%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ARI579_2 : 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 : n008.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 09:33:24 AM UTC 2026
% Result : Theorem 3.67s 1.25s
% Output : Refutation 3.67s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 1
% Syntax : Number of formulae : 7 ( 1 unt; 0 typ; 0 def)
% Number of atoms : 19 ( 0 equ)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 25 ( 13 ~; 8 |; 4 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number arithmetic : 80 ( 18 atm; 18 fun; 34 num; 10 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 : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 2 usr; 7 con; 0-2 aty)
% Number of variables : 10 ( 6 !; 4 ?; 10 :)
% Comments :
%------------------------------------------------------------------------------
tff(func_def_8,type,
'$inst0': $rat ).
tff(func_def_9,type,
'$inst1': $rat ).
tff(f1,conjecture,
? [X1: $rat,X0: $rat] :
( $less($sum($product(3/1,X0),$product(4/1,X1)),6/1)
& $less(0/1,X1)
& $less(0/1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ineq_sys_rat_solvable) ).
tff(f2,negated_conjecture,
~ ? [X1: $rat,X0: $rat] :
( $less($sum($product(3/1,X0),$product(4/1,X1)),6/1)
& $less(0/1,X1)
& $less(0/1,X0) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
tff(f20,plain,
! [X1: $rat,X0: $rat] :
( ~ $less(0/1,X0)
| ~ $less($sum($product(3/1,X0),$product(4/1,X1)),6/1)
| ~ $less(0/1,X1) ),
inference(ennf_transformation,[],[f2]) ).
tff(f21,plain,
! [X0: $rat,X1: $rat] :
( ~ $less(0/1,X1)
| ~ $less($sum($product(3/1,X1),$product(4/1,X0)),6/1)
| ~ $less(0/1,X0) ),
inference(rectify,[],[f20]) ).
tff(f22,plain,
! [X0: $rat,X1: $rat] :
( ~ $less($sum($product(3/1,X1),$product(4/1,X0)),6/1)
| ~ $less(0/1,X1)
| ~ $less(0/1,X0) ),
inference(cnf_transformation,[],[f21]) ).
tff(f24,plain,
( ~ $less($sum($product(3/1,3/4),$product(4/1,3/4)),6/1)
| ~ $less(0/1,3/4)
| ~ $less(0/1,3/4) ),
inference(instantiation,[],[f22]) ).
tff(f25,plain,
$false,
inference(interpreted_simplification,[],[f24]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ARI579_2 : TPTP v9.3.1. Released v5.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.19 % Computer : n008.cluster.edu
% 0.08/0.19 % Model : x86_64 x86_64
% 0.08/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.19 % Memory : 8046.5625MB
% 0.08/0.19 % OS : Linux 6.8.0-71-generic
% 0.08/0.19 % CPULimit : 300
% 0.08/0.19 % WCLimit : 300
% 0.08/0.19 % DateTime : Mon Sep 28 20:53:25 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.22 Running first-order theorem proving
% 0.08/0.22 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
% 3.67/1.24 % (2632170)Detected arithmetic, will pick strategies from an ALASCA-aware ARI schedule.
% 3.67/1.24 % (2632221)dis+21_64_to=kbo:sil=128000:si=on:sp=weighted_frequency:uwa=alasca_can_abstract:random_seed=999863632:i=4:rtra=on_2999 on theBenchmark for (2999ds/4Mi)
% 3.67/1.24 % (2632221)Instruction limit reached!
% 3.67/1.24 % (2632221)------------------------------
% 3.67/1.24 % (2632221)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.67/1.24 % (2632221)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.67/1.24 % (2632221)CaDiCaL version: 2.1.3
% 3.67/1.24 % (2632221)Termination reason: Instruction limit
% 3.67/1.24 % (2632221)Termination phase: Saturation
% 3.67/1.24 % (2632221)Time elapsed: 0.002 s
% 3.67/1.24 % (2632221)Peak memory usage: 88 MB
% 3.67/1.24 % (2632221)Instructions burned: 4 (million)
% 3.67/1.24 % (2632218)dis+1002_1_to=kbo:sil=128000:tgt=ground:sas=z3:si=on:spb=units:tha=off:random_seed=1716293819:i=307:kws=precedence:nm=0:rtra=on_2999 on theBenchmark for (2999ds/307Mi)
% 3.67/1.24 % (2632217)dis+1002_16:1_to=lpo:sil=64000:sas=z3:si=on:norm_ineq=on:gve=force:uwa=one_side_constant:random_seed=3450510738:i=12:doe=on:rtra=on:gtg=exists_top:ss=axioms_2999 on theBenchmark for (2999ds/12Mi)
% 3.67/1.24 % (2632219)dis+10_3_slsqr=1,4:to=lpo:sil=128000:thi=strong:si=on:uwa=off:s2agt=20:slsqc=1:slsq=on:random_seed=2701951040:i=201:slsql=off:asg=cautious:rtra=on:gtg=all:ss=axioms:sgt=16_2999 on theBenchmark for (2999ds/201Mi)
% 3.67/1.24 % (2632220)lrs+1002_4:1_to=lpo:sil=64000:si=on:br=off:random_seed=3607032800:s2a=on:i=7:rtra=on:inst=on_2999 on theBenchmark for (2999ds/7Mi)
% 3.67/1.24 % (2632222)lrs+10_1_to=lpo:sas=z3:si=on:tha=off:random_seed=3286828377:i=46:rtra=on_2999 on theBenchmark for (2999ds/46Mi)
% 3.67/1.24 % (2632223)lrs+10_1_tgt=ground:sas=z3:si=on:random_seed=3745815500:i=33:rtra=on_2999 on theBenchmark for (2999ds/33Mi)
% 3.67/1.24 % (2632220)Instruction limit reached!
% 3.67/1.24 % (2632220)------------------------------
% 3.67/1.24 % (2632220)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.67/1.24 % (2632220)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.67/1.24 % (2632220)CaDiCaL version: 2.1.3
% 3.67/1.24 % (2632220)Termination reason: Instruction limit
% 3.67/1.24 % (2632220)Termination phase: Saturation
% 3.67/1.24 % (2632220)Time elapsed: 0.005 s
% 3.67/1.24 % (2632220)Peak memory usage: 88 MB
% 3.67/1.24 % (2632220)Instructions burned: 8 (million)
% 3.67/1.24 % (2632218)Refutation not found, incomplete strategy
% 3.67/1.24 % (2632218)------------------------------
% 3.67/1.24 % (2632218)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.67/1.24 % (2632218)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.67/1.24 % (2632218)CaDiCaL version: 2.1.3
% 3.67/1.24 % (2632218)Termination reason: Refutation not found, incomplete strategy
% 3.67/1.24 % (2632218)Time elapsed: 0.027 s
% 3.67/1.24 % (2632218)Peak memory usage: 111 MB
% 3.67/1.24 % (2632218)Instructions burned: 5 (million)
% 3.67/1.24 % (2632217)Instruction limit reached!
% 3.67/1.24 % (2632217)------------------------------
% 3.67/1.24 % (2632217)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.67/1.24 % (2632217)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.67/1.24 % (2632217)CaDiCaL version: 2.1.3
% 3.67/1.25 % (2632217)Termination reason: Instruction limit
% 3.67/1.25 % (2632217)Termination phase: Saturation
% 3.67/1.25 % (2632217)Time elapsed: 0.029 s
% 3.67/1.25 % (2632217)Peak memory usage: 112 MB
% 3.67/1.25 % (2632217)Instructions burned: 12 (million)
% 3.67/1.25 % (2632219)First to succeed.
% 3.67/1.25 % (2632219)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2632170"
% 3.67/1.25 % (2632222)Refutation not found, incomplete strategy
% 3.67/1.25 % (2632222)------------------------------
% 3.67/1.25 % (2632222)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.67/1.25 % (2632222)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.67/1.25 % (2632222)CaDiCaL version: 2.1.3
% 3.67/1.25 % (2632222)Termination reason: Refutation not found, incomplete strategy
% 3.67/1.25 % (2632222)Time elapsed: 0.027 s
% 3.67/1.25 % (2632222)Peak memory usage: 111 MB
% 3.67/1.25 % (2632222)Instructions burned: 5 (million)
% 3.67/1.25 % (2632225)dis+11_3_anc=none:drc=ordering:si=on:urr=ec_only:bce=on:tha=off:sac=on:random_seed=1500784630:st=5:i=14:sd=10:rtra=on:ss=axioms:rawr=on_2998 on theBenchmark for (2998ds/14Mi)
% 3.67/1.25 % (2632225)Refutation not found, incomplete strategy
% 3.67/1.25 % (2632225)------------------------------
% 3.67/1.25 % (2632225)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.67/1.25 % (2632225)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.67/1.25 % (2632225)CaDiCaL version: 2.1.3
% 3.67/1.25 % (2632225)Termination reason: Refutation not found, incomplete strategy
% 3.67/1.25 % (2632225)Time elapsed: 0.0000 s
% 3.67/1.25 % (2632225)Peak memory usage: 88 MB
% 3.67/1.25 % (2632223)Instruction limit reached!
% 3.67/1.25 % (2632223)------------------------------
% 3.67/1.25 % (2632223)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.67/1.25 % (2632223)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.67/1.25 % (2632223)CaDiCaL version: 2.1.3
% 3.67/1.25 % (2632223)Termination reason: Instruction limit
% 3.67/1.25 % (2632223)Termination phase: Saturation
% 3.67/1.25 % (2632223)Time elapsed: 0.044 s
% 3.67/1.25 % (2632223)Peak memory usage: 112 MB
% 3.67/1.25 % (2632223)Instructions burned: 33 (million)
% 3.67/1.25 % (2632232)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=3326633941:i=29:thsqd=64:nm=0:thsqc=8:rtra=on:thsq=on:ev=off_2998 on theBenchmark for (2998ds/29Mi)
% 3.67/1.25 % (2632233)ott+21_1024_to=lakbo:sil=128000:bsd=on:si=on:alasca=on:uwa=alasca_main:nwc=0.5:random_seed=3717653295:cond=on:i=16:fgj=on:ep=RS:asg=force:nm=10:rtra=on:rawr=on_2998 on theBenchmark for (2998ds/16Mi)
% 3.67/1.25 % (2632232)Instruction limit reached!
% 3.67/1.25 % (2632232)------------------------------
% 3.67/1.25 % (2632232)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.67/1.25 % (2632232)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.67/1.25 % (2632232)CaDiCaL version: 2.1.3
% 3.67/1.25 % (2632232)Termination reason: Instruction limit
% 3.67/1.25 % (2632232)Termination phase: Saturation
% 3.67/1.25 % (2632232)Time elapsed: 0.018 s
% 3.67/1.25 % (2632232)Peak memory usage: 88 MB
% 3.67/1.25 % (2632232)Instructions burned: 30 (million)
% 3.67/1.25 % (2632233)Also succeeded, but the first one will report.
% 3.67/1.25 % (2632225)------------------------------
% 3.67/1.25 % (2632225)------------------------------
% 3.67/1.25 % (2632235)dis+1011_1_prc=on:drc=off:si=on:sac=on:random_seed=1129543709:i=24:canc=force:rtra=on_2997 on theBenchmark for (2997ds/24Mi)
% 3.67/1.25 % (2632235)Instruction limit reached!
% 3.67/1.25 % (2632235)------------------------------
% 3.67/1.25 % (2632235)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.67/1.25 % (2632235)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.67/1.25 % (2632235)CaDiCaL version: 2.1.3
% 3.67/1.25 % (2632235)Termination reason: Instruction limit
% 3.67/1.25 % (2632235)Termination phase: Saturation
% 3.67/1.25 % (2632235)Time elapsed: 0.017 s
% 3.67/1.25 % (2632235)Peak memory usage: 89 MB
% 3.67/1.25 % (2632235)Instructions burned: 25 (million)
% 3.67/1.25 % (2632218)------------------------------
% 3.67/1.25 % (2632218)------------------------------
% 3.67/1.25 % (2632240)dis+1002_24_to=kbo:sil=128000:si=on:random_seed=1588395337:i=85:gtgl=4:rtra=on:gtg=exists_sym_2996 on theBenchmark for (2996ds/85Mi)
% 3.67/1.25 % (2632219)Refutation found. Thanks to Tanya!
% 3.67/1.25 % SZS status Theorem for theBenchmark
% 3.67/1.25 % SZS output start Proof for theBenchmark
% See solution above
% 3.67/1.25 % (2632219)------------------------------
% 3.67/1.25 % (2632219)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.67/1.25 % (2632219)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.67/1.25 % (2632219)CaDiCaL version: 2.1.3
% 3.67/1.25 % (2632219)Termination reason: Refutation
% 3.67/1.25 % (2632219)Time elapsed: 0.030 s
% 3.67/1.25 % (2632219)Peak memory usage: 116 MB
% 3.67/1.25 % (2632219)Instructions burned: 7 (million)
% 3.67/1.25 % (2632219)------------------------------
% 3.67/1.25 % (2632219)------------------------------
% 3.67/1.25 % (2632170)Success in time 0.442 s
% 3.67/1.25 % Vampire exiting
%------------------------------------------------------------------------------