ).
tff(f104,axiom,
number_ring(int),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Int_Onumber__ring) ).
tff(f110,axiom,
! [X0: int] :
( ( ord_less_eq(int,zero_zero(int),X0)
& ord_less(int,X0,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)))
& zcong(s1,X0,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int))) )
=> thesis ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
tff(f111,conjecture,
thesis,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_1) ).
tff(f112,negated_conjecture,
~ thesis,
inference(negated_conjecture,[status(cth)],[f111]) ).
tff(f113,plain,
? [X0: int] :
( ord_less_eq(int,zero_zero(int),X0)
& ord_less(int,X0,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)))
& zcong(s1,X0,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)))
& ! [X1: int] :
( ( ord_less_eq(int,zero_zero(int),X1)
& ord_less(int,X1,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)))
& zcong(s1,X1,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int))) )
=> ( X0 = X1 ) ) ),
inference(rectify,[],[f1]) ).
tff(f114,plain,
~ thesis,
inference(flattening,[],[f112]) ).
tff(f116,plain,
? [X0: int] :
( ord_less_eq(int,zero_zero(int),X0)
& ord_less(int,X0,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)))
& zcong(s1,X0,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)))
& ! [X1: int] :
( ( X0 = X1 )
| ~ ord_less_eq(int,zero_zero(int),X1)
| ~ ord_less(int,X1,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)))
| ~ zcong(s1,X1,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int))) ) ),
inference(ennf_transformation,[],[f113]) ).
tff(f117,plain,
? [X0: int] :
( ord_less_eq(int,zero_zero(int),X0)
& ord_less(int,X0,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)))
& zcong(s1,X0,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)))
& ! [X1: int] :
( ( X0 = X1 )
| ~ ord_less_eq(int,zero_zero(int),X1)
| ~ ord_less(int,X1,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)))
| ~ zcong(s1,X1,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int))) ) ),
inference(flattening,[],[f116]) ).
tff(f153,plain,
! [X0: $tType] :
( ( number_number_of(X0,bit1(pls)) = one_one(X0) )
| ~ number_ring(X0) ),
inference(ennf_transformation,[],[f55]) ).
tff(f167,plain,
! [X0: $tType] :
( ! [X1: X0] : ( times_times(X0,number_number_of(X0,bit1(pls)),X1) = X1 )
| ~ number_ring(X0) ),
inference(ennf_transformation,[],[f97]) ).
tff(f169,plain,
! [X0: int] :
( thesis
| ~ ord_less_eq(int,zero_zero(int),X0)
| ~ ord_less(int,X0,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)))
| ~ zcong(s1,X0,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int))) ),
inference(ennf_transformation,[],[f110]) ).
tff(f170,plain,
! [X0: int] :
( thesis
| ~ ord_less_eq(int,zero_zero(int),X0)
| ~ ord_less(int,X0,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)))
| ~ zcong(s1,X0,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int))) ),
inference(flattening,[],[f169]) ).
tff(f171,plain,
( ord_less_eq(int,zero_zero(int),sK0)
& ord_less(int,sK0,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)))
& zcong(s1,sK0,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)))
& ! [X1: int] :
( ( sK0 = X1 )
| ~ ord_less_eq(int,zero_zero(int),X1)
| ~ ord_less(int,X1,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)))
| ~ zcong(s1,X1,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int))) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[f117]) ).
tff(f223,plain,
zcong(s1,sK0,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int))),
inference(cnf_transformation,[],[f171]) ).
tff(f224,plain,
ord_less(int,sK0,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int))),
inference(cnf_transformation,[],[f171]) ).
tff(f225,plain,
ord_less_eq(int,zero_zero(int),sK0),
inference(cnf_transformation,[],[f171]) ).
tff(f276,plain,
! [X0: int,X1: int] : ( times_times(int,bit0(X1),X0) = bit0(times_times(int,X1,X0)) ),
inference(cnf_transformation,[],[f34]) ).
tff(f306,plain,
! [X0: int,X1: int] : ( bit1(plus_plus(int,X1,X0)) = plus_plus(int,bit0(X1),bit1(X0)) ),
inference(cnf_transformation,[],[f54]) ).
tff(f307,plain,
! [X0: $tType] :
( ~ number_ring(X0)
| ( one_one(X0) = number_number_of(X0,bit1(pls)) ) ),
inference(cnf_transformation,[],[f153]) ).
tff(f319,plain,
! [X0: int] : ( number_number_of(int,X0) = X0 ),
inference(cnf_transformation,[],[f62]) ).
tff(f320,plain,
zero_zero(int) = pls,
inference(cnf_transformation,[],[f63]) ).
tff(f332,plain,
! [X0: int] : ( plus_plus(int,X0,pls) = X0 ),
inference(cnf_transformation,[],[f69]) ).
tff(f370,plain,
! [X0: $tType,X1: X0] :
( ~ number_ring(X0)
| ( times_times(X0,number_number_of(X0,bit1(pls)),X1) = X1 ) ),
inference(cnf_transformation,[],[f167]) ).
tff(f377,plain,
number_ring(int),
inference(cnf_transformation,[],[f104]) ).
tff(f383,plain,
! [X0: int] :
( thesis
| ~ ord_less_eq(int,zero_zero(int),X0)
| ~ ord_less(int,X0,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)))
| ~ zcong(s1,X0,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int))) ),
inference(cnf_transformation,[],[f170]) ).
tff(f384,plain,
~ thesis,
inference(cnf_transformation,[],[f114]) ).
tff(f396,definition,
( spl1_1
<=> ! [X0: int] :
( ~ ord_less_eq(int,zero_zero(int),X0)
| ~ zcong(s1,X0,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)))
| ~ ord_less(int,X0,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int))) ) ),
introduced(definition,[new_symbols(definition,[spl1_1])],[avatar_definition]) ).
tff(f397,plain,
( ! [X0: int] :
( ~ ord_less_eq(int,zero_zero(int),X0)
| ~ zcong(s1,X0,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)))
| ~ ord_less(int,X0,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int))) )
| ~ spl1_1 ),
inference(avatar_component_clause,[],[f396]) ).
tff(f399,definition,
( spl1_2
<=> thesis ),
introduced(definition,[new_symbols(definition,[spl1_2])],[avatar_definition]) ).
tff(f402,plain,
( spl1_1
| spl1_2 ),
inference(avatar_split_clause,[],[f383,f399,f396]) ).
tff(f403,plain,
~ spl1_2,
inference(avatar_split_clause,[],[f384,f399]) ).
tff(f404,plain,
( ! [X0: int] :
( ~ ord_less_eq(int,pls,X0)
| ~ zcong(s1,X0,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)))
| ~ ord_less(int,X0,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int))) )
| ~ spl1_1 ),
inference(superposition,[],[f397,f320]) ).
tff(f405,plain,
ord_less_eq(int,pls,sK0),
inference(forward_demodulation,[],[f225,f320]) ).
tff(f466,plain,
one_one(int) = number_number_of(int,bit1(pls)),
inference(resolution,[],[f307,f377]) ).
tff(f467,plain,
bit1(pls) = one_one(int),
inference(forward_demodulation,[],[f466,f319]) ).
tff(f610,plain,
! [X0: int] : ( times_times(int,number_number_of(int,bit1(pls)),X0) = X0 ),
inference(resolution,[],[f370,f377]) ).
tff(f611,plain,
! [X0: int] : ( times_times(int,bit1(pls),X0) = X0 ),
inference(forward_demodulation,[],[f610,f319]) ).
tff(f936,plain,
zcong(s1,sK0,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),bit1(pls))),
inference(forward_demodulation,[],[f223,f467]) ).
tff(f937,plain,
zcong(s1,sK0,plus_plus(int,times_times(int,bit0(bit0(bit1(pls))),m),bit1(pls))),
inference(forward_demodulation,[],[f936,f319]) ).
tff(f938,plain,
zcong(s1,sK0,plus_plus(int,bit0(times_times(int,bit0(bit1(pls)),m)),bit1(pls))),
inference(forward_demodulation,[],[f937,f276]) ).
tff(f939,plain,
zcong(s1,sK0,bit1(plus_plus(int,times_times(int,bit0(bit1(pls)),m),pls))),
inference(forward_demodulation,[],[f938,f306]) ).
tff(f940,plain,
zcong(s1,sK0,bit1(times_times(int,bit0(bit1(pls)),m))),
inference(forward_demodulation,[],[f939,f332]) ).
tff(f941,plain,
zcong(s1,sK0,bit1(bit0(times_times(int,bit1(pls),m)))),
inference(forward_demodulation,[],[f940,f276]) ).
tff(f942,plain,
zcong(s1,sK0,bit1(bit0(m))),
inference(forward_demodulation,[],[f941,f611]) ).
tff(f943,plain,
ord_less(int,sK0,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),bit1(pls))),
inference(forward_demodulation,[],[f224,f467]) ).
tff(f944,plain,
ord_less(int,sK0,plus_plus(int,times_times(int,bit0(bit0(bit1(pls))),m),bit1(pls))),
inference(forward_demodulation,[],[f943,f319]) ).
tff(f945,plain,
ord_less(int,sK0,plus_plus(int,bit0(times_times(int,bit0(bit1(pls)),m)),bit1(pls))),
inference(forward_demodulation,[],[f944,f276]) ).
tff(f946,plain,
ord_less(int,sK0,bit1(plus_plus(int,times_times(int,bit0(bit1(pls)),m),pls))),
inference(forward_demodulation,[],[f945,f306]) ).
tff(f947,plain,
ord_less(int,sK0,bit1(times_times(int,bit0(bit1(pls)),m))),
inference(forward_demodulation,[],[f946,f332]) ).
tff(f948,plain,
ord_less(int,sK0,bit1(bit0(times_times(int,bit1(pls),m)))),
inference(forward_demodulation,[],[f947,f276]) ).
tff(f949,plain,
ord_less(int,sK0,bit1(bit0(m))),
inference(forward_demodulation,[],[f948,f611]) ).
tff(f2289,plain,
( ! [X0: int] :
( ~ zcong(s1,X0,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),bit1(pls)))
| ~ ord_less_eq(int,pls,X0)
| ~ ord_less(int,X0,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int))) )
| ~ spl1_1 ),
inference(forward_demodulation,[],[f404,f467]) ).
tff(f2290,plain,
( ! [X0: int] :
( ~ zcong(s1,X0,plus_plus(int,times_times(int,bit0(bit0(bit1(pls))),m),bit1(pls)))
| ~ ord_less_eq(int,pls,X0)
| ~ ord_less(int,X0,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int))) )
| ~ spl1_1 ),
inference(forward_demodulation,[],[f2289,f319]) ).
tff(f2291,plain,
( ! [X0: int] :
( ~ zcong(s1,X0,plus_plus(int,bit0(times_times(int,bit0(bit1(pls)),m)),bit1(pls)))
| ~ ord_less_eq(int,pls,X0)
| ~ ord_less(int,X0,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int))) )
| ~ spl1_1 ),
inference(forward_demodulation,[],[f2290,f276]) ).
tff(f2292,plain,
( ! [X0: int] :
( ~ zcong(s1,X0,bit1(plus_plus(int,times_times(int,bit0(bit1(pls)),m),pls)))
| ~ ord_less_eq(int,pls,X0)
| ~ ord_less(int,X0,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int))) )
| ~ spl1_1 ),
inference(forward_demodulation,[],[f2291,f306]) ).
tff(f2293,plain,
( ! [X0: int] :
( ~ zcong(s1,X0,bit1(times_times(int,bit0(bit1(pls)),m)))
| ~ ord_less_eq(int,pls,X0)
| ~ ord_less(int,X0,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int))) )
| ~ spl1_1 ),
inference(forward_demodulation,[],[f2292,f332]) ).
tff(f2294,plain,
( ! [X0: int] :
( ~ zcong(s1,X0,bit1(bit0(times_times(int,bit1(pls),m))))
| ~ ord_less_eq(int,pls,X0)
| ~ ord_less(int,X0,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int))) )
| ~ spl1_1 ),
inference(forward_demodulation,[],[f2293,f276]) ).
tff(f2295,plain,
( ! [X0: int] :
( ~ zcong(s1,X0,bit1(bit0(m)))
| ~ ord_less_eq(int,pls,X0)
| ~ ord_less(int,X0,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int))) )
| ~ spl1_1 ),
inference(forward_demodulation,[],[f2294,f611]) ).
tff(f2296,plain,
( ! [X0: int] :
( ~ ord_less(int,X0,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),bit1(pls)))
| ~ zcong(s1,X0,bit1(bit0(m)))
| ~ ord_less_eq(int,pls,X0) )
| ~ spl1_1 ),
inference(forward_demodulation,[],[f2295,f467]) ).
tff(f2297,plain,
( ! [X0: int] :
( ~ ord_less(int,X0,plus_plus(int,times_times(int,bit0(bit0(bit1(pls))),m),bit1(pls)))
| ~ zcong(s1,X0,bit1(bit0(m)))
| ~ ord_less_eq(int,pls,X0) )
| ~ spl1_1 ),
inference(forward_demodulation,[],[f2296,f319]) ).
tff(f2298,plain,
( ! [X0: int] :
( ~ ord_less(int,X0,plus_plus(int,bit0(times_times(int,bit0(bit1(pls)),m)),bit1(pls)))
| ~ zcong(s1,X0,bit1(bit0(m)))
| ~ ord_less_eq(int,pls,X0) )
| ~ spl1_1 ),
inference(forward_demodulation,[],[f2297,f276]) ).
tff(f2299,plain,
( ! [X0: int] :
( ~ ord_less(int,X0,bit1(plus_plus(int,times_times(int,bit0(bit1(pls)),m),pls)))
| ~ zcong(s1,X0,bit1(bit0(m)))
| ~ ord_less_eq(int,pls,X0) )
| ~ spl1_1 ),
inference(forward_demodulation,[],[f2298,f306]) ).
tff(f2300,plain,
( ! [X0: int] :
( ~ ord_less(int,X0,bit1(times_times(int,bit0(bit1(pls)),m)))
| ~ zcong(s1,X0,bit1(bit0(m)))
| ~ ord_less_eq(int,pls,X0) )
| ~ spl1_1 ),
inference(forward_demodulation,[],[f2299,f332]) ).
tff(f2301,plain,
( ! [X0: int] :
( ~ ord_less(int,X0,bit1(bit0(times_times(int,bit1(pls),m))))
| ~ zcong(s1,X0,bit1(bit0(m)))
| ~ ord_less_eq(int,pls,X0) )
| ~ spl1_1 ),
inference(forward_demodulation,[],[f2300,f276]) ).
tff(f2302,plain,
( ! [X0: int] :
( ~ zcong(s1,X0,bit1(bit0(m)))
| ~ ord_less(int,X0,bit1(bit0(m)))
| ~ ord_less_eq(int,pls,X0) )
| ~ spl1_1 ),
inference(forward_demodulation,[],[f2301,f611]) ).
tff(f2303,plain,
( ~ ord_less(int,sK0,bit1(bit0(m)))
| ~ ord_less_eq(int,pls,sK0)
| ~ spl1_1 ),
inference(resolution,[],[f2302,f942]) ).
tff(f2304,plain,
( ~ ord_less_eq(int,pls,sK0)
| ~ spl1_1 ),
inference(forward_subsumption_resolution,[],[f2303,f949]) ).
tff(f2305,plain,
( $false
| ~ spl1_1 ),
inference(forward_subsumption_resolution,[],[f2304,f405]) ).
tff(f2306,plain,
~ spl1_1,
inference(avatar_contradiction_clause,[],[f2305]) ).
cnf(s1,plain,
( spl1_1
| spl1_2 ),
inference(sat_conversion,[],[f402]) ).
cnf(s2,plain,
~ spl1_2,
inference(sat_conversion,[],[f403]) ).
cnf(s43,plain,
~ spl1_1,
inference(sat_conversion,[],[f2306]) ).
cnf(s44,plain,
$false,
inference(rat,[],[s1,s2,s43]) ).
tff(f2307,plain,
$false,
inference(avatar_sat_refutation,[],[s44]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : NUM948_5 : TPTP v9.3.1. Released v6.0.0.
% 0.00/0.08 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.15/0.42 % Computer : n010.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
% 0.15/0.42 % CPULimit : 300
% 0.15/0.42 % WCLimit : 300
% 0.15/0.42 % DateTime : Sun Sep 27 21:48:02 UTC 2026
% 0.15/0.42 % CPUTime :
% 0.15/0.42 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.21/0.48 Running first-order theorem proving
% 0.21/0.48 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
% 2.05/1.76 % (1337833)Detected formulas, will run a generic FOF schedule.
% 2.05/1.76 % (1337851)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=901194860:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.05/1.76 % (1337851)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 2.05/1.76 % (1337849)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=3921790435:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.05/1.76 % (1337855)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=812069166:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.05/1.76 % (1337850)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=1863974156:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.05/1.76 % (1337856)dis-21_1_sil=8000:lcm=predicate:random_seed=822872901: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)
% 2.05/1.76 % (1337852)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1875007562:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.05/1.76 % (1337854)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3058255488:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.05/1.76 % (1337852)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 2.05/1.76 % (1337855)First to succeed.
% 2.05/1.76 % (1337855)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-1337833"
% 2.05/1.76 % (1337852)Instruction limit reached!
% 2.05/1.76 % (1337852)------------------------------
% 2.05/1.76 % (1337852)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.05/1.76 % (1337852)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.05/1.76 % (1337852)CaDiCaL version: 2.1.3
% 2.05/1.76 % (1337852)Termination reason: Instruction limit
% 2.05/1.76 % (1337852)Termination phase: Saturation
% 2.05/1.76 % (1337852)Time elapsed: 0.107 s
% 2.05/1.76 % (1337852)Peak memory usage: 89 MB
% 2.05/1.76 % (1337852)Instructions burned: 109 (million)
% 2.05/1.76 % (1337854)Also succeeded, but the first one will report.
% 2.05/1.76 % (1337856)Instruction limit reached!
% 2.05/1.76 % (1337856)------------------------------
% 2.05/1.76 % (1337856)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.05/1.76 % (1337856)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.05/1.76 % (1337856)CaDiCaL version: 2.1.3
% 2.05/1.76 % (1337856)Termination reason: Instruction limit
% 2.05/1.76 % (1337856)Termination phase: Saturation
% 2.05/1.76 % (1337856)Time elapsed: 0.127 s
% 2.05/1.76 % (1337856)Peak memory usage: 89 MB
% 2.05/1.76 % (1337856)Instructions burned: 130 (million)
% 2.05/1.76 % (1337851)Aborted by signal SIGSEGV on /export/starexec/sandbox2/benchmark/theBenchmark.p
% 2.05/1.76 % (1337851)------------------------------
% 2.05/1.76 % (1337851)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.05/1.76 % (1337851)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.05/1.76 % (1337851)CaDiCaL version: 2.1.3
% 2.05/1.76 % (1337851)Termination reason: Unknown
% 2.05/1.76 % (1337851)Termination phase: Saturation
% 2.05/1.76 % (1337851)Time elapsed: 0.321 s
% 2.05/1.76 % (1337851)Peak memory usage: 113 MB
% 2.05/1.76 % (1337851)Instructions burned: 542 (million)
% 2.05/1.76 % (1337874)lrs+10_1_sil=8000:sp=occurrence:random_seed=3506593655:i=285:sd=3:ss=axioms:sgt=8_2996 on theBenchmark for (2996ds/285Mi)
% 2.05/1.76 % (1337875)lrs+10_1_sil=32000:urr=on:br=off:random_seed=1709003892:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2996 on theBenchmark for (2996ds/157Mi)
% 2.05/1.76 % (1337875)Refutation not found, incomplete strategy
% 2.05/1.76 % (1337875)------------------------------
% 2.05/1.76 % (1337875)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.05/1.76 % (1337875)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.05/1.76 % (1337875)CaDiCaL version: 2.1.3
% 2.05/1.76 % (1337875)Termination reason: Refutation not found, incomplete strategy
% 2.05/1.76 % (1337875)Time elapsed: 0.002 s
% 2.05/1.76 % (1337875)Peak memory usage: 87 MB
% 2.05/1.76 % (1337875)Instructions burned: 1 (million)
% 2.05/1.76 % (1337855)Refutation found. Thanks to Tanya!
% 2.05/1.76 % SZS status Theorem for theBenchmark
% 2.05/1.76 % SZS output start Proof for theBenchmark
% See solution above
% 5.90/1.97 % (1337855)------------------------------
% 5.90/1.97 % (1337855)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.90/1.97 % (1337855)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.90/1.97 % (1337855)CaDiCaL version: 2.1.3
% 5.90/1.97 % (1337855)Termination reason: Refutation
% 5.90/1.97 % (1337855)Time elapsed: 0.084 s
% 5.90/1.97 % (1337855)Peak memory usage: 90 MB
% 5.90/1.97 % (1337855)Instructions burned: 78 (million)
% 5.90/1.97 % (1337855)------------------------------
% 5.90/1.97 % (1337855)------------------------------
% 5.90/1.97 % (1337833)Success in time 0.73 s
% 5.90/1.98 % Vampire exiting
%------------------------------------------------------------------------------