%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ARI605_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 : n007.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 09:33:28 AM UTC 2026
% Result : Theorem 0.20s 1.31s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 15
% Syntax : Number of formulae : 40 ( 20 unt; 0 typ; 11 def)
% Number of atoms : 64 ( 15 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 42 ( 18 ~; 10 |; 4 &)
% ( 7 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number arithmetic : 73 ( 28 atm; 23 fun; 5 num; 17 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 : 11 ( 7 usr; 8 prp; 0-2 aty)
% Number of functors : 9 ( 7 usr; 7 con; 0-2 aty)
% Number of variables : 17 ( 14 !; 3 ?; 17 :)
% Comments :
%------------------------------------------------------------------------------
tff(func_def_0,type,
a: $int ).
tff(func_def_1,type,
b: $int ).
tff(func_def_2,type,
f: $int > $int ).
tff(func_def_7,type,
sF0: $int ).
tff(func_def_8,type,
sF1: $int ).
tff(func_def_9,type,
sF2: $int ).
tff(func_def_10,type,
sF3: $int ).
tff(f1,conjecture,
( ! [X0: $int] : $greater(f(X0),X0)
=> ? [X1: $int] :
( $less(X1,$sum(f(a),f(b)))
& $less($sum(a,b),X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fX_gt_X_implies_f_a_b) ).
tff(f2,negated_conjecture,
~ ( ! [X0: $int] : $greater(f(X0),X0)
=> ? [X1: $int] :
( $less(X1,$sum(f(a),f(b)))
& $less($sum(a,b),X1) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
tff(f3,plain,
~ ( ! [X0: $int] : $less(X0,f(X0))
=> ? [X1: $int] :
( $less(X1,$sum(f(a),f(b)))
& $less($sum(a,b),X1) ) ),
inference(theory_normalization,[],[f2]) ).
tff(f4,plain,
! [X0: $int,X1: $int] : ( $sum(X0,X1) = $sum(X1,X0) ),
introduced(definition,[],[tha_commutativity]) ).
tff(f9,plain,
! [X0: $int] : ~ $less(X0,X0),
introduced(definition,[],[tha_non-reflexivity]) ).
tff(f13,plain,
! [X0: $int,X1: $int] :
( $less(X1,$sum(X0,1))
| $less(X0,X1) ),
introduced(definition,[],[tha_order_plus_one_dichotomy]) ).
tff(f16,plain,
( ! [X0: $int] : $less(X0,f(X0))
& ! [X1: $int] :
( ~ $less(X1,$sum(f(a),f(b)))
| ~ $less($sum(a,b),X1) ) ),
inference(ennf_transformation,[],[f3]) ).
tff(f17,plain,
! [X1: $int] :
( ~ $less(X1,$sum(f(a),f(b)))
| ~ $less($sum(a,b),X1) ),
inference(cnf_transformation,[],[f16]) ).
tff(f18,plain,
! [X0: $int] : $less(X0,f(X0)),
inference(cnf_transformation,[],[f16]) ).
tff(f19,definition,
sF0 = f(a),
introduced(definition,[new_symbols(definition,[sF0])],[function_definition]) ).
tff(f20,plain,
f(a) = sF0,
inference(reorient_equations,[],[f19]) ).
tff(f21,definition,
sF1 = f(b),
introduced(definition,[new_symbols(definition,[sF1])],[function_definition]) ).
tff(f22,plain,
f(b) = sF1,
inference(reorient_equations,[],[f21]) ).
tff(f23,definition,
sF2 = $sum(sF0,sF1),
introduced(definition,[new_symbols(definition,[sF2])],[function_definition]) ).
tff(f24,plain,
$sum(sF0,sF1) = sF2,
inference(reorient_equations,[],[f23]) ).
tff(f25,definition,
sF3 = $sum(a,b),
introduced(definition,[new_symbols(definition,[sF3])],[function_definition]) ).
tff(f26,plain,
$sum(a,b) = sF3,
inference(reorient_equations,[],[f25]) ).
tff(f27,plain,
! [X1: $int] :
( ~ $less(sF3,X1)
| ~ $less(X1,sF2) ),
inference(definition_folding,[],[f17,f26,f24,f22,f20]) ).
tff(f29,definition,
( spl4_1
<=> ( $sum(a,b) = sF3 ) ),
introduced(definition,[new_symbols(definition,[spl4_1])],[avatar_definition]) ).
tff(f32,plain,
spl4_1,
inference(avatar_split_clause,[],[f26,f29]) ).
tff(f34,definition,
( spl4_2
<=> ( f(a) = sF0 ) ),
introduced(definition,[new_symbols(definition,[spl4_2])],[avatar_definition]) ).
tff(f36,plain,
( ( f(a) = sF0 )
| ~ spl4_2 ),
inference(avatar_component_clause,[],[f34]) ).
tff(f37,plain,
spl4_2,
inference(avatar_split_clause,[],[f20,f34]) ).
tff(f39,definition,
( spl4_3
<=> ( f(b) = sF1 ) ),
introduced(definition,[new_symbols(definition,[spl4_3])],[avatar_definition]) ).
tff(f41,plain,
( ( f(b) = sF1 )
| ~ spl4_3 ),
inference(avatar_component_clause,[],[f39]) ).
tff(f42,plain,
spl4_3,
inference(avatar_split_clause,[],[f22,f39]) ).
tff(f44,definition,
( spl4_4
<=> ( $sum(sF0,sF1) = sF2 ) ),
introduced(definition,[new_symbols(definition,[spl4_4])],[avatar_definition]) ).
tff(f47,plain,
spl4_4,
inference(avatar_split_clause,[],[f24,f44]) ).
tff(f60,plain,
( $less(a,sF0)
| ~ spl4_2 ),
inference(superposition,[],[f18,f36]) ).
tff(f62,definition,
( spl4_7
<=> $less(a,sF0) ),
introduced(definition,[new_symbols(definition,[spl4_7])],[avatar_definition]) ).
tff(f65,plain,
( spl4_7
| ~ spl4_2 ),
inference(avatar_split_clause,[],[f60,f34,f62]) ).
tff(f66,plain,
( $less(b,sF1)
| ~ spl4_3 ),
inference(superposition,[],[f18,f41]) ).
tff(f68,definition,
( spl4_8
<=> $less(b,sF1) ),
introduced(definition,[new_symbols(definition,[spl4_8])],[avatar_definition]) ).
tff(f71,plain,
( spl4_8
| ~ spl4_3 ),
inference(avatar_split_clause,[],[f66,f39,f68]) ).
tff(f79,plain,
! [X0: $int] : $less(X0,$sum(X0,1)),
inference(resolution,[],[f13,f9]) ).
tff(f199,plain,
~ $less($sum(sF3,1),sF2),
inference(resolution,[],[f79,f27]) ).
tff(f203,plain,
~ $less($sum(1,sF3),sF2),
inference(forward_demodulation,[],[f199,f4]) ).
tff(f205,definition,
( spl4_13
<=> $less($sum(1,sF3),sF2) ),
introduced(definition,[new_symbols(definition,[spl4_13])],[avatar_definition]) ).
tff(f208,plain,
~ spl4_13,
inference(avatar_split_clause,[],[f203,f205]) ).
tff(f209,plain,
$false,
inference(avatar_smt_refutation,[],[f208,f71,f65,f47,f42,f37,f32]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ARI605_1 : TPTP v9.3.1. Released v5.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.19 % Computer : n007.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 20:51:26 UTC 2026
% 0.07/0.19 % CPUTime :
% 0.07/0.20 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.23 Running first-order theorem proving
% 0.07/0.23 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
% 0.20/1.31 % (2808359)Detected arithmetic, will pick strategies from an ALASCA-aware ARI schedule.
% 0.20/1.31 % (2808368)dis+21_64_to=kbo:sil=128000:si=on:sp=weighted_frequency:uwa=alasca_can_abstract:random_seed=4128024768:i=4:rtra=on_2999 on theBenchmark for (2999ds/4Mi)
% 0.20/1.31 % (2808368)Instruction limit reached!
% 0.20/1.31 % (2808368)------------------------------
% 0.20/1.31 % (2808368)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.20/1.31 % (2808368)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/1.31 % (2808368)CaDiCaL version: 2.1.3
% 0.20/1.31 % (2808368)Termination reason: Instruction limit
% 0.20/1.31 % (2808368)Termination phase: Saturation
% 0.20/1.31 % (2808368)Time elapsed: 0.003 s
% 0.20/1.31 % (2808368)Peak memory usage: 88 MB
% 0.20/1.31 % (2808368)Instructions burned: 7 (million)
% 0.20/1.31 % (2808369)lrs+10_1_to=lpo:sas=z3:si=on:tha=off:random_seed=232414470:i=46:rtra=on_2999 on theBenchmark for (2999ds/46Mi)
% 0.20/1.31 % (2808367)lrs+1002_4:1_to=lpo:sil=64000:si=on:br=off:random_seed=3774944952:s2a=on:i=7:rtra=on:inst=on_2999 on theBenchmark for (2999ds/7Mi)
% 0.20/1.31 % (2808365)dis+1002_1_to=kbo:sil=128000:tgt=ground:sas=z3:si=on:spb=units:tha=off:random_seed=3721190615:i=307:kws=precedence:nm=0:rtra=on_2999 on theBenchmark for (2999ds/307Mi)
% 0.20/1.31 % (2808370)lrs+10_1_tgt=ground:sas=z3:si=on:random_seed=3431811731:i=33:rtra=on_2999 on theBenchmark for (2999ds/33Mi)
% 0.20/1.31 % (2808364)dis+1002_16:1_to=lpo:sil=64000:sas=z3:si=on:norm_ineq=on:gve=force:uwa=one_side_constant:random_seed=1193725546:i=12:doe=on:rtra=on:gtg=exists_top:ss=axioms_2999 on theBenchmark for (2999ds/12Mi)
% 0.20/1.31 % (2808366)dis+10_3_slsqr=1,4:to=lpo:sil=128000:thi=strong:si=on:uwa=off:s2agt=20:slsqc=1:slsq=on:random_seed=2778674724:i=201:slsql=off:asg=cautious:rtra=on:gtg=all:ss=axioms:sgt=16_2999 on theBenchmark for (2999ds/201Mi)
% 0.20/1.31 % (2808367)Instruction limit reached!
% 0.20/1.31 % (2808367)------------------------------
% 0.20/1.31 % (2808367)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.20/1.31 % (2808367)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/1.31 % (2808367)CaDiCaL version: 2.1.3
% 0.20/1.31 % (2808367)Termination reason: Instruction limit
% 0.20/1.31 % (2808367)Termination phase: Saturation
% 0.20/1.31 % (2808367)Time elapsed: 0.005 s
% 0.20/1.31 % (2808367)Peak memory usage: 88 MB
% 0.20/1.31 % (2808367)Instructions burned: 7 (million)
% 0.20/1.31 % (2808369)Refutation not found, incomplete strategy
% 0.20/1.31 % (2808369)------------------------------
% 0.20/1.31 % (2808369)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.20/1.31 % (2808369)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/1.31 % (2808369)CaDiCaL version: 2.1.3
% 0.20/1.31 % (2808369)Termination reason: Refutation not found, incomplete strategy
% 0.20/1.31 % (2808369)Time elapsed: 0.027 s
% 0.20/1.31 % (2808369)Peak memory usage: 112 MB
% 0.20/1.31 % (2808369)Instructions burned: 5 (million)
% 0.20/1.31 % (2808364)Refutation not found, incomplete strategy
% 0.20/1.31 % (2808364)------------------------------
% 0.20/1.31 % (2808364)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.20/1.31 % (2808364)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/1.31 % (2808364)CaDiCaL version: 2.1.3
% 0.20/1.31 % (2808364)Termination reason: Refutation not found, incomplete strategy
% 0.20/1.31 % (2808364)Time elapsed: 0.031 s
% 0.20/1.31 % (2808364)Peak memory usage: 116 MB
% 0.20/1.31 % (2808364)Instructions burned: 10 (million)
% 0.20/1.31 % (2808365)Refutation not found, incomplete strategy
% 0.20/1.31 % (2808365)------------------------------
% 0.20/1.31 % (2808365)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.20/1.31 % (2808365)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/1.31 % (2808365)CaDiCaL version: 2.1.3
% 0.20/1.31 % (2808365)Termination reason: Refutation not found, incomplete strategy
% 0.20/1.31 % (2808365)Time elapsed: 0.032 s
% 0.20/1.31 % (2808365)Peak memory usage: 116 MB
% 0.20/1.31 % (2808365)Instructions burned: 10 (million)
% 0.20/1.31 % (2808370)First to succeed.
% 0.20/1.31 % (2808370)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2808359"
% 0.20/1.31 % (2808372)dis+11_3_anc=none:drc=ordering:si=on:urr=ec_only:bce=on:tha=off:sac=on:random_seed=307972484:st=5:i=14:sd=10:rtra=on:ss=axioms:rawr=on_2998 on theBenchmark for (2998ds/14Mi)
% 0.20/1.31 % (2808372)Refutation not found, incomplete strategy
% 0.20/1.31 % (2808372)------------------------------
% 0.20/1.31 % (2808372)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.20/1.31 % (2808372)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/1.31 % (2808372)CaDiCaL version: 2.1.3
% 0.20/1.31 % (2808372)Termination reason: Refutation not found, incomplete strategy
% 0.20/1.31 % (2808372)Time elapsed: 0.0000 s
% 0.20/1.31 % (2808372)Peak memory usage: 88 MB
% 0.20/1.31 % (2808366)Also succeeded, but the first one will report.
% 0.20/1.31 % (2808379)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=1380021370:i=29:thsqd=64:nm=0:thsqc=8:rtra=on:thsq=on:ev=off_2998 on theBenchmark for (2998ds/29Mi)
% 0.20/1.31 % (2808379)Instruction limit reached!
% 0.20/1.31 % (2808379)------------------------------
% 0.20/1.31 % (2808379)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.20/1.31 % (2808379)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/1.31 % (2808379)CaDiCaL version: 2.1.3
% 0.20/1.31 % (2808379)Termination reason: Instruction limit
% 0.20/1.31 % (2808379)Termination phase: Saturation
% 0.20/1.31 % (2808379)Time elapsed: 0.022 s
% 0.20/1.31 % (2808379)Peak memory usage: 88 MB
% 0.20/1.31 % (2808379)Instructions burned: 29 (million)
% 0.20/1.31 % (2808372)------------------------------
% 0.20/1.31 % (2808372)------------------------------
% 0.20/1.31 % (2808369)------------------------------
% 0.20/1.31 % (2808369)------------------------------
% 0.20/1.31 % (2808364)------------------------------
% 0.20/1.31 % (2808364)------------------------------
% 0.20/1.31 % (2808365)------------------------------
% 0.20/1.31 % (2808365)------------------------------
% 0.20/1.31 % (2808370)Refutation found. Thanks to Tanya!
% 0.20/1.31 % SZS status Theorem for theBenchmark
% 0.20/1.31 % SZS output start Proof for theBenchmark
% See solution above
% 0.20/1.31 % (2808370)------------------------------
% 0.20/1.31 % (2808370)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.20/1.31 % (2808370)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/1.31 % (2808370)CaDiCaL version: 2.1.3
% 0.20/1.31 % (2808370)Termination reason: Refutation
% 0.20/1.31 % (2808370)Time elapsed: 0.043 s
% 0.20/1.31 % (2808370)Peak memory usage: 117 MB
% 0.20/1.31 % (2808370)Instructions burned: 23 (million)
% 0.20/1.31 % (2808370)------------------------------
% 0.20/1.31 % (2808370)------------------------------
% 0.20/1.31 % (2808359)Success in time 0.451 s
% 0.20/1.31 % Vampire exiting
%------------------------------------------------------------------------------