%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ARI633_1 : TPTP v9.3.1. Released v6.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n018.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 09:33:32 AM UTC 2026
% Result : Theorem 5.71s 1.84s
% Output : Refutation 5.71s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 16
% Syntax : Number of formulae : 39 ( 28 unt; 0 typ; 12 def)
% Number of atoms : 50 ( 12 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 23 ( 12 ~; 3 |; 0 &)
% ( 8 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 3 ( 2 avg)
% Maximal term depth : 4 ( 1 avg)
% Number arithmetic : 50 ( 18 atm; 20 fun; 9 num; 3 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 ( 8 usr; 9 prp; 0-2 aty)
% Number of functors : 13 ( 9 usr; 10 con; 0-2 aty)
% Number of variables : 3 ( 3 !; 0 ?; 3 :)
% Comments :
%------------------------------------------------------------------------------
tff(func_def_0,type,
u: $real ).
tff(func_def_1,type,
v: $real ).
tff(func_def_2,type,
w: $real ).
tff(func_def_3,type,
x: $real ).
tff(func_def_4,type,
f: $real > $real ).
tff(func_def_9,type,
sF0: $real ).
tff(func_def_10,type,
sF1: $real ).
tff(func_def_11,type,
sF2: $real ).
tff(func_def_12,type,
sF3: $real ).
tff(f1,axiom,
! [X0: $real] : $lesseq(f(X0),1/1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f_less_equal_1) ).
tff(f2,axiom,
$less(u,v),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hypothesis) ).
tff(f3,axiom,
$greater(w,0/1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hypothesis_01) ).
tff(f4,conjecture,
$less($sum(u,$product(w,f(x))),$sum(v,w)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conclusion) ).
tff(f5,negated_conjecture,
~ $less($sum(u,$product(w,f(x))),$sum(v,w)),
inference(negated_conjecture,[status(cth)],[f4]) ).
tff(f6,plain,
$less(0/1,w),
inference(theory_normalization,[],[f3]) ).
tff(f7,plain,
! [X0: $real] : ~ $less(1/1,f(X0)),
inference(theory_normalization,[],[f1]) ).
tff(f8,plain,
~ $less($sum(u,$product(w,f(x))),$sum(v,w)),
inference(flattening,[],[f5]) ).
tff(f9,plain,
~ $less($sum(u,$product(w,f(x))),$sum(v,w)),
inference(cnf_transformation,[],[f8]) ).
tff(f10,plain,
! [X0: $real] : ~ $less(1/1,f(X0)),
inference(cnf_transformation,[],[f7]) ).
tff(f11,plain,
$less(u,v),
inference(cnf_transformation,[],[f2]) ).
tff(f12,plain,
$less(0/1,w),
inference(cnf_transformation,[],[f6]) ).
tff(f13,definition,
sF0 = f(x),
introduced(definition,[new_symbols(definition,[sF0])],[function_definition]) ).
tff(f14,plain,
f(x) = sF0,
inference(reorient_equations,[],[f13]) ).
tff(f15,definition,
sF1 = $product(w,sF0),
introduced(definition,[new_symbols(definition,[sF1])],[function_definition]) ).
tff(f16,definition,
sF2 = $sum(u,sF1),
introduced(definition,[new_symbols(definition,[sF2])],[function_definition]) ).
tff(f17,plain,
$sum(u,sF1) = sF2,
inference(reorient_equations,[],[f16]) ).
tff(f18,definition,
sF3 = $sum(v,w),
introduced(definition,[new_symbols(definition,[sF3])],[function_definition]) ).
tff(f19,plain,
$sum(v,w) = sF3,
inference(reorient_equations,[],[f18]) ).
tff(f20,plain,
~ $less(sF2,sF3),
inference(definition_folding,[],[f9,f19,f17,f15,f14]) ).
tff(f22,definition,
( spl4_1
<=> $less(0/1,w) ),
introduced(definition,[new_symbols(definition,[spl4_1])],[avatar_definition]) ).
tff(f25,plain,
spl4_1,
inference(avatar_split_clause,[],[f12,f22]) ).
tff(f27,definition,
( spl4_2
<=> ( f(x) = sF0 ) ),
introduced(definition,[new_symbols(definition,[spl4_2])],[avatar_definition]) ).
tff(f29,plain,
( ( f(x) = sF0 )
| ~ spl4_2 ),
inference(avatar_component_clause,[],[f27]) ).
tff(f30,plain,
spl4_2,
inference(avatar_split_clause,[],[f14,f27]) ).
tff(f32,definition,
( spl4_3
<=> ( $sum(u,sF1) = sF2 ) ),
introduced(definition,[new_symbols(definition,[spl4_3])],[avatar_definition]) ).
tff(f35,plain,
spl4_3,
inference(avatar_split_clause,[],[f17,f32]) ).
tff(f37,definition,
( spl4_4
<=> ( $sum(v,w) = sF3 ) ),
introduced(definition,[new_symbols(definition,[spl4_4])],[avatar_definition]) ).
tff(f40,plain,
spl4_4,
inference(avatar_split_clause,[],[f19,f37]) ).
tff(f42,definition,
( spl4_5
<=> ( sF1 = $product(w,sF0) ) ),
introduced(definition,[new_symbols(definition,[spl4_5])],[avatar_definition]) ).
tff(f45,plain,
spl4_5,
inference(avatar_split_clause,[],[f15,f42]) ).
tff(f47,definition,
( spl4_6
<=> $less(u,v) ),
introduced(definition,[new_symbols(definition,[spl4_6])],[avatar_definition]) ).
tff(f50,plain,
spl4_6,
inference(avatar_split_clause,[],[f11,f47]) ).
tff(f52,definition,
( spl4_7
<=> $less(sF2,sF3) ),
introduced(definition,[new_symbols(definition,[spl4_7])],[avatar_definition]) ).
tff(f55,plain,
~ spl4_7,
inference(avatar_split_clause,[],[f20,f52]) ).
tff(f56,plain,
( ~ $less(1/1,sF0)
| ~ spl4_2 ),
inference(superposition,[],[f10,f29]) ).
tff(f58,definition,
( spl4_8
<=> $less(1/1,sF0) ),
introduced(definition,[new_symbols(definition,[spl4_8])],[avatar_definition]) ).
tff(f61,plain,
( ~ spl4_8
| ~ spl4_2 ),
inference(avatar_split_clause,[],[f56,f27,f58]) ).
tff(f62,plain,
$false,
inference(avatar_smt_refutation,[],[f61,f55,f50,f45,f40,f35,f30,f25]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : ARI633_1 : TPTP v9.3.1. Released v6.3.0.
% 0.00/0.08 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.27 % Computer : n018.cluster.edu
% 0.10/0.27 % Model : x86_64 x86_64
% 0.10/0.27 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.27 % Memory : 8046.5625MB
% 0.10/0.27 % OS : Linux 6.8.0-71-generic
% 0.10/0.27 % CPULimit : 300
% 0.10/0.27 % WCLimit : 300
% 0.10/0.27 % DateTime : Mon Sep 28 20:56:25 UTC 2026
% 0.26/0.28 % CPUTime :
% 0.26/0.28 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.26/0.32 Running first-order theorem proving
% 0.26/0.32 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 5.71/1.84 % (3771562)Detected arithmetic, will pick strategies from an ALASCA-aware ARI schedule.
% 5.71/1.84 % (3771572)dis+1002_16:1_to=lpo:sil=64000:sas=z3:si=on:norm_ineq=on:gve=force:uwa=one_side_constant:random_seed=1402834725:i=12:doe=on:rtra=on:gtg=exists_top:ss=axioms_2999 on theBenchmark for (2999ds/12Mi)
% 5.71/1.84 % (3771572)Instruction limit reached!
% 5.71/1.84 % (3771572)------------------------------
% 5.71/1.84 % (3771572)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.71/1.84 % (3771572)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.71/1.84 % (3771572)CaDiCaL version: 2.1.3
% 5.71/1.84 % (3771572)Termination reason: Instruction limit
% 5.71/1.84 % (3771572)Termination phase: Saturation
% 5.71/1.84 % (3771572)Time elapsed: 0.027 s
% 5.71/1.84 % (3771572)Peak memory usage: 117 MB
% 5.71/1.84 % (3771572)Instructions burned: 13 (million)
% 5.71/1.84 % (3771577)lrs+10_1_to=lpo:sas=z3:si=on:tha=off:random_seed=225014988:i=46:rtra=on_2999 on theBenchmark for (2999ds/46Mi)
% 5.71/1.84 % (3771573)dis+1002_1_to=kbo:sil=128000:tgt=ground:sas=z3:si=on:spb=units:tha=off:random_seed=671216179:i=307:kws=precedence:nm=0:rtra=on_2999 on theBenchmark for (2999ds/307Mi)
% 5.71/1.84 % (3771574)dis+10_3_slsqr=1,4:to=lpo:sil=128000:thi=strong:si=on:uwa=off:s2agt=20:slsqc=1:slsq=on:random_seed=1352120622:i=201:slsql=off:asg=cautious:rtra=on:gtg=all:ss=axioms:sgt=16_2999 on theBenchmark for (2999ds/201Mi)
% 5.71/1.84 % (3771576)dis+21_64_to=kbo:sil=128000:si=on:sp=weighted_frequency:uwa=alasca_can_abstract:random_seed=2392049378:i=4:rtra=on_2999 on theBenchmark for (2999ds/4Mi)
% 5.71/1.84 % (3771575)lrs+1002_4:1_to=lpo:sil=64000:si=on:br=off:random_seed=916950964:s2a=on:i=7:rtra=on:inst=on_2999 on theBenchmark for (2999ds/7Mi)
% 5.71/1.84 % (3771576)Instruction limit reached!
% 5.71/1.84 % (3771576)------------------------------
% 5.71/1.84 % (3771576)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.71/1.84 % (3771576)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.71/1.84 % (3771576)CaDiCaL version: 2.1.3
% 5.71/1.84 % (3771576)Termination reason: Instruction limit
% 5.71/1.84 % (3771576)Termination phase: Saturation
% 5.71/1.84 % (3771576)Time elapsed: 0.005 s
% 5.71/1.84 % (3771576)Peak memory usage: 88 MB
% 5.71/1.84 % (3771576)Instructions burned: 4 (million)
% 5.71/1.84 % (3771577)Refutation not found, incomplete strategy
% 5.71/1.84 % (3771577)------------------------------
% 5.71/1.84 % (3771577)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.71/1.84 % (3771577)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.71/1.84 % (3771577)CaDiCaL version: 2.1.3
% 5.71/1.84 % (3771577)Termination reason: Refutation not found, incomplete strategy
% 5.71/1.84 % (3771577)Time elapsed: 0.043 s
% 5.71/1.84 % (3771577)Peak memory usage: 116 MB
% 5.71/1.84 % (3771577)Instructions burned: 7 (million)
% 5.71/1.84 % (3771575)Instruction limit reached!
% 5.71/1.84 % (3771575)------------------------------
% 5.71/1.84 % (3771575)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.71/1.84 % (3771575)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.71/1.84 % (3771575)CaDiCaL version: 2.1.3
% 5.71/1.84 % (3771575)Termination reason: Instruction limit
% 5.71/1.84 % (3771575)Termination phase: Saturation
% 5.71/1.84 % (3771575)Time elapsed: 0.008 s
% 5.71/1.84 % (3771575)Peak memory usage: 88 MB
% 5.71/1.84 % (3771575)Instructions burned: 7 (million)
% 5.71/1.84 % (3771573)First to succeed.
% 5.71/1.84 % (3771573)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3771562"
% 5.71/1.84 % (3771578)lrs+10_1_tgt=ground:sas=z3:si=on:random_seed=32083261:i=33:rtra=on_2999 on theBenchmark for (2999ds/33Mi)
% 5.71/1.84 % (3771578)Also succeeded, but the first one will report.
% 5.71/1.84 % (3771581)dis+11_3_anc=none:drc=ordering:si=on:urr=ec_only:bce=on:tha=off:sac=on:random_seed=593607561:st=5:i=14:sd=10:rtra=on:ss=axioms:rawr=on_2997 on theBenchmark for (2997ds/14Mi)
% 5.71/1.84 % (3771581)Refutation not found, incomplete strategy
% 5.71/1.84 % (3771581)------------------------------
% 5.71/1.84 % (3771581)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.71/1.84 % (3771581)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.71/1.84 % (3771581)CaDiCaL version: 2.1.3
% 5.71/1.84 % (3771581)Termination reason: Refutation not found, incomplete strategy
% 5.71/1.84 % (3771581)Time elapsed: 0.001 s
% 5.71/1.84 % (3771581)Peak memory usage: 88 MB
% 5.71/1.84 % (3771574)Instruction limit reached!
% 5.71/1.84 % (3771574)------------------------------
% 5.71/1.84 % (3771574)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.71/1.84 % (3771574)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.71/1.84 % (3771574)CaDiCaL version: 2.1.3
% 5.71/1.84 % (3771574)Termination reason: Instruction limit
% 5.71/1.84 % (3771574)Termination phase: Saturation
% 5.71/1.84 % (3771574)Time elapsed: 0.270 s
% 5.71/1.84 % (3771574)Peak memory usage: 117 MB
% 5.71/1.84 % (3771574)Instructions burned: 202 (million)
% 5.71/1.84 % (3771587)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=98399582:i=29:thsqd=64:nm=0:thsqc=8:rtra=on:thsq=on:ev=off_2997 on theBenchmark for (2997ds/29Mi)
% 5.71/1.84 % (3771588)ott+21_1024_to=lakbo:sil=128000:bsd=on:si=on:alasca=on:uwa=alasca_main:nwc=0.5:random_seed=4026607113:cond=on:i=16:fgj=on:ep=RS:asg=force:nm=10:rtra=on:rawr=on_2997 on theBenchmark for (2997ds/16Mi)
% 5.71/1.84 % (3771588)Instruction limit reached!
% 5.71/1.84 % (3771588)------------------------------
% 5.71/1.84 % (3771588)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.71/1.84 % (3771588)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.71/1.84 % (3771588)CaDiCaL version: 2.1.3
% 5.71/1.84 % (3771588)Termination reason: Instruction limit
% 5.71/1.84 % (3771588)Termination phase: Saturation
% 5.71/1.84 % (3771588)Time elapsed: 0.015 s
% 5.71/1.84 % (3771588)Peak memory usage: 90 MB
% 5.71/1.84 % (3771588)Instructions burned: 16 (million)
% 5.71/1.84 % (3771587)Instruction limit reached!
% 5.71/1.84 % (3771587)------------------------------
% 5.71/1.84 % (3771587)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.71/1.84 % (3771587)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.71/1.84 % (3771587)CaDiCaL version: 2.1.3
% 5.71/1.84 % (3771587)Termination reason: Instruction limit
% 5.71/1.84 % (3771587)Termination phase: Saturation
% 5.71/1.84 % (3771587)Time elapsed: 0.032 s
% 5.71/1.84 % (3771587)Peak memory usage: 88 MB
% 5.71/1.84 % (3771587)Instructions burned: 29 (million)
% 5.71/1.84 % (3771581)------------------------------
% 5.71/1.84 % (3771581)------------------------------
% 5.71/1.84 % (3771573)Refutation found. Thanks to Tanya!
% 5.71/1.84 % SZS status Theorem for theBenchmark
% 5.71/1.84 % SZS output start Proof for theBenchmark
% See solution above
% 5.71/1.84 % (3771573)------------------------------
% 5.71/1.84 % (3771573)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.71/1.84 % (3771573)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.71/1.84 % (3771573)CaDiCaL version: 2.1.3
% 5.71/1.84 % (3771573)Termination reason: Refutation
% 5.71/1.84 % (3771573)Time elapsed: 0.050 s
% 5.71/1.84 % (3771573)Peak memory usage: 117 MB
% 5.71/1.84 % (3771573)Instructions burned: 12 (million)
% 5.71/1.84 % (3771573)------------------------------
% 5.71/1.84 % (3771573)------------------------------
% 5.71/1.84 % (3771562)Success in time 0.677 s
% 5.71/1.84 % Vampire exiting
%------------------------------------------------------------------------------