%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ARI607_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 : n015.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 5.49s 1.41s
% Output : Refutation 5.49s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 16
% Syntax : Number of formulae : 48 ( 21 unt; 0 typ; 15 def)
% Number of atoms : 90 ( 21 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 76 ( 34 ~; 25 |; 2 &)
% ( 9 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number arithmetic : 109 ( 32 atm; 17 fun; 46 num; 14 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 : 13 ( 9 usr; 10 prp; 0-2 aty)
% Number of functors : 12 ( 7 usr; 10 con; 0-2 aty)
% Number of variables : 14 ( 14 !; 0 ?; 14 :)
% Comments :
%------------------------------------------------------------------------------
tff(func_def_0,type,
f: $int > $int ).
tff(func_def_9,type,
sF0: $int ).
tff(func_def_10,type,
sF1: $int ).
tff(func_def_11,type,
sF2: $int ).
tff(func_def_12,type,
sF3: $int ).
tff(func_def_13,type,
sF4: $int ).
tff(func_def_14,type,
sF5: $int ).
tff(f1,conjecture,
( ! [X0: $int,X1: $int] :
( $lesseq(X0,X1)
=> $lesseq(f(X0),f(X1)) )
=> $lesseq($sum(f(2),f(5)),$sum(f(7),f(3))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f_mon_implies_f2plusf5_gt_f7plusf3) ).
tff(f2,negated_conjecture,
~ ( ! [X0: $int,X1: $int] :
( $lesseq(X0,X1)
=> $lesseq(f(X0),f(X1)) )
=> $lesseq($sum(f(2),f(5)),$sum(f(7),f(3))) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
tff(f3,plain,
~ ( ! [X0: $int,X1: $int] :
( ~ $less(X1,X0)
=> ~ $less(f(X1),f(X0)) )
=> ~ $less($sum(f(7),f(3)),$sum(f(2),f(5))) ),
inference(theory_normalization,[],[f2]) ).
tff(f16,plain,
( $less($sum(f(7),f(3)),$sum(f(2),f(5)))
& ! [X1: $int,X0: $int] :
( $less(X1,X0)
| ~ $less(f(X1),f(X0)) ) ),
inference(ennf_transformation,[],[f3]) ).
tff(f17,plain,
( $less($sum(f(7),f(3)),$sum(f(2),f(5)))
& ! [X0: $int,X1: $int] :
( $less(X0,X1)
| ~ $less(f(X0),f(X1)) ) ),
inference(rectify,[],[f16]) ).
tff(f18,plain,
! [X0: $int,X1: $int] :
( ~ $less(f(X0),f(X1))
| $less(X0,X1) ),
inference(cnf_transformation,[],[f17]) ).
tff(f19,plain,
$less($sum(f(7),f(3)),$sum(f(2),f(5))),
inference(cnf_transformation,[],[f17]) ).
tff(f20,definition,
sF0 = f(7),
introduced(definition,[new_symbols(definition,[sF0])],[function_definition]) ).
tff(f21,plain,
f(7) = sF0,
inference(reorient_equations,[],[f20]) ).
tff(f22,definition,
sF1 = f(3),
introduced(definition,[new_symbols(definition,[sF1])],[function_definition]) ).
tff(f23,plain,
f(3) = sF1,
inference(reorient_equations,[],[f22]) ).
tff(f24,definition,
sF2 = $sum(sF0,sF1),
introduced(definition,[new_symbols(definition,[sF2])],[function_definition]) ).
tff(f25,plain,
$sum(sF0,sF1) = sF2,
inference(reorient_equations,[],[f24]) ).
tff(f26,definition,
sF3 = f(2),
introduced(definition,[new_symbols(definition,[sF3])],[function_definition]) ).
tff(f27,plain,
f(2) = sF3,
inference(reorient_equations,[],[f26]) ).
tff(f28,definition,
sF4 = f(5),
introduced(definition,[new_symbols(definition,[sF4])],[function_definition]) ).
tff(f29,plain,
f(5) = sF4,
inference(reorient_equations,[],[f28]) ).
tff(f30,definition,
sF5 = $sum(sF3,sF4),
introduced(definition,[new_symbols(definition,[sF5])],[function_definition]) ).
tff(f31,plain,
$less(sF2,sF5),
inference(definition_folding,[],[f19,f30,f29,f27,f25,f23,f21]) ).
tff(f33,definition,
( spl6_1
<=> ( f(7) = sF0 ) ),
introduced(definition,[new_symbols(definition,[spl6_1])],[avatar_definition]) ).
tff(f35,plain,
( ( f(7) = sF0 )
| ~ spl6_1 ),
inference(avatar_component_clause,[],[f33]) ).
tff(f36,plain,
spl6_1,
inference(avatar_split_clause,[],[f21,f33]) ).
tff(f38,definition,
( spl6_2
<=> ( sF5 = $sum(sF3,sF4) ) ),
introduced(definition,[new_symbols(definition,[spl6_2])],[avatar_definition]) ).
tff(f41,plain,
spl6_2,
inference(avatar_split_clause,[],[f30,f38]) ).
tff(f43,definition,
( spl6_3
<=> ( f(3) = sF1 ) ),
introduced(definition,[new_symbols(definition,[spl6_3])],[avatar_definition]) ).
tff(f45,plain,
( ( f(3) = sF1 )
| ~ spl6_3 ),
inference(avatar_component_clause,[],[f43]) ).
tff(f46,plain,
spl6_3,
inference(avatar_split_clause,[],[f23,f43]) ).
tff(f48,definition,
( spl6_4
<=> ( $sum(sF0,sF1) = sF2 ) ),
introduced(definition,[new_symbols(definition,[spl6_4])],[avatar_definition]) ).
tff(f51,plain,
spl6_4,
inference(avatar_split_clause,[],[f25,f48]) ).
tff(f53,definition,
( spl6_5
<=> ( f(5) = sF4 ) ),
introduced(definition,[new_symbols(definition,[spl6_5])],[avatar_definition]) ).
tff(f55,plain,
( ( f(5) = sF4 )
| ~ spl6_5 ),
inference(avatar_component_clause,[],[f53]) ).
tff(f56,plain,
spl6_5,
inference(avatar_split_clause,[],[f29,f53]) ).
tff(f58,definition,
( spl6_6
<=> ( f(2) = sF3 ) ),
introduced(definition,[new_symbols(definition,[spl6_6])],[avatar_definition]) ).
tff(f60,plain,
( ( f(2) = sF3 )
| ~ spl6_6 ),
inference(avatar_component_clause,[],[f58]) ).
tff(f61,plain,
spl6_6,
inference(avatar_split_clause,[],[f27,f58]) ).
tff(f63,definition,
( spl6_7
<=> $less(sF2,sF5) ),
introduced(definition,[new_symbols(definition,[spl6_7])],[avatar_definition]) ).
tff(f66,plain,
spl6_7,
inference(avatar_split_clause,[],[f31,f63]) ).
tff(f74,plain,
( ! [X0: $int] :
( ~ $less(sF0,f(X0))
| $less(7,X0) )
| ~ spl6_1 ),
inference(superposition,[],[f18,f35]) ).
tff(f79,plain,
( ! [X0: $int] :
( ~ $less(sF1,f(X0))
| $less(3,X0) )
| ~ spl6_3 ),
inference(superposition,[],[f18,f45]) ).
tff(f89,plain,
( $less(7,5)
| ~ $less(sF0,sF4)
| ~ spl6_1
| ~ spl6_5 ),
inference(superposition,[],[f74,f55]) ).
tff(f93,plain,
( ~ $less(sF0,sF4)
| ~ spl6_1
| ~ spl6_5 ),
inference(evaluation,[],[f89]) ).
tff(f95,definition,
( spl6_10
<=> $less(sF0,sF4) ),
introduced(definition,[new_symbols(definition,[spl6_10])],[avatar_definition]) ).
tff(f98,plain,
( ~ spl6_10
| ~ spl6_1
| ~ spl6_5 ),
inference(avatar_split_clause,[],[f93,f53,f33,f95]) ).
tff(f121,plain,
( ~ $less(sF1,sF3)
| $less(3,2)
| ~ spl6_3
| ~ spl6_6 ),
inference(superposition,[],[f79,f60]) ).
tff(f126,plain,
( ~ $less(sF1,sF3)
| ~ spl6_3
| ~ spl6_6 ),
inference(evaluation,[],[f121]) ).
tff(f128,definition,
( spl6_13
<=> $less(sF1,sF3) ),
introduced(definition,[new_symbols(definition,[spl6_13])],[avatar_definition]) ).
tff(f131,plain,
( ~ spl6_13
| ~ spl6_3
| ~ spl6_6 ),
inference(avatar_split_clause,[],[f126,f58,f43,f128]) ).
tff(f132,plain,
$false,
inference(avatar_smt_refutation,[],[f131,f98,f66,f61,f56,f51,f46,f41,f36]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ARI607_1 : TPTP v9.3.1. Released v5.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.18 % Computer : n015.cluster.edu
% 0.09/0.18 % Model : x86_64 x86_64
% 0.09/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.18 % Memory : 8046.5625MB
% 0.09/0.18 % OS : Linux 6.8.0-71-generic
% 0.09/0.18 % CPULimit : 300
% 0.09/0.18 % WCLimit : 300
% 0.09/0.18 % DateTime : Mon Sep 28 20:56:47 UTC 2026
% 0.09/0.18 % CPUTime :
% 0.09/0.18 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.21 Running first-order theorem proving
% 0.09/0.21 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
% 4.23/1.17 % (3008397)Detected arithmetic, will pick strategies from an ALASCA-aware ARI schedule.
% 4.23/1.17 % (3008472)lrs+10_1_to=lpo:sas=z3:si=on:tha=off:random_seed=3796284095:i=46:rtra=on_3000 on theBenchmark for (3000ds/46Mi)
% 4.23/1.17 % (3008468)dis+1002_1_to=kbo:sil=128000:tgt=ground:sas=z3:si=on:spb=units:tha=off:random_seed=555350901:i=307:kws=precedence:nm=0:rtra=on_3000 on theBenchmark for (3000ds/307Mi)
% 4.23/1.17 % (3008471)dis+21_64_to=kbo:sil=128000:si=on:sp=weighted_frequency:uwa=alasca_can_abstract:random_seed=375911624:i=4:rtra=on_3000 on theBenchmark for (3000ds/4Mi)
% 4.23/1.17 % (3008471)Instruction limit reached!
% 4.23/1.17 % (3008471)------------------------------
% 4.23/1.17 % (3008471)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.23/1.17 % (3008471)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.23/1.17 % (3008471)CaDiCaL version: 2.1.3
% 4.23/1.17 % (3008471)Termination reason: Instruction limit
% 4.23/1.17 % (3008471)Termination phase: Saturation
% 4.23/1.17 % (3008471)Time elapsed: 0.005 s
% 4.23/1.17 % (3008471)Peak memory usage: 88 MB
% 4.23/1.18 % (3008471)Instructions burned: 4 (million)
% 4.23/1.18 % (3008470)lrs+1002_4:1_to=lpo:sil=64000:si=on:br=off:random_seed=1976784454:s2a=on:i=7:rtra=on:inst=on_3000 on theBenchmark for (3000ds/7Mi)
% 4.23/1.18 % (3008469)dis+10_3_slsqr=1,4:to=lpo:sil=128000:thi=strong:si=on:uwa=off:s2agt=20:slsqc=1:slsq=on:random_seed=787381598:i=201:slsql=off:asg=cautious:rtra=on:gtg=all:ss=axioms:sgt=16_3000 on theBenchmark for (3000ds/201Mi)
% 4.23/1.18 % (3008473)lrs+10_1_tgt=ground:sas=z3:si=on:random_seed=1276898872:i=33:rtra=on_3000 on theBenchmark for (3000ds/33Mi)
% 4.23/1.18 % (3008467)dis+1002_16:1_to=lpo:sil=64000:sas=z3:si=on:norm_ineq=on:gve=force:uwa=one_side_constant:random_seed=3476704156:i=12:doe=on:rtra=on:gtg=exists_top:ss=axioms_3000 on theBenchmark for (3000ds/12Mi)
% 4.23/1.18 % (3008472)Refutation not found, incomplete strategy
% 4.23/1.18 % (3008472)------------------------------
% 4.23/1.18 % (3008472)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.23/1.18 % (3008472)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.23/1.18 % (3008472)CaDiCaL version: 2.1.3
% 4.23/1.18 % (3008472)Termination reason: Refutation not found, incomplete strategy
% 4.23/1.18 % (3008472)Time elapsed: 0.026 s
% 4.23/1.18 % (3008472)Peak memory usage: 115 MB
% 4.23/1.18 % (3008472)Instructions burned: 6 (million)
% 4.23/1.18 % (3008470)Instruction limit reached!
% 4.23/1.18 % (3008470)------------------------------
% 4.23/1.18 % (3008470)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.23/1.18 % (3008470)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.23/1.18 % (3008470)CaDiCaL version: 2.1.3
% 4.23/1.18 % (3008470)Termination reason: Instruction limit
% 4.23/1.18 % (3008470)Termination phase: Saturation
% 4.23/1.18 % (3008470)Time elapsed: 0.009 s
% 4.23/1.18 % (3008470)Peak memory usage: 88 MB
% 4.23/1.18 % (3008470)Instructions burned: 8 (million)
% 4.23/1.18 % (3008468)Refutation not found, incomplete strategy
% 4.23/1.18 % (3008468)------------------------------
% 4.23/1.18 % (3008468)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.23/1.18 % (3008468)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.23/1.18 % (3008468)CaDiCaL version: 2.1.3
% 4.23/1.18 % (3008468)Termination reason: Refutation not found, incomplete strategy
% 4.23/1.18 % (3008468)Time elapsed: 0.046 s
% 4.23/1.18 % (3008468)Peak memory usage: 116 MB
% 4.23/1.18 % (3008468)Instructions burned: 10 (million)
% 4.23/1.18 % (3008467)Refutation not found, incomplete strategy
% 4.23/1.18 % (3008467)------------------------------
% 4.23/1.18 % (3008467)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.23/1.18 % (3008467)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.23/1.18 % (3008467)CaDiCaL version: 2.1.3
% 4.23/1.18 % (3008467)Termination reason: Refutation not found, incomplete strategy
% 4.23/1.18 % (3008467)Time elapsed: 0.047 s
% 4.23/1.18 % (3008467)Peak memory usage: 116 MB
% 4.23/1.18 % (3008467)Instructions burned: 11 (million)
% 4.23/1.18 % (3008473)First to succeed.
% 4.23/1.18 % (3008473)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3008397"
% 4.23/1.18 % (3008472)------------------------------
% 4.23/1.18 % (3008472)------------------------------
% 4.23/1.18 % (3008469)Instruction limit reached!
% 4.23/1.18 % (3008469)------------------------------
% 5.49/1.41 % (3008469)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.49/1.41 % (3008469)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.49/1.41 % (3008469)CaDiCaL version: 2.1.3
% 5.49/1.41 % (3008469)Termination reason: Instruction limit
% 5.49/1.41 % (3008469)Termination phase: Saturation
% 5.49/1.41 % (3008469)Time elapsed: 0.263 s
% 5.49/1.41 % (3008469)Peak memory usage: 117 MB
% 5.49/1.41 % (3008469)Instructions burned: 201 (million)
% 5.49/1.41 % (3008496)dis+11_3_anc=none:drc=ordering:si=on:urr=ec_only:bce=on:tha=off:sac=on:random_seed=2526288504:st=5:i=14:sd=10:rtra=on:ss=axioms:rawr=on_2997 on theBenchmark for (2997ds/14Mi)
% 5.49/1.41 % (3008496)Refutation not found, incomplete strategy
% 5.49/1.41 % (3008496)------------------------------
% 5.49/1.41 % (3008496)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.49/1.41 % (3008496)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.49/1.41 % (3008496)CaDiCaL version: 2.1.3
% 5.49/1.41 % (3008496)Termination reason: Refutation not found, incomplete strategy
% 5.49/1.41 % (3008496)Time elapsed: 0.002 s
% 5.49/1.41 % (3008496)Peak memory usage: 88 MB
% 5.49/1.41 % (3008498)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=1680272706:i=29:thsqd=64:nm=0:thsqc=8:rtra=on:thsq=on:ev=off_2997 on theBenchmark for (2997ds/29Mi)
% 5.49/1.41 % (3008498)Instruction limit reached!
% 5.49/1.41 % (3008498)------------------------------
% 5.49/1.41 % (3008498)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.49/1.41 % (3008498)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.49/1.41 % (3008498)CaDiCaL version: 2.1.3
% 5.49/1.41 % (3008498)Termination reason: Instruction limit
% 5.49/1.41 % (3008498)Termination phase: Saturation
% 5.49/1.41 % (3008498)Time elapsed: 0.033 s
% 5.49/1.41 % (3008498)Peak memory usage: 88 MB
% 5.49/1.41 % (3008498)Instructions burned: 29 (million)
% 5.49/1.41 % (3008507)ott+21_1024_to=lakbo:sil=128000:bsd=on:si=on:alasca=on:uwa=alasca_main:nwc=0.5:random_seed=2656843055:cond=on:i=16:fgj=on:ep=RS:asg=force:nm=10:rtra=on:rawr=on_2995 on theBenchmark for (2995ds/16Mi)
% 5.49/1.41 % (3008507)Instruction limit reached!
% 5.49/1.41 % (3008507)------------------------------
% 5.49/1.41 % (3008507)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.49/1.41 % (3008507)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.49/1.41 % (3008507)CaDiCaL version: 2.1.3
% 5.49/1.41 % (3008507)Termination reason: Instruction limit
% 5.49/1.41 % (3008507)Termination phase: Saturation
% 5.49/1.41 % (3008507)Time elapsed: 0.010 s
% 5.49/1.41 % (3008507)Peak memory usage: 90 MB
% 5.49/1.41 % (3008507)Instructions burned: 18 (million)
% 5.49/1.41 % (3008468)------------------------------
% 5.49/1.41 % (3008468)------------------------------
% 5.49/1.41 % (3008467)------------------------------
% 5.49/1.41 % (3008467)------------------------------
% 5.49/1.41 % (3008473)Refutation found. Thanks to Tanya!
% 5.49/1.41 % SZS status Theorem for theBenchmark
% 5.49/1.41 % SZS output start Proof for theBenchmark
% See solution above
% 5.49/1.41 % (3008473)------------------------------
% 5.49/1.41 % (3008473)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.49/1.41 % (3008473)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.49/1.41 % (3008473)CaDiCaL version: 2.1.3
% 5.49/1.41 % (3008473)Termination reason: Refutation
% 5.49/1.41 % (3008473)Time elapsed: 0.058 s
% 5.49/1.41 % (3008473)Peak memory usage: 116 MB
% 5.49/1.41 % (3008473)Instructions burned: 19 (million)
% 5.49/1.41 % (3008473)------------------------------
% 5.49/1.41 % (3008473)------------------------------
% 5.49/1.41 % (3008397)Success in time 0.709 s
% 5.49/1.41 % Vampire exiting
%------------------------------------------------------------------------------