%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ARI601_1 : TPTP v9.3.1. Released v5.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n001.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 09:33:27 AM UTC 2026
% Result : Theorem 4.79s 1.52s
% Output : Refutation 4.79s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 8
% Syntax : Number of formulae : 26 ( 13 unt; 0 typ; 7 def)
% Number of atoms : 44 ( 7 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 28 ( 10 ~; 3 |; 4 &)
% ( 5 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number arithmetic : 62 ( 23 atm; 9 fun; 24 num; 6 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 : 9 ( 5 usr; 6 prp; 0-2 aty)
% Number of functors : 8 ( 4 usr; 6 con; 0-2 aty)
% Number of variables : 6 ( 6 !; 0 ?; 6 :)
% Comments :
%------------------------------------------------------------------------------
tff(func_def_0,type,
a: $int ).
tff(func_def_1,type,
f: $int > $int ).
tff(func_def_6,type,
sF0: $int ).
tff(func_def_7,type,
sF1: $int ).
tff(f1,conjecture,
( ! [X0: $int] : $greater(f(X0),X0)
=> ( $less(3,a)
=> $less(4,f($sum(a,1))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fX_gt_X_implies_ineq) ).
tff(f2,negated_conjecture,
~ ( ! [X0: $int] : $greater(f(X0),X0)
=> ( $less(3,a)
=> $less(4,f($sum(a,1))) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
tff(f3,plain,
~ ( ! [X0: $int] : $less(X0,f(X0))
=> ( $less(3,a)
=> $less(4,f($sum(a,1))) ) ),
inference(theory_normalization,[],[f2]) ).
tff(f4,plain,
( ~ $less(4,f($sum(a,1)))
& $less(3,a)
& ! [X0: $int] : $less(X0,f(X0)) ),
inference(ennf_transformation,[],[f3]) ).
tff(f5,plain,
( $less(3,a)
& ! [X0: $int] : $less(X0,f(X0))
& ~ $less(4,f($sum(a,1))) ),
inference(flattening,[],[f4]) ).
tff(f6,plain,
~ $less(4,f($sum(a,1))),
inference(cnf_transformation,[],[f5]) ).
tff(f7,plain,
! [X0: $int] : $less(X0,f(X0)),
inference(cnf_transformation,[],[f5]) ).
tff(f8,plain,
$less(3,a),
inference(cnf_transformation,[],[f5]) ).
tff(f9,definition,
sF0 = $sum(a,1),
introduced(definition,[new_symbols(definition,[sF0])],[function_definition]) ).
tff(f10,plain,
$sum(a,1) = sF0,
inference(reorient_equations,[],[f9]) ).
tff(f11,definition,
sF1 = f(sF0),
introduced(definition,[new_symbols(definition,[sF1])],[function_definition]) ).
tff(f12,plain,
f(sF0) = sF1,
inference(reorient_equations,[],[f11]) ).
tff(f13,plain,
~ $less(4,sF1),
inference(definition_folding,[],[f6,f12,f10]) ).
tff(f15,definition,
( spl2_1
<=> $less(3,a) ),
introduced(definition,[new_symbols(definition,[spl2_1])],[avatar_definition]) ).
tff(f18,plain,
spl2_1,
inference(avatar_split_clause,[],[f8,f15]) ).
tff(f20,definition,
( spl2_2
<=> ( $sum(a,1) = sF0 ) ),
introduced(definition,[new_symbols(definition,[spl2_2])],[avatar_definition]) ).
tff(f23,plain,
spl2_2,
inference(avatar_split_clause,[],[f10,f20]) ).
tff(f25,definition,
( spl2_3
<=> $less(4,sF1) ),
introduced(definition,[new_symbols(definition,[spl2_3])],[avatar_definition]) ).
tff(f28,plain,
~ spl2_3,
inference(avatar_split_clause,[],[f13,f25]) ).
tff(f30,definition,
( spl2_4
<=> ( f(sF0) = sF1 ) ),
introduced(definition,[new_symbols(definition,[spl2_4])],[avatar_definition]) ).
tff(f32,plain,
( ( f(sF0) = sF1 )
| ~ spl2_4 ),
inference(avatar_component_clause,[],[f30]) ).
tff(f33,plain,
spl2_4,
inference(avatar_split_clause,[],[f12,f30]) ).
tff(f34,plain,
( $less(sF0,sF1)
| ~ spl2_4 ),
inference(superposition,[],[f7,f32]) ).
tff(f36,definition,
( spl2_5
<=> $less(sF0,sF1) ),
introduced(definition,[new_symbols(definition,[spl2_5])],[avatar_definition]) ).
tff(f39,plain,
( spl2_5
| ~ spl2_4 ),
inference(avatar_split_clause,[],[f34,f30,f36]) ).
tff(f40,plain,
$false,
inference(avatar_smt_refutation,[],[f39,f33,f28,f23,f18]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ARI601_1 : TPTP v9.3.1. Released v5.1.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.20 % Computer : n001.cluster.edu
% 0.08/0.20 % Model : x86_64 x86_64
% 0.08/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.20 % Memory : 8046.5625MB
% 0.08/0.20 % OS : Linux 6.8.0-71-generic
% 0.08/0.20 % CPULimit : 300
% 0.08/0.20 % WCLimit : 300
% 0.08/0.20 % DateTime : Mon Sep 28 20:59:04 UTC 2026
% 0.08/0.21 % CPUTime :
% 0.08/0.21 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.24 Running first-order theorem proving
% 0.08/0.24 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
% 4.79/1.52 % (734734)Detected arithmetic, will pick strategies from an ALASCA-aware ARI schedule.
% 4.79/1.52 % (734826)dis+21_64_to=kbo:sil=128000:si=on:sp=weighted_frequency:uwa=alasca_can_abstract:random_seed=1495909182:i=4:rtra=on_2999 on theBenchmark for (2999ds/4Mi)
% 4.79/1.52 % (734826)Instruction limit reached!
% 4.79/1.52 % (734826)------------------------------
% 4.79/1.52 % (734826)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.79/1.52 % (734826)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.79/1.52 % (734826)CaDiCaL version: 2.1.3
% 4.79/1.52 % (734826)Termination reason: Instruction limit
% 4.79/1.52 % (734826)Termination phase: Saturation
% 4.79/1.52 % (734826)Time elapsed: 0.002 s
% 4.79/1.52 % (734826)Peak memory usage: 88 MB
% 4.79/1.52 % (734826)Instructions burned: 4 (million)
% 4.79/1.52 % (734824)dis+10_3_slsqr=1,4:to=lpo:sil=128000:thi=strong:si=on:uwa=off:s2agt=20:slsqc=1:slsq=on:random_seed=2929586255:i=201:slsql=off:asg=cautious:rtra=on:gtg=all:ss=axioms:sgt=16_2999 on theBenchmark for (2999ds/201Mi)
% 4.79/1.52 % (734825)lrs+1002_4:1_to=lpo:sil=64000:si=on:br=off:random_seed=720813555:s2a=on:i=7:rtra=on:inst=on_2999 on theBenchmark for (2999ds/7Mi)
% 4.79/1.52 % (734821)dis+1002_16:1_to=lpo:sil=64000:sas=z3:si=on:norm_ineq=on:gve=force:uwa=one_side_constant:random_seed=81782254:i=12:doe=on:rtra=on:gtg=exists_top:ss=axioms_2999 on theBenchmark for (2999ds/12Mi)
% 4.79/1.52 % (734823)dis+1002_1_to=kbo:sil=128000:tgt=ground:sas=z3:si=on:spb=units:tha=off:random_seed=1068080680:i=307:kws=precedence:nm=0:rtra=on_2999 on theBenchmark for (2999ds/307Mi)
% 4.79/1.52 % (734825)Instruction limit reached!
% 4.79/1.52 % (734825)------------------------------
% 4.79/1.52 % (734825)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.79/1.52 % (734825)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.79/1.52 % (734825)CaDiCaL version: 2.1.3
% 4.79/1.52 % (734825)Termination reason: Instruction limit
% 4.79/1.52 % (734825)Termination phase: Saturation
% 4.79/1.52 % (734825)Time elapsed: 0.005 s
% 4.79/1.52 % (734825)Peak memory usage: 88 MB
% 4.79/1.52 % (734825)Instructions burned: 7 (million)
% 4.79/1.52 % (734828)lrs+10_1_tgt=ground:sas=z3:si=on:random_seed=3213206492:i=33:rtra=on_2999 on theBenchmark for (2999ds/33Mi)
% 4.79/1.52 % (734823)First to succeed.
% 4.79/1.52 % (734823)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-734734"
% 4.79/1.52 % (734821)Refutation not found, incomplete strategy
% 4.79/1.52 % (734821)------------------------------
% 4.79/1.52 % (734821)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.79/1.52 % (734821)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.79/1.52 % (734821)CaDiCaL version: 2.1.3
% 4.79/1.52 % (734821)Termination reason: Refutation not found, incomplete strategy
% 4.79/1.52 % (734821)Time elapsed: 0.035 s
% 4.79/1.52 % (734821)Peak memory usage: 115 MB
% 4.79/1.52 % (734821)Instructions burned: 13 (million)
% 4.79/1.52 % (734827)lrs+10_1_to=lpo:sas=z3:si=on:tha=off:random_seed=2820780469:i=46:rtra=on_2999 on theBenchmark for (2999ds/46Mi)
% 4.79/1.52 % (734828)Also succeeded, but the first one will report.
% 4.79/1.52 % (734827)Refutation not found, incomplete strategy
% 4.79/1.52 % (734827)------------------------------
% 4.79/1.52 % (734827)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.79/1.52 % (734827)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.79/1.52 % (734827)CaDiCaL version: 2.1.3
% 4.79/1.52 % (734827)Termination reason: Refutation not found, incomplete strategy
% 4.79/1.52 % (734827)Time elapsed: 0.033 s
% 4.79/1.52 % (734827)Peak memory usage: 115 MB
% 4.79/1.52 % (734827)Instructions burned: 6 (million)
% 4.79/1.52 % (734853)dis+11_3_anc=none:drc=ordering:si=on:urr=ec_only:bce=on:tha=off:sac=on:random_seed=323843893:st=5:i=14:sd=10:rtra=on:ss=axioms:rawr=on_2998 on theBenchmark for (2998ds/14Mi)
% 4.79/1.52 % (734853)Refutation not found, incomplete strategy
% 4.79/1.52 % (734853)------------------------------
% 4.79/1.52 % (734853)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.79/1.52 % (734853)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.79/1.52 % (734853)CaDiCaL version: 2.1.3
% 4.79/1.52 % (734853)Termination reason: Refutation not found, incomplete strategy
% 4.79/1.52 % (734853)Time elapsed: 0.002 s
% 4.79/1.52 % (734853)Peak memory usage: 88 MB
% 4.79/1.52 % (734870)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=2606072258:i=29:thsqd=64:nm=0:thsqc=8:rtra=on:thsq=on:ev=off_2998 on theBenchmark for (2998ds/29Mi)
% 4.79/1.52 % (734870)Instruction limit reached!
% 4.79/1.52 % (734870)------------------------------
% 4.79/1.52 % (734870)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.79/1.52 % (734870)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.79/1.52 % (734870)CaDiCaL version: 2.1.3
% 4.79/1.52 % (734870)Termination reason: Instruction limit
% 4.79/1.52 % (734870)Termination phase: Saturation
% 4.79/1.52 % (734870)Time elapsed: 0.019 s
% 4.79/1.52 % (734870)Peak memory usage: 88 MB
% 4.79/1.52 % (734870)Instructions burned: 30 (million)
% 4.79/1.52 % (734824)Instruction limit reached!
% 4.79/1.52 % (734824)------------------------------
% 4.79/1.52 % (734824)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.79/1.52 % (734824)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.79/1.52 % (734824)CaDiCaL version: 2.1.3
% 4.79/1.52 % (734824)Termination reason: Instruction limit
% 4.79/1.52 % (734824)Termination phase: Saturation
% 4.79/1.52 % (734824)Time elapsed: 0.243 s
% 4.79/1.52 % (734824)Peak memory usage: 117 MB
% 4.79/1.52 % (734824)Instructions burned: 201 (million)
% 4.79/1.52 % (734823)Refutation found. Thanks to Tanya!
% 4.79/1.52 % SZS status Theorem for theBenchmark
% 4.79/1.52 % SZS output start Proof for theBenchmark
% See solution above
% 4.79/1.52 % (734823)------------------------------
% 4.79/1.52 % (734823)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.79/1.52 % (734823)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.79/1.52 % (734823)CaDiCaL version: 2.1.3
% 4.79/1.52 % (734823)Termination reason: Refutation
% 4.79/1.52 % (734823)Time elapsed: 0.033 s
% 4.79/1.52 % (734823)Peak memory usage: 116 MB
% 4.79/1.52 % (734823)Instructions burned: 9 (million)
% 4.79/1.52 % (734823)------------------------------
% 4.79/1.52 % (734823)------------------------------
% 4.79/1.52 % (734734)Success in time 0.615 s
% 4.79/1.52 % Vampire exiting
%------------------------------------------------------------------------------