%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ARI668_1 : TPTP v9.3.1. Released v6.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n011.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 09:33:37 AM UTC 2026
% Result : Theorem 0.19s 1.51s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 9
% Syntax : Number of formulae : 26 ( 17 unt; 0 typ; 6 def)
% Number of atoms : 35 ( 6 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 16 ( 7 ~; 3 |; 1 &)
% ( 5 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number arithmetic : 63 ( 18 atm; 22 fun; 23 num; 0 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 ( 5 usr; 6 prp; 0-2 aty)
% Number of functors : 11 ( 4 usr; 9 con; 0-2 aty)
% Number of variables : 0 ( 0 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(func_def_0,type,
a: $int ).
tff(func_def_1,type,
b: $int ).
tff(func_def_2,type,
c: $int ).
tff(func_def_10,type,
sF0: $int ).
tff(f1,axiom,
$sum($product(11,a),$product(7,b)) = 1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj) ).
tff(f2,axiom,
$lesseq(a,c),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_001) ).
tff(f3,conjecture,
( $lesseq(4,$product(a,c))
| $greatereq(0,$product(a,c)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_002) ).
tff(f4,negated_conjecture,
~ ( $lesseq(4,$product(a,c))
| $greatereq(0,$product(a,c)) ),
inference(negated_conjecture,[status(cth)],[f3]) ).
tff(f5,plain,
~ ( ~ $less($product(a,c),4)
| ~ $less(0,$product(a,c)) ),
inference(theory_normalization,[],[f4]) ).
tff(f6,plain,
~ $less(c,a),
inference(theory_normalization,[],[f2]) ).
tff(f7,plain,
( $less(0,$product(a,c))
& $less($product(a,c),4) ),
inference(ennf_transformation,[],[f5]) ).
tff(f8,plain,
$less($product(a,c),4),
inference(cnf_transformation,[],[f7]) ).
tff(f9,plain,
$less(0,$product(a,c)),
inference(cnf_transformation,[],[f7]) ).
tff(f10,plain,
~ $less(c,a),
inference(cnf_transformation,[],[f6]) ).
tff(f11,plain,
$sum($product(11,a),$product(7,b)) = 1,
inference(cnf_transformation,[],[f1]) ).
tff(f12,definition,
sF0 = $product(a,c),
introduced(definition,[new_symbols(definition,[sF0])],[function_definition]) ).
tff(f13,plain,
$product(a,c) = sF0,
inference(reorient_equations,[],[f12]) ).
tff(f14,plain,
$less(0,sF0),
inference(definition_folding,[],[f9,f13]) ).
tff(f15,plain,
$less(sF0,4),
inference(definition_folding,[],[f8,f13]) ).
tff(f17,definition,
( spl1_1
<=> ( $product(a,c) = sF0 ) ),
introduced(definition,[new_symbols(definition,[spl1_1])],[avatar_definition]) ).
tff(f20,plain,
spl1_1,
inference(avatar_split_clause,[],[f13,f17]) ).
tff(f22,definition,
( spl1_2
<=> $less(0,sF0) ),
introduced(definition,[new_symbols(definition,[spl1_2])],[avatar_definition]) ).
tff(f25,plain,
spl1_2,
inference(avatar_split_clause,[],[f14,f22]) ).
tff(f27,definition,
( spl1_3
<=> $less(sF0,4) ),
introduced(definition,[new_symbols(definition,[spl1_3])],[avatar_definition]) ).
tff(f30,plain,
spl1_3,
inference(avatar_split_clause,[],[f15,f27]) ).
tff(f32,definition,
( spl1_4
<=> ( $sum($product(11,a),$product(7,b)) = 1 ) ),
introduced(definition,[new_symbols(definition,[spl1_4])],[avatar_definition]) ).
tff(f35,plain,
spl1_4,
inference(avatar_split_clause,[],[f11,f32]) ).
tff(f37,definition,
( spl1_5
<=> $less(c,a) ),
introduced(definition,[new_symbols(definition,[spl1_5])],[avatar_definition]) ).
tff(f40,plain,
~ spl1_5,
inference(avatar_split_clause,[],[f10,f37]) ).
tff(f41,plain,
$false,
inference(avatar_smt_refutation,[],[f40,f35,f30,f25,f20]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ARI668_1 : TPTP v9.3.1. Released v6.3.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.20 % Computer : n011.cluster.edu
% 0.09/0.20 % Model : x86_64 x86_64
% 0.09/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.20 % Memory : 8046.5625MB
% 0.09/0.20 % OS : Linux 6.8.0-71-generic
% 0.09/0.20 % CPULimit : 300
% 0.09/0.20 % WCLimit : 300
% 0.09/0.20 % DateTime : Mon Sep 28 20:55:31 UTC 2026
% 0.09/0.20 % CPUTime :
% 0.09/0.20 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.24 Running first-order theorem proving
% 0.09/0.24 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
% 0.19/1.51 % (3777253)Detected arithmetic, will pick strategies from an ALASCA-aware ARI schedule.
% 0.19/1.51 % (3777329)dis+1002_16:1_to=lpo:sil=64000:sas=z3:si=on:norm_ineq=on:gve=force:uwa=one_side_constant:random_seed=2073017752:i=12:doe=on:rtra=on:gtg=exists_top:ss=axioms_2999 on theBenchmark for (2999ds/12Mi)
% 0.19/1.51 % (3777329)Instruction limit reached!
% 0.19/1.51 % (3777329)------------------------------
% 0.19/1.51 % (3777329)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.19/1.51 % (3777329)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/1.51 % (3777329)CaDiCaL version: 2.1.3
% 0.19/1.51 % (3777329)Termination reason: Instruction limit
% 0.19/1.51 % (3777329)Termination phase: Saturation
% 0.19/1.51 % (3777329)Time elapsed: 0.021 s
% 0.19/1.51 % (3777329)Peak memory usage: 116 MB
% 0.19/1.51 % (3777329)Instructions burned: 14 (million)
% 0.19/1.51 % (3777333)lrs+1002_4:1_to=lpo:sil=64000:si=on:br=off:random_seed=606026488:s2a=on:i=7:rtra=on:inst=on_2999 on theBenchmark for (2999ds/7Mi)
% 0.19/1.51 % (3777331)dis+1002_1_to=kbo:sil=128000:tgt=ground:sas=z3:si=on:spb=units:tha=off:random_seed=3746748208:i=307:kws=precedence:nm=0:rtra=on_2999 on theBenchmark for (2999ds/307Mi)
% 0.19/1.51 % (3777332)dis+10_3_slsqr=1,4:to=lpo:sil=128000:thi=strong:si=on:uwa=off:s2agt=20:slsqc=1:slsq=on:random_seed=2337237860:i=201:slsql=off:asg=cautious:rtra=on:gtg=all:ss=axioms:sgt=16_2999 on theBenchmark for (2999ds/201Mi)
% 0.19/1.51 % (3777335)dis+21_64_to=kbo:sil=128000:si=on:sp=weighted_frequency:uwa=alasca_can_abstract:random_seed=2240316263:i=4:rtra=on_2999 on theBenchmark for (2999ds/4Mi)
% 0.19/1.51 % (3777335)Instruction limit reached!
% 0.19/1.51 % (3777335)------------------------------
% 0.19/1.51 % (3777335)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.19/1.51 % (3777335)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/1.51 % (3777335)CaDiCaL version: 2.1.3
% 0.19/1.51 % (3777335)Termination reason: Instruction limit
% 0.19/1.51 % (3777335)Termination phase: Saturation
% 0.19/1.51 % (3777335)Time elapsed: 0.004 s
% 0.19/1.51 % (3777335)Peak memory usage: 88 MB
% 0.19/1.51 % (3777335)Instructions burned: 4 (million)
% 0.19/1.51 % (3777333)Instruction limit reached!
% 0.19/1.51 % (3777333)------------------------------
% 0.19/1.51 % (3777333)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.19/1.51 % (3777333)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/1.51 % (3777333)CaDiCaL version: 2.1.3
% 0.19/1.51 % (3777333)Termination reason: Instruction limit
% 0.19/1.51 % (3777333)Termination phase: Saturation
% 0.19/1.51 % (3777333)Time elapsed: 0.006 s
% 0.19/1.51 % (3777333)Peak memory usage: 88 MB
% 0.19/1.51 % (3777333)Instructions burned: 8 (million)
% 0.19/1.51 % (3777338)lrs+10_1_tgt=ground:sas=z3:si=on:random_seed=3878388650:i=33:rtra=on_2999 on theBenchmark for (2999ds/33Mi)
% 0.19/1.51 % (3777336)lrs+10_1_to=lpo:sas=z3:si=on:tha=off:random_seed=3967712554:i=46:rtra=on_2999 on theBenchmark for (2999ds/46Mi)
% 0.19/1.51 % (3777331)First to succeed.
% 0.19/1.51 % (3777331)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3777253"
% 0.19/1.51 % (3777338)Also succeeded, but the first one will report.
% 0.19/1.51 % (3777336)Also succeeded, but the first one will report.
% 0.19/1.51 % (3777365)dis+11_3_anc=none:drc=ordering:si=on:urr=ec_only:bce=on:tha=off:sac=on:random_seed=584338909:st=5:i=14:sd=10:rtra=on:ss=axioms:rawr=on_2998 on theBenchmark for (2998ds/14Mi)
% 0.19/1.51 % (3777365)Refutation not found, incomplete strategy
% 0.19/1.51 % (3777365)------------------------------
% 0.19/1.51 % (3777365)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.19/1.51 % (3777365)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/1.51 % (3777365)CaDiCaL version: 2.1.3
% 0.19/1.51 % (3777365)Termination reason: Refutation not found, incomplete strategy
% 0.19/1.51 % (3777365)Time elapsed: 0.001 s
% 0.19/1.51 % (3777365)Peak memory usage: 88 MB
% 0.19/1.51 % (3777332)Instruction limit reached!
% 0.19/1.51 % (3777332)------------------------------
% 0.19/1.51 % (3777332)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.19/1.51 % (3777332)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/1.51 % (3777332)CaDiCaL version: 2.1.3
% 0.19/1.51 % (3777332)Termination reason: Instruction limit
% 0.19/1.51 % (3777332)Termination phase: Saturation
% 0.19/1.51 % (3777332)Time elapsed: 0.177 s
% 0.19/1.51 % (3777332)Peak memory usage: 117 MB
% 0.19/1.51 % (3777332)Instructions burned: 201 (million)
% 0.19/1.51 % (3777374)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=975384840:i=29:thsqd=64:nm=0:thsqc=8:rtra=on:thsq=on:ev=off_2998 on theBenchmark for (2998ds/29Mi)
% 0.19/1.51 % (3777375)ott+21_1024_to=lakbo:sil=128000:bsd=on:si=on:alasca=on:uwa=alasca_main:nwc=0.5:random_seed=3875025246:cond=on:i=16:fgj=on:ep=RS:asg=force:nm=10:rtra=on:rawr=on_2998 on theBenchmark for (2998ds/16Mi)
% 0.19/1.51 % (3777375)Instruction limit reached!
% 0.19/1.51 % (3777375)------------------------------
% 0.19/1.51 % (3777375)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.19/1.51 % (3777375)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/1.51 % (3777375)CaDiCaL version: 2.1.3
% 0.19/1.51 % (3777375)Termination reason: Instruction limit
% 0.19/1.51 % (3777375)Termination phase: Saturation
% 0.19/1.51 % (3777375)Time elapsed: 0.019 s
% 0.19/1.51 % (3777375)Peak memory usage: 90 MB
% 0.19/1.51 % (3777375)Instructions burned: 16 (million)
% 0.19/1.51 % (3777374)Instruction limit reached!
% 0.19/1.51 % (3777374)------------------------------
% 0.19/1.51 % (3777374)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.19/1.51 % (3777374)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/1.51 % (3777374)CaDiCaL version: 2.1.3
% 0.19/1.51 % (3777374)Termination reason: Instruction limit
% 0.19/1.51 % (3777374)Termination phase: Saturation
% 0.19/1.51 % (3777374)Time elapsed: 0.034 s
% 0.19/1.51 % (3777374)Peak memory usage: 88 MB
% 0.19/1.51 % (3777374)Instructions burned: 30 (million)
% 0.19/1.51 % (3777365)------------------------------
% 0.19/1.51 % (3777365)------------------------------
% 0.19/1.51 % (3777331)Refutation found. Thanks to Tanya!
% 0.19/1.51 % SZS status Theorem for theBenchmark
% 0.19/1.51 % SZS output start Proof for theBenchmark
% See solution above
% 0.19/1.51 % (3777331)------------------------------
% 0.19/1.51 % (3777331)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.19/1.51 % (3777331)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/1.51 % (3777331)CaDiCaL version: 2.1.3
% 0.19/1.51 % (3777331)Termination reason: Refutation
% 0.19/1.51 % (3777331)Time elapsed: 0.041 s
% 0.19/1.51 % (3777331)Peak memory usage: 117 MB
% 0.19/1.51 % (3777331)Instructions burned: 17 (million)
% 0.19/1.51 % (3777331)------------------------------
% 0.19/1.51 % (3777331)------------------------------
% 0.19/1.51 % (3777253)Success in time 0.597 s
% 0.19/1.51 % Vampire exiting
%------------------------------------------------------------------------------