%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ARI614_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 : n003.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 09:33:29 AM UTC 2026
% Result : Theorem 4.08s 1.32s
% Output : Refutation 4.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 12
% Syntax : Number of formulae : 40 ( 10 unt; 0 typ; 5 def)
% Number of atoms : 108 ( 17 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 104 ( 36 ~; 39 |; 15 &)
% ( 5 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number arithmetic : 154 ( 29 atm; 34 fun; 47 num; 44 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 : 10 ( 7 usr; 6 prp; 0-2 aty)
% Number of functors : 5 ( 1 usr; 3 con; 0-2 aty)
% Number of variables : 44 ( 38 !; 6 ?; 44 :)
% Comments :
%------------------------------------------------------------------------------
tff(func_def_0,type,
a: $int ).
tff(pred_def_1,type,
p: $int > $o ).
tff(pred_def_2,type,
q: $int > $o ).
tff(f1,conjecture,
( ( ! [X0: $int] :
( $less(X0,0)
=> q(X0) )
& ! [X0: $int] :
( $less(a,X0)
=> p(X0) ) )
=> ? [X0: $int,X1: $int] :
( ( $sum(X0,X1) = 0 )
& q(X1)
& p(X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',interv_a_infty_and_neginfty_1_contain_compl) ).
tff(f2,negated_conjecture,
~ ( ( ! [X0: $int] :
( $less(X0,0)
=> q(X0) )
& ! [X0: $int] :
( $less(a,X0)
=> p(X0) ) )
=> ? [X0: $int,X1: $int] :
( ( $sum(X0,X1) = 0 )
& q(X1)
& p(X0) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
tff(f3,plain,
! [X0: $int,X1: $int] : ( $sum(X0,X1) = $sum(X1,X0) ),
introduced(definition,[],[tha_commutativity]) ).
tff(f5,plain,
! [X0: $int] : ( $sum(X0,0) = X0 ),
introduced(definition,[],[tha_right_identity]) ).
tff(f7,plain,
! [X0: $int] : ( 0 = $sum(X0,$uminus(X0)) ),
introduced(definition,[],[tha_inverse_op_unit]) ).
tff(f8,plain,
! [X0: $int] : ~ $less(X0,X0),
introduced(definition,[],[tha_non-reflexivity]) ).
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(f15,plain,
~ ( ( ! [X0: $int] :
( $less(X0,0)
=> q(X0) )
& ! [X1: $int] :
( $less(a,X1)
=> p(X1) ) )
=> ? [X2: $int,X3: $int] :
( ( 0 = $sum(X2,X3) )
& p(X2)
& q(X3) ) ),
inference(rectify,[],[f2]) ).
tff(f16,plain,
( ! [X2: $int,X3: $int] :
( ~ q(X3)
| ~ p(X2)
| ( 0 != $sum(X2,X3) ) )
& ! [X0: $int] :
( q(X0)
| ~ $less(X0,0) )
& ! [X1: $int] :
( p(X1)
| ~ $less(a,X1) ) ),
inference(ennf_transformation,[],[f15]) ).
tff(f17,plain,
( ! [X1: $int] :
( p(X1)
| ~ $less(a,X1) )
& ! [X0: $int] :
( q(X0)
| ~ $less(X0,0) )
& ! [X2: $int,X3: $int] :
( ~ q(X3)
| ~ p(X2)
| ( 0 != $sum(X2,X3) ) ) ),
inference(flattening,[],[f16]) ).
tff(f18,plain,
( ! [X0: $int] :
( p(X0)
| ~ $less(a,X0) )
& ! [X1: $int] :
( q(X1)
| ~ $less(X1,0) )
& ! [X2: $int,X3: $int] :
( ~ q(X3)
| ~ p(X2)
| ( 0 != $sum(X2,X3) ) ) ),
inference(rectify,[],[f17]) ).
tff(f19,plain,
! [X2: $int,X3: $int] :
( ( 0 != $sum(X2,X3) )
| ~ p(X2)
| ~ q(X3) ),
inference(cnf_transformation,[],[f18]) ).
tff(f20,plain,
! [X1: $int] :
( ~ $less(X1,0)
| q(X1) ),
inference(cnf_transformation,[],[f18]) ).
tff(f21,plain,
! [X0: $int] :
( ~ $less(a,X0)
| p(X0) ),
inference(cnf_transformation,[],[f18]) ).
tff(f32,plain,
! [X0: $int] :
( ( 0 != 0 )
| ~ q($uminus(X0))
| ~ p(X0) ),
inference(superposition,[],[f19,f7]) ).
tff(f33,plain,
! [X0: $int] :
( ~ q($uminus(X0))
| ~ p(X0) ),
inference(trivial_inequality_removal,[],[f32]) ).
tff(f43,plain,
! [X0: $int] : $less(X0,$sum(X0,1)),
inference(resolution,[],[f12,f8]) ).
tff(f44,plain,
! [X0: $int] :
( p($sum(X0,1))
| $less(X0,a) ),
inference(resolution,[],[f12,f21]) ).
tff(f47,plain,
! [X0: $int] :
( p($sum(1,X0))
| $less(X0,a) ),
inference(superposition,[],[f44,f3]) ).
tff(f52,plain,
( $less(0,a)
| p(1) ),
inference(superposition,[],[f47,f5]) ).
tff(f67,definition,
( spl0_5
<=> p(1) ),
introduced(definition,[new_symbols(definition,[spl0_5])],[avatar_definition]) ).
tff(f69,plain,
( p(1)
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f67]) ).
tff(f71,definition,
( spl0_6
<=> $less(0,a) ),
introduced(definition,[new_symbols(definition,[spl0_6])],[avatar_definition]) ).
tff(f74,plain,
( spl0_5
| spl0_6 ),
inference(avatar_split_clause,[],[f52,f71,f67]) ).
tff(f77,plain,
! [X0: $int] :
( q(X0)
| $less(0,X0)
| ( 0 = X0 ) ),
inference(resolution,[],[f10,f20]) ).
tff(f117,plain,
! [X0: $int] :
( ~ p(X0)
| $less(0,$uminus(X0))
| ( 0 = $uminus(X0) ) ),
inference(resolution,[],[f77,f33]) ).
tff(f184,plain,
p($sum(a,1)),
inference(resolution,[],[f43,f21]) ).
tff(f188,plain,
p($sum(1,a)),
inference(forward_demodulation,[],[f184,f3]) ).
tff(f190,definition,
( spl0_9
<=> p($sum(1,a)) ),
introduced(definition,[new_symbols(definition,[spl0_9])],[avatar_definition]) ).
tff(f192,plain,
( p($sum(1,a))
| ~ spl0_9 ),
inference(avatar_component_clause,[],[f190]) ).
tff(f193,plain,
spl0_9,
inference(avatar_split_clause,[],[f188,f190]) ).
tff(f207,plain,
( ( 0 = $uminus($sum(1,a)) )
| $less(0,$uminus($sum(1,a)))
| ~ spl0_9 ),
inference(resolution,[],[f117,f192]) ).
tff(f208,plain,
( ( 0 = $uminus(1) )
| $less(0,$uminus(1))
| ~ spl0_5 ),
inference(resolution,[],[f117,f69]) ).
tff(f209,plain,
( $false
| ~ spl0_5 ),
inference(evaluation,[],[f208]) ).
tff(f210,plain,
~ spl0_5,
inference(avatar_contradiction_clause,[],[f209]) ).
tff(f212,definition,
( spl0_10
<=> ( 0 = $uminus($sum(1,a)) ) ),
introduced(definition,[new_symbols(definition,[spl0_10])],[avatar_definition]) ).
tff(f216,definition,
( spl0_11
<=> $less(0,$uminus($sum(1,a))) ),
introduced(definition,[new_symbols(definition,[spl0_11])],[avatar_definition]) ).
tff(f219,plain,
( spl0_10
| spl0_11
| ~ spl0_9 ),
inference(avatar_split_clause,[],[f207,f190,f216,f212]) ).
tff(f220,plain,
$false,
inference(avatar_smt_refutation,[],[f219,f210,f193,f74]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ARI614_1 : TPTP v9.3.1. Released v5.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.17 % Computer : n003.cluster.edu
% 0.07/0.17 % Model : x86_64 x86_64
% 0.07/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.17 % Memory : 8046.5625MB
% 0.07/0.17 % OS : Linux 6.8.0-71-generic
% 0.07/0.17 % CPULimit : 300
% 0.07/0.17 % WCLimit : 300
% 0.07/0.17 % DateTime : Mon Sep 28 20:55:27 UTC 2026
% 0.07/0.17 % CPUTime :
% 0.07/0.17 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.20 Running first-order theorem proving
% 0.07/0.20 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
% 4.08/1.32 % (2003962)Detected arithmetic, will pick strategies from an ALASCA-aware ARI schedule.
% 4.08/1.32 % (2003967)dis+1002_16:1_to=lpo:sil=64000:sas=z3:si=on:norm_ineq=on:gve=force:uwa=one_side_constant:random_seed=3595971971:i=12:doe=on:rtra=on:gtg=exists_top:ss=axioms_2999 on theBenchmark for (2999ds/12Mi)
% 4.08/1.32 % (2003967)Refutation not found, incomplete strategy
% 4.08/1.32 % (2003967)------------------------------
% 4.08/1.32 % (2003967)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.08/1.32 % (2003967)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.08/1.32 % (2003967)CaDiCaL version: 2.1.3
% 4.08/1.32 % (2003967)Termination reason: Refutation not found, incomplete strategy
% 4.08/1.32 % (2003967)Time elapsed: 0.020 s
% 4.08/1.32 % (2003967)Peak memory usage: 116 MB
% 4.08/1.32 % (2003967)Instructions burned: 11 (million)
% 4.08/1.32 % (2003972)lrs+10_1_to=lpo:sas=z3:si=on:tha=off:random_seed=213111625:i=46:rtra=on_2999 on theBenchmark for (2999ds/46Mi)
% 4.08/1.32 % (2003971)dis+21_64_to=kbo:sil=128000:si=on:sp=weighted_frequency:uwa=alasca_can_abstract:random_seed=2446577177:i=4:rtra=on_2999 on theBenchmark for (2999ds/4Mi)
% 4.08/1.32 % (2003968)dis+1002_1_to=kbo:sil=128000:tgt=ground:sas=z3:si=on:spb=units:tha=off:random_seed=4086856772:i=307:kws=precedence:nm=0:rtra=on_2999 on theBenchmark for (2999ds/307Mi)
% 4.08/1.32 % (2003969)dis+10_3_slsqr=1,4:to=lpo:sil=128000:thi=strong:si=on:uwa=off:s2agt=20:slsqc=1:slsq=on:random_seed=768409538:i=201:slsql=off:asg=cautious:rtra=on:gtg=all:ss=axioms:sgt=16_2999 on theBenchmark for (2999ds/201Mi)
% 4.08/1.32 % (2003973)lrs+10_1_tgt=ground:sas=z3:si=on:random_seed=3616440521:i=33:rtra=on_2999 on theBenchmark for (2999ds/33Mi)
% 4.08/1.32 % (2003970)lrs+1002_4:1_to=lpo:sil=64000:si=on:br=off:random_seed=4014605588:s2a=on:i=7:rtra=on:inst=on_2999 on theBenchmark for (2999ds/7Mi)
% 4.08/1.32 % (2003971)Instruction limit reached!
% 4.08/1.32 % (2003971)------------------------------
% 4.08/1.32 % (2003971)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.08/1.32 % (2003971)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.08/1.32 % (2003971)CaDiCaL version: 2.1.3
% 4.08/1.32 % (2003971)Termination reason: Instruction limit
% 4.08/1.32 % (2003971)Termination phase: Saturation
% 4.08/1.32 % (2003971)Time elapsed: 0.004 s
% 4.08/1.32 % (2003971)Peak memory usage: 88 MB
% 4.08/1.32 % (2003971)Instructions burned: 6 (million)
% 4.08/1.32 % (2003970)Instruction limit reached!
% 4.08/1.32 % (2003970)------------------------------
% 4.08/1.32 % (2003970)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.08/1.32 % (2003970)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.08/1.32 % (2003970)CaDiCaL version: 2.1.3
% 4.08/1.32 % (2003970)Termination reason: Instruction limit
% 4.08/1.32 % (2003970)Termination phase: Saturation
% 4.08/1.32 % (2003970)Time elapsed: 0.007 s
% 4.08/1.32 % (2003970)Peak memory usage: 88 MB
% 4.08/1.32 % (2003970)Instructions burned: 8 (million)
% 4.08/1.32 % (2003972)Refutation not found, incomplete strategy
% 4.08/1.32 % (2003972)------------------------------
% 4.08/1.32 % (2003972)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.08/1.32 % (2003972)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.08/1.32 % (2003972)CaDiCaL version: 2.1.3
% 4.08/1.32 % (2003972)Termination reason: Refutation not found, incomplete strategy
% 4.08/1.32 % (2003972)Time elapsed: 0.027 s
% 4.08/1.32 % (2003968)Refutation not found, incomplete strategy
% 4.08/1.32 % (2003968)------------------------------
% 4.08/1.32 % (2003968)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.08/1.32 % (2003968)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.08/1.32 % (2003972)Peak memory usage: 111 MB
% 4.08/1.32 % (2003972)Instructions burned: 5 (million)
% 4.08/1.32 % (2003968)CaDiCaL version: 2.1.3
% 4.08/1.32 % (2003968)Termination reason: Refutation not found, incomplete strategy
% 4.08/1.32 % (2003968)Time elapsed: 0.027 s
% 4.08/1.32 % (2003968)Peak memory usage: 111 MB
% 4.08/1.32 % (2003968)Instructions burned: 5 (million)
% 4.08/1.32 % (2003973)First to succeed.
% 4.08/1.32 % (2003973)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2003962"
% 4.08/1.32 % (2003967)------------------------------
% 4.08/1.32 % (2003967)------------------------------
% 4.08/1.32 % (2003981)dis+11_3_anc=none:drc=ordering:si=on:urr=ec_only:bce=on:tha=off:sac=on:random_seed=3385780787:st=5:i=14:sd=10:rtra=on:ss=axioms:rawr=on_2998 on theBenchmark for (2998ds/14Mi)
% 4.08/1.32 % (2003982)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=3323557714:i=29:thsqd=64:nm=0:thsqc=8:rtra=on:thsq=on:ev=off_2998 on theBenchmark for (2998ds/29Mi)
% 4.08/1.32 % (2003981)Refutation not found, incomplete strategy
% 4.08/1.32 % (2003981)------------------------------
% 4.08/1.32 % (2003981)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.08/1.32 % (2003981)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.08/1.32 % (2003981)CaDiCaL version: 2.1.3
% 4.08/1.32 % (2003981)Termination reason: Refutation not found, incomplete strategy
% 4.08/1.32 % (2003981)Time elapsed: 0.001 s
% 4.08/1.32 % (2003981)Peak memory usage: 88 MB
% 4.08/1.32 % (2003969)Also succeeded, but the first one will report.
% 4.08/1.32 % (2003982)Instruction limit reached!
% 4.08/1.32 % (2003982)------------------------------
% 4.08/1.32 % (2003982)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.08/1.32 % (2003982)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.08/1.32 % (2003982)CaDiCaL version: 2.1.3
% 4.08/1.32 % (2003982)Termination reason: Instruction limit
% 4.08/1.32 % (2003982)Termination phase: Saturation
% 4.08/1.32 % (2003982)Time elapsed: 0.015 s
% 4.08/1.32 % (2003982)Peak memory usage: 88 MB
% 4.08/1.32 % (2003982)Instructions burned: 29 (million)
% 4.08/1.32 % (2003983)ott+21_1024_to=lakbo:sil=128000:bsd=on:si=on:alasca=on:uwa=alasca_main:nwc=0.5:random_seed=2372768196:cond=on:i=16:fgj=on:ep=RS:asg=force:nm=10:rtra=on:rawr=on_2997 on theBenchmark for (2997ds/16Mi)
% 4.08/1.32 % (2003983)Also succeeded, but the first one will report.
% 4.08/1.32 % (2003972)------------------------------
% 4.08/1.32 % (2003972)------------------------------
% 4.08/1.32 % (2003968)------------------------------
% 4.08/1.32 % (2003968)------------------------------
% 4.08/1.32 % (2003973)Refutation found. Thanks to Tanya!
% 4.08/1.32 % SZS status Theorem for theBenchmark
% 4.08/1.32 % SZS output start Proof for theBenchmark
% See solution above
% 4.08/1.32 % (2003973)------------------------------
% 4.08/1.32 % (2003973)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.08/1.32 % (2003973)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.08/1.32 % (2003973)CaDiCaL version: 2.1.3
% 4.08/1.32 % (2003973)Termination reason: Refutation
% 4.08/1.32 % (2003973)Time elapsed: 0.041 s
% 4.08/1.32 % (2003973)Peak memory usage: 116 MB
% 4.08/1.32 % (2003973)Instructions burned: 19 (million)
% 4.08/1.32 % (2003973)------------------------------
% 4.08/1.32 % (2003973)------------------------------
% 4.08/1.32 % (2003962)Success in time 0.49 s
% 4.08/1.32 % Vampire exiting
%------------------------------------------------------------------------------