%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM962_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 12:17:42 PM UTC 2026
% Result : Theorem 5.93s 2.00s
% Output : Refutation 5.93s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 7
% Syntax : Number of formulae : 25 ( 22 unt; 0 typ; 0 def)
% Number of atoms : 28 ( 22 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 13 ( 10 ~; 2 |; 0 &)
% ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 10 ( 3 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 : 16 ( 14 usr; 1 prp; 0-3 aty)
% Number of functors : 15 ( 15 usr; 7 con; 0-3 aty)
% Number of variables : 19 ( 19 !; 0 ?; 19 :)
% 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,
minus_minus:
!>[X0: $tType] : ( ( X0 * X0 ) > X0 ) ).
tff(func_def_1,type,
one_one:
!>[X0: $tType] : X0 ).
tff(func_def_2,type,
plus_plus:
!>[X0: $tType] : ( ( X0 * X0 ) > X0 ) ).
tff(func_def_3,type,
times_times:
!>[X0: $tType] : ( ( X0 * X0 ) > 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,
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,
m: int ).
tff(func_def_12,type,
s: int ).
tff(func_def_13,type,
t: int ).
tff(func_def_14,type,
sK0: int ).
tff(pred_def_1,type,
number:
!>[X0: $tType] : $o ).
tff(pred_def_2,type,
ring:
!>[X0: $tType] : $o ).
tff(pred_def_3,type,
semiring:
!>[X0: $tType] : $o ).
tff(pred_def_4,type,
number_ring:
!>[X0: $tType] : $o ).
tff(pred_def_5,type,
ring_char_0:
!>[X0: $tType] : $o ).
tff(pred_def_6,type,
semiring_1:
!>[X0: $tType] : $o ).
tff(pred_def_7,type,
monoid_mult:
!>[X0: $tType] : $o ).
tff(pred_def_8,type,
number_semiring:
!>[X0: $tType] : $o ).
tff(pred_def_9,type,
comm_semiring_1:
!>[X0: $tType] : $o ).
tff(pred_def_10,type,
linordered_idom:
!>[X0: $tType] : $o ).
tff(pred_def_11,type,
zprime: int > $o ).
tff(pred_def_12,type,
ord_less:
!>[X0: $tType] : ( ( X0 * X0 ) > $o ) ).
tff(pred_def_13,type,
twoSqu1567020053sum2sq: int > $o ).
tff(pred_def_14,type,
pp: bool > $o ).
tff(f25,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_24_mult__Bit0) ).
tff(f49,axiom,
! [X0: int] : ( number_number_of(int,X0) = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_48_number__of__is__id) ).
tff(f59,axiom,
! [X0: int,X1: int,X2: int] : ( times_times(int,minus_minus(int,X2,X1),X0) = minus_minus(int,times_times(int,X2,X0),times_times(int,X1,X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_58_int__distrib_I3_J) ).
tff(f73,axiom,
one_one(int) = number_number_of(int,bit1(pls)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_72_one__is__num__one) ).
tff(f82,axiom,
! [X0: $tType] :
( monoid_mult(X0)
=> ! [X1: X0] : ( power_power(X0,X1,number_number_of(nat,bit0(bit1(pls)))) = times_times(X0,X1,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_81_power2__eq__square) ).
tff(f102,axiom,
monoid_mult(int),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Omonoid__mult) ).
tff(f127,conjecture,
power_power(int,minus_minus(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),one_one(int)),number_number_of(nat,bit0(bit1(pls)))) = minus_minus(int,times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),minus_minus(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),one_one(int))),times_times(int,one_one(int),minus_minus(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),one_one(int)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
tff(f128,negated_conjecture,
( ( ~ power_power(int,minus_minus(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),one_one(int)),number_number_of(nat,bit0(bit1(pls)))) ) = minus_minus(int,times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),minus_minus(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),one_one(int))),times_times(int,one_one(int),minus_minus(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),one_one(int)))) ),
inference(negated_conjecture,[status(cth)],[f127]) ).
tff(f129,plain,
power_power(int,minus_minus(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),one_one(int)),number_number_of(nat,bit0(bit1(pls)))) != minus_minus(int,times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),minus_minus(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),one_one(int))),times_times(int,one_one(int),minus_minus(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),one_one(int)))),
inference(flattening,[],[f128]) ).
tff(f175,plain,
! [X0: $tType] :
( ! [X1: X0] : ( power_power(X0,X1,number_number_of(nat,bit0(bit1(pls)))) = times_times(X0,X1,X1) )
| ~ monoid_mult(X0) ),
inference(ennf_transformation,[],[f82]) ).
tff(f221,plain,
! [X0: int,X1: int] : ( bit0(times_times(int,X1,X0)) = times_times(int,bit0(X1),X0) ),
inference(cnf_transformation,[],[f25]) ).
tff(f245,plain,
! [X0: int] : ( number_number_of(int,X0) = X0 ),
inference(cnf_transformation,[],[f49]) ).
tff(f255,plain,
! [X2: int,X0: int,X1: int] : ( times_times(int,minus_minus(int,X2,X1),X0) = minus_minus(int,times_times(int,X2,X0),times_times(int,X1,X0)) ),
inference(cnf_transformation,[],[f59]) ).
tff(f269,plain,
one_one(int) = number_number_of(int,bit1(pls)),
inference(cnf_transformation,[],[f73]) ).
tff(f278,plain,
! [X0: $tType,X1: X0] :
( ~ monoid_mult(X0)
| ( power_power(X0,X1,number_number_of(nat,bit0(bit1(pls)))) = times_times(X0,X1,X1) ) ),
inference(cnf_transformation,[],[f175]) ).
tff(f300,plain,
monoid_mult(int),
inference(cnf_transformation,[],[f102]) ).
tff(f325,plain,
power_power(int,minus_minus(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),one_one(int)),number_number_of(nat,bit0(bit1(pls)))) != minus_minus(int,times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),minus_minus(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),one_one(int))),times_times(int,one_one(int),minus_minus(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),one_one(int)))),
inference(cnf_transformation,[],[f129]) ).
tff(f339,plain,
bit1(pls) = one_one(int),
inference(forward_demodulation,[],[f269,f245]) ).
tff(f340,plain,
power_power(int,minus_minus(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),bit1(pls)),bit1(pls)),number_number_of(nat,bit0(bit1(pls)))) != minus_minus(int,times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),bit1(pls)),minus_minus(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),bit1(pls)),bit1(pls))),times_times(int,bit1(pls),minus_minus(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),bit1(pls)),bit1(pls)))),
inference(superposition,[],[f325,f339]) ).
tff(f341,plain,
power_power(int,minus_minus(int,plus_plus(int,times_times(int,bit0(bit0(bit1(pls))),m),bit1(pls)),bit1(pls)),number_number_of(nat,bit0(bit1(pls)))) != minus_minus(int,times_times(int,plus_plus(int,times_times(int,bit0(bit0(bit1(pls))),m),bit1(pls)),minus_minus(int,plus_plus(int,times_times(int,bit0(bit0(bit1(pls))),m),bit1(pls)),bit1(pls))),times_times(int,bit1(pls),minus_minus(int,plus_plus(int,times_times(int,bit0(bit0(bit1(pls))),m),bit1(pls)),bit1(pls)))),
inference(forward_demodulation,[],[f340,f245]) ).
tff(f366,plain,
power_power(int,minus_minus(int,plus_plus(int,bit0(times_times(int,bit0(bit1(pls)),m)),bit1(pls)),bit1(pls)),number_number_of(nat,bit0(bit1(pls)))) != minus_minus(int,times_times(int,plus_plus(int,bit0(times_times(int,bit0(bit1(pls)),m)),bit1(pls)),minus_minus(int,plus_plus(int,bit0(times_times(int,bit0(bit1(pls)),m)),bit1(pls)),bit1(pls))),times_times(int,bit1(pls),minus_minus(int,plus_plus(int,bit0(times_times(int,bit0(bit1(pls)),m)),bit1(pls)),bit1(pls)))),
inference(superposition,[],[f341,f221]) ).
tff(f367,plain,
power_power(int,minus_minus(int,plus_plus(int,bit0(bit0(times_times(int,bit1(pls),m))),bit1(pls)),bit1(pls)),number_number_of(nat,bit0(bit1(pls)))) != minus_minus(int,times_times(int,plus_plus(int,bit0(bit0(times_times(int,bit1(pls),m))),bit1(pls)),minus_minus(int,plus_plus(int,bit0(bit0(times_times(int,bit1(pls),m))),bit1(pls)),bit1(pls))),times_times(int,bit1(pls),minus_minus(int,plus_plus(int,bit0(bit0(times_times(int,bit1(pls),m))),bit1(pls)),bit1(pls)))),
inference(forward_demodulation,[],[f366,f221]) ).
tff(f519,plain,
! [X0: int] : ( power_power(int,X0,number_number_of(nat,bit0(bit1(pls)))) = times_times(int,X0,X0) ),
inference(resolution,[],[f278,f300]) ).
tff(f720,plain,
power_power(int,minus_minus(int,plus_plus(int,bit0(bit0(times_times(int,bit1(pls),m))),bit1(pls)),bit1(pls)),number_number_of(nat,bit0(bit1(pls)))) != times_times(int,minus_minus(int,plus_plus(int,bit0(bit0(times_times(int,bit1(pls),m))),bit1(pls)),bit1(pls)),minus_minus(int,plus_plus(int,bit0(bit0(times_times(int,bit1(pls),m))),bit1(pls)),bit1(pls))),
inference(superposition,[],[f367,f255]) ).
tff(f721,plain,
$false,
inference(forward_subsumption_resolution,[],[f720,f519]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM962_5 : TPTP v9.3.1. Released v6.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.14/0.39 % Computer : n014.cluster.edu
% 0.14/0.39 % Model : x86_64 x86_64
% 0.14/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.39 % Memory : 8046.5625MB
% 0.14/0.39 % OS : Linux 6.8.0-71-generic
% 0.14/0.39 % CPULimit : 300
% 0.14/0.39 % WCLimit : 300
% 0.14/0.39 % DateTime : Sun Sep 27 21:48:16 UTC 2026
% 0.14/0.39 % CPUTime :
% 0.14/0.39 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.14/0.44 Running first-order theorem proving
% 0.14/0.44 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
% 2.04/1.77 % (1200536)Detected formulas, will run a generic FOF schedule.
% 2.04/1.77 % (1200546)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=3171902304:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.04/1.77 % (1200549)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=16860483:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.04/1.77 % (1200548)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=4058877282:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.04/1.77 % (1200547)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=1327770665:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.04/1.77 % (1200545)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=3913198591:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.04/1.77 % (1200551)dis-21_1_sil=8000:lcm=predicate:random_seed=3715224658: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)
% 2.04/1.77 % (1200550)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3994918286:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.04/1.77 % (1200548)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 2.04/1.77 % (1200547)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 2.04/1.77 % (1200551)Refutation not found, incomplete strategy
% 2.04/1.77 % (1200551)------------------------------
% 2.04/1.77 % (1200551)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.04/1.77 % (1200551)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.04/1.77 % (1200551)CaDiCaL version: 2.1.3
% 2.04/1.77 % (1200551)Termination reason: Refutation not found, incomplete strategy
% 2.04/1.77 % (1200551)Time elapsed: 0.017 s
% 2.04/1.77 % (1200551)Peak memory usage: 88 MB
% 2.04/1.77 % (1200551)Instructions burned: 17 (million)
% 2.04/1.77 % (1200550)First to succeed.
% 2.04/1.77 % (1200550)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-1200536"
% 2.04/1.77 % (1200548)Instruction limit reached!
% 2.04/1.77 % (1200548)------------------------------
% 2.04/1.77 % (1200548)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.04/1.77 % (1200548)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.04/1.77 % (1200548)CaDiCaL version: 2.1.3
% 2.04/1.77 % (1200548)Termination reason: Instruction limit
% 2.04/1.77 % (1200548)Termination phase: Saturation
% 2.04/1.77 % (1200548)Time elapsed: 0.104 s
% 2.04/1.77 % (1200548)Peak memory usage: 89 MB
% 2.04/1.77 % (1200548)Instructions burned: 110 (million)
% 2.04/1.77 % (1200549)Instruction limit reached!
% 2.04/1.77 % (1200549)------------------------------
% 2.04/1.77 % (1200549)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.04/1.77 % (1200549)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.04/1.77 % (1200549)CaDiCaL version: 2.1.3
% 2.04/1.77 % (1200549)Termination reason: Instruction limit
% 2.04/1.77 % (1200549)Termination phase: Saturation
% 2.04/1.77 % (1200549)Time elapsed: 0.106 s
% 2.04/1.77 % (1200549)Peak memory usage: 88 MB
% 2.04/1.77 % (1200549)Instructions burned: 119 (million)
% 2.04/1.77 % (1200546)Aborted by signal SIGSEGV on /export/starexec/sandbox2/benchmark/theBenchmark.p
% 2.04/1.77 % (1200546)------------------------------
% 2.04/1.77 % (1200546)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.04/1.77 % (1200546)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.04/1.77 % (1200546)CaDiCaL version: 2.1.3
% 2.04/1.77 % (1200546)Termination reason: Unknown
% 2.04/1.77 % (1200546)Termination phase: Saturation
% 2.04/1.77 % (1200546)Time elapsed: 0.275 s
% 2.04/1.77 % (1200546)Peak memory usage: 114 MB
% 2.04/1.77 % (1200546)Instructions burned: 547 (million)
% 2.04/1.77 % (1200562)lrs+10_1_sil=8000:sp=occurrence:random_seed=1691182223:i=285:sd=3:ss=axioms:sgt=8_2996 on theBenchmark for (2996ds/285Mi)
% 2.04/1.77 % (1200564)lrs+1011_1_sil=32000:sp=occurrence:random_seed=2327992621:i=325:sd=1:ss=axioms:sgt=32_2995 on theBenchmark for (2995ds/325Mi)
% 2.04/1.77 % (1200563)lrs+10_1_sil=32000:urr=on:br=off:random_seed=1040208398:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2995 on theBenchmark for (2995ds/157Mi)
% 5.93/2.00 % (1200551)------------------------------
% 5.93/2.00 % (1200551)------------------------------
% 5.93/2.00 % (1200550)Refutation found. Thanks to Tanya!
% 5.93/2.00 % SZS status Theorem for theBenchmark
% 5.93/2.00 % SZS output start Proof for theBenchmark
% See solution above
% 5.93/2.00 % (1200550)------------------------------
% 5.93/2.00 % (1200550)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.93/2.00 % (1200550)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.93/2.00 % (1200550)CaDiCaL version: 2.1.3
% 5.93/2.00 % (1200550)Termination reason: Refutation
% 5.93/2.00 % (1200550)Time elapsed: 0.035 s
% 5.93/2.00 % (1200550)Peak memory usage: 89 MB
% 5.93/2.00 % (1200550)Instructions burned: 33 (million)
% 5.93/2.00 % (1200550)------------------------------
% 5.93/2.00 % (1200550)------------------------------
% 5.93/2.00 % (1200536)Success in time 0.735 s
% 5.93/2.01 % Vampire exiting
%------------------------------------------------------------------------------