%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM926+1 : TPTP v9.3.1. Released v5.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n008.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 12:17:35 PM UTC 2026
% Result : Theorem 1.78s 1.75s
% Output : Refutation 4.62s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 11
% Syntax : Number of formulae : 54 ( 18 unt; 6 def)
% Number of atoms : 104 ( 23 equ)
% Maximal formula atoms : 6 ( 1 avg)
% Number of connectives : 91 ( 41 ~; 36 |; 5 &)
% ( 7 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 7 ( 3 avg)
% Number of predicates : 10 ( 8 usr; 6 prp; 0-2 aty)
% Number of functors : 15 ( 15 usr; 8 con; 0-2 aty)
% Number of variables : 34 ( 0 sgn 22 !; 12 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
ord_less_eq_int(one_one_int,t),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0_tpos) ).
fof(f2,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/sandbox/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(f3,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/sandbox/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(f29,axiom,
! [X0,X1] :
( ord_less_int(X0,X1)
<=> ( ord_less_eq_int(X0,X1)
& X0 != X1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_28_zless__le) ).
fof(f124,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/sandbox/benchmark/theBenchmark.p',conj_0) ).
fof(f125,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)],[f124]) ).
fof(f128,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)
| one_one_int != t ),
inference(ennf_transformation,[],[f2]) ).
fof(f129,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,[],[f3]) ).
fof(f143,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,[],[f125]) ).
fof(f144,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)))))
| one_one_int != t ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f128]) ).
fof(f145,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)],[f129]) ).
fof(f147,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,[],[f29]) ).
fof(f148,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,[],[f147]) ).
fof(f184,plain,
ord_less_eq_int(one_one_int,t),
inference(cnf_transformation,[],[f1]) ).
fof(f185,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)))))
| one_one_int != t ),
inference(cnf_transformation,[],[f144]) ).
fof(f186,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,[],[f145]) ).
fof(f213,plain,
! [X0,X1] :
( ord_less_int(X0,X1)
| ~ ord_less_eq_int(X0,X1)
| X0 = X1 ),
inference(cnf_transformation,[],[f148]) ).
fof(f344,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,[],[f143]) ).
fof(f353,definition,
! [X0,X1] :
( sQ5_eqProxy(X0,X1)
<=> X0 = X1 ),
introduced(definition,[new_symbols(definition,[sQ5_eqProxy])],[equality_proxy_definition]) ).
fof(f354,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(one_one_int,t) ),
inference(equality_proxy_replacement,[],[f185,f353,f353]) ).
fof(f355,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,[],[f186,f353]) ).
fof(f376,plain,
! [X0,X1] :
( sQ5_eqProxy(X0,X1)
| ~ ord_less_eq_int(X0,X1)
| ord_less_int(X0,X1) ),
inference(equality_proxy_replacement,[],[f213,f353]) ).
fof(f439,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,[],[f344,f353]) ).
fof(f441,plain,
! [X0,X1] :
( sQ5_eqProxy(X1,X0)
| ~ sQ5_eqProxy(X0,X1) ),
inference(equality_proxy_axiom,[],[f353]) ).
fof(f443,definition,
( spl6_1
<=> ord_less_int(one_one_int,t) ),
introduced(definition,[new_symbols(definition,[spl6_1])],[avatar_definition]) ).
fof(f446,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(f447,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,[],[f446]) ).
fof(f448,plain,
( ~ spl6_1
| spl6_2 ),
inference(avatar_split_clause,[],[f355,f446,f443]) ).
fof(f450,definition,
( spl6_3
<=> sQ5_eqProxy(one_one_int,t) ),
introduced(definition,[new_symbols(definition,[spl6_3])],[avatar_definition]) ).
fof(f451,plain,
( ~ sQ5_eqProxy(one_one_int,t)
| spl6_3 ),
inference(avatar_component_clause,[],[f450]) ).
fof(f453,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(f454,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,[],[f453]) ).
fof(f455,plain,
( ~ spl6_3
| spl6_4 ),
inference(avatar_split_clause,[],[f354,f453,f450]) ).
fof(f456,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,[],[f441,f439]) ).
fof(f611,definition,
( spl6_7
<=> ord_less_eq_int(one_one_int,t) ),
introduced(definition,[new_symbols(definition,[spl6_7])],[avatar_definition]) ).
fof(f612,plain,
( ~ ord_less_eq_int(one_one_int,t)
| spl6_7 ),
inference(avatar_component_clause,[],[f611]) ).
fof(f614,plain,
( $false
| spl6_7 ),
inference(resolution,[],[f612,f184]) ).
fof(f620,plain,
spl6_7,
inference(avatar_contradiction_clause,[],[f614]) ).
fof(f626,plain,
( $false
| ~ spl6_4 ),
inference(resolution,[],[f454,f456]) ).
fof(f627,plain,
~ spl6_4,
inference(avatar_contradiction_clause,[],[f626]) ).
fof(f628,plain,
( ~ ord_less_eq_int(one_one_int,t)
| ord_less_int(one_one_int,t)
| spl6_3 ),
inference(resolution,[],[f451,f376]) ).
fof(f630,plain,
( spl6_1
| ~ spl6_7
| spl6_3 ),
inference(avatar_split_clause,[],[f628,f450,f611,f443]) ).
fof(f631,plain,
( $false
| ~ spl6_2 ),
inference(resolution,[],[f447,f456]) ).
fof(f632,plain,
~ spl6_2,
inference(avatar_contradiction_clause,[],[f631]) ).
cnf(s1,plain,
( ~ spl6_1
| spl6_2 ),
inference(sat_conversion,[],[f448]) ).
cnf(s2,plain,
( ~ spl6_3
| spl6_4 ),
inference(sat_conversion,[],[f455]) ).
cnf(s5,plain,
spl6_7,
inference(sat_conversion,[],[f620]) ).
cnf(s6,plain,
~ spl6_4,
inference(sat_conversion,[],[f627]) ).
cnf(s7,plain,
( spl6_1
| spl6_3
| ~ spl6_7 ),
inference(sat_conversion,[],[f630]) ).
cnf(s8,plain,
~ spl6_2,
inference(sat_conversion,[],[f632]) ).
cnf(s10,plain,
~ spl6_3,
inference(rat,[],[s2,s6]) ).
cnf(s11,plain,
spl6_1,
inference(rat,[],[s7,s5,s10]) ).
cnf(s12,plain,
$false,
inference(rat,[],[s1,s8,s11]) ).
fof(f633,plain,
$false,
inference(avatar_sat_refutation,[],[s12]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM926+1 : TPTP v9.3.1. Released v5.3.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.13/0.39 % Computer : n008.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 21:42:54 UTC 2026
% 0.13/0.40 % CPUTime :
% 0.13/0.40 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.13/0.46 Running first-order theorem proving
% 0.13/0.46 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
% 1.78/1.75 % (1630550)Detected formulas, will run a generic FOF schedule.
% 1.78/1.75 % (1630561)dis-21_1_sil=8000:lcm=predicate:random_seed=3979437935: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)
% 1.78/1.75 % (1630561)First to succeed.
% 1.78/1.75 % (1630561)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-1630550"
% 1.78/1.75 % (1630555)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=3485400374:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 1.78/1.75 % (1630557)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=3845592024:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 1.78/1.75 % (1630556)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=1881946327:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 1.78/1.75 % (1630558)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3422176751:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 1.78/1.75 % (1630559)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3382786406:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 1.78/1.75 % (1630560)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1029010757:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 1.78/1.75 % (1630558)Instruction limit reached!
% 1.78/1.75 % (1630558)------------------------------
% 1.78/1.75 % (1630558)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 1.78/1.75 % (1630558)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.78/1.75 % (1630558)CaDiCaL version: 2.1.3
% 1.78/1.75 % (1630558)Termination reason: Instruction limit
% 1.78/1.75 % (1630558)Termination phase: Saturation
% 1.78/1.75 % (1630558)Time elapsed: 0.099 s
% 1.78/1.75 % (1630558)Peak memory usage: 89 MB
% 1.78/1.75 % (1630558)Instructions burned: 110 (million)
% 1.78/1.75 % (1630559)Instruction limit reached!
% 1.78/1.75 % (1630559)------------------------------
% 1.78/1.75 % (1630559)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 1.78/1.75 % (1630559)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.78/1.75 % (1630559)CaDiCaL version: 2.1.3
% 1.78/1.75 % (1630559)Termination reason: Instruction limit
% 1.78/1.75 % (1630559)Termination phase: Saturation
% 1.78/1.75 % (1630559)Time elapsed: 0.108 s
% 1.78/1.75 % (1630559)Peak memory usage: 88 MB
% 1.78/1.75 % (1630559)Instructions burned: 119 (million)
% 1.78/1.75 % (1630560)Also succeeded, but the first one will report.
% 1.78/1.75 % (1630561)Refutation found. Thanks to Tanya!
% 1.78/1.75 % SZS status Theorem for theBenchmark
% 1.78/1.75 % SZS output start Proof for theBenchmark
% See solution above
% 4.62/2.05 % (1630561)------------------------------
% 4.62/2.05 % (1630561)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.62/2.05 % (1630561)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.62/2.05 % (1630561)CaDiCaL version: 2.1.3
% 4.62/2.05 % (1630561)Termination reason: Refutation
% 4.62/2.05 % (1630561)Time elapsed: 0.008 s
% 4.62/2.05 % (1630561)Peak memory usage: 89 MB
% 4.62/2.05 % (1630561)Instructions burned: 12 (million)
% 4.62/2.05 % (1630561)------------------------------
% 4.62/2.05 % (1630561)------------------------------
% 4.62/2.05 % (1630550)Success in time 0.512 s
% 4.62/2.05 % Vampire exiting
%------------------------------------------------------------------------------