%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM954_5 : TPTP v9.3.1. Released v6.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n001.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 12:17:41 PM UTC 2026
% Result : Theorem 2.95s 1.11s
% Output : Refutation 3.67s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 10
% Syntax : Number of formulae : 44 ( 36 unt; 0 typ; 0 def)
% Number of atoms : 58 ( 33 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 31 ( 17 ~; 9 |; 3 &)
% ( 1 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of types : 4 ( 3 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 15 ( 13 usr; 1 prp; 0-3 aty)
% Number of functors : 22 ( 22 usr; 9 con; 0-4 aty)
% Number of variables : 43 ( 37 !; 6 ?; 43 :)
% Comments :
%------------------------------------------------------------------------------
tff(type_def_5,type,
bool: $tType ).
tff(type_def_6,type,
int: $tType ).
tff(type_def_7,type,
nat: $tType ).
tff(type_def_8,type,
product_prod: ( $tType * $tType ) > $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,
bit0: int > int ).
tff(func_def_4,type,
bit1: int > int ).
tff(func_def_5,type,
min: 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,
power_power:
!>[X0: $tType] : ( ( X0 * nat ) > X0 ) ).
tff(func_def_9,type,
product_Pair:
!>[X0: $tType,X1: $tType] : ( ( X0 * X1 ) > product_prod(X0,X1) ) ).
tff(func_def_10,type,
legendre: ( int * int ) > int ).
tff(func_def_11,type,
twoSqu196287499sum2sq: product_prod(int,int) > int ).
tff(func_def_12,type,
fFalse: bool ).
tff(func_def_13,type,
fTrue: bool ).
tff(func_def_14,type,
m: int ).
tff(func_def_15,type,
s1: int ).
tff(func_def_16,type,
s: int ).
tff(func_def_17,type,
t: int ).
tff(func_def_18,type,
sK0: int > int ).
tff(func_def_19,type,
sK1: int > int ).
tff(func_def_20,type,
sK2: 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,
semiring_1:
!>[X0: $tType] : $o ).
tff(pred_def_6,type,
monoid_mult:
!>[X0: $tType] : $o ).
tff(pred_def_7,type,
number_semiring:
!>[X0: $tType] : $o ).
tff(pred_def_8,type,
zcong: ( int * int * int ) > $o ).
tff(pred_def_9,type,
zprime: int > $o ).
tff(pred_def_10,type,
quadRes: ( int * int ) > $o ).
tff(pred_def_11,type,
dvd_dvd:
!>[X0: $tType] : ( ( X0 * X0 ) > $o ) ).
tff(pred_def_12,type,
twoSqu1567020053sum2sq: int > $o ).
tff(pred_def_13,type,
pp: bool > $o ).
tff(f1,axiom,
twoSqu196287499sum2sq(product_Pair(int,int,s,one_one(int))) = times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),t),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0__096sum2sq_A_Is_M_A1_J_A_061_A_I4_A_K_Am_A_L_A1_J_A_K_At_096) ).
tff(f9,axiom,
! [X0: int,X1: int] : ( plus_plus(int,bit0(X1),bit1(X0)) = bit1(plus_plus(int,X1,X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8_add__Bit0__Bit1) ).
tff(f27,axiom,
! [X0: int,X1: int] : ( times_times(int,bit0(X1),X0) = bit0(times_times(int,X1,X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_26_mult__Bit0) ).
tff(f32,axiom,
! [X0: int] : ( number_number_of(int,X0) = X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_31_number__of__is__id) ).
tff(f33,axiom,
! [X0: int] : ( plus_plus(int,X0,pls) = X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_32_add__Pls__right) ).
tff(f46,axiom,
! [X0: $tType] :
( number_ring(X0)
=> ! [X1: X0] : ( times_times(X0,number_number_of(X0,bit1(pls)),X1) = X1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_45_mult__numeral__1) ).
tff(f49,axiom,
one_one(int) = number_number_of(int,bit1(pls)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_48_one__is__num__one) ).
tff(f59,axiom,
! [X0: int] :
( twoSqu1567020053sum2sq(X0)
<=> ? [X1: int,X2: int] : ( twoSqu196287499sum2sq(product_Pair(int,int,X1,X2)) = X0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_58_is__sum2sq__def) ).
tff(f102,axiom,
number_ring(int),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Int_Onumber__ring) ).
tff(f112,conjecture,
twoSqu1567020053sum2sq(times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),t)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
tff(f113,negated_conjecture,
~ twoSqu1567020053sum2sq(times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),t)),
inference(negated_conjecture,[status(cth)],[f112]) ).
tff(f114,plain,
~ twoSqu1567020053sum2sq(times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),t)),
inference(flattening,[],[f113]) ).
tff(f143,plain,
! [X0: $tType] :
( ! [X1: X0] : ( times_times(X0,number_number_of(X0,bit1(pls)),X1) = X1 )
| ~ number_ring(X0) ),
inference(ennf_transformation,[],[f46]) ).
tff(f172,plain,
! [X0: int] :
( ( twoSqu1567020053sum2sq(X0)
| ! [X1: int,X2: int] : ( twoSqu196287499sum2sq(product_Pair(int,int,X1,X2)) != X0 ) )
& ( ? [X1: int,X2: int] : ( twoSqu196287499sum2sq(product_Pair(int,int,X1,X2)) = X0 )
| ~ twoSqu1567020053sum2sq(X0) ) ),
inference(nnf_transformation,[],[f59]) ).
tff(f173,plain,
! [X0: int] :
( ( twoSqu1567020053sum2sq(X0)
| ! [X1: int,X2: int] : ( twoSqu196287499sum2sq(product_Pair(int,int,X1,X2)) != X0 ) )
& ( ? [X3: int,X4: int] : ( twoSqu196287499sum2sq(product_Pair(int,int,X3,X4)) = X0 )
| ~ twoSqu1567020053sum2sq(X0) ) ),
inference(rectify,[],[f172]) ).
tff(f174,plain,
! [X0: int] :
( ( twoSqu1567020053sum2sq(X0)
| ! [X1: int,X2: int] : ( twoSqu196287499sum2sq(product_Pair(int,int,X1,X2)) != X0 ) )
& ( ( twoSqu196287499sum2sq(product_Pair(int,int,sK0(X0),sK1(X0))) = X0 )
| ~ twoSqu1567020053sum2sq(X0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X3,sK0(X0)),skolemize(X4,sK1(X0))],[f173]) ).
tff(f182,plain,
twoSqu196287499sum2sq(product_Pair(int,int,s,one_one(int))) = times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),t),
inference(cnf_transformation,[],[f1]) ).
tff(f190,plain,
! [X0: int,X1: int] : ( plus_plus(int,bit0(X1),bit1(X0)) = bit1(plus_plus(int,X1,X0)) ),
inference(cnf_transformation,[],[f9]) ).
tff(f213,plain,
! [X0: int,X1: int] : ( bit0(times_times(int,X1,X0)) = times_times(int,bit0(X1),X0) ),
inference(cnf_transformation,[],[f27]) ).
tff(f219,plain,
! [X0: int] : ( number_number_of(int,X0) = X0 ),
inference(cnf_transformation,[],[f32]) ).
tff(f220,plain,
! [X0: int] : ( plus_plus(int,X0,pls) = X0 ),
inference(cnf_transformation,[],[f33]) ).
tff(f233,plain,
! [X0: $tType,X1: X0] :
( ~ number_ring(X0)
| ( times_times(X0,number_number_of(X0,bit1(pls)),X1) = X1 ) ),
inference(cnf_transformation,[],[f143]) ).
tff(f236,plain,
one_one(int) = number_number_of(int,bit1(pls)),
inference(cnf_transformation,[],[f49]) ).
tff(f247,plain,
! [X2: int,X0: int,X1: int] :
( twoSqu1567020053sum2sq(X0)
| ( twoSqu196287499sum2sq(product_Pair(int,int,X1,X2)) != X0 ) ),
inference(cnf_transformation,[],[f174]) ).
tff(f293,plain,
number_ring(int),
inference(cnf_transformation,[],[f102]) ).
tff(f303,plain,
~ twoSqu1567020053sum2sq(times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),t)),
inference(cnf_transformation,[],[f114]) ).
tff(f311,plain,
! [X2: int,X1: int] : twoSqu1567020053sum2sq(twoSqu196287499sum2sq(product_Pair(int,int,X1,X2))),
inference(equality_resolution,[],[f247]) ).
tff(f327,plain,
one_one(int) = bit1(pls),
inference(forward_demodulation,[],[f236,f219]) ).
tff(f329,plain,
~ twoSqu1567020053sum2sq(times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),bit1(pls)),t)),
inference(superposition,[],[f303,f327]) ).
tff(f330,plain,
~ twoSqu1567020053sum2sq(times_times(int,plus_plus(int,times_times(int,bit0(bit0(bit1(pls))),m),bit1(pls)),t)),
inference(forward_demodulation,[],[f329,f219]) ).
tff(f364,plain,
! [X0: int] : ( times_times(int,number_number_of(int,bit1(pls)),X0) = X0 ),
inference(resolution,[],[f233,f293]) ).
tff(f365,plain,
! [X0: int] : ( times_times(int,bit1(pls),X0) = X0 ),
inference(forward_demodulation,[],[f364,f219]) ).
tff(f366,plain,
! [X0: int] : ( bit0(X0) = times_times(int,bit0(bit1(pls)),X0) ),
inference(superposition,[],[f213,f365]) ).
tff(f398,plain,
! [X0: int] : ( times_times(int,bit0(bit0(bit1(pls))),X0) = bit0(bit0(X0)) ),
inference(superposition,[],[f213,f366]) ).
tff(f448,plain,
~ twoSqu1567020053sum2sq(times_times(int,plus_plus(int,bit0(bit0(m)),bit1(pls)),t)),
inference(superposition,[],[f330,f398]) ).
tff(f452,plain,
~ twoSqu1567020053sum2sq(times_times(int,bit1(plus_plus(int,bit0(m),pls)),t)),
inference(forward_demodulation,[],[f448,f190]) ).
tff(f455,plain,
~ twoSqu1567020053sum2sq(times_times(int,bit1(bit0(m)),t)),
inference(forward_demodulation,[],[f452,f220]) ).
tff(f1140,plain,
times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),bit1(pls)),t) = twoSqu196287499sum2sq(product_Pair(int,int,s,bit1(pls))),
inference(forward_demodulation,[],[f182,f327]) ).
tff(f1141,plain,
times_times(int,plus_plus(int,times_times(int,bit0(bit0(bit1(pls))),m),bit1(pls)),t) = twoSqu196287499sum2sq(product_Pair(int,int,s,bit1(pls))),
inference(forward_demodulation,[],[f1140,f219]) ).
tff(f1142,plain,
times_times(int,plus_plus(int,bit0(bit0(m)),bit1(pls)),t) = twoSqu196287499sum2sq(product_Pair(int,int,s,bit1(pls))),
inference(forward_demodulation,[],[f1141,f398]) ).
tff(f1143,plain,
times_times(int,bit1(plus_plus(int,bit0(m),pls)),t) = twoSqu196287499sum2sq(product_Pair(int,int,s,bit1(pls))),
inference(forward_demodulation,[],[f1142,f190]) ).
tff(f1144,plain,
times_times(int,bit1(bit0(m)),t) = twoSqu196287499sum2sq(product_Pair(int,int,s,bit1(pls))),
inference(forward_demodulation,[],[f1143,f220]) ).
tff(f1145,plain,
twoSqu1567020053sum2sq(times_times(int,bit1(bit0(m)),t)),
inference(superposition,[],[f311,f1144]) ).
tff(f1146,plain,
$false,
inference(forward_subsumption_resolution,[],[f1145,f455]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM954_5 : TPTP v9.3.1. Released v6.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.38 % Computer : n001.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Sun Sep 27 21:53:32 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.42 Running first-order theorem proving
% 0.11/0.42 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.95/1.11 % (3992669)Detected formulas, will run a generic FOF schedule.
% 2.95/1.11 % (3992752)dis-21_1_sil=8000:lcm=predicate:random_seed=1575879185: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)
% 2.95/1.11 % (3992752)Instruction limit reached!
% 2.95/1.11 % (3992752)------------------------------
% 2.95/1.11 % (3992752)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.95/1.11 % (3992752)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.95/1.11 % (3992752)CaDiCaL version: 2.1.3
% 2.95/1.11 % (3992752)Termination reason: Instruction limit
% 2.95/1.11 % (3992752)Termination phase: Saturation
% 2.95/1.11 % (3992752)Time elapsed: 0.036 s
% 2.95/1.11 % (3992752)Peak memory usage: 89 MB
% 2.95/1.11 % (3992752)Instructions burned: 129 (million)
% 2.95/1.11 % (3992749)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=758449844:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.95/1.11 % (3992747)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=3022237901:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.95/1.11 % (3992750)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=518403159:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.95/1.11 % (3992748)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1759071233:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.95/1.11 % (3992744)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=393433965:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.95/1.11 % (3992746)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=1410498448:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.95/1.11 % (3992748)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 2.95/1.11 % (3992748)Refutation not found, incomplete strategy
% 2.95/1.11 % (3992748)------------------------------
% 2.95/1.11 % (3992748)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.95/1.11 % (3992748)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.95/1.11 % (3992748)CaDiCaL version: 2.1.3
% 2.95/1.11 % (3992748)Termination reason: Refutation not found, incomplete strategy
% 2.95/1.11 % (3992748)Time elapsed: 0.003 s
% 2.95/1.11 % (3992748)Peak memory usage: 88 MB
% 2.95/1.11 % (3992748)Instructions burned: 3 (million)
% 2.95/1.11 % (3992747)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 2.95/1.11 % (3992750)First to succeed.
% 2.95/1.11 % (3992750)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3992669"
% 2.95/1.11 % (3992749)Instruction limit reached!
% 2.95/1.11 % (3992749)------------------------------
% 2.95/1.11 % (3992749)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.95/1.11 % (3992749)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.95/1.11 % (3992749)CaDiCaL version: 2.1.3
% 2.95/1.11 % (3992749)Termination reason: Instruction limit
% 2.95/1.11 % (3992749)Termination phase: Saturation
% 2.95/1.11 % (3992749)Time elapsed: 0.067 s
% 2.95/1.11 % (3992749)Peak memory usage: 88 MB
% 2.95/1.11 % (3992749)Instructions burned: 120 (million)
% 2.95/1.11 % (3992788)lrs+10_1_sil=8000:sp=occurrence:random_seed=3780044074:i=285:sd=3:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/285Mi)
% 2.95/1.11 % (3992788)Also succeeded, but the first one will report.
% 2.95/1.11 % (3992790)lrs+10_1_sil=32000:urr=on:br=off:random_seed=2169274699:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 2.95/1.11 % (3992790)Also succeeded, but the first one will report.
% 2.95/1.11 % (3992748)------------------------------
% 2.95/1.11 % (3992748)------------------------------
% 2.95/1.11 % (3992750)Refutation found. Thanks to Tanya!
% 2.95/1.11 % SZS status Theorem for theBenchmark
% 2.95/1.11 % SZS output start Proof for theBenchmark
% See solution above
% 3.67/1.33 % (3992750)------------------------------
% 3.67/1.33 % (3992750)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.67/1.33 % (3992750)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.67/1.33 % (3992750)CaDiCaL version: 2.1.3
% 3.67/1.33 % (3992750)Termination reason: Refutation
% 3.67/1.33 % (3992750)Time elapsed: 0.031 s
% 3.67/1.33 % (3992750)Peak memory usage: 89 MB
% 3.67/1.33 % (3992750)Instructions burned: 47 (million)
% 3.67/1.33 % (3992750)------------------------------
% 3.67/1.33 % (3992750)------------------------------
% 3.67/1.33 % (3992669)Success in time 0.464 s
% 3.67/1.33 % Vampire exiting
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