%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM925_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 : n017.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 12:17:34 PM UTC 2026
% Result : Theorem 0.19s 1.50s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 11
% Syntax : Number of formulae : 43 ( 30 unt; 0 typ; 0 def)
% Number of atoms : 97 ( 51 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 102 ( 48 ~; 40 |; 10 &)
% ( 3 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 3 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of FOOLs : 1 ( 1 fml; 0 var)
% 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 : 14 ( 14 usr; 6 con; 0-3 aty)
% Number of variables : 34 ( 34 !; 0 ?; 34 :)
% 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(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,
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,
semiring_1_of_nat:
!>[X0: $tType] : ( nat > X0 ) ).
tff(func_def_8,type,
power_power:
!>[X0: $tType] : ( ( X0 * nat ) > X0 ) ).
tff(func_def_9,type,
fFalse: bool ).
tff(func_def_10,type,
fTrue: bool ).
tff(func_def_11,type,
m1: int ).
tff(func_def_12,type,
n: nat ).
tff(func_def_13,type,
t: int ).
tff(pred_def_1,type,
number:
!>[X0: $tType] : $o ).
tff(pred_def_2,type,
power:
!>[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,
semiring_0:
!>[X0: $tType] : $o ).
tff(pred_def_7,type,
semiring_1:
!>[X0: $tType] : $o ).
tff(pred_def_8,type,
zero_neq_one:
!>[X0: $tType] : $o ).
tff(pred_def_9,type,
number_semiring:
!>[X0: $tType] : $o ).
tff(pred_def_10,type,
linordered_idom:
!>[X0: $tType] : $o ).
tff(pred_def_11,type,
no_zero_divisors:
!>[X0: $tType] : $o ).
tff(pred_def_12,type,
linordered_semidom:
!>[X0: $tType] : $o ).
tff(pred_def_13,type,
ring_11004092258visors:
!>[X0: $tType] : $o ).
tff(pred_def_14,type,
linord219039673up_add:
!>[X0: $tType] : $o ).
tff(pred_def_15,type,
ord_less:
!>[X0: $tType] : ( ( X0 * X0 ) > $o ) ).
tff(pred_def_16,type,
pp: bool > $o ).
tff(f1,axiom,
ord_less(int,zero_zero(int),plus_plus(int,one_one(int),semiring_1_of_nat(int,n))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0_n1pos) ).
tff(f27,axiom,
~ ord_less(int,pls,pls),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_26_rel__simps_I2_J) ).
tff(f72,axiom,
pls = zero_zero(int),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_71_Pls__def) ).
tff(f73,axiom,
! [X0: int] : ( plus_plus(int,X0,pls) = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_72_add__Pls__right) ).
tff(f81,axiom,
! [X0: int] : ( bit1(X0) = plus_plus(int,plus_plus(int,one_one(int),X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_80_Bit1__def) ).
tff(f98,axiom,
! [X0: $tType] :
( ( power(X0)
& mult_zero(X0)
& no_zero_divisors(X0)
& zero_neq_one(X0) )
=> ! [X1: nat,X2: X0] :
( ( power_power(X0,X2,X1) = zero_zero(X0) )
<=> ( ( X2 = zero_zero(X0) )
& ( X1 != zero_zero(nat) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_97_power__eq__0__iff) ).
tff(f102,axiom,
no_zero_divisors(int),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Ono__zero__divisors) ).
tff(f105,axiom,
zero_neq_one(int),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Ozero__neq__one) ).
tff(f108,axiom,
mult_zero(int),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Omult__zero) ).
tff(f111,axiom,
power(int),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Power_Opower) ).
tff(f138,conjecture,
power_power(int,plus_plus(int,one_one(int),semiring_1_of_nat(int,n)),number_number_of(nat,bit0(bit1(pls)))) != zero_zero(int),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
tff(f139,negated_conjecture,
( ( ~ power_power(int,plus_plus(int,one_one(int),semiring_1_of_nat(int,n)),number_number_of(nat,bit0(bit1(pls)))) ) != zero_zero(int) ),
inference(negated_conjecture,[status(cth)],[f138]) ).
tff(f140,plain,
zero_zero(int) = power_power(int,plus_plus(int,one_one(int),semiring_1_of_nat(int,n)),number_number_of(nat,bit0(bit1(pls)))),
inference(flattening,[],[f139]) ).
tff(f190,plain,
! [X0: $tType] :
( ! [X1: nat,X2: X0] :
( ( power_power(X0,X2,X1) = zero_zero(X0) )
<=> ( ( X2 = zero_zero(X0) )
& ( X1 != zero_zero(nat) ) ) )
| ~ power(X0)
| ~ mult_zero(X0)
| ~ no_zero_divisors(X0)
| ~ zero_neq_one(X0) ),
inference(ennf_transformation,[],[f98]) ).
tff(f191,plain,
! [X0: $tType] :
( ! [X1: nat,X2: X0] :
( ( power_power(X0,X2,X1) = zero_zero(X0) )
<=> ( ( X2 = zero_zero(X0) )
& ( X1 != zero_zero(nat) ) ) )
| ~ power(X0)
| ~ mult_zero(X0)
| ~ no_zero_divisors(X0)
| ~ zero_neq_one(X0) ),
inference(flattening,[],[f190]) ).
tff(f233,plain,
! [X0: $tType] :
( ! [X1: nat,X2: X0] :
( ( ( power_power(X0,X2,X1) = zero_zero(X0) )
| ( zero_zero(X0) != X2 )
| ( zero_zero(nat) = X1 ) )
& ( ( ( X2 = zero_zero(X0) )
& ( X1 != zero_zero(nat) ) )
| ( zero_zero(X0) != power_power(X0,X2,X1) ) ) )
| ~ power(X0)
| ~ mult_zero(X0)
| ~ no_zero_divisors(X0)
| ~ zero_neq_one(X0) ),
inference(nnf_transformation,[],[f191]) ).
tff(f234,plain,
! [X0: $tType] :
( ! [X1: nat,X2: X0] :
( ( ( power_power(X0,X2,X1) = zero_zero(X0) )
| ( zero_zero(X0) != X2 )
| ( zero_zero(nat) = X1 ) )
& ( ( ( X2 = zero_zero(X0) )
& ( X1 != zero_zero(nat) ) )
| ( zero_zero(X0) != power_power(X0,X2,X1) ) ) )
| ~ power(X0)
| ~ mult_zero(X0)
| ~ no_zero_divisors(X0)
| ~ zero_neq_one(X0) ),
inference(flattening,[],[f233]) ).
tff(f235,plain,
ord_less(int,zero_zero(int),plus_plus(int,one_one(int),semiring_1_of_nat(int,n))),
inference(cnf_transformation,[],[f1]) ).
tff(f270,plain,
~ ord_less(int,pls,pls),
inference(cnf_transformation,[],[f27]) ).
tff(f343,plain,
zero_zero(int) = pls,
inference(cnf_transformation,[],[f72]) ).
tff(f344,plain,
! [X0: int] : ( plus_plus(int,X0,pls) = X0 ),
inference(cnf_transformation,[],[f73]) ).
tff(f352,plain,
! [X0: int] : ( bit1(X0) = plus_plus(int,plus_plus(int,one_one(int),X0),X0) ),
inference(cnf_transformation,[],[f81]) ).
tff(f377,plain,
! [X0: $tType,X2: X0,X1: nat] :
( ~ no_zero_divisors(X0)
| ( zero_zero(X0) != power_power(X0,X2,X1) )
| ~ power(X0)
| ~ mult_zero(X0)
| ( zero_zero(X0) = X2 )
| ~ zero_neq_one(X0) ),
inference(cnf_transformation,[],[f234]) ).
tff(f382,plain,
no_zero_divisors(int),
inference(cnf_transformation,[],[f102]) ).
tff(f385,plain,
zero_neq_one(int),
inference(cnf_transformation,[],[f105]) ).
tff(f388,plain,
mult_zero(int),
inference(cnf_transformation,[],[f108]) ).
tff(f391,plain,
power(int),
inference(cnf_transformation,[],[f111]) ).
tff(f418,plain,
zero_zero(int) = power_power(int,plus_plus(int,one_one(int),semiring_1_of_nat(int,n)),number_number_of(nat,bit0(bit1(pls)))),
inference(cnf_transformation,[],[f140]) ).
tff(f512,plain,
ord_less(int,pls,plus_plus(int,one_one(int),semiring_1_of_nat(int,n))),
inference(forward_demodulation,[],[f235,f343]) ).
tff(f525,plain,
bit1(pls) = plus_plus(int,one_one(int),pls),
inference(superposition,[],[f344,f352]) ).
tff(f528,plain,
one_one(int) = bit1(pls),
inference(forward_demodulation,[],[f525,f344]) ).
tff(f540,plain,
ord_less(int,pls,plus_plus(int,bit1(pls),semiring_1_of_nat(int,n))),
inference(superposition,[],[f512,f528]) ).
tff(f936,plain,
! [X0: int,X1: nat] :
( ( zero_zero(int) != power_power(int,X0,X1) )
| ~ power(int)
| ~ mult_zero(int)
| ( zero_zero(int) = X0 )
| ~ zero_neq_one(int) ),
inference(resolution,[],[f377,f382]) ).
tff(f941,plain,
! [X0: int,X1: nat] :
( ( zero_zero(int) != power_power(int,X0,X1) )
| ~ mult_zero(int)
| ( zero_zero(int) = X0 )
| ~ zero_neq_one(int) ),
inference(forward_subsumption_resolution,[],[f936,f391]) ).
tff(f944,plain,
! [X0: int,X1: nat] :
( ( zero_zero(int) != power_power(int,X0,X1) )
| ( zero_zero(int) = X0 )
| ~ zero_neq_one(int) ),
inference(forward_subsumption_resolution,[],[f941,f388]) ).
tff(f947,plain,
! [X0: int,X1: nat] :
( ( zero_zero(int) != power_power(int,X0,X1) )
| ( zero_zero(int) = X0 ) ),
inference(forward_subsumption_resolution,[],[f944,f385]) ).
tff(f948,plain,
! [X0: int,X1: nat] :
( ( pls != power_power(int,X0,X1) )
| ( zero_zero(int) = X0 ) ),
inference(forward_demodulation,[],[f947,f343]) ).
tff(f949,plain,
! [X0: int,X1: nat] :
( ( pls != power_power(int,X0,X1) )
| ( pls = X0 ) ),
inference(forward_demodulation,[],[f948,f343]) ).
tff(f1003,plain,
( ( zero_zero(int) != pls )
| ( plus_plus(int,one_one(int),semiring_1_of_nat(int,n)) = pls ) ),
inference(superposition,[],[f949,f418]) ).
tff(f1011,plain,
plus_plus(int,one_one(int),semiring_1_of_nat(int,n)) = pls,
inference(forward_subsumption_resolution,[],[f1003,f343]) ).
tff(f1012,plain,
pls = plus_plus(int,bit1(pls),semiring_1_of_nat(int,n)),
inference(forward_demodulation,[],[f1011,f528]) ).
tff(f1013,plain,
ord_less(int,pls,pls),
inference(superposition,[],[f540,f1012]) ).
tff(f1016,plain,
$false,
inference(forward_subsumption_resolution,[],[f1013,f270]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM925_5 : TPTP v9.3.1. Released v6.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.13/0.39 % Computer : n017.cluster.edu
% 0.13/0.39 % Model : x86_64 x86_64
% 0.13/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.39 % Memory : 8046.5625MB
% 0.13/0.39 % OS : Linux 6.8.0-71-generic
% 0.13/0.39 % CPULimit : 300
% 0.13/0.39 % WCLimit : 300
% 0.13/0.39 % DateTime : Sun Sep 27 21:38:32 UTC 2026
% 0.13/0.40 % CPUTime :
% 0.13/0.40 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.13/0.43 Running first-order theorem proving
% 0.13/0.43 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
% 2.79/1.31 % (2961541)Detected formulas, will run a generic FOF schedule.
% 2.79/1.31 % (2961635)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1415829697:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.79/1.31 % (2961635)Instruction limit reached!
% 2.79/1.31 % (2961635)------------------------------
% 2.79/1.31 % (2961635)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.79/1.31 % (2961635)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.79/1.31 % (2961635)CaDiCaL version: 2.1.3
% 2.79/1.31 % (2961635)Termination reason: Instruction limit
% 2.79/1.31 % (2961635)Termination phase: Saturation
% 2.79/1.31 % (2961635)Time elapsed: 0.037 s
% 2.79/1.31 % (2961635)Peak memory usage: 88 MB
% 2.79/1.31 % (2961635)Instructions burned: 122 (million)
% 2.79/1.31 % (2961636)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3759580178:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.79/1.31 % (2961633)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=2262814679:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.79/1.31 % (2961637)dis-21_1_sil=8000:lcm=predicate:random_seed=3857145387: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)
% 2.79/1.31 % (2961631)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=2878191117:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.79/1.31 % (2961632)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=1964945953:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.79/1.31 % (2961634)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=259882722:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.79/1.31 % (2961634)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 2.79/1.31 % (2961633)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 2.79/1.31 % (2961634)Refutation not found, incomplete strategy
% 2.79/1.31 % (2961634)------------------------------
% 2.79/1.31 % (2961634)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.79/1.31 % (2961634)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.79/1.31 % (2961634)CaDiCaL version: 2.1.3
% 2.79/1.31 % (2961634)Termination reason: Refutation not found, incomplete strategy
% 2.79/1.31 % (2961634)Time elapsed: 0.004 s
% 2.79/1.31 % (2961634)Peak memory usage: 89 MB
% 2.79/1.31 % (2961634)Instructions burned: 5 (million)
% 2.79/1.31 % (2961636)First to succeed.
% 2.79/1.31 % (2961636)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2961541"
% 2.79/1.31 % (2961637)Instruction limit reached!
% 2.79/1.31 % (2961637)------------------------------
% 2.79/1.31 % (2961637)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.79/1.31 % (2961637)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.79/1.31 % (2961637)CaDiCaL version: 2.1.3
% 2.79/1.31 % (2961637)Termination reason: Instruction limit
% 2.79/1.31 % (2961637)Termination phase: Saturation
% 2.79/1.31 % (2961637)Time elapsed: 0.072 s
% 2.79/1.31 % (2961637)Peak memory usage: 90 MB
% 2.79/1.31 % (2961637)Instructions burned: 129 (million)
% 2.79/1.31 % (2961639)lrs+10_1_sil=8000:sp=occurrence:random_seed=2738989882:i=285:sd=3:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/285Mi)
% 2.79/1.31 % (2961639)Instruction limit reached!
% 2.79/1.31 % (2961639)------------------------------
% 2.79/1.31 % (2961639)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.79/1.31 % (2961639)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.79/1.31 % (2961639)CaDiCaL version: 2.1.3
% 2.79/1.31 % (2961639)Termination reason: Instruction limit
% 2.79/1.31 % (2961639)Termination phase: Saturation
% 2.79/1.31 % (2961639)Time elapsed: 0.087 s
% 2.79/1.31 % (2961639)Peak memory usage: 91 MB
% 2.79/1.31 % (2961639)Instructions burned: 286 (million)
% 2.79/1.31 % (2961646)lrs+10_1_sil=32000:urr=on:br=off:random_seed=4149708738:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 2.79/1.31 % (2961634)------------------------------
% 0.19/1.50 % (2961634)------------------------------
% 0.19/1.50 % (2961648)lrs+1011_1_sil=32000:sp=occurrence:random_seed=2840778644:i=325:sd=1:ss=axioms:sgt=32_2996 on theBenchmark for (2996ds/325Mi)
% 0.19/1.50 % (2961636)Refutation found. Thanks to Tanya!
% 0.19/1.50 % SZS status Theorem for theBenchmark
% 0.19/1.50 % SZS output start Proof for theBenchmark
% See solution above
% 0.19/1.50 % (2961636)------------------------------
% 0.19/1.50 % (2961636)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.19/1.50 % (2961636)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/1.50 % (2961636)CaDiCaL version: 2.1.3
% 0.19/1.50 % (2961636)Termination reason: Refutation
% 0.19/1.50 % (2961636)Time elapsed: 0.027 s
% 0.19/1.50 % (2961636)Peak memory usage: 89 MB
% 0.19/1.50 % (2961636)Instructions burned: 38 (million)
% 0.19/1.50 % (2961636)------------------------------
% 0.19/1.50 % (2961636)------------------------------
% 0.19/1.50 % (2961541)Success in time 0.432 s
% 0.19/1.50 % Vampire exiting
%------------------------------------------------------------------------------