%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM926+5 : TPTP v9.3.1. Released v5.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n015.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 12:17:37 PM UTC 2026
% Result : Theorem 2.72s 1.26s
% Output : Refutation 3.54s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 11
% Syntax : Number of formulae : 56 ( 18 unt; 6 def)
% Number of atoms : 108 ( 23 equ)
% Maximal formula atoms : 6 ( 1 avg)
% Number of connectives : 94 ( 42 ~; 38 |; 5 &)
% ( 7 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 10 ( 8 usr; 6 prp; 0-3 aty)
% Number of functors : 16 ( 16 usr; 9 con; 0-3 aty)
% Number of variables : 34 ( 0 sgn 22 !; 12 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f28,axiom,
ord_less_eq(int,one_one(int),t),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0_tpos) ).
fof(f29,axiom,
( t = one_one(int)
=> ? [X0,X1] : 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',fact_1__096t_A_061_A1_A_061_061_062_AEX_Ax_Ay_O_Ax_A_094_A2_A_L_Ay_A_094_A2_A_06) ).
fof(f30,axiom,
( ord_less(int,one_one(int),t)
=> ? [X0,X1] : 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',fact_2__0961_A_060_At_A_061_061_062_AEX_Ax_Ay_O_Ax_A_094_A2_A_L_Ay_A_094_A2_A_06) ).
fof(f50,axiom,
! [X0,X1] :
( ord_less(int,X0,X1)
<=> ( ord_less_eq(int,X0,X1)
& X0 != X1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_22_zless__le) ).
fof(f142,conjecture,
? [X0,X1] : 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) ).
fof(f143,negated_conjecture,
~ ? [X0,X1] : 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)],[f142]) ).
fof(f164,plain,
( ? [X0,X1] : 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))
| t != one_one(int) ),
inference(ennf_transformation,[],[f29]) ).
fof(f165,plain,
( ? [X0,X1] : 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))
| ~ ord_less(int,one_one(int),t) ),
inference(ennf_transformation,[],[f30]) ).
fof(f215,plain,
! [X0,X1] : 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(ennf_transformation,[],[f143]) ).
fof(f222,plain,
( plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)) = plus_plus(int,power_power(int,sK0,number_number_of(nat,bit0(bit1(pls)))),power_power(int,sK1,number_number_of(nat,bit0(bit1(pls)))))
| t != one_one(int) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f164]) ).
fof(f223,plain,
( plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)) = plus_plus(int,power_power(int,sK2,number_number_of(nat,bit0(bit1(pls)))),power_power(int,sK3,number_number_of(nat,bit0(bit1(pls)))))
| ~ ord_less(int,one_one(int),t) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3]),skolemize(X0,sK2),skolemize(X1,sK3)],[f165]) ).
fof(f225,plain,
! [X0,X1] :
( ( ord_less(int,X0,X1)
| ~ ord_less_eq(int,X0,X1)
| X0 = X1 )
& ( ( ord_less_eq(int,X0,X1)
& X0 != X1 )
| ~ ord_less(int,X0,X1) ) ),
inference(nnf_transformation,[],[f50]) ).
fof(f226,plain,
! [X0,X1] :
( ( ord_less(int,X0,X1)
| ~ ord_less_eq(int,X0,X1)
| X0 = X1 )
& ( ( ord_less_eq(int,X0,X1)
& X0 != X1 )
| ~ ord_less(int,X0,X1) ) ),
inference(flattening,[],[f225]) ).
fof(f293,plain,
ord_less_eq(int,one_one(int),t),
inference(cnf_transformation,[],[f28]) ).
fof(f294,plain,
( plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)) = plus_plus(int,power_power(int,sK0,number_number_of(nat,bit0(bit1(pls)))),power_power(int,sK1,number_number_of(nat,bit0(bit1(pls)))))
| t != one_one(int) ),
inference(cnf_transformation,[],[f222]) ).
fof(f295,plain,
( plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)) = plus_plus(int,power_power(int,sK2,number_number_of(nat,bit0(bit1(pls)))),power_power(int,sK3,number_number_of(nat,bit0(bit1(pls)))))
| ~ ord_less(int,one_one(int),t) ),
inference(cnf_transformation,[],[f223]) ).
fof(f317,plain,
! [X0,X1] :
( ord_less(int,X0,X1)
| ~ ord_less_eq(int,X0,X1)
| X0 = X1 ),
inference(cnf_transformation,[],[f226]) ).
fof(f444,plain,
! [X0,X1] : 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(cnf_transformation,[],[f215]) ).
fof(f449,definition,
! [X0,X1] :
( sQ5_eqProxy(X0,X1)
<=> X0 = X1 ),
introduced(definition,[new_symbols(definition,[sQ5_eqProxy])],[equality_proxy_definition]) ).
fof(f471,plain,
( sQ5_eqProxy(plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),plus_plus(int,power_power(int,sK0,number_number_of(nat,bit0(bit1(pls)))),power_power(int,sK1,number_number_of(nat,bit0(bit1(pls))))))
| ~ sQ5_eqProxy(t,one_one(int)) ),
inference(equality_proxy_replacement,[],[f294,f449,f449]) ).
fof(f472,plain,
( sQ5_eqProxy(plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),plus_plus(int,power_power(int,sK2,number_number_of(nat,bit0(bit1(pls)))),power_power(int,sK3,number_number_of(nat,bit0(bit1(pls))))))
| ~ ord_less(int,one_one(int),t) ),
inference(equality_proxy_replacement,[],[f295,f449]) ).
fof(f487,plain,
! [X0,X1] :
( sQ5_eqProxy(X0,X1)
| ~ ord_less_eq(int,X0,X1)
| ord_less(int,X0,X1) ),
inference(equality_proxy_replacement,[],[f317,f449]) ).
fof(f532,plain,
! [X0,X1] : ~ sQ5_eqProxy(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(equality_proxy_replacement,[],[f444,f449]) ).
fof(f534,plain,
! [X0,X1] :
( sQ5_eqProxy(X1,X0)
| ~ sQ5_eqProxy(X0,X1) ),
inference(equality_proxy_axiom,[],[f449]) ).
fof(f536,definition,
( spl6_1
<=> ord_less(int,one_one(int),t) ),
introduced(definition,[new_symbols(definition,[spl6_1])],[avatar_definition]) ).
fof(f539,definition,
( spl6_2
<=> sQ5_eqProxy(plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),plus_plus(int,power_power(int,sK2,number_number_of(nat,bit0(bit1(pls)))),power_power(int,sK3,number_number_of(nat,bit0(bit1(pls)))))) ),
introduced(definition,[new_symbols(definition,[spl6_2])],[avatar_definition]) ).
fof(f540,plain,
( sQ5_eqProxy(plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),plus_plus(int,power_power(int,sK2,number_number_of(nat,bit0(bit1(pls)))),power_power(int,sK3,number_number_of(nat,bit0(bit1(pls))))))
| ~ spl6_2 ),
inference(avatar_component_clause,[],[f539]) ).
fof(f541,plain,
( ~ spl6_1
| spl6_2 ),
inference(avatar_split_clause,[],[f472,f539,f536]) ).
fof(f543,definition,
( spl6_3
<=> sQ5_eqProxy(t,one_one(int)) ),
introduced(definition,[new_symbols(definition,[spl6_3])],[avatar_definition]) ).
fof(f544,plain,
( ~ sQ5_eqProxy(t,one_one(int))
| spl6_3 ),
inference(avatar_component_clause,[],[f543]) ).
fof(f546,definition,
( spl6_4
<=> sQ5_eqProxy(plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),plus_plus(int,power_power(int,sK0,number_number_of(nat,bit0(bit1(pls)))),power_power(int,sK1,number_number_of(nat,bit0(bit1(pls)))))) ),
introduced(definition,[new_symbols(definition,[spl6_4])],[avatar_definition]) ).
fof(f547,plain,
( sQ5_eqProxy(plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),plus_plus(int,power_power(int,sK0,number_number_of(nat,bit0(bit1(pls)))),power_power(int,sK1,number_number_of(nat,bit0(bit1(pls))))))
| ~ spl6_4 ),
inference(avatar_component_clause,[],[f546]) ).
fof(f548,plain,
( ~ spl6_3
| spl6_4 ),
inference(avatar_split_clause,[],[f471,f546,f543]) ).
fof(f551,plain,
( ~ sQ5_eqProxy(one_one(int),t)
| spl6_3 ),
inference(resolution,[],[f534,f544]) ).
fof(f552,plain,
! [X0,X1] : ~ sQ5_eqProxy(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(resolution,[],[f534,f532]) ).
fof(f649,plain,
( ~ ord_less_eq(int,one_one(int),t)
| ord_less(int,one_one(int),t)
| spl6_3 ),
inference(resolution,[],[f487,f551]) ).
fof(f666,definition,
( spl6_7
<=> ord_less_eq(int,one_one(int),t) ),
introduced(definition,[new_symbols(definition,[spl6_7])],[avatar_definition]) ).
fof(f667,plain,
( ~ ord_less_eq(int,one_one(int),t)
| spl6_7 ),
inference(avatar_component_clause,[],[f666]) ).
fof(f668,plain,
( spl6_1
| ~ spl6_7
| spl6_3 ),
inference(avatar_split_clause,[],[f649,f543,f666,f536]) ).
fof(f672,plain,
( $false
| spl6_7 ),
inference(resolution,[],[f667,f293]) ).
fof(f676,plain,
spl6_7,
inference(avatar_contradiction_clause,[],[f672]) ).
fof(f677,plain,
( $false
| ~ spl6_4 ),
inference(resolution,[],[f547,f552]) ).
fof(f678,plain,
~ spl6_4,
inference(avatar_contradiction_clause,[],[f677]) ).
fof(f681,plain,
( $false
| ~ spl6_2 ),
inference(resolution,[],[f540,f552]) ).
fof(f682,plain,
~ spl6_2,
inference(avatar_contradiction_clause,[],[f681]) ).
cnf(s1,plain,
( ~ spl6_1
| spl6_2 ),
inference(sat_conversion,[],[f541]) ).
cnf(s2,plain,
( ~ spl6_3
| spl6_4 ),
inference(sat_conversion,[],[f548]) ).
cnf(s4,plain,
( spl6_1
| spl6_3
| ~ spl6_7 ),
inference(sat_conversion,[],[f668]) ).
cnf(s5,plain,
spl6_7,
inference(sat_conversion,[],[f676]) ).
cnf(s6,plain,
~ spl6_4,
inference(sat_conversion,[],[f678]) ).
cnf(s7,plain,
~ spl6_2,
inference(sat_conversion,[],[f682]) ).
cnf(s8,plain,
( spl6_1
| spl6_3 ),
inference(rat,[],[s4,s5]) ).
cnf(s9,plain,
~ spl6_3,
inference(rat,[],[s2,s6]) ).
cnf(s10,plain,
spl6_1,
inference(rat,[],[s8,s9]) ).
cnf(s11,plain,
$false,
inference(rat,[],[s1,s7,s10]) ).
fof(f683,plain,
$false,
inference(avatar_sat_refutation,[],[s11]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM926+5 : TPTP v9.3.1. Released v5.3.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.38 % Computer : n015.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 21:48:01 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.41 Running first-order theorem proving
% 0.11/0.41 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
% 2.72/1.26 % (2034949)Detected formulas, will run a generic FOF schedule.
% 2.72/1.26 % (2034958)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1124143431:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.72/1.26 % (2034958)Instruction limit reached!
% 2.72/1.26 % (2034958)------------------------------
% 2.72/1.26 % (2034958)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.72/1.26 % (2034958)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.72/1.26 % (2034958)CaDiCaL version: 2.1.3
% 2.72/1.26 % (2034958)Termination reason: Instruction limit
% 2.72/1.26 % (2034958)Termination phase: Saturation
% 2.72/1.26 % (2034958)Time elapsed: 0.035 s
% 2.72/1.26 % (2034958)Peak memory usage: 88 MB
% 2.72/1.26 % (2034958)Instructions burned: 124 (million)
% 2.72/1.26 % (2034959)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1017806569:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.72/1.26 % (2034955)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=3961946591:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.72/1.26 % (2034956)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=1357299259:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.72/1.26 % (2034954)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=1540134632:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.72/1.26 % (2034957)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3713559289:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.72/1.26 % (2034960)dis-21_1_sil=8000:lcm=predicate:random_seed=1624069791: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)
% 2.72/1.26 % (2034960)First to succeed.
% 2.72/1.26 % (2034960)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2034949"
% 2.72/1.26 % (2034959)Also succeeded, but the first one will report.
% 2.72/1.26 % (2034957)Instruction limit reached!
% 2.72/1.26 % (2034957)------------------------------
% 2.72/1.26 % (2034957)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.72/1.26 % (2034957)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.72/1.26 % (2034957)CaDiCaL version: 2.1.3
% 2.72/1.26 % (2034957)Termination reason: Instruction limit
% 2.72/1.26 % (2034957)Termination phase: Saturation
% 2.72/1.26 % (2034957)Time elapsed: 0.054 s
% 2.72/1.26 % (2034957)Peak memory usage: 88 MB
% 2.72/1.26 % (2034957)Instructions burned: 109 (million)
% 2.72/1.26 % (2034962)lrs+10_1_sil=8000:sp=occurrence:random_seed=3189307944:i=285:sd=3:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/285Mi)
% 2.72/1.26 % (2034962)Instruction limit reached!
% 2.72/1.26 % (2034962)------------------------------
% 2.72/1.26 % (2034962)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.72/1.26 % (2034962)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.72/1.26 % (2034962)CaDiCaL version: 2.1.3
% 2.72/1.26 % (2034962)Termination reason: Instruction limit
% 2.72/1.26 % (2034962)Termination phase: Saturation
% 2.72/1.26 % (2034962)Time elapsed: 0.088 s
% 2.72/1.26 % (2034962)Peak memory usage: 90 MB
% 2.72/1.26 % (2034962)Instructions burned: 286 (million)
% 2.72/1.26 % (2034969)lrs+10_1_sil=32000:urr=on:br=off:random_seed=201597780:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 2.72/1.26 % (2034971)lrs+1011_1_sil=32000:sp=occurrence:random_seed=4060136096:i=325:sd=1:ss=axioms:sgt=32_2996 on theBenchmark for (2996ds/325Mi)
% 2.72/1.26 % (2034960)Refutation found. Thanks to Tanya!
% 2.72/1.26 % SZS status Theorem for theBenchmark
% 2.72/1.26 % SZS output start Proof for theBenchmark
% See solution above
% 3.54/1.45 % (2034960)------------------------------
% 3.54/1.45 % (2034960)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.54/1.45 % (2034960)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.54/1.45 % (2034960)CaDiCaL version: 2.1.3
% 3.54/1.45 % (2034960)Termination reason: Refutation
% 3.54/1.45 % (2034960)Time elapsed: 0.009 s
% 3.54/1.45 % (2034960)Peak memory usage: 89 MB
% 3.54/1.45 % (2034960)Instructions burned: 15 (million)
% 3.54/1.45 % (2034960)------------------------------
% 3.54/1.45 % (2034960)------------------------------
% 3.54/1.45 % (2034949)Success in time 0.42 s
% 3.54/1.45 % Vampire exiting
%------------------------------------------------------------------------------