%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : NUM925+2 : TPTP v9.3.1. Released v5.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n020.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 12:26:09 PM UTC 2026
% Result : Theorem 0.19s 0.49s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 8
% Syntax : Number of formulae : 27 ( 22 unt; 0 def)
% Number of atoms : 32 ( 24 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 17 ( 12 ~; 4 |; 0 &)
% ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 15 ( 15 usr; 6 con; 0-2 aty)
% Number of variables : 22 ( 22 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f73,axiom,
! [X0,X1] : hAPP_int_int(plus_plus_int(X0),X1) = hAPP_int_int(plus_plus_int(X1),X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_67_zadd__commute) ).
fof(f89,axiom,
! [X0] : ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(semiri1621563631at_int,X0)),zero_zero_int)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_83_int__less__0__conv) ).
fof(f104,axiom,
pls = zero_zero_int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_98_Pls__def) ).
fof(f109,axiom,
! [X0] : bit0(X0) = hAPP_int_int(plus_plus_int(X0),X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_103_Bit0__def) ).
fof(f134,axiom,
! [X0] : bit1(X0) = hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),X0)),X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_128_Bit1__def) ).
fof(f237,axiom,
! [X0,X1] :
( X1 != zero_zero_int
=> hAPP_nat_int(power_power_int(X1),X0) != zero_zero_int ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_231_field__power__not__zero) ).
fof(f276,axiom,
! [X0] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),hAPP_int_int(plus_plus_int(X0),one_one_int))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_270_less__add__one) ).
fof(f708,conjecture,
hAPP_nat_int(power_power_int(hAPP_int_int(plus_plus_int(one_one_int),hAPP_nat_int(semiri1621563631at_int,n))),number_number_of_nat(bit0(bit1(pls)))) != zero_zero_int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
fof(f709,negated_conjecture,
~ ( hAPP_nat_int(power_power_int(hAPP_int_int(plus_plus_int(one_one_int),hAPP_nat_int(semiri1621563631at_int,n))),number_number_of_nat(bit0(bit1(pls)))) != zero_zero_int ),
inference(negated_conjecture,[status(cth)],[f708]) ).
fof(f712,plain,
zero_zero_int = hAPP_nat_int(power_power_int(hAPP_int_int(plus_plus_int(one_one_int),hAPP_nat_int(semiri1621563631at_int,n))),number_number_of_nat(bit0(bit1(pls)))),
inference(flattening,[],[f709]) ).
fof(f761,plain,
! [X0,X1] :
( hAPP_nat_int(power_power_int(X1),X0) != zero_zero_int
| zero_zero_int = X1 ),
inference(ennf_transformation,[],[f237]) ).
fof(f1494,plain,
! [X0,X1] : hAPP_int_int(plus_plus_int(X0),X1) = hAPP_int_int(plus_plus_int(X1),X0),
inference(cnf_transformation,[],[f73]) ).
fof(f1524,plain,
! [X0] : ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(semiri1621563631at_int,X0)),zero_zero_int)),
inference(cnf_transformation,[],[f89]) ).
fof(f1548,plain,
zero_zero_int = pls,
inference(cnf_transformation,[],[f104]) ).
fof(f1553,plain,
! [X0] : bit0(X0) = hAPP_int_int(plus_plus_int(X0),X0),
inference(cnf_transformation,[],[f109]) ).
fof(f1584,plain,
! [X0] : bit1(X0) = hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),X0)),X0),
inference(cnf_transformation,[],[f134]) ).
fof(f1738,plain,
! [X0,X1] :
( zero_zero_int != hAPP_nat_int(power_power_int(X1),X0)
| zero_zero_int = X1 ),
inference(cnf_transformation,[],[f761]) ).
fof(f1780,plain,
! [X0] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),hAPP_int_int(plus_plus_int(X0),one_one_int))),
inference(cnf_transformation,[],[f276]) ).
fof(f2379,plain,
zero_zero_int = hAPP_nat_int(power_power_int(hAPP_int_int(plus_plus_int(one_one_int),hAPP_nat_int(semiri1621563631at_int,n))),number_number_of_nat(bit0(bit1(pls)))),
inference(cnf_transformation,[],[f712]) ).
fof(f2455,plain,
! [X0] : ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(semiri1621563631at_int,X0)),pls)),
inference(definition_unfolding,[],[f1524,f1548]) ).
fof(f2528,plain,
! [X0,X1] :
( pls != hAPP_nat_int(power_power_int(X1),X0)
| pls = X1 ),
inference(definition_unfolding,[],[f1738,f1548,f1548]) ).
fof(f2705,plain,
pls = hAPP_nat_int(power_power_int(hAPP_int_int(plus_plus_int(one_one_int),hAPP_nat_int(semiri1621563631at_int,n))),number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)))),
inference(definition_unfolding,[],[f2379,f1548,f1553,f1584]) ).
fof(f2968,plain,
! [X0] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),hAPP_int_int(plus_plus_int(one_one_int),X0))),
inference(superposition,[],[f1780,f1494]) ).
fof(f3001,plain,
( pls != pls
| hAPP_int_int(plus_plus_int(one_one_int),hAPP_nat_int(semiri1621563631at_int,n)) = pls ),
inference(superposition,[],[f2528,f2705]) ).
fof(f3006,plain,
hAPP_int_int(plus_plus_int(one_one_int),hAPP_nat_int(semiri1621563631at_int,n)) = pls,
inference(trivial_inequality_removal,[],[f3001]) ).
fof(f3065,plain,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(semiri1621563631at_int,n)),pls)),
inference(superposition,[],[f2968,f3006]) ).
fof(f3069,plain,
$false,
inference(forward_subsumption_resolution,[],[f3065,f2455]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM925+2 : TPTP v9.3.1. Released v5.3.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.11/0.37 % Computer : n020.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Sun Sep 27 21:42:50 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.11/0.41 Running first-order model finding
% 0.11/0.41 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.49 % (3783179)Will run a generic schedule for satisfiability detection.
% 0.19/0.49 % (3783187)dis+10_1_sil=32000:sp=arity:random_seed=1222606164:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.19/0.49 % (3783185)% WARNING: option uhcvi not known.
% 0.19/0.49 % (3783184)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2949347748_2999 on theBenchmark for (2999ds/0Mi)
% 0.19/0.49 % (3783185)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=351226680:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.19/0.49 % (3783186)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2145871004:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.19/0.49 % (3783188)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3449767709:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.19/0.49 % (3783189)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=2785567912:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.19/0.49 % (3783190)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=3799190028:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.19/0.49 % (3783187) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3783179-3783187"...
% 0.19/0.49 % (3783187)...printing done.
% 0.19/0.49 % (3783187)Refutation found. Thanks to Tanya!
% 0.19/0.49 % SZS status Theorem for theBenchmark
% 0.19/0.49 % SZS output start Proof for theBenchmark
% See solution above
% 0.19/0.49 % (3783187)------------------------------
% 0.19/0.49 % (3783187)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.49 % (3783187)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.49 % (3783187)CaDiCaL version: 2.1.3
% 0.19/0.49 % (3783187)Termination reason: Refutation
% 0.19/0.49 % (3783187)Time elapsed: 0.020 s
% 0.19/0.49 % (3783187)Peak memory usage: 13 MB
% 0.19/0.49 % (3783187)Instructions burned: 73 (million)
% 0.19/0.49 % (3783179)Success in time 0.07 s
% 0.19/0.49 % Vampire exiting
%------------------------------------------------------------------------------