%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM925+1 : 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 : 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 12:17:32 PM UTC 2026
% Result : Theorem 2.77s 1.38s
% Output : Refutation 2.77s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 13
% Syntax : Number of formulae : 48 ( 33 unt; 0 def)
% Number of atoms : 74 ( 42 equ)
% Maximal formula atoms : 6 ( 1 avg)
% Number of connectives : 44 ( 18 ~; 19 |; 5 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 4 con; 0-2 aty)
% Number of variables : 47 ( 47 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f37,axiom,
~ ord_less_int(pls,pls),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_36_rel__simps_I2_J) ).
fof(f51,axiom,
! [X0,X1,X2] : plus_plus_int(plus_plus_int(X0,X1),X2) = plus_plus_int(X0,plus_plus_int(X1,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_50_zadd__assoc) ).
fof(f52,axiom,
! [X0,X1,X2] : plus_plus_int(X0,plus_plus_int(X1,X2)) = plus_plus_int(X1,plus_plus_int(X0,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_51_zadd__left__commute) ).
fof(f53,axiom,
! [X0,X1] : plus_plus_int(X0,X1) = plus_plus_int(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_52_zadd__commute) ).
fof(f66,axiom,
! [X0,X1] :
( ord_less_int(X0,plus_plus_int(X1,one_one_int))
<=> ( ord_less_int(X0,X1)
| X0 = X1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_65_zless__add1__eq) ).
fof(f67,axiom,
! [X0] : ~ ord_less_int(semiri1621563631at_int(X0),zero_zero_int),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_66_int__less__0__conv) ).
fof(f79,axiom,
pls = zero_zero_int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_78_Pls__def) ).
fof(f81,axiom,
! [X0] : plus_plus_int(X0,pls) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_80_add__Pls__right) ).
fof(f82,axiom,
! [X0] : plus_plus_int(pls,X0) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_81_add__Pls) ).
fof(f84,axiom,
! [X0] : bit0(X0) = plus_plus_int(X0,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_83_Bit0__def) ).
fof(f100,axiom,
! [X0] : bit1(X0) = plus_plus_int(plus_plus_int(one_one_int,X0),X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_99_Bit1__def) ).
fof(f104,axiom,
! [X0] :
( ord_less_int(zero_zero_int,power_power_int(X0,number_number_of_nat(bit0(bit1(pls)))))
<=> X0 != zero_zero_int ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_103_zero__less__power2) ).
fof(f107,conjecture,
power_power_int(plus_plus_int(one_one_int,semiri1621563631at_int(n)),number_number_of_nat(bit0(bit1(pls)))) != zero_zero_int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
fof(f108,negated_conjecture,
~ ( power_power_int(plus_plus_int(one_one_int,semiri1621563631at_int(n)),number_number_of_nat(bit0(bit1(pls)))) != zero_zero_int ),
inference(negated_conjecture,[status(cth)],[f107]) ).
fof(f109,plain,
zero_zero_int = power_power_int(plus_plus_int(one_one_int,semiri1621563631at_int(n)),number_number_of_nat(bit0(bit1(pls)))),
inference(flattening,[],[f108]) ).
fof(f118,plain,
! [X0,X1] :
( ( ord_less_int(X0,plus_plus_int(X1,one_one_int))
| ( ~ ord_less_int(X0,X1)
& X0 != X1 ) )
& ( ord_less_int(X0,X1)
| X0 = X1
| ~ ord_less_int(X0,plus_plus_int(X1,one_one_int)) ) ),
inference(nnf_transformation,[],[f66]) ).
fof(f119,plain,
! [X0,X1] :
( ( ord_less_int(X0,plus_plus_int(X1,one_one_int))
| ( ~ ord_less_int(X0,X1)
& X0 != X1 ) )
& ( ord_less_int(X0,X1)
| X0 = X1
| ~ ord_less_int(X0,plus_plus_int(X1,one_one_int)) ) ),
inference(flattening,[],[f118]) ).
fof(f134,plain,
! [X0] :
( ( ord_less_int(zero_zero_int,power_power_int(X0,number_number_of_nat(bit0(bit1(pls)))))
| zero_zero_int = X0 )
& ( X0 != zero_zero_int
| ~ ord_less_int(zero_zero_int,power_power_int(X0,number_number_of_nat(bit0(bit1(pls))))) ) ),
inference(nnf_transformation,[],[f104]) ).
fof(f147,plain,
zero_zero_int = power_power_int(plus_plus_int(one_one_int,semiri1621563631at_int(n)),number_number_of_nat(bit0(bit1(pls)))),
inference(cnf_transformation,[],[f109]) ).
fof(f150,plain,
zero_zero_int = pls,
inference(cnf_transformation,[],[f79]) ).
fof(f161,plain,
! [X0] : bit1(X0) = plus_plus_int(plus_plus_int(one_one_int,X0),X0),
inference(cnf_transformation,[],[f100]) ).
fof(f170,plain,
! [X0,X1] :
( ord_less_int(X0,plus_plus_int(X1,one_one_int))
| X0 != X1 ),
inference(cnf_transformation,[],[f119]) ).
fof(f182,plain,
! [X0] : ~ ord_less_int(semiri1621563631at_int(X0),zero_zero_int),
inference(cnf_transformation,[],[f67]) ).
fof(f185,plain,
! [X0] : plus_plus_int(pls,X0) = X0,
inference(cnf_transformation,[],[f82]) ).
fof(f186,plain,
! [X0] : plus_plus_int(X0,pls) = X0,
inference(cnf_transformation,[],[f81]) ).
fof(f187,plain,
! [X0,X1] : plus_plus_int(X0,X1) = plus_plus_int(X1,X0),
inference(cnf_transformation,[],[f53]) ).
fof(f188,plain,
! [X2,X0,X1] : plus_plus_int(X0,plus_plus_int(X1,X2)) = plus_plus_int(X1,plus_plus_int(X0,X2)),
inference(cnf_transformation,[],[f52]) ).
fof(f189,plain,
! [X2,X0,X1] : plus_plus_int(plus_plus_int(X0,X1),X2) = plus_plus_int(X0,plus_plus_int(X1,X2)),
inference(cnf_transformation,[],[f51]) ).
fof(f196,plain,
! [X0] : bit0(X0) = plus_plus_int(X0,X0),
inference(cnf_transformation,[],[f84]) ).
fof(f226,plain,
! [X0] :
( ord_less_int(zero_zero_int,power_power_int(X0,number_number_of_nat(bit0(bit1(pls)))))
| zero_zero_int = X0 ),
inference(cnf_transformation,[],[f134]) ).
fof(f238,plain,
~ ord_less_int(pls,pls),
inference(cnf_transformation,[],[f37]) ).
fof(f266,plain,
pls = power_power_int(plus_plus_int(one_one_int,semiri1621563631at_int(n)),number_number_of_nat(plus_plus_int(plus_plus_int(plus_plus_int(one_one_int,pls),pls),plus_plus_int(plus_plus_int(one_one_int,pls),pls)))),
inference(definition_unfolding,[],[f147,f150,f196,f161]) ).
fof(f295,plain,
! [X0] : ~ ord_less_int(semiri1621563631at_int(X0),pls),
inference(definition_unfolding,[],[f182,f150]) ).
fof(f328,plain,
! [X0] :
( ord_less_int(pls,power_power_int(X0,number_number_of_nat(plus_plus_int(plus_plus_int(plus_plus_int(one_one_int,pls),pls),plus_plus_int(plus_plus_int(one_one_int,pls),pls)))))
| pls = X0 ),
inference(definition_unfolding,[],[f226,f150,f196,f161,f150]) ).
fof(f353,plain,
! [X1] : ord_less_int(X1,plus_plus_int(X1,one_one_int)),
inference(equality_resolution,[],[f170]) ).
fof(f371,plain,
pls = power_power_int(plus_plus_int(one_one_int,semiri1621563631at_int(n)),number_number_of_nat(plus_plus_int(plus_plus_int(one_one_int,pls),plus_plus_int(one_one_int,pls)))),
inference(superposition,[],[f266,f186]) ).
fof(f372,plain,
pls = power_power_int(plus_plus_int(one_one_int,semiri1621563631at_int(n)),number_number_of_nat(plus_plus_int(one_one_int,one_one_int))),
inference(forward_demodulation,[],[f371,f186]) ).
fof(f382,plain,
! [X0] : ord_less_int(X0,plus_plus_int(one_one_int,X0)),
inference(superposition,[],[f353,f187]) ).
fof(f2676,plain,
! [X0] :
( ord_less_int(pls,power_power_int(X0,number_number_of_nat(plus_plus_int(plus_plus_int(one_one_int,pls),plus_plus_int(plus_plus_int(plus_plus_int(one_one_int,pls),pls),pls)))))
| pls = X0 ),
inference(forward_demodulation,[],[f328,f188]) ).
fof(f2677,plain,
! [X0] :
( ord_less_int(pls,power_power_int(X0,number_number_of_nat(plus_plus_int(one_one_int,plus_plus_int(pls,plus_plus_int(plus_plus_int(plus_plus_int(one_one_int,pls),pls),pls))))))
| pls = X0 ),
inference(forward_demodulation,[],[f2676,f189]) ).
fof(f2678,plain,
! [X0] :
( ord_less_int(pls,power_power_int(X0,number_number_of_nat(plus_plus_int(one_one_int,plus_plus_int(plus_plus_int(plus_plus_int(one_one_int,pls),pls),pls)))))
| pls = X0 ),
inference(forward_demodulation,[],[f2677,f185]) ).
fof(f2679,plain,
! [X0] :
( ord_less_int(pls,power_power_int(X0,number_number_of_nat(plus_plus_int(one_one_int,plus_plus_int(plus_plus_int(one_one_int,pls),pls)))))
| pls = X0 ),
inference(forward_demodulation,[],[f2678,f186]) ).
fof(f2680,plain,
! [X0] :
( ord_less_int(pls,power_power_int(X0,number_number_of_nat(plus_plus_int(one_one_int,plus_plus_int(one_one_int,pls)))))
| pls = X0 ),
inference(forward_demodulation,[],[f2679,f186]) ).
fof(f2681,plain,
! [X0] :
( ord_less_int(pls,power_power_int(X0,number_number_of_nat(plus_plus_int(one_one_int,one_one_int))))
| pls = X0 ),
inference(forward_demodulation,[],[f2680,f186]) ).
fof(f2682,plain,
( ord_less_int(pls,pls)
| plus_plus_int(one_one_int,semiri1621563631at_int(n)) = pls ),
inference(superposition,[],[f2681,f372]) ).
fof(f2684,plain,
plus_plus_int(one_one_int,semiri1621563631at_int(n)) = pls,
inference(forward_subsumption_resolution,[],[f2682,f238]) ).
fof(f2689,plain,
ord_less_int(semiri1621563631at_int(n),pls),
inference(superposition,[],[f382,f2684]) ).
fof(f2757,plain,
$false,
inference(forward_subsumption_resolution,[],[f2689,f295]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM925+1 : TPTP v9.3.1. Released v5.3.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.38 % Computer : n017.cluster.edu
% 0.10/0.38 % Model : x86_64 x86_64
% 0.10/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.38 % Memory : 8046.5625MB
% 0.10/0.38 % OS : Linux 6.8.0-71-generic
% 0.10/0.38 % CPULimit : 300
% 0.10/0.38 % WCLimit : 300
% 0.10/0.38 % DateTime : Sun Sep 27 21:37:06 UTC 2026
% 0.10/0.39 % CPUTime :
% 0.10/0.39 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.42 Running first-order theorem proving
% 0.10/0.42 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
% 2.77/1.38 % (2959465)Detected formulas, will run a generic FOF schedule.
% 2.77/1.38 % (2959474)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=423601438:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.77/1.38 % (2959474)First to succeed.
% 2.77/1.38 % (2959474)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2959465"
% 2.77/1.38 % (2959471)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=2798229513:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.77/1.38 % (2959470)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=2391201856:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.77/1.38 % (2959473)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=833222837:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.77/1.38 % (2959472)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=1345815533:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.77/1.38 % (2959476)dis-21_1_sil=8000:lcm=predicate:random_seed=3267417459: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)
% 2.77/1.38 % (2959475)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2179363109:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.77/1.38 % (2959475)Also succeeded, but the first one will report.
% 2.77/1.38 % (2959473)Instruction limit reached!
% 2.77/1.38 % (2959473)------------------------------
% 2.77/1.38 % (2959473)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.77/1.38 % (2959473)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.77/1.38 % (2959473)CaDiCaL version: 2.1.3
% 2.77/1.38 % (2959473)Termination reason: Instruction limit
% 2.77/1.38 % (2959473)Termination phase: Saturation
% 2.77/1.38 % (2959473)Time elapsed: 0.060 s
% 2.77/1.38 % (2959473)Peak memory usage: 89 MB
% 2.77/1.38 % (2959473)Instructions burned: 110 (million)
% 2.77/1.38 % (2959476)Instruction limit reached!
% 2.77/1.38 % (2959476)------------------------------
% 2.77/1.38 % (2959476)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.77/1.38 % (2959476)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.77/1.38 % (2959476)CaDiCaL version: 2.1.3
% 2.77/1.38 % (2959476)Termination reason: Instruction limit
% 2.77/1.38 % (2959476)Termination phase: Saturation
% 2.77/1.38 % (2959476)Time elapsed: 0.074 s
% 2.77/1.38 % (2959476)Peak memory usage: 89 MB
% 2.77/1.38 % (2959476)Instructions burned: 129 (million)
% 2.77/1.38 % (2959474)Refutation found. Thanks to Tanya!
% 2.77/1.38 % SZS status Theorem for theBenchmark
% 2.77/1.38 % SZS output start Proof for theBenchmark
% See solution above
% 2.77/1.38 % (2959474)------------------------------
% 2.77/1.38 % (2959474)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.77/1.38 % (2959474)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.77/1.38 % (2959474)CaDiCaL version: 2.1.3
% 2.77/1.38 % (2959474)Termination reason: Refutation
% 2.77/1.38 % (2959474)Time elapsed: 0.025 s
% 2.77/1.38 % (2959474)Peak memory usage: 89 MB
% 2.77/1.38 % (2959474)Instructions burned: 77 (million)
% 2.77/1.38 % (2959474)------------------------------
% 2.77/1.38 % (2959474)------------------------------
% 2.77/1.38 % (2959465)Success in time 0.317 s
% 2.77/1.38 % Vampire exiting
%------------------------------------------------------------------------------