%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM919_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 : n005.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 12:17:26 PM UTC 2026
% Result : Theorem 0.15s 1.51s
% Output : Refutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 4
% Syntax : Number of formulae : 20 ( 8 unt; 0 typ; 2 def)
% Number of atoms : 36 ( 2 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 26 ( 10 ~; 8 |; 6 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 8 ( 2 avg)
% Number arithmetic : 129 ( 29 atm; 53 fun; 30 num; 17 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 : 5 ( 2 usr; 3 prp; 0-2 aty)
% Number of functors : 7 ( 2 usr; 4 con; 0-2 aty)
% Number of variables : 17 ( 11 !; 6 ?; 17 :)
% Comments :
%------------------------------------------------------------------------------
tff(func_def_4,type,
sK0: $int ).
tff(func_def_5,type,
sK1: $int > $int ).
tff(f1,conjecture,
! [X0: $int] :
? [X1: $int] :
( ~ ? [X2: $int] :
( $less(X2,X0)
& $less(X1,X2) )
& $less(X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1) ).
tff(f2,negated_conjecture,
~ ! [X0: $int] :
? [X1: $int] :
( ~ ? [X2: $int] :
( $less(X2,X0)
& $less(X1,X2) )
& $less(X1,X0) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
tff(f8,plain,
! [X0: $int] : ~ $less(X0,X0),
introduced(definition,[],[tha_non-reflexivity]) ).
tff(f15,plain,
? [X0: $int] :
! [X1: $int] :
( ~ $less(X1,X0)
| ? [X2: $int] :
( $less(X2,X0)
& $less(X1,X2) ) ),
inference(ennf_transformation,[],[f2]) ).
tff(f16,plain,
! [X1: $int] :
( ~ $less(X1,sK0)
| ( $less(sK1(X1),sK0)
& $less(X1,sK1(X1)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X2,sK1(X1))],[f15]) ).
tff(f17,plain,
! [X1: $int] :
( $less(X1,sK1(X1))
| ~ $less(X1,sK0) ),
inference(cnf_transformation,[],[f16]) ).
tff(f18,plain,
! [X1: $int] :
( $less(sK1(X1),sK0)
| ~ $less(X1,sK0) ),
inference(cnf_transformation,[],[f16]) ).
tff(f19,plain,
! [X1: $int] :
( $less(0,$sum($sum(X1,1),$uminus(sK0)))
| $less(0,$sum(sK0,$uminus(sK1(X1)))) ),
inference(evaluation,[],[f18]) ).
tff(f20,plain,
! [X1: $int] :
( $less(0,$sum($sum(X1,1),$uminus(sK0)))
| $less(0,$sum(sK1(X1),$uminus(X1))) ),
inference(evaluation,[],[f17]) ).
tff(f21,plain,
! [X0: $int] :
( $less(0,$sum(sK1(X0),$uminus(X0)))
| ( 0 != $sum($sum(X0,1),$uminus(sK0)) ) ),
inference(constrained_resolution,[],[f8,f20]) ).
tff(f22,plain,
! [X0: $int] :
( ( 0 != $sum($sum(X0,1),$uminus(sK0)) )
| $less(0,$sum(sK0,$uminus(sK1(X0)))) ),
inference(constrained_resolution,[],[f8,f19]) ).
tff(f23,plain,
$less(0,$sum(sK0,$uminus(sK1($sum($sum(0,$uminus($uminus(sK0))),$uminus(1)))))),
inference(gaussian_variable_elimination,[],[f22]) ).
tff(f24,plain,
$less(0,$sum(sK0,$uminus(sK1($sum(sK0,-1))))),
inference(evaluation,[],[f23]) ).
tff(f25,plain,
$less(0,$sum(sK1($sum($sum(0,$uminus($uminus(sK0))),$uminus(1))),$uminus($sum($sum(0,$uminus($uminus(sK0))),$uminus(1))))),
inference(gaussian_variable_elimination,[],[f21]) ).
tff(f26,plain,
$less(0,$sum(sK1($sum(sK0,-1)),$uminus($sum(sK0,-1)))),
inference(evaluation,[],[f25]) ).
tff(f28,definition,
( spl2_1
<=> $less(0,$sum(sK0,$uminus(sK1($sum(sK0,-1))))) ),
introduced(definition,[new_symbols(definition,[spl2_1])],[avatar_definition]) ).
tff(f31,plain,
spl2_1,
inference(avatar_split_clause,[],[f24,f28]) ).
tff(f33,definition,
( spl2_2
<=> $less(0,$sum(sK1($sum(sK0,-1)),$uminus($sum(sK0,-1)))) ),
introduced(definition,[new_symbols(definition,[spl2_2])],[avatar_definition]) ).
tff(f36,plain,
spl2_2,
inference(avatar_split_clause,[],[f26,f33]) ).
tff(f37,plain,
$false,
inference(avatar_smt_refutation,[],[f36,f31]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM919_1 : TPTP v9.3.1. Released v5.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.35 % Computer : n005.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Sun Sep 27 21:39:16 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.13/0.39 Running first-order theorem proving
% 0.13/0.39 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
% 0.15/1.51 % (195153)Detected arithmetic, will pick strategies from an ALASCA-aware ARI schedule.
% 0.15/1.51 % (195164)lrs+10_1_to=lpo:sas=z3:si=on:tha=off:random_seed=2627963571:i=46:rtra=on_2999 on theBenchmark for (2999ds/46Mi)
% 0.15/1.51 % (195164)Refutation not found, incomplete strategy
% 0.15/1.51 % (195164)------------------------------
% 0.15/1.51 % (195164)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.15/1.51 % (195164)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.15/1.51 % (195164)CaDiCaL version: 2.1.3
% 0.15/1.51 % (195164)Termination reason: Refutation not found, incomplete strategy
% 0.15/1.51 % (195164)Time elapsed: 0.017 s
% 0.15/1.51 % (195164)Peak memory usage: 112 MB
% 0.15/1.51 % (195164)Instructions burned: 5 (million)
% 0.15/1.51 % (195161)dis+10_3_slsqr=1,4:to=lpo:sil=128000:thi=strong:si=on:uwa=off:s2agt=20:slsqc=1:slsq=on:random_seed=556487488:i=201:slsql=off:asg=cautious:rtra=on:gtg=all:ss=axioms:sgt=16_2999 on theBenchmark for (2999ds/201Mi)
% 0.15/1.51 % (195162)lrs+1002_4:1_to=lpo:sil=64000:si=on:br=off:random_seed=3342369729:s2a=on:i=7:rtra=on:inst=on_2999 on theBenchmark for (2999ds/7Mi)
% 0.15/1.51 % (195165)lrs+10_1_tgt=ground:sas=z3:si=on:random_seed=4214202479:i=33:rtra=on_2999 on theBenchmark for (2999ds/33Mi)
% 0.15/1.51 % (195160)dis+1002_1_to=kbo:sil=128000:tgt=ground:sas=z3:si=on:spb=units:tha=off:random_seed=431593779:i=307:kws=precedence:nm=0:rtra=on_2999 on theBenchmark for (2999ds/307Mi)
% 0.15/1.51 % (195159)dis+1002_16:1_to=lpo:sil=64000:sas=z3:si=on:norm_ineq=on:gve=force:uwa=one_side_constant:random_seed=3649306088:i=12:doe=on:rtra=on:gtg=exists_top:ss=axioms_2999 on theBenchmark for (2999ds/12Mi)
% 0.15/1.51 % (195163)dis+21_64_to=kbo:sil=128000:si=on:sp=weighted_frequency:uwa=alasca_can_abstract:random_seed=2037996215:i=4:rtra=on_2999 on theBenchmark for (2999ds/4Mi)
% 0.15/1.51 % (195163)Instruction limit reached!
% 0.15/1.51 % (195163)------------------------------
% 0.15/1.51 % (195163)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.15/1.51 % (195163)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.15/1.51 % (195163)CaDiCaL version: 2.1.3
% 0.15/1.51 % (195163)Termination reason: Instruction limit
% 0.15/1.51 % (195163)Termination phase: Saturation
% 0.15/1.51 % (195163)Time elapsed: 0.004 s
% 0.15/1.51 % (195163)Peak memory usage: 88 MB
% 0.15/1.51 % (195163)Instructions burned: 5 (million)
% 0.15/1.51 % (195162)Instruction limit reached!
% 0.15/1.51 % (195162)------------------------------
% 0.15/1.51 % (195162)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.15/1.51 % (195162)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.15/1.51 % (195162)CaDiCaL version: 2.1.3
% 0.15/1.51 % (195162)Termination reason: Instruction limit
% 0.15/1.51 % (195162)Termination phase: Saturation
% 0.15/1.51 % (195162)Time elapsed: 0.006 s
% 0.15/1.51 % (195162)Peak memory usage: 88 MB
% 0.15/1.51 % (195162)Instructions burned: 7 (million)
% 0.15/1.51 % (195160)Refutation not found, incomplete strategy
% 0.15/1.51 % (195160)------------------------------
% 0.15/1.51 % (195160)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.15/1.51 % (195160)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.15/1.51 % (195160)CaDiCaL version: 2.1.3
% 0.15/1.51 % (195160)Termination reason: Refutation not found, incomplete strategy
% 0.15/1.51 % (195160)Time elapsed: 0.027 s
% 0.15/1.51 % (195160)Peak memory usage: 112 MB
% 0.15/1.51 % (195160)Instructions burned: 5 (million)
% 0.15/1.51 % (195159)First to succeed.
% 0.15/1.51 % (195159)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-195153"
% 0.15/1.51 % (195165)Instruction limit reached!
% 0.15/1.51 % (195165)------------------------------
% 0.15/1.51 % (195165)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.15/1.51 % (195165)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.15/1.51 % (195165)CaDiCaL version: 2.1.3
% 0.15/1.51 % (195165)Termination reason: Instruction limit
% 0.15/1.51 % (195165)Termination phase: Saturation
% 0.15/1.51 % (195165)Time elapsed: 0.046 s
% 0.15/1.51 % (195165)Peak memory usage: 115 MB
% 0.15/1.51 % (195165)Instructions burned: 34 (million)
% 0.15/1.51 % (195164)------------------------------
% 0.15/1.51 % (195164)------------------------------
% 0.15/1.51 % (195161)Instruction limit reached!
% 0.15/1.51 % (195161)------------------------------
% 0.15/1.51 % (195161)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.15/1.51 % (195161)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.15/1.51 % (195161)CaDiCaL version: 2.1.3
% 0.15/1.51 % (195161)Termination reason: Instruction limit
% 0.15/1.51 % (195161)Termination phase: Saturation
% 0.15/1.51 % (195161)Time elapsed: 0.158 s
% 0.15/1.51 % (195161)Peak memory usage: 118 MB
% 0.15/1.51 % (195161)Instructions burned: 201 (million)
% 0.15/1.51 % (195174)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=3710635875:i=29:thsqd=64:nm=0:thsqc=8:rtra=on:thsq=on:ev=off_2998 on theBenchmark for (2998ds/29Mi)
% 0.15/1.51 % (195173)dis+11_3_anc=none:drc=ordering:si=on:urr=ec_only:bce=on:tha=off:sac=on:random_seed=700443155:st=5:i=14:sd=10:rtra=on:ss=axioms:rawr=on_2998 on theBenchmark for (2998ds/14Mi)
% 0.15/1.51 % (195173)Refutation not found, incomplete strategy
% 0.15/1.51 % (195173)------------------------------
% 0.15/1.51 % (195173)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.15/1.51 % (195173)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.15/1.51 % (195173)CaDiCaL version: 2.1.3
% 0.15/1.51 % (195173)Termination reason: Refutation not found, incomplete strategy
% 0.15/1.51 % (195173)Time elapsed: 0.001 s
% 0.15/1.51 % (195173)Peak memory usage: 88 MB
% 0.15/1.51 % (195174)Instruction limit reached!
% 0.15/1.51 % (195174)------------------------------
% 0.15/1.51 % (195174)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.15/1.51 % (195174)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.15/1.51 % (195174)CaDiCaL version: 2.1.3
% 0.15/1.51 % (195174)Termination reason: Instruction limit
% 0.15/1.51 % (195174)Termination phase: Saturation
% 0.15/1.51 % (195174)Time elapsed: 0.021 s
% 0.15/1.51 % (195174)Peak memory usage: 88 MB
% 0.15/1.51 % (195174)Instructions burned: 30 (million)
% 0.15/1.51 % (195175)ott+21_1024_to=lakbo:sil=128000:bsd=on:si=on:alasca=on:uwa=alasca_main:nwc=0.5:random_seed=1212371470:cond=on:i=16:fgj=on:ep=RS:asg=force:nm=10:rtra=on:rawr=on_2997 on theBenchmark for (2997ds/16Mi)
% 0.15/1.51 % (195175)Instruction limit reached!
% 0.15/1.51 % (195175)------------------------------
% 0.15/1.51 % (195175)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.15/1.51 % (195175)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.15/1.51 % (195175)CaDiCaL version: 2.1.3
% 0.15/1.51 % (195175)Termination reason: Instruction limit
% 0.15/1.51 % (195175)Termination phase: Saturation
% 0.15/1.51 % (195175)Time elapsed: 0.009 s
% 0.15/1.51 % (195175)Peak memory usage: 90 MB
% 0.15/1.51 % (195175)Instructions burned: 16 (million)
% 0.15/1.51 % (195160)------------------------------
% 0.15/1.51 % (195160)------------------------------
% 0.15/1.51 % (195176)dis+1011_1_prc=on:drc=off:si=on:sac=on:random_seed=2024011289:i=24:canc=force:rtra=on_2996 on theBenchmark for (2996ds/24Mi)
% 0.15/1.51 % (195159)Refutation found. Thanks to Tanya!
% 0.15/1.51 % SZS status Theorem for theBenchmark
% 0.15/1.51 % SZS output start Proof for theBenchmark
% See solution above
% 0.15/1.51 % (195159)------------------------------
% 0.15/1.51 % (195159)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.15/1.51 % (195159)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.15/1.51 % (195159)CaDiCaL version: 2.1.3
% 0.15/1.51 % (195159)Termination reason: Refutation
% 0.15/1.51 % (195159)Time elapsed: 0.031 s
% 0.15/1.51 % (195159)Peak memory usage: 116 MB
% 0.15/1.51 % (195159)Instructions burned: 9 (million)
% 0.15/1.51 % (195159)------------------------------
% 0.15/1.51 % (195159)------------------------------
% 0.15/1.51 % (195153)Success in time 0.469 s
% 0.15/1.51 % Vampire exiting
%------------------------------------------------------------------------------