%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ARI185_1 : TPTP v9.3.1. Released v5.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n004.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 09:32:39 AM UTC 2026
% Result : Theorem 5.47s 1.59s
% Output : Refutation 5.47s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 11
% Syntax : Number of formulae : 28 ( 15 unt; 0 typ; 10 def)
% Number of atoms : 41 ( 11 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 22 ( 9 ~; 3 |; 1 &)
% ( 6 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 5 ( 2 avg)
% Number arithmetic : 77 ( 14 atm; 20 fun; 38 num; 5 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 : 10 ( 6 usr; 7 prp; 0-2 aty)
% Number of functors : 14 ( 5 usr; 9 con; 0-2 aty)
% Number of variables : 5 ( 5 !; 0 ?; 5 :)
% Comments :
%------------------------------------------------------------------------------
tff(func_def_0,type,
f: $int > $int ).
tff(func_def_10,type,
sF0: $int ).
tff(func_def_11,type,
sF1: $int ).
tff(func_def_12,type,
sF2: $int ).
tff(func_def_13,type,
sF3: $int ).
tff(f1,conjecture,
( ! [X0: $int] : $greater(f(X0),1)
=> $less($difference(7,$product(2,f(3))),4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1) ).
tff(f2,negated_conjecture,
~ ( ! [X0: $int] : $greater(f(X0),1)
=> $less($difference(7,$product(2,f(3))),4) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
tff(f3,plain,
~ ( ! [X0: $int] : $less(1,f(X0))
=> $less($sum(7,$uminus($product(2,f(3)))),4) ),
inference(theory_normalization,[],[f2]) ).
tff(f4,plain,
( ~ $less($sum(7,$uminus($product(2,f(3)))),4)
& ! [X0: $int] : $less(1,f(X0)) ),
inference(ennf_transformation,[],[f3]) ).
tff(f5,plain,
! [X0: $int] : $less(1,f(X0)),
inference(cnf_transformation,[],[f4]) ).
tff(f6,plain,
~ $less($sum(7,$uminus($product(2,f(3)))),4),
inference(cnf_transformation,[],[f4]) ).
tff(f7,definition,
sF0 = f(3),
introduced(definition,[new_symbols(definition,[sF0])],[function_definition]) ).
tff(f8,plain,
f(3) = sF0,
inference(reorient_equations,[],[f7]) ).
tff(f9,definition,
sF1 = $product(2,sF0),
introduced(definition,[new_symbols(definition,[sF1])],[function_definition]) ).
tff(f10,definition,
sF2 = $uminus(sF1),
introduced(definition,[new_symbols(definition,[sF2])],[function_definition]) ).
tff(f11,definition,
sF3 = $sum(7,sF2),
introduced(definition,[new_symbols(definition,[sF3])],[function_definition]) ).
tff(f12,plain,
$sum(7,sF2) = sF3,
inference(reorient_equations,[],[f11]) ).
tff(f13,plain,
~ $less(sF3,4),
inference(definition_folding,[],[f6,f12,f10,f9,f8]) ).
tff(f15,definition,
( spl4_1
<=> ( f(3) = sF0 ) ),
introduced(definition,[new_symbols(definition,[spl4_1])],[avatar_definition]) ).
tff(f17,plain,
( ( f(3) = sF0 )
| ~ spl4_1 ),
inference(avatar_component_clause,[],[f15]) ).
tff(f18,plain,
spl4_1,
inference(avatar_split_clause,[],[f8,f15]) ).
tff(f20,definition,
( spl4_2
<=> ( sF1 = $product(2,sF0) ) ),
introduced(definition,[new_symbols(definition,[spl4_2])],[avatar_definition]) ).
tff(f23,plain,
spl4_2,
inference(avatar_split_clause,[],[f9,f20]) ).
tff(f25,definition,
( spl4_3
<=> $less(sF3,4) ),
introduced(definition,[new_symbols(definition,[spl4_3])],[avatar_definition]) ).
tff(f28,plain,
~ spl4_3,
inference(avatar_split_clause,[],[f13,f25]) ).
tff(f30,definition,
( spl4_4
<=> ( $sum(7,sF2) = sF3 ) ),
introduced(definition,[new_symbols(definition,[spl4_4])],[avatar_definition]) ).
tff(f33,plain,
spl4_4,
inference(avatar_split_clause,[],[f12,f30]) ).
tff(f35,definition,
( spl4_5
<=> ( sF2 = $uminus(sF1) ) ),
introduced(definition,[new_symbols(definition,[spl4_5])],[avatar_definition]) ).
tff(f38,plain,
spl4_5,
inference(avatar_split_clause,[],[f10,f35]) ).
tff(f39,plain,
( $less(1,sF0)
| ~ spl4_1 ),
inference(superposition,[],[f5,f17]) ).
tff(f41,definition,
( spl4_6
<=> $less(1,sF0) ),
introduced(definition,[new_symbols(definition,[spl4_6])],[avatar_definition]) ).
tff(f44,plain,
( spl4_6
| ~ spl4_1 ),
inference(avatar_split_clause,[],[f39,f15,f41]) ).
tff(f45,plain,
$false,
inference(avatar_smt_refutation,[],[f44,f38,f33,f28,f23,f18]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ARI185_1 : TPTP v9.3.1. Released v5.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.19 % Computer : n004.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 20:44:22 UTC 2026
% 0.09/0.19 % CPUTime :
% 0.09/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.22 Running first-order theorem proving
% 0.09/0.22 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
% 5.47/1.59 % (741897)Detected arithmetic, will pick strategies from an ALASCA-aware ARI schedule.
% 5.47/1.59 % (742022)dis+1002_16:1_to=lpo:sil=64000:sas=z3:si=on:norm_ineq=on:gve=force:uwa=one_side_constant:random_seed=727408688:i=12:doe=on:rtra=on:gtg=exists_top:ss=axioms_2999 on theBenchmark for (2999ds/12Mi)
% 5.47/1.59 % (742022)Instruction limit reached!
% 5.47/1.59 % (742022)------------------------------
% 5.47/1.59 % (742022)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.47/1.59 % (742022)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.47/1.59 % (742022)CaDiCaL version: 2.1.3
% 5.47/1.59 % (742022)Termination reason: Instruction limit
% 5.47/1.59 % (742022)Termination phase: Saturation
% 5.47/1.59 % (742022)Time elapsed: 0.026 s
% 5.47/1.59 % (742022)Peak memory usage: 115 MB
% 5.47/1.59 % (742022)Instructions burned: 12 (million)
% 5.47/1.59 % (742024)dis+10_3_slsqr=1,4:to=lpo:sil=128000:thi=strong:si=on:uwa=off:s2agt=20:slsqc=1:slsq=on:random_seed=1162680319:i=201:slsql=off:asg=cautious:rtra=on:gtg=all:ss=axioms:sgt=16_2999 on theBenchmark for (2999ds/201Mi)
% 5.47/1.59 % (742027)lrs+10_1_to=lpo:sas=z3:si=on:tha=off:random_seed=4221501190:i=46:rtra=on_2999 on theBenchmark for (2999ds/46Mi)
% 5.47/1.59 % (742025)lrs+1002_4:1_to=lpo:sil=64000:si=on:br=off:random_seed=1873726268:s2a=on:i=7:rtra=on:inst=on_2999 on theBenchmark for (2999ds/7Mi)
% 5.47/1.59 % (742028)lrs+10_1_tgt=ground:sas=z3:si=on:random_seed=3539342465:i=33:rtra=on_2999 on theBenchmark for (2999ds/33Mi)
% 5.47/1.59 % (742026)dis+21_64_to=kbo:sil=128000:si=on:sp=weighted_frequency:uwa=alasca_can_abstract:random_seed=2829566043:i=4:rtra=on_2999 on theBenchmark for (2999ds/4Mi)
% 5.47/1.59 % (742023)dis+1002_1_to=kbo:sil=128000:tgt=ground:sas=z3:si=on:spb=units:tha=off:random_seed=3036781274:i=307:kws=precedence:nm=0:rtra=on_2999 on theBenchmark for (2999ds/307Mi)
% 5.47/1.59 % (742026)Instruction limit reached!
% 5.47/1.59 % (742026)------------------------------
% 5.47/1.59 % (742026)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.47/1.59 % (742026)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.47/1.59 % (742026)CaDiCaL version: 2.1.3
% 5.47/1.59 % (742026)Termination reason: Instruction limit
% 5.47/1.59 % (742026)Termination phase: Saturation
% 5.47/1.59 % (742026)Time elapsed: 0.006 s
% 5.47/1.59 % (742026)Peak memory usage: 89 MB
% 5.47/1.59 % (742026)Instructions burned: 4 (million)
% 5.47/1.59 % (742025)Instruction limit reached!
% 5.47/1.59 % (742025)------------------------------
% 5.47/1.59 % (742025)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.47/1.59 % (742025)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.47/1.59 % (742025)CaDiCaL version: 2.1.3
% 5.47/1.59 % (742025)Termination reason: Instruction limit
% 5.47/1.59 % (742025)Termination phase: Saturation
% 5.47/1.59 % (742025)Time elapsed: 0.008 s
% 5.47/1.59 % (742025)Peak memory usage: 88 MB
% 5.47/1.59 % (742025)Instructions burned: 7 (million)
% 5.47/1.59 % (742027)Refutation not found, incomplete strategy
% 5.47/1.59 % (742027)------------------------------
% 5.47/1.59 % (742027)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.47/1.59 % (742027)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.47/1.59 % (742027)CaDiCaL version: 2.1.3
% 5.47/1.59 % (742027)Termination reason: Refutation not found, incomplete strategy
% 5.47/1.59 % (742027)Time elapsed: 0.040 s
% 5.47/1.59 % (742027)Peak memory usage: 114 MB
% 5.47/1.59 % (742027)Instructions burned: 6 (million)
% 5.47/1.59 % (742023)First to succeed.
% 5.47/1.59 % (742028)Also succeeded, but the first one will report.
% 5.47/1.59 % (742023)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-741897"
% 5.47/1.59 % (742032)dis+11_3_anc=none:drc=ordering:si=on:urr=ec_only:bce=on:tha=off:sac=on:random_seed=3998616730:st=5:i=14:sd=10:rtra=on:ss=axioms:rawr=on_2998 on theBenchmark for (2998ds/14Mi)
% 5.47/1.59 % (742032)Refutation not found, incomplete strategy
% 5.47/1.59 % (742032)------------------------------
% 5.47/1.59 % (742032)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.47/1.59 % (742032)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.47/1.59 % (742032)CaDiCaL version: 2.1.3
% 5.47/1.59 % (742032)Termination reason: Refutation not found, incomplete strategy
% 5.47/1.59 % (742032)Time elapsed: 0.001 s
% 5.47/1.59 % (742032)Peak memory usage: 88 MB
% 5.47/1.59 % (742024)Instruction limit reached!
% 5.47/1.59 % (742024)------------------------------
% 5.47/1.59 % (742024)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.47/1.59 % (742024)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.47/1.59 % (742024)CaDiCaL version: 2.1.3
% 5.47/1.59 % (742024)Termination reason: Instruction limit
% 5.47/1.59 % (742024)Termination phase: Saturation
% 5.47/1.59 % (742024)Time elapsed: 0.242 s
% 5.47/1.59 % (742024)Peak memory usage: 118 MB
% 5.47/1.59 % (742024)Instructions burned: 201 (million)
% 5.47/1.59 % (742039)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=2091693431:i=29:thsqd=64:nm=0:thsqc=8:rtra=on:thsq=on:ev=off_2997 on theBenchmark for (2997ds/29Mi)
% 5.47/1.59 % (742040)ott+21_1024_to=lakbo:sil=128000:bsd=on:si=on:alasca=on:uwa=alasca_main:nwc=0.5:random_seed=564026778:cond=on:i=16:fgj=on:ep=RS:asg=force:nm=10:rtra=on:rawr=on_2997 on theBenchmark for (2997ds/16Mi)
% 5.47/1.59 % (742040)Also succeeded, but the first one will report.
% 5.47/1.59 % (742039)Instruction limit reached!
% 5.47/1.59 % (742039)------------------------------
% 5.47/1.59 % (742039)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.47/1.59 % (742039)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.47/1.59 % (742039)CaDiCaL version: 2.1.3
% 5.47/1.59 % (742039)Termination reason: Instruction limit
% 5.47/1.59 % (742039)Termination phase: Saturation
% 5.47/1.59 % (742039)Time elapsed: 0.033 s
% 5.47/1.59 % (742039)Peak memory usage: 88 MB
% 5.47/1.59 % (742039)Instructions burned: 30 (million)
% 5.47/1.59 % (742032)------------------------------
% 5.47/1.59 % (742032)------------------------------
% 5.47/1.59 % (742023)Refutation found. Thanks to Tanya!
% 5.47/1.59 % SZS status Theorem for theBenchmark
% 5.47/1.59 % SZS output start Proof for theBenchmark
% See solution above
% 5.47/1.59 % (742023)------------------------------
% 5.47/1.59 % (742023)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.47/1.59 % (742023)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.47/1.59 % (742023)CaDiCaL version: 2.1.3
% 5.47/1.59 % (742023)Termination reason: Refutation
% 5.47/1.59 % (742023)Time elapsed: 0.047 s
% 5.47/1.59 % (742023)Peak memory usage: 116 MB
% 5.47/1.59 % (742023)Instructions burned: 10 (million)
% 5.47/1.59 % (742023)------------------------------
% 5.47/1.59 % (742023)------------------------------
% 5.47/1.59 % (741897)Success in time 0.688 s
% 5.47/1.59 % Vampire exiting
%------------------------------------------------------------------------------