%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ARI611_1 : TPTP v9.3.1. Released v5.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n016.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 09:33:28 AM UTC 2026
% Result : Theorem 4.06s 1.46s
% Output : Refutation 4.06s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 2
% Syntax : Number of formulae : 20 ( 3 unt; 0 typ; 0 def)
% Number of atoms : 109 ( 0 equ)
% Maximal formula atoms : 14 ( 5 avg)
% Number of connectives : 130 ( 41 ~; 38 |; 38 &)
% ( 10 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number arithmetic : 165 ( 60 atm; 4 fun; 69 num; 32 var)
% Number of types : 2 ( 0 usr; 1 ari; 0 dat; 0 cdt)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 1 usr; 8 con; 0-2 aty)
% Number of variables : 32 ( 29 !; 3 ?; 32 :)
% Comments :
%------------------------------------------------------------------------------
tff(func_def_8,type,
'$inst0': $int ).
tff(func_def_10,type,
-1: $int > $int ).
tff(pred_def_1,type,
p: $int > $o ).
tff(pred_def_2,type,
q: $int > $o ).
tff(f1,conjecture,
( ( ! [X0: $int] :
( ( $less(X0,18)
& $less(8,X0) )
<=> q(X0) )
& ! [X0: $int] :
( ( $less(X0,15)
& $less(5,X0) )
<=> p(X0) ) )
=> ? [X0: $int] :
( p(X0)
& q(X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',interv_5_15_and_8_18_intersect) ).
tff(f2,negated_conjecture,
~ ( ( ! [X0: $int] :
( ( $less(X0,18)
& $less(8,X0) )
<=> q(X0) )
& ! [X0: $int] :
( ( $less(X0,15)
& $less(5,X0) )
<=> p(X0) ) )
=> ? [X0: $int] :
( p(X0)
& q(X0) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
tff(f12,plain,
! [X0: $int,X1: $int] :
( $less(X1,$sum(X0,1))
| $less(X0,X1) ),
introduced(definition,[],[tha_order_plus_one_dichotomy]) ).
tff(f15,plain,
~ ( ( ! [X1: $int] :
( p(X1)
<=> ( $less(X1,15)
& $less(5,X1) ) )
& ! [X0: $int] :
( ( $less(X0,18)
& $less(8,X0) )
<=> q(X0) ) )
=> ? [X2: $int] :
( p(X2)
& q(X2) ) ),
inference(rectify,[],[f2]) ).
tff(f16,plain,
( ! [X2: $int] :
( ~ p(X2)
| ~ q(X2) )
& ! [X1: $int] :
( p(X1)
<=> ( $less(X1,15)
& $less(5,X1) ) )
& ! [X0: $int] :
( ( $less(X0,18)
& $less(8,X0) )
<=> q(X0) ) ),
inference(ennf_transformation,[],[f15]) ).
tff(f17,plain,
( ! [X1: $int] :
( p(X1)
<=> ( $less(X1,15)
& $less(5,X1) ) )
& ! [X2: $int] :
( ~ p(X2)
| ~ q(X2) )
& ! [X0: $int] :
( ( $less(X0,18)
& $less(8,X0) )
<=> q(X0) ) ),
inference(flattening,[],[f16]) ).
tff(f18,plain,
( ! [X1: $int] :
( ( p(X1)
| ~ $less(X1,15)
| ~ $less(5,X1) )
& ( ( $less(X1,15)
& $less(5,X1) )
| ~ p(X1) ) )
& ! [X2: $int] :
( ~ p(X2)
| ~ q(X2) )
& ! [X0: $int] :
( ( ( $less(X0,18)
& $less(8,X0) )
| ~ q(X0) )
& ( q(X0)
| ~ $less(X0,18)
| ~ $less(8,X0) ) ) ),
inference(nnf_transformation,[],[f17]) ).
tff(f19,plain,
( ! [X1: $int] :
( ( p(X1)
| ~ $less(X1,15)
| ~ $less(5,X1) )
& ( ( $less(X1,15)
& $less(5,X1) )
| ~ p(X1) ) )
& ! [X2: $int] :
( ~ p(X2)
| ~ q(X2) )
& ! [X0: $int] :
( ( ( $less(X0,18)
& $less(8,X0) )
| ~ q(X0) )
& ( q(X0)
| ~ $less(X0,18)
| ~ $less(8,X0) ) ) ),
inference(flattening,[],[f18]) ).
tff(f20,plain,
( ! [X0: $int] :
( ( p(X0)
| ~ $less(X0,15)
| ~ $less(5,X0) )
& ( ( $less(X0,15)
& $less(5,X0) )
| ~ p(X0) ) )
& ! [X1: $int] :
( ~ p(X1)
| ~ q(X1) )
& ! [X2: $int] :
( ( ( $less(X2,18)
& $less(8,X2) )
| ~ q(X2) )
& ( q(X2)
| ~ $less(X2,18)
| ~ $less(8,X2) ) ) ),
inference(rectify,[],[f19]) ).
tff(f21,plain,
! [X2: $int] :
( ~ $less(8,X2)
| q(X2)
| ~ $less(X2,18) ),
inference(cnf_transformation,[],[f20]) ).
tff(f24,plain,
! [X1: $int] :
( ~ q(X1)
| ~ p(X1) ),
inference(cnf_transformation,[],[f20]) ).
tff(f27,plain,
! [X0: $int] :
( ~ $less(5,X0)
| p(X0)
| ~ $less(X0,15) ),
inference(cnf_transformation,[],[f20]) ).
tff(f264,plain,
( ~ $less(8,9)
| q(9)
| ~ $less(9,18) ),
inference(instantiation,[],[f21]) ).
tff(f265,plain,
q(9),
inference(interpreted_simplification,[],[f264]) ).
tff(f417,plain,
~ p(9),
inference(resolution,[],[f265,f24]) ).
tff(f634,plain,
! [X0: $int] :
( $less(X0,$sum(5,1))
| p(X0)
| ~ $less(X0,15) ),
inference(resolution,[],[f12,f27]) ).
tff(f639,plain,
! [X0: $int] :
( ~ $less(X0,15)
| p(X0)
| $less(X0,6) ),
inference(evaluation,[],[f634]) ).
tff(f644,plain,
! [X0: $int] :
( p(X0)
| $less(X0,6)
| $less(15,$sum(X0,1)) ),
inference(resolution,[],[f639,f12]) ).
tff(f1024,plain,
( $less(15,$sum(9,1))
| $less(9,6) ),
inference(resolution,[],[f644,f417]) ).
tff(f1025,plain,
$false,
inference(evaluation,[],[f1024]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ARI611_1 : TPTP v9.3.1. Released v5.1.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.20 % Computer : n016.cluster.edu
% 0.09/0.20 % Model : x86_64 x86_64
% 0.09/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.20 % Memory : 8046.5625MB
% 0.09/0.20 % OS : Linux 6.8.0-71-generic
% 0.09/0.20 % CPULimit : 300
% 0.09/0.20 % WCLimit : 300
% 0.09/0.20 % DateTime : Mon Sep 28 20:58:33 UTC 2026
% 0.09/0.20 % CPUTime :
% 0.09/0.20 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.24 Running first-order theorem proving
% 0.09/0.24 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
% 4.06/1.46 % (3997183)Detected arithmetic, will pick strategies from an ALASCA-aware ARI schedule.
% 4.06/1.46 % (3997307)lrs+1002_4:1_to=lpo:sil=64000:si=on:br=off:random_seed=1477757140:s2a=on:i=7:rtra=on:inst=on_2999 on theBenchmark for (2999ds/7Mi)
% 4.06/1.46 % (3997307)Instruction limit reached!
% 4.06/1.46 % (3997307)------------------------------
% 4.06/1.46 % (3997307)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.06/1.46 % (3997307)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.06/1.46 % (3997307)CaDiCaL version: 2.1.3
% 4.06/1.46 % (3997307)Termination reason: Instruction limit
% 4.06/1.46 % (3997307)Termination phase: Saturation
% 4.06/1.46 % (3997307)Time elapsed: 0.004 s
% 4.06/1.46 % (3997307)Peak memory usage: 88 MB
% 4.06/1.46 % (3997307)Instructions burned: 10 (million)
% 4.06/1.46 % (3997305)dis+1002_1_to=kbo:sil=128000:tgt=ground:sas=z3:si=on:spb=units:tha=off:random_seed=1429052469:i=307:kws=precedence:nm=0:rtra=on_2999 on theBenchmark for (2999ds/307Mi)
% 4.06/1.46 % (3997304)dis+1002_16:1_to=lpo:sil=64000:sas=z3:si=on:norm_ineq=on:gve=force:uwa=one_side_constant:random_seed=1629491166:i=12:doe=on:rtra=on:gtg=exists_top:ss=axioms_2999 on theBenchmark for (2999ds/12Mi)
% 4.06/1.46 % (3997306)dis+10_3_slsqr=1,4:to=lpo:sil=128000:thi=strong:si=on:uwa=off:s2agt=20:slsqc=1:slsq=on:random_seed=1896686571:i=201:slsql=off:asg=cautious:rtra=on:gtg=all:ss=axioms:sgt=16_2999 on theBenchmark for (2999ds/201Mi)
% 4.06/1.46 % (3997308)dis+21_64_to=kbo:sil=128000:si=on:sp=weighted_frequency:uwa=alasca_can_abstract:random_seed=3786423506:i=4:rtra=on_2999 on theBenchmark for (2999ds/4Mi)
% 4.06/1.46 % (3997308)Instruction limit reached!
% 4.06/1.46 % (3997308)------------------------------
% 4.06/1.46 % (3997308)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.06/1.46 % (3997308)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.06/1.46 % (3997308)CaDiCaL version: 2.1.3
% 4.06/1.46 % (3997308)Termination reason: Instruction limit
% 4.06/1.46 % (3997308)Termination phase: Saturation
% 4.06/1.46 % (3997308)Time elapsed: 0.004 s
% 4.06/1.46 % (3997308)Peak memory usage: 88 MB
% 4.06/1.46 % (3997308)Instructions burned: 4 (million)
% 4.06/1.46 % (3997305)Refutation not found, incomplete strategy
% 4.06/1.46 % (3997305)------------------------------
% 4.06/1.46 % (3997305)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.06/1.46 % (3997305)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.06/1.46 % (3997305)CaDiCaL version: 2.1.3
% 4.06/1.46 % (3997305)Termination reason: Refutation not found, incomplete strategy
% 4.06/1.46 % (3997305)Time elapsed: 0.029 s
% 4.06/1.46 % (3997305)Peak memory usage: 114 MB
% 4.06/1.46 % (3997305)Instructions burned: 6 (million)
% 4.06/1.46 % (3997304)Refutation not found, incomplete strategy
% 4.06/1.46 % (3997304)------------------------------
% 4.06/1.46 % (3997304)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.06/1.46 % (3997304)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.06/1.46 % (3997304)CaDiCaL version: 2.1.3
% 4.06/1.46 % (3997304)Termination reason: Refutation not found, incomplete strategy
% 4.06/1.46 % (3997304)Time elapsed: 0.032 s
% 4.06/1.46 % (3997304)Peak memory usage: 115 MB
% 4.06/1.46 % (3997304)Instructions burned: 10 (million)
% 4.06/1.46 % (3997310)lrs+10_1_tgt=ground:sas=z3:si=on:random_seed=1615485110:i=33:rtra=on_2999 on theBenchmark for (2999ds/33Mi)
% 4.06/1.46 % (3997306)First to succeed.
% 4.06/1.46 % (3997306)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3997183"
% 4.06/1.46 % (3997309)lrs+10_1_to=lpo:sas=z3:si=on:tha=off:random_seed=1123974767:i=46:rtra=on_2999 on theBenchmark for (2999ds/46Mi)
% 4.06/1.46 % (3997310)Also succeeded, but the first one will report.
% 4.06/1.46 % (3997312)dis+11_3_anc=none:drc=ordering:si=on:urr=ec_only:bce=on:tha=off:sac=on:random_seed=114297199:st=5:i=14:sd=10:rtra=on:ss=axioms:rawr=on_2998 on theBenchmark for (2998ds/14Mi)
% 4.06/1.46 % (3997312)Refutation not found, incomplete strategy
% 4.06/1.46 % (3997312)------------------------------
% 4.06/1.46 % (3997312)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.06/1.46 % (3997312)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.06/1.46 % (3997312)CaDiCaL version: 2.1.3
% 4.06/1.46 % (3997312)Termination reason: Refutation not found, incomplete strategy
% 4.06/1.46 % (3997312)Time elapsed: 0.001 s
% 4.06/1.46 % (3997312)Peak memory usage: 88 MB
% 4.06/1.46 % (3997309)Refutation not found, incomplete strategy
% 4.06/1.46 % (3997309)------------------------------
% 4.06/1.46 % (3997309)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.06/1.46 % (3997309)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.06/1.46 % (3997309)CaDiCaL version: 2.1.3
% 4.06/1.46 % (3997309)Termination reason: Refutation not found, incomplete strategy
% 4.06/1.46 % (3997309)Time elapsed: 0.038 s
% 4.06/1.46 % (3997309)Peak memory usage: 111 MB
% 4.06/1.46 % (3997309)Instructions burned: 5 (million)
% 4.06/1.46 % (3997317)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=4040302477:i=29:thsqd=64:nm=0:thsqc=8:rtra=on:thsq=on:ev=off_2998 on theBenchmark for (2998ds/29Mi)
% 4.06/1.46 % (3997317)Instruction limit reached!
% 4.06/1.46 % (3997317)------------------------------
% 4.06/1.46 % (3997317)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.06/1.46 % (3997317)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.06/1.46 % (3997317)CaDiCaL version: 2.1.3
% 4.06/1.46 % (3997317)Termination reason: Instruction limit
% 4.06/1.46 % (3997317)Termination phase: Saturation
% 4.06/1.46 % (3997317)Time elapsed: 0.020 s
% 4.06/1.46 % (3997317)Peak memory usage: 88 MB
% 4.06/1.46 % (3997317)Instructions burned: 30 (million)
% 4.06/1.46 % (3997312)------------------------------
% 4.06/1.46 % (3997312)------------------------------
% 4.06/1.46 % (3997304)------------------------------
% 4.06/1.46 % (3997304)------------------------------
% 4.06/1.46 % (3997305)------------------------------
% 4.06/1.46 % (3997305)------------------------------
% 4.06/1.46 % (3997306)Refutation found. Thanks to Tanya!
% 4.06/1.46 % SZS status Theorem for theBenchmark
% 4.06/1.46 % SZS output start Proof for theBenchmark
% See solution above
% 4.06/1.46 % (3997306)------------------------------
% 4.06/1.46 % (3997306)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.06/1.46 % (3997306)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.06/1.46 % (3997306)CaDiCaL version: 2.1.3
% 4.06/1.46 % (3997306)Termination reason: Refutation
% 4.06/1.46 % (3997306)Time elapsed: 0.059 s
% 4.06/1.46 % (3997306)Peak memory usage: 116 MB
% 4.06/1.46 % (3997306)Instructions burned: 49 (million)
% 4.06/1.46 % (3997306)------------------------------
% 4.06/1.46 % (3997306)------------------------------
% 4.06/1.46 % (3997183)Success in time 0.487 s
% 4.06/1.46 % Vampire exiting
%------------------------------------------------------------------------------