%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM960_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 : n016.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 4.14s 1.74s
% Output : Refutation 4.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 8
% Syntax : Number of formulae : 35 ( 27 unt; 0 typ; 0 def)
% Number of atoms : 46 ( 11 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 26 ( 15 ~; 6 |; 3 &)
% ( 1 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 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 : 17 ( 15 usr; 1 prp; 0-3 aty)
% Number of functors : 18 ( 18 usr; 9 con; 0-3 aty)
% Number of variables : 21 ( 21 !; 0 ?; 21 :)
% Comments :
%------------------------------------------------------------------------------
tff(type_def_5,type,
bool: $tType ).
tff(type_def_6,type,
int: $tType ).
tff(type_def_7,type,
nat: $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,
zero_zero:
!>[X0: $tType] : X0 ).
tff(func_def_5,type,
bit0: int > int ).
tff(func_def_6,type,
bit1: int > int ).
tff(func_def_7,type,
pls: int ).
tff(func_def_8,type,
number_number_of:
!>[X0: $tType] : ( int > X0 ) ).
tff(func_def_9,type,
power_power:
!>[X0: $tType] : ( ( X0 * nat ) > X0 ) ).
tff(func_def_10,type,
fFalse: bool ).
tff(func_def_11,type,
fTrue: bool ).
tff(func_def_12,type,
m: int ).
tff(func_def_13,type,
s1: int ).
tff(func_def_14,type,
s: int ).
tff(func_def_15,type,
t: int ).
tff(func_def_16,type,
sK0: int ).
tff(func_def_17,type,
sK1: 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,
linorder:
!>[X0: $tType] : $o ).
tff(pred_def_7,type,
number_semiring:
!>[X0: $tType] : $o ).
tff(pred_def_8,type,
linordered_idom:
!>[X0: $tType] : $o ).
tff(pred_def_9,type,
linord219039673up_add:
!>[X0: $tType] : $o ).
tff(pred_def_10,type,
zcong: ( int * int * int ) > $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,
ord_less_eq:
!>[X0: $tType] : ( ( X0 * X0 ) > $o ) ).
tff(pred_def_14,type,
twoSqu1567020053sum2sq: int > $o ).
tff(pred_def_15,type,
pp: bool > $o ).
tff(f1,axiom,
( ord_less_eq(int,zero_zero(int),s)
& ord_less(int,s,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)))
& zcong(s1,s,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0_s0p) ).
tff(f11,axiom,
! [X0: $tType] :
( number_ring(X0)
=> ( number_number_of(X0,bit1(pls)) = one_one(X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_10_numeral__1__eq__1) ).
tff(f35,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_34_mult__Bit0) ).
tff(f58,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_57_add__Bit0__Bit1) ).
tff(f64,axiom,
! [X0: int,X1: int] :
( ord_less_eq(int,X1,minus_minus(int,X0,one_one(int)))
<=> ord_less(int,X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_63_zle__diff1__eq) ).
tff(f91,axiom,
! [X0: int] : ( number_number_of(int,X0) = X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_90_number__of__is__id) ).
tff(f104,axiom,
number_ring(int),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Int_Onumber__ring) ).
tff(f115,conjecture,
ord_less_eq(int,s,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/sandbox/benchmark/theBenchmark.p',conj_0) ).
tff(f116,negated_conjecture,
~ ord_less_eq(int,s,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)],[f115]) ).
tff(f117,plain,
~ ord_less_eq(int,s,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,[],[f116]) ).
tff(f127,plain,
! [X0: $tType] :
( ( number_number_of(X0,bit1(pls)) = one_one(X0) )
| ~ number_ring(X0) ),
inference(ennf_transformation,[],[f11]) ).
tff(f200,plain,
! [X0: int,X1: int] :
( ( ord_less_eq(int,X1,minus_minus(int,X0,one_one(int)))
| ~ ord_less(int,X1,X0) )
& ( ord_less(int,X1,X0)
| ~ ord_less_eq(int,X1,minus_minus(int,X0,one_one(int))) ) ),
inference(nnf_transformation,[],[f64]) ).
tff(f228,plain,
ord_less(int,s,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int))),
inference(cnf_transformation,[],[f1]) ).
tff(f240,plain,
! [X0: $tType] :
( ~ number_ring(X0)
| ( one_one(X0) = number_number_of(X0,bit1(pls)) ) ),
inference(cnf_transformation,[],[f127]) ).
tff(f274,plain,
! [X0: int,X1: int] : ( bit0(times_times(int,X1,X0)) = times_times(int,bit0(X1),X0) ),
inference(cnf_transformation,[],[f35]) ).
tff(f307,plain,
! [X0: int,X1: int] : ( bit1(plus_plus(int,X1,X0)) = plus_plus(int,bit0(X1),bit1(X0)) ),
inference(cnf_transformation,[],[f58]) ).
tff(f319,plain,
! [X0: int,X1: int] :
( ord_less_eq(int,X1,minus_minus(int,X0,one_one(int)))
| ~ ord_less(int,X1,X0) ),
inference(cnf_transformation,[],[f200]) ).
tff(f371,plain,
! [X0: int] : ( number_number_of(int,X0) = X0 ),
inference(cnf_transformation,[],[f91]) ).
tff(f387,plain,
number_ring(int),
inference(cnf_transformation,[],[f104]) ).
tff(f398,plain,
~ ord_less_eq(int,s,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,[],[f117]) ).
tff(f424,plain,
~ ord_less_eq(int,s,minus_minus(int,plus_plus(int,times_times(int,bit0(bit0(bit1(pls))),m),one_one(int)),one_one(int))),
inference(superposition,[],[f398,f371]) ).
tff(f437,plain,
one_one(int) = number_number_of(int,bit1(pls)),
inference(resolution,[],[f240,f387]) ).
tff(f438,plain,
bit1(pls) = one_one(int),
inference(forward_demodulation,[],[f437,f371]) ).
tff(f548,plain,
~ ord_less_eq(int,s,minus_minus(int,plus_plus(int,bit0(times_times(int,bit0(bit1(pls)),m)),one_one(int)),one_one(int))),
inference(superposition,[],[f424,f274]) ).
tff(f549,plain,
~ ord_less_eq(int,s,minus_minus(int,plus_plus(int,bit0(times_times(int,bit0(bit1(pls)),m)),bit1(pls)),bit1(pls))),
inference(forward_demodulation,[],[f548,f438]) ).
tff(f552,plain,
~ ord_less_eq(int,s,minus_minus(int,plus_plus(int,bit0(bit0(times_times(int,bit1(pls),m))),bit1(pls)),bit1(pls))),
inference(forward_demodulation,[],[f549,f274]) ).
tff(f623,plain,
! [X0: int,X1: int] :
( ord_less_eq(int,X1,minus_minus(int,X0,bit1(pls)))
| ~ ord_less(int,X1,X0) ),
inference(forward_demodulation,[],[f319,f438]) ).
tff(f714,plain,
~ ord_less(int,s,plus_plus(int,bit0(bit0(times_times(int,bit1(pls),m))),bit1(pls))),
inference(resolution,[],[f623,f552]) ).
tff(f719,plain,
~ ord_less(int,s,bit1(plus_plus(int,bit0(times_times(int,bit1(pls),m)),pls))),
inference(forward_demodulation,[],[f714,f307]) ).
tff(f889,plain,
ord_less(int,s,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),bit1(pls))),
inference(forward_demodulation,[],[f228,f438]) ).
tff(f890,plain,
ord_less(int,s,plus_plus(int,times_times(int,bit0(bit0(bit1(pls))),m),bit1(pls))),
inference(forward_demodulation,[],[f889,f371]) ).
tff(f891,plain,
ord_less(int,s,plus_plus(int,bit0(times_times(int,bit0(bit1(pls)),m)),bit1(pls))),
inference(forward_demodulation,[],[f890,f274]) ).
tff(f892,plain,
ord_less(int,s,bit1(plus_plus(int,times_times(int,bit0(bit1(pls)),m),pls))),
inference(forward_demodulation,[],[f891,f307]) ).
tff(f893,plain,
ord_less(int,s,bit1(plus_plus(int,bit0(times_times(int,bit1(pls),m)),pls))),
inference(forward_demodulation,[],[f892,f274]) ).
tff(f894,plain,
$false,
inference(forward_subsumption_resolution,[],[f893,f719]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM960_5 : TPTP v9.3.1. Released v6.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.40 % Computer : n016.cluster.edu
% 0.12/0.40 % Model : x86_64 x86_64
% 0.12/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.40 % Memory : 8046.5625MB
% 0.12/0.40 % OS : Linux 6.8.0-71-generic
% 0.12/0.40 % CPULimit : 300
% 0.12/0.40 % WCLimit : 300
% 0.12/0.40 % DateTime : Sun Sep 27 21:52:47 UTC 2026
% 0.12/0.40 % CPUTime :
% 0.12/0.40 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.46 Running first-order theorem proving
% 0.12/0.46 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
% 4.14/1.74 % (3022554)Detected formulas, will run a generic FOF schedule.
% 4.14/1.74 % (3022575)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=949332387:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 4.14/1.74 % (3022575)First to succeed.
% 4.14/1.74 % (3022575)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3022554"
% 4.14/1.74 % (3022570)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=4110802545:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 4.14/1.74 % (3022573)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3133099277:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 4.14/1.74 % (3022574)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2809998698:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 4.14/1.74 % (3022572)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=3769466276:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 4.14/1.74 % (3022571)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=2106326987:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 4.14/1.74 % (3022573)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 4.14/1.74 % (3022572)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 4.14/1.74 % (3022573)Refutation not found, incomplete strategy
% 4.14/1.74 % (3022573)------------------------------
% 4.14/1.74 % (3022573)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.14/1.74 % (3022573)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.14/1.74 % (3022573)CaDiCaL version: 2.1.3
% 4.14/1.74 % (3022573)Termination reason: Refutation not found, incomplete strategy
% 4.14/1.74 % (3022573)Time elapsed: 0.012 s
% 4.14/1.74 % (3022573)Peak memory usage: 88 MB
% 4.14/1.74 % (3022573)Instructions burned: 10 (million)
% 4.14/1.74 % (3022576)dis-21_1_sil=8000:lcm=predicate:random_seed=1849275522: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)
% 4.14/1.74 % (3022574)Also succeeded, but the first one will report.
% 4.14/1.74 % (3022576)Also succeeded, but the first one will report.
% 4.14/1.74 % (3022575)Refutation found. Thanks to Tanya!
% 4.14/1.74 % SZS status Theorem for theBenchmark
% 4.14/1.74 % SZS output start Proof for theBenchmark
% See solution above
% 4.14/1.74 % (3022575)------------------------------
% 4.14/1.74 % (3022575)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.14/1.74 % (3022575)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.14/1.74 % (3022575)CaDiCaL version: 2.1.3
% 4.14/1.74 % (3022575)Termination reason: Refutation
% 4.14/1.74 % (3022575)Time elapsed: 0.026 s
% 4.14/1.74 % (3022575)Peak memory usage: 89 MB
% 4.14/1.74 % (3022575)Instructions burned: 32 (million)
% 4.14/1.74 % (3022575)------------------------------
% 4.14/1.74 % (3022575)------------------------------
% 4.14/1.74 % (3022554)Success in time 0.468 s
% 4.14/1.74 % Vampire exiting
%------------------------------------------------------------------------------