%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ARI588_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 : n010.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 09:33:25 AM UTC 2026
% Result : Theorem 0.21s 1.30s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 3
% Syntax : Number of formulae : 21 ( 5 unt; 0 typ; 0 def)
% Number of atoms : 41 ( 2 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 42 ( 22 ~; 14 |; 2 &)
% ( 4 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 4 ( 2 avg)
% Number arithmetic : 211 ( 38 atm; 87 fun; 60 num; 26 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 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 1 usr; 4 con; 0-2 aty)
% Number of variables : 26 ( 21 !; 5 ?; 26 :)
% Comments :
%------------------------------------------------------------------------------
tff(func_def_6,type,
sK0: $int > $int ).
tff(f1,conjecture,
? [X0: $int] :
! [X1: $int] :
~ ( $less(X1,$sum(X0,-1))
<=> $lesseq($sum(3,$uminus(X0)),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',exists_X_complementary_halflines) ).
tff(f2,negated_conjecture,
~ ? [X0: $int] :
! [X1: $int] :
~ ( $less(X1,$sum(X0,-1))
<=> $lesseq($sum(3,$uminus(X0)),X1) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
tff(f3,plain,
~ ? [X0: $int] :
! [X1: $int] :
~ ( $less(X1,$sum(X0,-1))
<=> ~ $less(X1,$sum(3,$uminus(X0))) ),
inference(theory_normalization,[],[f2]) ).
tff(f5,plain,
! [X2: $int,X0: $int,X1: $int] : ( $sum(X0,$sum(X1,X2)) = $sum($sum(X0,X1),X2) ),
introduced(definition,[],[tha_associativity]) ).
tff(f7,plain,
! [X0: $int,X1: $int] : ( $sum($uminus(X1),$uminus(X0)) = $uminus($sum(X0,X1)) ),
introduced(definition,[],[tha_inverse_op_op_inverses]) ).
tff(f16,plain,
! [X0: $int] :
? [X1: $int] :
( $less(X1,$sum(X0,-1))
<=> ~ $less(X1,$sum(3,$uminus(X0))) ),
inference(ennf_transformation,[],[f3]) ).
tff(f17,plain,
! [X0: $int] :
? [X1: $int] :
( ( $less(X1,$sum(X0,-1))
| $less(X1,$sum(3,$uminus(X0))) )
& ( ~ $less(X1,$sum(3,$uminus(X0)))
| ~ $less(X1,$sum(X0,-1)) ) ),
inference(nnf_transformation,[],[f16]) ).
tff(f18,plain,
! [X0: $int] :
( ( $less(sK0(X0),$sum(X0,-1))
| $less(sK0(X0),$sum(3,$uminus(X0))) )
& ( ~ $less(sK0(X0),$sum(3,$uminus(X0)))
| ~ $less(sK0(X0),$sum(X0,-1)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X1,sK0(X0))],[f17]) ).
tff(f19,plain,
! [X0: $int] :
( ~ $less(sK0(X0),$sum(3,$uminus(X0)))
| ~ $less(sK0(X0),$sum(X0,-1)) ),
inference(cnf_transformation,[],[f18]) ).
tff(f20,plain,
! [X0: $int] :
( $less(sK0(X0),$sum(3,$uminus(X0)))
| $less(sK0(X0),$sum(X0,-1)) ),
inference(cnf_transformation,[],[f18]) ).
tff(f120,plain,
! [X0: $int,X1: $int] :
( $less(sK0($sum(X1,X0)),$sum(3,$sum($uminus(X0),$uminus(X1))))
| $less(sK0($sum(X1,X0)),$sum($sum(X1,X0),-1)) ),
inference(superposition,[],[f20,f7]) ).
tff(f121,plain,
! [X0: $int,X1: $int] :
( ~ $less(sK0($sum(X1,X0)),$sum(3,$sum($uminus(X0),$uminus(X1))))
| ~ $less(sK0($sum(X1,X0)),$sum($sum(X1,X0),-1)) ),
inference(superposition,[],[f19,f7]) ).
tff(f130,plain,
! [X0: $int,X1: $int] :
( ~ $less(sK0($sum(X1,X0)),$sum(3,$sum($uminus(X0),$uminus(X1))))
| ~ $less(sK0($sum(X1,X0)),$sum(X1,$sum(X0,-1))) ),
inference(forward_demodulation,[],[f121,f5]) ).
tff(f132,plain,
! [X0: $int,X1: $int] :
( $less(sK0($sum(X1,X0)),$sum(3,$sum($uminus(X0),$uminus(X1))))
| $less(sK0($sum(X1,X0)),$sum(X1,$sum(X0,-1))) ),
inference(forward_demodulation,[],[f120,f5]) ).
tff(f187,plain,
( ~ $less(sK0($sum(1,1)),$sum(1,$sum(1,-1)))
| ~ $less(sK0($sum(1,1)),$sum(3,$sum($uminus(1),$uminus(1)))) ),
inference(instantiation,[],[f130]) ).
tff(f190,plain,
( ~ $less(sK0(2),1)
| ~ $less(sK0(2),1) ),
inference(evaluation,[],[f187]) ).
tff(f191,plain,
~ $less(sK0(2),1),
inference(duplicate_literal_removal,[],[f190]) ).
tff(f227,plain,
( $less(sK0($sum(-1,3)),$sum(-1,$sum(3,-1)))
| $less(sK0($sum(-1,3)),$sum(3,$sum($uminus(3),$uminus(-1)))) ),
inference(instantiation,[],[f132]) ).
tff(f238,plain,
( $less(sK0(2),1)
| $less(sK0(2),1) ),
inference(evaluation,[],[f227]) ).
tff(f239,plain,
$less(sK0(2),1),
inference(duplicate_literal_removal,[],[f238]) ).
tff(f248,plain,
$false,
inference(forward_subsumption_resolution,[],[f239,f191]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ARI588_1 : TPTP v9.3.1. Released v5.1.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.19 % Computer : n010.cluster.edu
% 0.09/0.19 % Model : x86_64 x86_64
% 0.09/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.19 % Memory : 8046.5625MB
% 0.09/0.19 % OS : Linux 6.8.0-71-generic
% 0.09/0.19 % CPULimit : 300
% 0.09/0.19 % WCLimit : 300
% 0.09/0.19 % DateTime : Mon Sep 28 20:53:17 UTC 2026
% 0.09/0.19 % CPUTime :
% 0.09/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.23 Running first-order theorem proving
% 0.09/0.23 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
% 0.21/1.30 % (2318375)Detected arithmetic, will pick strategies from an ALASCA-aware ARI schedule.
% 0.21/1.30 % (2318526)dis+10_3_slsqr=1,4:to=lpo:sil=128000:thi=strong:si=on:uwa=off:s2agt=20:slsqc=1:slsq=on:random_seed=2777574512:i=201:slsql=off:asg=cautious:rtra=on:gtg=all:ss=axioms:sgt=16_2999 on theBenchmark for (2999ds/201Mi)
% 0.21/1.30 % (2318529)dis+21_64_to=kbo:sil=128000:si=on:sp=weighted_frequency:uwa=alasca_can_abstract:random_seed=203458281:i=4:rtra=on_2999 on theBenchmark for (2999ds/4Mi)
% 0.21/1.30 % (2318523)dis+1002_16:1_to=lpo:sil=64000:sas=z3:si=on:norm_ineq=on:gve=force:uwa=one_side_constant:random_seed=2466052268:i=12:doe=on:rtra=on:gtg=exists_top:ss=axioms_2999 on theBenchmark for (2999ds/12Mi)
% 0.21/1.30 % (2318530)lrs+10_1_to=lpo:sas=z3:si=on:tha=off:random_seed=3124331191:i=46:rtra=on_2999 on theBenchmark for (2999ds/46Mi)
% 0.21/1.30 % (2318524)dis+1002_1_to=kbo:sil=128000:tgt=ground:sas=z3:si=on:spb=units:tha=off:random_seed=3541819469:i=307:kws=precedence:nm=0:rtra=on_2999 on theBenchmark for (2999ds/307Mi)
% 0.21/1.30 % (2318528)lrs+1002_4:1_to=lpo:sil=64000:si=on:br=off:random_seed=1253676720:s2a=on:i=7:rtra=on:inst=on_2999 on theBenchmark for (2999ds/7Mi)
% 0.21/1.30 % (2318529)Instruction limit reached!
% 0.21/1.30 % (2318529)------------------------------
% 0.21/1.30 % (2318529)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.21/1.30 % (2318529)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/1.30 % (2318529)CaDiCaL version: 2.1.3
% 0.21/1.30 % (2318529)Termination reason: Instruction limit
% 0.21/1.30 % (2318529)Termination phase: Saturation
% 0.21/1.30 % (2318529)Time elapsed: 0.004 s
% 0.21/1.30 % (2318529)Peak memory usage: 88 MB
% 0.21/1.30 % (2318529)Instructions burned: 4 (million)
% 0.21/1.30 % (2318528)First to succeed.
% 0.21/1.30 % (2318528)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2318375"
% 0.21/1.30 % (2318532)lrs+10_1_tgt=ground:sas=z3:si=on:random_seed=2499158714:i=33:rtra=on_2999 on theBenchmark for (2999ds/33Mi)
% 0.21/1.30 % (2318524)Refutation not found, incomplete strategy
% 0.21/1.30 % (2318524)------------------------------
% 0.21/1.30 % (2318524)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.21/1.30 % (2318524)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/1.30 % (2318524)CaDiCaL version: 2.1.3
% 0.21/1.30 % (2318524)Termination reason: Refutation not found, incomplete strategy
% 0.21/1.30 % (2318524)Time elapsed: 0.027 s
% 0.21/1.30 % (2318524)Peak memory usage: 112 MB
% 0.21/1.30 % (2318530)Refutation not found, incomplete strategy
% 0.21/1.30 % (2318530)------------------------------
% 0.21/1.30 % (2318530)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.21/1.30 % (2318524)Instructions burned: 5 (million)
% 0.21/1.30 % (2318530)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/1.30 % (2318530)CaDiCaL version: 2.1.3
% 0.21/1.30 % (2318530)Termination reason: Refutation not found, incomplete strategy
% 0.21/1.30 % (2318530)Time elapsed: 0.027 s
% 0.21/1.30 % (2318530)Peak memory usage: 112 MB
% 0.21/1.30 % (2318530)Instructions burned: 5 (million)
% 0.21/1.30 % (2318523)Instruction limit reached!
% 0.21/1.30 % (2318523)------------------------------
% 0.21/1.30 % (2318523)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.21/1.30 % (2318523)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/1.30 % (2318523)CaDiCaL version: 2.1.3
% 0.21/1.30 % (2318523)Termination reason: Instruction limit
% 0.21/1.30 % (2318523)Termination phase: Saturation
% 0.21/1.30 % (2318523)Time elapsed: 0.029 s
% 0.21/1.30 % (2318523)Peak memory usage: 112 MB
% 0.21/1.30 % (2318523)Instructions burned: 13 (million)
% 0.21/1.30 % (2318526)Instruction limit reached!
% 0.21/1.30 % (2318526)------------------------------
% 0.21/1.30 % (2318526)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.21/1.30 % (2318526)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/1.30 % (2318526)CaDiCaL version: 2.1.3
% 0.21/1.30 % (2318526)Termination reason: Instruction limit
% 0.21/1.30 % (2318526)Termination phase: Saturation
% 0.21/1.30 % (2318526)Time elapsed: 0.097 s
% 0.21/1.30 % (2318526)Peak memory usage: 117 MB
% 0.21/1.30 % (2318526)Instructions burned: 201 (million)
% 0.21/1.30 % (2318532)Instruction limit reached!
% 0.21/1.30 % (2318532)------------------------------
% 0.21/1.30 % (2318532)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.21/1.30 % (2318532)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/1.30 % (2318532)CaDiCaL version: 2.1.3
% 0.21/1.30 % (2318532)Termination reason: Instruction limit
% 0.21/1.30 % (2318532)Termination phase: Saturation
% 0.21/1.30 % (2318532)Time elapsed: 0.047 s
% 0.21/1.30 % (2318532)Peak memory usage: 115 MB
% 0.21/1.30 % (2318532)Instructions burned: 34 (million)
% 0.21/1.30 % (2318599)dis+11_3_anc=none:drc=ordering:si=on:urr=ec_only:bce=on:tha=off:sac=on:random_seed=335882240:st=5:i=14:sd=10:rtra=on:ss=axioms:rawr=on_2998 on theBenchmark for (2998ds/14Mi)
% 0.21/1.30 % (2318599)Refutation not found, incomplete strategy
% 0.21/1.30 % (2318599)------------------------------
% 0.21/1.30 % (2318599)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.21/1.30 % (2318599)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/1.30 % (2318599)CaDiCaL version: 2.1.3
% 0.21/1.30 % (2318599)Termination reason: Refutation not found, incomplete strategy
% 0.21/1.30 % (2318599)Time elapsed: 0.001 s
% 0.21/1.30 % (2318599)Peak memory usage: 88 MB
% 0.21/1.30 % (2318621)ott+21_1024_to=lakbo:sil=128000:bsd=on:si=on:alasca=on:uwa=alasca_main:nwc=0.5:random_seed=1879379504:cond=on:i=16:fgj=on:ep=RS:asg=force:nm=10:rtra=on:rawr=on_2997 on theBenchmark for (2997ds/16Mi)
% 0.21/1.30 % (2318621)Instruction limit reached!
% 0.21/1.30 % (2318621)------------------------------
% 0.21/1.30 % (2318621)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.21/1.30 % (2318621)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/1.30 % (2318621)CaDiCaL version: 2.1.3
% 0.21/1.30 % (2318621)Termination reason: Instruction limit
% 0.21/1.30 % (2318621)Termination phase: Saturation
% 0.21/1.30 % (2318621)Time elapsed: 0.005 s
% 0.21/1.30 % (2318621)Peak memory usage: 90 MB
% 0.21/1.30 % (2318621)Instructions burned: 19 (million)
% 0.21/1.30 % (2318609)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=1348834107:i=29:thsqd=64:nm=0:thsqc=8:rtra=on:thsq=on:ev=off_2998 on theBenchmark for (2998ds/29Mi)
% 0.21/1.30 % (2318609)Instruction limit reached!
% 0.21/1.30 % (2318609)------------------------------
% 0.21/1.30 % (2318609)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.21/1.30 % (2318609)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/1.30 % (2318609)CaDiCaL version: 2.1.3
% 0.21/1.30 % (2318609)Termination reason: Instruction limit
% 0.21/1.30 % (2318609)Termination phase: Saturation
% 0.21/1.30 % (2318609)Time elapsed: 0.020 s
% 0.21/1.30 % (2318609)Peak memory usage: 88 MB
% 0.21/1.30 % (2318609)Instructions burned: 29 (million)
% 0.21/1.30 % (2318625)dis+1011_1_prc=on:drc=off:si=on:sac=on:random_seed=1238881922:i=24:canc=force:rtra=on_2997 on theBenchmark for (2997ds/24Mi)
% 0.21/1.30 % (2318625)Instruction limit reached!
% 0.21/1.30 % (2318625)------------------------------
% 0.21/1.30 % (2318625)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.21/1.30 % (2318625)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/1.30 % (2318625)CaDiCaL version: 2.1.3
% 0.21/1.30 % (2318625)Termination reason: Instruction limit
% 0.21/1.30 % (2318625)Termination phase: Saturation
% 0.21/1.30 % (2318625)Time elapsed: 0.017 s
% 0.21/1.30 % (2318625)Peak memory usage: 89 MB
% 0.21/1.30 % (2318625)Instructions burned: 24 (million)
% 0.21/1.30 % (2318528)Refutation found. Thanks to Tanya!
% 0.21/1.30 % SZS status Theorem for theBenchmark
% 0.21/1.30 % SZS output start Proof for theBenchmark
% See solution above
% 0.21/1.30 % (2318528)------------------------------
% 0.21/1.30 % (2318528)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.21/1.30 % (2318528)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/1.30 % (2318528)CaDiCaL version: 2.1.3
% 0.21/1.30 % (2318528)Termination reason: Refutation
% 0.21/1.30 % (2318528)Time elapsed: 0.005 s
% 0.21/1.30 % (2318528)Peak memory usage: 89 MB
% 0.21/1.30 % (2318528)Instructions burned: 6 (million)
% 0.21/1.30 % (2318528)------------------------------
% 0.21/1.30 % (2318528)------------------------------
% 0.21/1.30 % (2318375)Success in time 0.414 s
% 0.21/1.30 % Vampire exiting
%------------------------------------------------------------------------------