%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM973_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 : n014.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 12:17:43 PM UTC 2026
% Result : Theorem 3.00s 1.34s
% Output : Refutation 3.87s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 9
% Syntax : Number of formulae : 38 ( 31 unt; 0 typ; 0 def)
% Number of atoms : 45 ( 33 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 19 ( 12 ~; 5 |; 0 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of types : 5 ( 4 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 18 ( 16 usr; 1 prp; 0-3 aty)
% Number of functors : 19 ( 19 usr; 9 con; 0-4 aty)
% Number of variables : 35 ( 31 !; 4 ?; 35 :)
% 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,
real: $tType ).
tff(type_def_9,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,
twoSqu196287499sum2sq: product_prod(int,int) > int ).
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,
s1: int ).
tff(func_def_15,type,
s: int ).
tff(func_def_16,type,
t: int ).
tff(func_def_17,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,
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,
comm_semiring_1:
!>[X0: $tType] : $o ).
tff(pred_def_9,type,
linordered_idom:
!>[X0: $tType] : $o ).
tff(pred_def_10,type,
linordered_semidom:
!>[X0: $tType] : $o ).
tff(pred_def_11,type,
zcong: ( int * int * int ) > $o ).
tff(pred_def_12,type,
zprime: int > $o ).
tff(pred_def_13,type,
ord_less:
!>[X0: $tType] : ( ( X0 * X0 ) > $o ) ).
tff(pred_def_14,type,
dvd_dvd:
!>[X0: $tType] : ( ( X0 * X0 ) > $o ) ).
tff(pred_def_15,type,
twoSqu1567020053sum2sq: int > $o ).
tff(pred_def_16,type,
pp: bool > $o ).
tff(f1,axiom,
t = one_one(int),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0__096t_A_061_A1_096) ).
tff(f12,axiom,
plus_plus(int,power_power(int,s,number_number_of(nat,bit0(bit1(pls)))),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/sandbox2/benchmark/theBenchmark.p',fact_11_t) ).
tff(f46,axiom,
! [X0: int] : ( number_number_of(int,X0) = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_45_number__of__is__id) ).
tff(f63,axiom,
! [X0: $tType] :
( number_ring(X0)
=> ! [X1: X0] : ( times_times(X0,X1,number_number_of(X0,bit1(pls))) = X1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_62_mult__numeral__1__right) ).
tff(f66,axiom,
one_one(int) = number_number_of(int,bit1(pls)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_65_one__is__num__one) ).
tff(f81,axiom,
! [X0: $tType] :
( monoid_mult(X0)
=> ! [X1: nat] : ( power_power(X0,one_one(X0),X1) = one_one(X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_80_power__one) ).
tff(f103,axiom,
monoid_mult(int),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Omonoid__mult) ).
tff(f106,axiom,
number_ring(int),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Int_Onumber__ring) ).
tff(f128,conjecture,
? [X0: int,X1: int] : ( plus_plus(int,power_power(int,X0,number_number_of(nat,bit0(bit1(pls)))),power_power(int,X1,number_number_of(nat,bit0(bit1(pls))))) = plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
tff(f129,negated_conjecture,
~ ? [X0: int,X1: int] : ( plus_plus(int,power_power(int,X0,number_number_of(nat,bit0(bit1(pls)))),power_power(int,X1,number_number_of(nat,bit0(bit1(pls))))) = plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)) ),
inference(negated_conjecture,[status(cth)],[f128]) ).
tff(f163,plain,
! [X0: $tType] :
( ! [X1: X0] : ( times_times(X0,X1,number_number_of(X0,bit1(pls))) = X1 )
| ~ number_ring(X0) ),
inference(ennf_transformation,[],[f63]) ).
tff(f176,plain,
! [X0: $tType] :
( ! [X1: nat] : ( power_power(X0,one_one(X0),X1) = one_one(X0) )
| ~ monoid_mult(X0) ),
inference(ennf_transformation,[],[f81]) ).
tff(f186,plain,
! [X0: int,X1: int] : ( plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)) != plus_plus(int,power_power(int,X0,number_number_of(nat,bit0(bit1(pls)))),power_power(int,X1,number_number_of(nat,bit0(bit1(pls))))) ),
inference(ennf_transformation,[],[f129]) ).
tff(f204,plain,
t = one_one(int),
inference(cnf_transformation,[],[f1]) ).
tff(f214,plain,
times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),t) = plus_plus(int,power_power(int,s,number_number_of(nat,bit0(bit1(pls)))),one_one(int)),
inference(cnf_transformation,[],[f12]) ).
tff(f253,plain,
! [X0: int] : ( number_number_of(int,X0) = X0 ),
inference(cnf_transformation,[],[f46]) ).
tff(f270,plain,
! [X0: $tType,X1: X0] :
( ( times_times(X0,X1,number_number_of(X0,bit1(pls))) = X1 )
| ~ number_ring(X0) ),
inference(cnf_transformation,[],[f163]) ).
tff(f273,plain,
one_one(int) = number_number_of(int,bit1(pls)),
inference(cnf_transformation,[],[f66]) ).
tff(f288,plain,
! [X0: $tType,X1: nat] :
( ~ monoid_mult(X0)
| ( one_one(X0) = power_power(X0,one_one(X0),X1) ) ),
inference(cnf_transformation,[],[f176]) ).
tff(f320,plain,
monoid_mult(int),
inference(cnf_transformation,[],[f103]) ).
tff(f323,plain,
number_ring(int),
inference(cnf_transformation,[],[f106]) ).
tff(f345,plain,
! [X0: int,X1: int] : ( plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)) != plus_plus(int,power_power(int,X0,number_number_of(nat,bit0(bit1(pls)))),power_power(int,X1,number_number_of(nat,bit0(bit1(pls))))) ),
inference(cnf_transformation,[],[f186]) ).
tff(f361,plain,
one_one(int) = bit1(pls),
inference(forward_demodulation,[],[f273,f253]) ).
tff(f362,plain,
t = bit1(pls),
inference(forward_demodulation,[],[f361,f204]) ).
tff(f365,plain,
! [X0: int,X1: int] : ( plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(t))),m),one_one(int)) != plus_plus(int,power_power(int,X0,number_number_of(nat,bit0(t))),power_power(int,X1,number_number_of(nat,bit0(t)))) ),
inference(superposition,[],[f345,f362]) ).
tff(f367,plain,
! [X0: int,X1: int] : ( plus_plus(int,power_power(int,X0,number_number_of(nat,bit0(t))),power_power(int,X1,number_number_of(nat,bit0(t)))) != plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(t))),m),t) ),
inference(forward_demodulation,[],[f365,f204]) ).
tff(f368,plain,
! [X0: int,X1: int] : ( plus_plus(int,times_times(int,bit0(bit0(t)),m),t) != plus_plus(int,power_power(int,X0,number_number_of(nat,bit0(t))),power_power(int,X1,number_number_of(nat,bit0(t)))) ),
inference(forward_demodulation,[],[f367,f253]) ).
tff(f397,plain,
! [X0: nat] : ( one_one(int) = power_power(int,one_one(int),X0) ),
inference(resolution,[],[f288,f320]) ).
tff(f400,plain,
! [X0: nat] : ( t = power_power(int,t,X0) ),
inference(forward_demodulation,[],[f397,f204]) ).
tff(f403,plain,
! [X0: int] : ( plus_plus(int,times_times(int,bit0(bit0(t)),m),t) != plus_plus(int,power_power(int,X0,number_number_of(nat,bit0(t))),t) ),
inference(superposition,[],[f368,f400]) ).
tff(f445,plain,
! [X0: $tType,X1: X0] :
( ~ number_ring(X0)
| ( times_times(X0,X1,number_number_of(X0,t)) = X1 ) ),
inference(forward_demodulation,[],[f270,f362]) ).
tff(f446,plain,
! [X0: int] : ( times_times(int,X0,number_number_of(int,t)) = X0 ),
inference(resolution,[],[f445,f323]) ).
tff(f449,plain,
! [X0: int] : ( times_times(int,X0,t) = X0 ),
inference(forward_demodulation,[],[f446,f253]) ).
tff(f1176,plain,
times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),t),t) = plus_plus(int,power_power(int,s,number_number_of(nat,bit0(bit1(pls)))),t),
inference(forward_demodulation,[],[f214,f204]) ).
tff(f1177,plain,
plus_plus(int,power_power(int,s,number_number_of(nat,bit0(t))),t) = times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(t))),m),t),t),
inference(forward_demodulation,[],[f1176,f362]) ).
tff(f1178,plain,
plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(t))),m),t) = plus_plus(int,power_power(int,s,number_number_of(nat,bit0(t))),t),
inference(forward_demodulation,[],[f1177,f449]) ).
tff(f1179,plain,
plus_plus(int,times_times(int,bit0(bit0(t)),m),t) = plus_plus(int,power_power(int,s,number_number_of(nat,bit0(t))),t),
inference(forward_demodulation,[],[f1178,f253]) ).
tff(f1180,plain,
$false,
inference(forward_subsumption_resolution,[],[f1179,f403]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM973_5 : TPTP v9.3.1. Released v6.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.39 % Computer : n014.cluster.edu
% 0.12/0.39 % Model : x86_64 x86_64
% 0.12/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.39 % Memory : 8046.5625MB
% 0.12/0.39 % OS : Linux 6.8.0-71-generic
% 0.12/0.39 % CPULimit : 300
% 0.12/0.39 % WCLimit : 300
% 0.12/0.39 % DateTime : Sun Sep 27 21:48:46 UTC 2026
% 0.12/0.39 % CPUTime :
% 0.12/0.39 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.43 Running first-order theorem proving
% 0.12/0.43 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
% 3.00/1.34 % (1201817)Detected formulas, will run a generic FOF schedule.
% 3.00/1.34 % (1201824)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=3012633866:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.00/1.34 % (1201824)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 3.00/1.34 % (1201825)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2742570153:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.00/1.34 % (1201828)dis-21_1_sil=8000:lcm=predicate:random_seed=2433384645: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)
% 3.00/1.34 % (1201827)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=4000677851:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.00/1.34 % (1201823)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=1115732321:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.00/1.34 % (1201822)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=2126297691:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.00/1.34 % (1201826)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3988730987:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.00/1.34 % (1201825)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 3.00/1.34 % (1201828)Refutation not found, incomplete strategy
% 3.00/1.34 % (1201828)------------------------------
% 3.00/1.34 % (1201828)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.00/1.34 % (1201828)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.00/1.34 % (1201828)CaDiCaL version: 2.1.3
% 3.00/1.34 % (1201828)Termination reason: Refutation not found, incomplete strategy
% 3.00/1.34 % (1201828)Time elapsed: 0.012 s
% 3.00/1.34 % (1201828)Peak memory usage: 88 MB
% 3.00/1.34 % (1201828)Instructions burned: 19 (million)
% 3.00/1.34 % (1201827)First to succeed.
% 3.00/1.34 % (1201827)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-1201817"
% 3.00/1.34 % (1201826)Instruction limit reached!
% 3.00/1.34 % (1201826)------------------------------
% 3.00/1.34 % (1201826)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.00/1.34 % (1201826)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.00/1.34 % (1201826)CaDiCaL version: 2.1.3
% 3.00/1.34 % (1201826)Termination reason: Instruction limit
% 3.00/1.34 % (1201826)Termination phase: Saturation
% 3.00/1.34 % (1201826)Time elapsed: 0.064 s
% 3.00/1.34 % (1201826)Peak memory usage: 88 MB
% 3.00/1.34 % (1201826)Instructions burned: 121 (million)
% 3.00/1.34 % (1201825)Instruction limit reached!
% 3.00/1.34 % (1201825)------------------------------
% 3.00/1.34 % (1201825)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.00/1.34 % (1201825)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.00/1.34 % (1201825)CaDiCaL version: 2.1.3
% 3.00/1.34 % (1201825)Termination reason: Instruction limit
% 3.00/1.34 % (1201825)Termination phase: Saturation
% 3.00/1.34 % (1201825)Time elapsed: 0.064 s
% 3.00/1.34 % (1201825)Peak memory usage: 89 MB
% 3.00/1.34 % (1201825)Instructions burned: 111 (million)
% 3.00/1.34 % Exception at run slice level
% 3.00/1.34 User error: GNN currently only supports monomorphic FOL.
% 3.00/1.34 % (1201837)lrs+10_1_sil=32000:urr=on:br=off:random_seed=1047694820:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 3.00/1.34 % (1201836)lrs+10_1_sil=8000:sp=occurrence:random_seed=640243854:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 3.00/1.34 % (1201828)------------------------------
% 3.00/1.34 % (1201828)------------------------------
% 3.00/1.34 % (1201838)lrs+1011_1_sil=32000:sp=occurrence:random_seed=3761695252:i=325:sd=1:ss=axioms:sgt=32_2996 on theBenchmark for (2996ds/325Mi)
% 3.00/1.34 % (1201827)Refutation found. Thanks to Tanya!
% 3.00/1.34 % SZS status Theorem for theBenchmark
% 3.00/1.34 % SZS output start Proof for theBenchmark
% See solution above
% 3.87/1.44 % (1201827)------------------------------
% 3.87/1.44 % (1201827)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.87/1.44 % (1201827)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.87/1.44 % (1201827)CaDiCaL version: 2.1.3
% 3.87/1.44 % (1201827)Termination reason: Refutation
% 3.87/1.44 % (1201827)Time elapsed: 0.037 s
% 3.87/1.44 % (1201827)Peak memory usage: 89 MB
% 3.87/1.44 % (1201827)Instructions burned: 59 (million)
% 3.87/1.44 % (1201827)------------------------------
% 3.87/1.44 % (1201827)------------------------------
% 3.87/1.44 % (1201817)Success in time 0.474 s
% 3.87/1.44 % Vampire exiting
%------------------------------------------------------------------------------