%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWX095_1 : TPTP v9.3.1. Released v9.1.0.
% 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 01:45:52 PM UTC 2026
% Result : Theorem 3.78s 1.32s
% Output : Refutation 3.78s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 2
% Syntax : Number of formulae : 13 ( 6 unt; 0 typ; 0 def)
% Number of atoms : 42 ( 0 equ)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 46 ( 17 ~; 14 |; 12 &)
% ( 3 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number arithmetic : 121 ( 27 atm; 36 fun; 42 num; 16 var)
% Number of types : 4 ( 2 usr; 1 ari; 0 dat; 0 cdt)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 15 ( 11 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 7 usr; 5 con; 0-2 aty)
% Number of variables : 16 ( 14 !; 2 ?; 16 :)
% Comments :
%------------------------------------------------------------------------------
tff(type_def_5,type,
general: $tType ).
tff(type_def_6,type,
symbol: $tType ).
tff(func_def_0,type,
f__integer__: $int > general ).
tff(func_def_1,type,
f__symbolic__: symbol > general ).
tff(func_def_2,type,
c__infimum__: general ).
tff(func_def_3,type,
c__supremum__: general ).
tff(func_def_4,type,
n_i: $int ).
tff(func_def_10,type,
sK0: general > symbol ).
tff(func_def_11,type,
sK1: general > $int ).
tff(pred_def_1,type,
p__is_integer__: general > $o ).
tff(pred_def_2,type,
p__is_symbolic__: general > $o ).
tff(pred_def_3,type,
p__less_equal__: ( general * general ) > $o ).
tff(pred_def_4,type,
p__less__: ( general * general ) > $o ).
tff(pred_def_5,type,
p__greater_equal__: ( general * general ) > $o ).
tff(pred_def_6,type,
p__greater__: ( general * general ) > $o ).
tff(pred_def_8,type,
three: general > $o ).
tff(pred_def_9,type,
sqrt: general > $o ).
tff(pred_def_10,type,
three_p: general > $o ).
tff(pred_def_11,type,
more_than_three: general > $o ).
tff(pred_def_12,type,
sqrt: ( general * general ) > $o ).
tff(f21,axiom,
! [X1: $int,X0: $int] :
( sqrt(f__integer__(X0),f__integer__(X1))
<=> ( $less(X1,$product($sum(X0,1),$sum(X0,1)))
& $greatereq(X0,0)
& $lesseq($product(X0,X0),X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',formula_5_unnamed_formula) ).
tff(f23,conjecture,
? [X0: $int] : sqrt(f__integer__(X0),f__integer__(0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',formula_7_base_case) ).
tff(f24,negated_conjecture,
~ ? [X0: $int] : sqrt(f__integer__(X0),f__integer__(0)),
inference(negated_conjecture,[status(cth)],[f23]) ).
tff(f30,plain,
! [X1: $int,X0: $int] :
( sqrt(f__integer__(X0),f__integer__(X1))
<=> ( $less(X1,$product($sum(X0,1),$sum(X0,1)))
& ~ $less(X0,0)
& ~ $less(X1,$product(X0,X0)) ) ),
inference(theory_normalization,[],[f21]) ).
tff(f59,plain,
! [X0: $int,X1: $int] :
( ( $less(X0,$product($sum(X1,1),$sum(X1,1)))
& ~ $less(X0,$product(X1,X1))
& ~ $less(X1,0) )
<=> sqrt(f__integer__(X1),f__integer__(X0)) ),
inference(rectify,[],[f30]) ).
tff(f71,plain,
! [X0: $int] : ~ sqrt(f__integer__(X0),f__integer__(0)),
inference(ennf_transformation,[],[f24]) ).
tff(f83,plain,
! [X0: $int,X1: $int] :
( ( ( $less(X0,$product($sum(X1,1),$sum(X1,1)))
& ~ $less(X0,$product(X1,X1))
& ~ $less(X1,0) )
| ~ sqrt(f__integer__(X1),f__integer__(X0)) )
& ( sqrt(f__integer__(X1),f__integer__(X0))
| ~ $less(X0,$product($sum(X1,1),$sum(X1,1)))
| $less(X0,$product(X1,X1))
| $less(X1,0) ) ),
inference(nnf_transformation,[],[f59]) ).
tff(f84,plain,
! [X0: $int,X1: $int] :
( ( ( $less(X0,$product($sum(X1,1),$sum(X1,1)))
& ~ $less(X0,$product(X1,X1))
& ~ $less(X1,0) )
| ~ sqrt(f__integer__(X1),f__integer__(X0)) )
& ( sqrt(f__integer__(X1),f__integer__(X0))
| ~ $less(X0,$product($sum(X1,1),$sum(X1,1)))
| $less(X0,$product(X1,X1))
| $less(X1,0) ) ),
inference(flattening,[],[f83]) ).
tff(f94,plain,
! [X0: $int] : ~ sqrt(f__integer__(X0),f__integer__(0)),
inference(cnf_transformation,[],[f71]) ).
tff(f100,plain,
! [X0: $int,X1: $int] :
( ~ $less(X0,$product($sum(X1,1),$sum(X1,1)))
| sqrt(f__integer__(X1),f__integer__(X0))
| $less(X0,$product(X1,X1))
| $less(X1,0) ),
inference(cnf_transformation,[],[f84]) ).
tff(f232,plain,
( sqrt(f__integer__(0),f__integer__(0))
| ~ $less(0,$product($sum(0,1),$sum(0,1)))
| $less(0,$product(0,0))
| $less(0,0) ),
inference(instantiation,[],[f100]) ).
tff(f239,plain,
sqrt(f__integer__(0),f__integer__(0)),
inference(evaluation,[],[f232]) ).
tff(f245,plain,
$false,
inference(forward_subsumption_resolution,[],[f239,f94]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWX095_1 : TPTP v9.3.1. Released v9.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.19 % Computer : n010.cluster.edu
% 0.07/0.19 % Model : x86_64 x86_64
% 0.07/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.19 % Memory : 8046.5625MB
% 0.07/0.19 % OS : Linux 6.8.0-71-generic
% 0.07/0.19 % CPULimit : 300
% 0.07/0.19 % WCLimit : 300
% 0.07/0.19 % DateTime : Mon Sep 28 15:01:32 UTC 2026
% 0.07/0.19 % CPUTime :
% 0.07/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.23 Running first-order theorem proving
% 0.07/0.23 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
% 3.78/1.32 % (1985382)Detected arithmetic, will pick strategies from an ALASCA-aware ARI schedule.
% 3.78/1.32 % (1985393)lrs+10_1_tgt=ground:sas=z3:si=on:random_seed=2183498404:i=33:rtra=on_2999 on theBenchmark for (2999ds/33Mi)
% 3.78/1.32 % (1985393)Instruction limit reached!
% 3.78/1.32 % (1985393)------------------------------
% 3.78/1.32 % (1985393)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.78/1.32 % (1985393)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.78/1.32 % (1985393)CaDiCaL version: 2.1.3
% 3.78/1.32 % (1985393)Termination reason: Instruction limit
% 3.78/1.32 % (1985393)Termination phase: Saturation
% 3.78/1.32 % (1985393)Time elapsed: 0.030 s
% 3.78/1.32 % (1985393)Peak memory usage: 115 MB
% 3.78/1.32 % (1985393)Instructions burned: 35 (million)
% 3.78/1.32 % (1985391)dis+21_64_to=kbo:sil=128000:si=on:sp=weighted_frequency:uwa=alasca_can_abstract:random_seed=4099195055:i=4:rtra=on_2999 on theBenchmark for (2999ds/4Mi)
% 3.78/1.32 % (1985389)dis+10_3_slsqr=1,4:to=lpo:sil=128000:thi=strong:si=on:uwa=off:s2agt=20:slsqc=1:slsq=on:random_seed=3515207248:i=201:slsql=off:asg=cautious:rtra=on:gtg=all:ss=axioms:sgt=16_2999 on theBenchmark for (2999ds/201Mi)
% 3.78/1.32 % (1985387)dis+1002_16:1_to=lpo:sil=64000:sas=z3:si=on:norm_ineq=on:gve=force:uwa=one_side_constant:random_seed=3435058285:i=12:doe=on:rtra=on:gtg=exists_top:ss=axioms_2999 on theBenchmark for (2999ds/12Mi)
% 3.78/1.32 % (1985388)dis+1002_1_to=kbo:sil=128000:tgt=ground:sas=z3:si=on:spb=units:tha=off:random_seed=511593869:i=307:kws=precedence:nm=0:rtra=on_2999 on theBenchmark for (2999ds/307Mi)
% 3.78/1.32 % (1985390)lrs+1002_4:1_to=lpo:sil=64000:si=on:br=off:random_seed=414302487:s2a=on:i=7:rtra=on:inst=on_2999 on theBenchmark for (2999ds/7Mi)
% 3.78/1.32 % (1985391)Instruction limit reached!
% 3.78/1.32 % (1985391)------------------------------
% 3.78/1.32 % (1985391)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.78/1.32 % (1985391)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.78/1.32 % (1985391)CaDiCaL version: 2.1.3
% 3.78/1.32 % (1985391)Termination reason: Instruction limit
% 3.78/1.32 % (1985391)Termination phase: Saturation
% 3.78/1.32 % (1985391)Time elapsed: 0.004 s
% 3.78/1.32 % (1985391)Peak memory usage: 88 MB
% 3.78/1.32 % (1985391)Instructions burned: 5 (million)
% 3.78/1.32 % (1985390)First to succeed.
% 3.78/1.32 % (1985390)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-1985382"
% 3.78/1.32 % (1985392)lrs+10_1_to=lpo:sas=z3:si=on:tha=off:random_seed=509640238:i=46:rtra=on_2999 on theBenchmark for (2999ds/46Mi)
% 3.78/1.32 % (1985387)Instruction limit reached!
% 3.78/1.32 % (1985387)------------------------------
% 3.78/1.32 % (1985387)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.78/1.32 % (1985387)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.78/1.32 % (1985387)CaDiCaL version: 2.1.3
% 3.78/1.32 % (1985387)Termination reason: Instruction limit
% 3.78/1.32 % (1985387)Termination phase: Saturation
% 3.78/1.32 % (1985387)Time elapsed: 0.030 s
% 3.78/1.32 % (1985387)Peak memory usage: 112 MB
% 3.78/1.32 % (1985387)Instructions burned: 12 (million)
% 3.78/1.32 % (1985392)Instruction limit reached!
% 3.78/1.32 % (1985392)------------------------------
% 3.78/1.32 % (1985392)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.78/1.32 % (1985392)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.78/1.32 % (1985392)CaDiCaL version: 2.1.3
% 3.78/1.32 % (1985392)Termination reason: Instruction limit
% 3.78/1.32 % (1985392)Termination phase: Saturation
% 3.78/1.32 % (1985392)Time elapsed: 0.054 s
% 3.78/1.32 % (1985392)Peak memory usage: 116 MB
% 3.78/1.32 % (1985392)Instructions burned: 47 (million)
% 3.78/1.32 % (1985389)Also succeeded, but the first one will report.
% 3.78/1.32 % (1985395)dis+11_3_anc=none:drc=ordering:si=on:urr=ec_only:bce=on:tha=off:sac=on:random_seed=1776096267:st=5:i=14:sd=10:rtra=on:ss=axioms:rawr=on_2998 on theBenchmark for (2998ds/14Mi)
% 3.78/1.32 % (1985395)Instruction limit reached!
% 3.78/1.32 % (1985395)------------------------------
% 3.78/1.32 % (1985395)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.78/1.32 % (1985395)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.78/1.32 % (1985395)CaDiCaL version: 2.1.3
% 3.78/1.32 % (1985395)Termination reason: Instruction limit
% 3.78/1.32 % (1985395)Termination phase: Saturation
% 3.78/1.32 % (1985395)Time elapsed: 0.006 s
% 3.78/1.32 % (1985395)Peak memory usage: 88 MB
% 3.78/1.32 % (1985395)Instructions burned: 17 (million)
% 3.78/1.32 % (1985402)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=2045975368:i=29:thsqd=64:nm=0:thsqc=8:rtra=on:thsq=on:ev=off_2998 on theBenchmark for (2998ds/29Mi)
% 3.78/1.32 % (1985402)Instruction limit reached!
% 3.78/1.32 % (1985402)------------------------------
% 3.78/1.32 % (1985402)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.78/1.32 % (1985402)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.78/1.32 % (1985402)CaDiCaL version: 2.1.3
% 3.78/1.32 % (1985402)Termination reason: Instruction limit
% 3.78/1.32 % (1985402)Termination phase: Saturation
% 3.78/1.32 % (1985402)Time elapsed: 0.022 s
% 3.78/1.32 % (1985402)Peak memory usage: 88 MB
% 3.78/1.32 % (1985402)Instructions burned: 29 (million)
% 3.78/1.32 % (1985403)ott+21_1024_to=lakbo:sil=128000:bsd=on:si=on:alasca=on:uwa=alasca_main:nwc=0.5:random_seed=3797175572:cond=on:i=16:fgj=on:ep=RS:asg=force:nm=10:rtra=on:rawr=on_2997 on theBenchmark for (2997ds/16Mi)
% 3.78/1.32 % (1985403)Instruction limit reached!
% 3.78/1.32 % (1985403)------------------------------
% 3.78/1.32 % (1985403)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.78/1.32 % (1985403)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.78/1.32 % (1985403)CaDiCaL version: 2.1.3
% 3.78/1.32 % (1985403)Termination reason: Instruction limit
% 3.78/1.32 % (1985403)Termination phase: Saturation
% 3.78/1.32 % (1985403)Time elapsed: 0.012 s
% 3.78/1.32 % (1985403)Peak memory usage: 90 MB
% 3.78/1.32 % (1985403)Instructions burned: 17 (million)
% 3.78/1.32 % (1985404)dis+1011_1_prc=on:drc=off:si=on:sac=on:random_seed=3816906561:i=24:canc=force:rtra=on_2997 on theBenchmark for (2997ds/24Mi)
% 3.78/1.32 % (1985406)ott+1010_8_to=lpo:sil=128000:si=on:norm_ineq=on:sp=unary_frequency:sos=on:gve=cautious:spb=goal_then_units:uwa=alasca_main_floor:tha=some:random_seed=2302482666:i=27:canc=cautious:fsr=off:rtra=on_2997 on theBenchmark for (2997ds/27Mi)
% 3.78/1.32 % (1985406)Refutation not found, incomplete strategy
% 3.78/1.32 % (1985406)------------------------------
% 3.78/1.32 % (1985406)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.78/1.32 % (1985406)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.78/1.32 % (1985406)CaDiCaL version: 2.1.3
% 3.78/1.32 % (1985406)Termination reason: Refutation not found, incomplete strategy
% 3.78/1.32 % (1985406)Time elapsed: 0.002 s
% 3.78/1.32 % (1985406)Peak memory usage: 89 MB
% 3.78/1.32 % (1985406)Instructions burned: 3 (million)
% 3.78/1.32 % (1985388)Instruction limit reached!
% 3.78/1.32 % (1985388)------------------------------
% 3.78/1.32 % (1985388)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.78/1.32 % (1985388)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.78/1.32 % (1985388)CaDiCaL version: 2.1.3
% 3.78/1.32 % (1985388)Termination reason: Instruction limit
% 3.78/1.32 % (1985388)Termination phase: Saturation
% 3.78/1.32 % (1985388)Time elapsed: 0.235 s
% 3.78/1.32 % (1985388)Peak memory usage: 117 MB
% 3.78/1.32 % (1985388)Instructions burned: 308 (million)
% 3.78/1.32 % (1985404)Also succeeded, but the first one will report.
% 3.78/1.32 % (1985390)Refutation found. Thanks to Tanya!
% 3.78/1.32 % SZS status Theorem for theBenchmark
% 3.78/1.32 % SZS output start Proof for theBenchmark
% See solution above
% 3.78/1.32 % (1985390)------------------------------
% 3.78/1.32 % (1985390)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.78/1.32 % (1985390)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.78/1.32 % (1985390)CaDiCaL version: 2.1.3
% 3.78/1.32 % (1985390)Termination reason: Refutation
% 3.78/1.32 % (1985390)Time elapsed: 0.006 s
% 3.78/1.32 % (1985390)Peak memory usage: 89 MB
% 3.78/1.32 % (1985390)Instructions burned: 6 (million)
% 3.78/1.32 % (1985390)------------------------------
% 3.78/1.32 % (1985390)------------------------------
% 3.78/1.32 % (1985382)Success in time 0.444 s
% 3.78/1.32 % Vampire exiting
%------------------------------------------------------------------------------