%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ARI591_1 : TPTP v9.3.1. Released v5.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n019.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 09:33:26 AM UTC 2026
% Result : Theorem 4.97s 1.52s
% Output : Refutation 4.97s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 7
% Syntax : Number of formulae : 23 ( 6 unt; 0 typ; 1 def)
% Number of atoms : 57 ( 20 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 54 ( 20 ~; 29 |; 4 &)
% ( 1 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number arithmetic : 118 ( 28 atm; 17 fun; 52 num; 21 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 : 4 ( 1 usr; 2 prp; 0-2 aty)
% Number of functors : 5 ( 1 usr; 4 con; 0-2 aty)
% Number of variables : 21 ( 18 !; 3 ?; 21 :)
% Comments :
%------------------------------------------------------------------------------
tff(func_def_5,type,
sK0: $int ).
tff(f1,conjecture,
! [X0: $int] :
? [X1: $int] :
( $less(X1,3)
& $less(0,X1)
& ( X0 != X1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',exists_X_0_3_noteq_Y) ).
tff(f2,negated_conjecture,
~ ! [X0: $int] :
? [X1: $int] :
( $less(X1,3)
& $less(0,X1)
& ( X0 != X1 ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
tff(f3,plain,
! [X0: $int,X1: $int] : ( $sum(X1,X0) = $sum(X0,X1) ),
introduced(definition,[],[tha_commutativity]) ).
tff(f5,plain,
! [X0: $int] : ( $sum(X0,0) = X0 ),
introduced(definition,[],[tha_right_identity]) ).
tff(f10,plain,
! [X0: $int,X1: $int] :
( $less(X1,X0)
| $less(X0,X1)
| ( X0 = X1 ) ),
introduced(definition,[],[tha_order_totality]) ).
tff(f12,plain,
! [X0: $int,X1: $int] :
( $less(X1,$sum(X0,1))
| $less(X0,X1) ),
introduced(definition,[],[tha_order_plus_one_dichotomy]) ).
tff(f14,plain,
! [X0: $int,X1: $int] :
( ~ $less(X1,$sum(X0,1))
| ~ $less(X0,X1) ),
introduced(definition,[],[tha_extra_integer_ordering]) ).
tff(f15,plain,
? [X0: $int] :
! [X1: $int] :
( ( X0 = X1 )
| ~ $less(X1,3)
| ~ $less(0,X1) ),
inference(ennf_transformation,[],[f2]) ).
tff(f16,plain,
! [X1: $int] :
( ( sK0 = X1 )
| ~ $less(X1,3)
| ~ $less(0,X1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[f15]) ).
tff(f17,plain,
! [X1: $int] :
( ~ $less(0,X1)
| ~ $less(X1,3)
| ( sK0 = X1 ) ),
inference(cnf_transformation,[],[f16]) ).
tff(f24,plain,
! [X0: $int] :
( ~ $less($sum(X0,1),3)
| ( $sum(X0,1) = sK0 )
| $less(X0,0) ),
inference(resolution,[],[f12,f17]) ).
tff(f31,plain,
! [X0: $int] :
( ~ $less($sum(1,X0),3)
| ( sK0 = $sum(1,X0) )
| $less(X0,0) ),
inference(superposition,[],[f24,f3]) ).
tff(f34,plain,
( ( sK0 = 1 )
| ~ $less(1,3)
| $less(0,0) ),
inference(superposition,[],[f31,f5]) ).
tff(f38,plain,
sK0 = 1,
inference(evaluation,[],[f34]) ).
tff(f40,definition,
( spl1_1
<=> ( sK0 = 1 ) ),
introduced(definition,[new_symbols(definition,[spl1_1])],[avatar_definition]) ).
tff(f42,plain,
( ( sK0 = 1 )
| ~ spl1_1 ),
inference(avatar_component_clause,[],[f40]) ).
tff(f43,plain,
spl1_1,
inference(avatar_split_clause,[],[f38,f40]) ).
tff(f47,plain,
! [X0: $int] :
( $less(X0,0)
| ( sK0 = $sum(1,X0) )
| $less(3,$sum(1,X0))
| ( 3 = $sum(1,X0) ) ),
inference(resolution,[],[f10,f31]) ).
tff(f56,plain,
( ! [X0: $int] :
( $less(3,$sum(1,X0))
| $less(X0,0)
| ( 1 = $sum(1,X0) )
| ( 3 = $sum(1,X0) ) )
| ~ spl1_1 ),
inference(forward_demodulation,[],[f47,f42]) ).
tff(f143,plain,
( ( $sum(1,1) = 1 )
| $less(1,0)
| ~ $less(1,3)
| ( 3 = $sum(1,1) )
| ~ spl1_1 ),
inference(resolution,[],[f56,f14]) ).
tff(f148,plain,
( $false
| ~ spl1_1 ),
inference(evaluation,[],[f143]) ).
tff(f149,plain,
~ spl1_1,
inference(avatar_contradiction_clause,[],[f148]) ).
tff(f150,plain,
$false,
inference(avatar_smt_refutation,[],[f149,f43]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ARI591_1 : TPTP v9.3.1. Released v5.1.0.
% 0.00/0.07 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.24 % Computer : n019.cluster.edu
% 0.09/0.24 % Model : x86_64 x86_64
% 0.09/0.24 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.24 % Memory : 8046.5625MB
% 0.09/0.24 % OS : Linux 6.8.0-71-generic
% 0.09/0.24 % CPULimit : 300
% 0.09/0.24 % WCLimit : 300
% 0.09/0.24 % DateTime : Mon Sep 28 20:53:03 UTC 2026
% 0.09/0.24 % CPUTime :
% 0.09/0.24 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.24/0.30 Running first-order theorem proving
% 0.24/0.30 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
% 4.97/1.52 % (266318)Detected arithmetic, will pick strategies from an ALASCA-aware ARI schedule.
% 4.97/1.52 % (266323)dis+1002_16:1_to=lpo:sil=64000:sas=z3:si=on:norm_ineq=on:gve=force:uwa=one_side_constant:random_seed=2394053930:i=12:doe=on:rtra=on:gtg=exists_top:ss=axioms_2999 on theBenchmark for (2999ds/12Mi)
% 4.97/1.52 % (266329)lrs+10_1_tgt=ground:sas=z3:si=on:random_seed=3259115448:i=33:rtra=on_2999 on theBenchmark for (2999ds/33Mi)
% 4.97/1.52 % (266323)Refutation not found, incomplete strategy
% 4.97/1.52 % (266323)------------------------------
% 4.97/1.52 % (266323)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.97/1.52 % (266323)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.97/1.52 % (266323)CaDiCaL version: 2.1.3
% 4.97/1.52 % (266323)Termination reason: Refutation not found, incomplete strategy
% 4.97/1.52 % (266323)Time elapsed: 0.026 s
% 4.97/1.52 % (266323)Peak memory usage: 116 MB
% 4.97/1.52 % (266323)Instructions burned: 10 (million)
% 4.97/1.52 % (266329)First to succeed.
% 4.97/1.52 % (266329)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-266318"
% 4.97/1.52 % (266327)dis+21_64_to=kbo:sil=128000:si=on:sp=weighted_frequency:uwa=alasca_can_abstract:random_seed=1910593730:i=4:rtra=on_2999 on theBenchmark for (2999ds/4Mi)
% 4.97/1.52 % (266325)dis+10_3_slsqr=1,4:to=lpo:sil=128000:thi=strong:si=on:uwa=off:s2agt=20:slsqc=1:slsq=on:random_seed=62917299:i=201:slsql=off:asg=cautious:rtra=on:gtg=all:ss=axioms:sgt=16_2999 on theBenchmark for (2999ds/201Mi)
% 4.97/1.52 % (266324)dis+1002_1_to=kbo:sil=128000:tgt=ground:sas=z3:si=on:spb=units:tha=off:random_seed=3794882322:i=307:kws=precedence:nm=0:rtra=on_2999 on theBenchmark for (2999ds/307Mi)
% 4.97/1.52 % (266326)lrs+1002_4:1_to=lpo:sil=64000:si=on:br=off:random_seed=277077957:s2a=on:i=7:rtra=on:inst=on_2999 on theBenchmark for (2999ds/7Mi)
% 4.97/1.52 % (266327)Instruction limit reached!
% 4.97/1.52 % (266327)------------------------------
% 4.97/1.52 % (266327)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.97/1.52 % (266327)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.97/1.52 % (266327)CaDiCaL version: 2.1.3
% 4.97/1.52 % (266327)Termination reason: Instruction limit
% 4.97/1.52 % (266327)Termination phase: Saturation
% 4.97/1.52 % (266327)Time elapsed: 0.006 s
% 4.97/1.52 % (266327)Peak memory usage: 88 MB
% 4.97/1.52 % (266327)Instructions burned: 4 (million)
% 4.97/1.52 % (266326)Instruction limit reached!
% 4.97/1.52 % (266326)------------------------------
% 4.97/1.52 % (266326)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.97/1.52 % (266326)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.97/1.52 % (266326)CaDiCaL version: 2.1.3
% 4.97/1.52 % (266326)Termination reason: Instruction limit
% 4.97/1.52 % (266326)Termination phase: Saturation
% 4.97/1.52 % (266326)Time elapsed: 0.009 s
% 4.97/1.52 % (266326)Peak memory usage: 88 MB
% 4.97/1.52 % (266326)Instructions burned: 7 (million)
% 4.97/1.52 % (266328)lrs+10_1_to=lpo:sas=z3:si=on:tha=off:random_seed=1307755347:i=46:rtra=on_2999 on theBenchmark for (2999ds/46Mi)
% 4.97/1.52 % (266324)Refutation not found, incomplete strategy
% 4.97/1.52 % (266324)------------------------------
% 4.97/1.52 % (266324)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.97/1.52 % (266324)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.97/1.52 % (266324)CaDiCaL version: 2.1.3
% 4.97/1.52 % (266324)Termination reason: Refutation not found, incomplete strategy
% 4.97/1.52 % (266324)Time elapsed: 0.037 s
% 4.97/1.52 % (266324)Peak memory usage: 112 MB
% 4.97/1.52 % (266324)Instructions burned: 5 (million)
% 4.97/1.52 % (266328)Refutation not found, incomplete strategy
% 4.97/1.52 % (266328)------------------------------
% 4.97/1.52 % (266328)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.97/1.52 % (266328)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.97/1.52 % (266328)CaDiCaL version: 2.1.3
% 4.97/1.52 % (266328)Termination reason: Refutation not found, incomplete strategy
% 4.97/1.52 % (266328)Time elapsed: 0.037 s
% 4.97/1.52 % (266328)Peak memory usage: 112 MB
% 4.97/1.52 % (266328)Instructions burned: 5 (million)
% 4.97/1.52 % (266325)Also succeeded, but the first one will report.
% 4.97/1.52 % (266323)------------------------------
% 4.97/1.52 % (266323)------------------------------
% 4.97/1.52 % (266336)dis+11_3_anc=none:drc=ordering:si=on:urr=ec_only:bce=on:tha=off:sac=on:random_seed=4250106334:st=5:i=14:sd=10:rtra=on:ss=axioms:rawr=on_2997 on theBenchmark for (2997ds/14Mi)
% 4.97/1.52 % (266337)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=2246886603:i=29:thsqd=64:nm=0:thsqc=8:rtra=on:thsq=on:ev=off_2997 on theBenchmark for (2997ds/29Mi)
% 4.97/1.52 % (266336)Refutation not found, incomplete strategy
% 4.97/1.52 % (266336)------------------------------
% 4.97/1.52 % (266336)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.97/1.52 % (266336)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.97/1.52 % (266336)CaDiCaL version: 2.1.3
% 4.97/1.52 % (266336)Termination reason: Refutation not found, incomplete strategy
% 4.97/1.52 % (266336)Time elapsed: 0.002 s
% 4.97/1.52 % (266336)Peak memory usage: 88 MB
% 4.97/1.52 % (266337)Refutation not found, incomplete strategy
% 4.97/1.52 % (266337)------------------------------
% 4.97/1.52 % (266337)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.97/1.52 % (266337)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.97/1.52 % (266337)CaDiCaL version: 2.1.3
% 4.97/1.52 % (266337)Termination reason: Refutation not found, incomplete strategy
% 4.97/1.52 % (266337)Time elapsed: 0.002 s
% 4.97/1.52 % (266337)Peak memory usage: 88 MB
% 4.97/1.52 % (266329)Refutation found. Thanks to Tanya!
% 4.97/1.52 % SZS status Theorem for theBenchmark
% 4.97/1.52 % SZS output start Proof for theBenchmark
% See solution above
% 4.97/1.52 % (266329)------------------------------
% 4.97/1.52 % (266329)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.97/1.52 % (266329)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.97/1.52 % (266329)CaDiCaL version: 2.1.3
% 4.97/1.52 % (266329)Termination reason: Refutation
% 4.97/1.52 % (266329)Time elapsed: 0.039 s
% 4.97/1.52 % (266329)Peak memory usage: 116 MB
% 4.97/1.52 % (266329)Instructions burned: 14 (million)
% 4.97/1.52 % (266329)------------------------------
% 4.97/1.52 % (266329)------------------------------
% 4.97/1.52 % (266318)Success in time 0.602 s
% 4.97/1.52 % Vampire exiting
%------------------------------------------------------------------------------