%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM894_1 : TPTP v9.3.1. Released v5.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/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 12:17:23 PM UTC 2026
% Result : Theorem 2.76s 1.36s
% Output : Refutation 2.76s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 5
% Syntax : Number of formulae : 19 ( 9 unt; 0 typ; 4 def)
% Number of atoms : 29 ( 3 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 15 ( 5 ~; 0 |; 3 &)
% ( 3 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 2 ( 1 avg)
% Number arithmetic : 53 ( 19 atm; 11 fun; 11 num; 12 var)
% Number of types : 1 ( 0 usr; 1 ari; 0 dat; 0 cdt)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 7 ( 3 usr; 4 prp; 0-2 aty)
% Number of functors : 5 ( 3 usr; 4 con; 0-2 aty)
% Number of variables : 12 ( 8 !; 4 ?; 12 :)
% Comments :
%------------------------------------------------------------------------------
tff(func_def_2,type,
sK0: $int ).
tff(func_def_3,type,
sK1: $int ).
tff(func_def_4,type,
sF2: $int ).
tff(f1,conjecture,
! [X1: $int,X0: $int] :
( $less(X1,$sum(X0,1))
=> $lesseq(X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',less_successor) ).
tff(f2,negated_conjecture,
~ ! [X1: $int,X0: $int] :
( $less(X1,$sum(X0,1))
=> $lesseq(X1,X0) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
tff(f3,plain,
~ ! [X1: $int,X0: $int] :
( $less(X1,$sum(X0,1))
=> ~ $less(X0,X1) ),
inference(theory_normalization,[],[f2]) ).
tff(f4,plain,
~ ! [X1: $int,X0: $int] :
( $less(X0,$sum(X1,1))
=> ~ $less(X1,X0) ),
inference(rectify,[],[f3]) ).
tff(f5,plain,
? [X1: $int,X0: $int] :
( $less(X1,X0)
& $less(X0,$sum(X1,1)) ),
inference(ennf_transformation,[],[f4]) ).
tff(f6,plain,
? [X0: $int,X1: $int] :
( $less(X0,X1)
& $less(X1,$sum(X0,1)) ),
inference(rectify,[],[f5]) ).
tff(f7,plain,
( $less(sK0,sK1)
& $less(sK1,$sum(sK0,1)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f6]) ).
tff(f8,plain,
$less(sK1,$sum(sK0,1)),
inference(cnf_transformation,[],[f7]) ).
tff(f9,plain,
$less(sK0,sK1),
inference(cnf_transformation,[],[f7]) ).
tff(f10,definition,
sF2 = $sum(sK0,1),
introduced(definition,[new_symbols(definition,[sF2])],[function_definition]) ).
tff(f11,plain,
$sum(sK0,1) = sF2,
inference(reorient_equations,[],[f10]) ).
tff(f12,plain,
$less(sK1,sF2),
inference(definition_folding,[],[f8,f11]) ).
tff(f14,definition,
( spl3_1
<=> ( $sum(sK0,1) = sF2 ) ),
introduced(definition,[new_symbols(definition,[spl3_1])],[avatar_definition]) ).
tff(f17,plain,
spl3_1,
inference(avatar_split_clause,[],[f11,f14]) ).
tff(f19,definition,
( spl3_2
<=> $less(sK0,sK1) ),
introduced(definition,[new_symbols(definition,[spl3_2])],[avatar_definition]) ).
tff(f22,plain,
spl3_2,
inference(avatar_split_clause,[],[f9,f19]) ).
tff(f24,definition,
( spl3_3
<=> $less(sK1,sF2) ),
introduced(definition,[new_symbols(definition,[spl3_3])],[avatar_definition]) ).
tff(f27,plain,
spl3_3,
inference(avatar_split_clause,[],[f12,f24]) ).
tff(f28,plain,
$false,
inference(avatar_smt_refutation,[],[f27,f22,f17]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM894_1 : TPTP v9.3.1. Released v5.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.38 % Computer : n015.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 21:41:46 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.42 Running first-order theorem proving
% 0.10/0.42 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
% 2.76/1.36 % (2030543)Detected arithmetic, will pick strategies from an ALASCA-aware ARI schedule.
% 2.76/1.36 % (2030549)dis+1002_1_to=kbo:sil=128000:tgt=ground:sas=z3:si=on:spb=units:tha=off:random_seed=3557824554:i=307:kws=precedence:nm=0:rtra=on_2999 on theBenchmark for (2999ds/307Mi)
% 2.76/1.36 % (2030549)First to succeed.
% 2.76/1.36 % (2030549)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2030543"
% 2.76/1.36 % (2030554)lrs+10_1_tgt=ground:sas=z3:si=on:random_seed=25319061:i=33:rtra=on_2999 on theBenchmark for (2999ds/33Mi)
% 2.76/1.36 % (2030551)lrs+1002_4:1_to=lpo:sil=64000:si=on:br=off:random_seed=3436335142:s2a=on:i=7:rtra=on:inst=on_2999 on theBenchmark for (2999ds/7Mi)
% 2.76/1.36 % (2030552)dis+21_64_to=kbo:sil=128000:si=on:sp=weighted_frequency:uwa=alasca_can_abstract:random_seed=388905787:i=4:rtra=on_2999 on theBenchmark for (2999ds/4Mi)
% 2.76/1.36 % (2030548)dis+1002_16:1_to=lpo:sil=64000:sas=z3:si=on:norm_ineq=on:gve=force:uwa=one_side_constant:random_seed=3274735198:i=12:doe=on:rtra=on:gtg=exists_top:ss=axioms_2999 on theBenchmark for (2999ds/12Mi)
% 2.76/1.36 % (2030550)dis+10_3_slsqr=1,4:to=lpo:sil=128000:thi=strong:si=on:uwa=off:s2agt=20:slsqc=1:slsq=on:random_seed=2007368242:i=201:slsql=off:asg=cautious:rtra=on:gtg=all:ss=axioms:sgt=16_2999 on theBenchmark for (2999ds/201Mi)
% 2.76/1.36 % (2030553)lrs+10_1_to=lpo:sas=z3:si=on:tha=off:random_seed=645983972:i=46:rtra=on_2999 on theBenchmark for (2999ds/46Mi)
% 2.76/1.36 % (2030552)Instruction limit reached!
% 2.76/1.36 % (2030552)------------------------------
% 2.76/1.36 % (2030552)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.76/1.36 % (2030552)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.76/1.36 % (2030552)CaDiCaL version: 2.1.3
% 2.76/1.36 % (2030552)Termination reason: Instruction limit
% 2.76/1.36 % (2030552)Termination phase: Saturation
% 2.76/1.36 % (2030552)Time elapsed: 0.004 s
% 2.76/1.36 % (2030552)Peak memory usage: 88 MB
% 2.76/1.36 % (2030552)Instructions burned: 4 (million)
% 2.76/1.36 % (2030551)Instruction limit reached!
% 2.76/1.36 % (2030551)------------------------------
% 2.76/1.36 % (2030551)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.76/1.36 % (2030551)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.76/1.36 % (2030551)CaDiCaL version: 2.1.3
% 2.76/1.36 % (2030551)Termination reason: Instruction limit
% 2.76/1.36 % (2030551)Termination phase: Saturation
% 2.76/1.36 % (2030551)Time elapsed: 0.005 s
% 2.76/1.36 % (2030551)Peak memory usage: 88 MB
% 2.76/1.36 % (2030551)Instructions burned: 7 (million)
% 2.76/1.36 % (2030554)Also succeeded, but the first one will report.
% 2.76/1.36 % (2030550)Also succeeded, but the first one will report.
% 2.76/1.36 % (2030548)Also succeeded, but the first one will report.
% 2.76/1.36 % (2030553)Also succeeded, but the first one will report.
% 2.76/1.36 % (2030562)dis+11_3_anc=none:drc=ordering:si=on:urr=ec_only:bce=on:tha=off:sac=on:random_seed=2921440035:st=5:i=14:sd=10:rtra=on:ss=axioms:rawr=on_2998 on theBenchmark for (2998ds/14Mi)
% 2.76/1.36 % (2030563)dis+1011_2:1_to=kbo:sil=128000:tgt=full:fde=none:si=on:norm_ineq=on:spb=goal_then_units:tha=some:nwc=2:sac=on:random_seed=3127966771:i=29:thsqd=64:nm=0:thsqc=8:rtra=on:thsq=on:ev=off_2998 on theBenchmark for (2998ds/29Mi)
% 2.76/1.36 % (2030562)Refutation not found, incomplete strategy
% 2.76/1.36 % (2030562)------------------------------
% 2.76/1.36 % (2030562)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.76/1.36 % (2030562)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.76/1.36 % (2030562)CaDiCaL version: 2.1.3
% 2.76/1.36 % (2030562)Termination reason: Refutation not found, incomplete strategy
% 2.76/1.36 % (2030562)Time elapsed: 0.001 s
% 2.76/1.36 % (2030562)Peak memory usage: 88 MB
% 2.76/1.36 % (2030549)Refutation found. Thanks to Tanya!
% 2.76/1.36 % SZS status Theorem for theBenchmark
% 2.76/1.36 % SZS output start Proof for theBenchmark
% See solution above
% 2.76/1.36 % (2030549)------------------------------
% 2.76/1.36 % (2030549)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.76/1.36 % (2030549)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.76/1.36 % (2030549)CaDiCaL version: 2.1.3
% 2.76/1.36 % (2030549)Termination reason: Refutation
% 2.76/1.36 % (2030549)Time elapsed: 0.020 s
% 2.76/1.36 % (2030549)Peak memory usage: 115 MB
% 2.76/1.36 % (2030549)Instructions burned: 8 (million)
% 2.76/1.36 % (2030549)------------------------------
% 2.76/1.36 % (2030549)------------------------------
% 2.76/1.36 % (2030543)Success in time 0.31 s
% 2.76/1.36 % Vampire exiting
%------------------------------------------------------------------------------