%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ARI632_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 : n012.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 2.47s 0.74s
% Output : Refutation 2.47s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 16
% Syntax : Number of formulae : 44 ( 25 unt; 0 typ; 12 def)
% Number of atoms : 70 ( 13 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 52 ( 26 ~; 16 |; 0 &)
% ( 8 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number arithmetic : 50 ( 28 atm; 13 fun; 0 num; 9 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 : 10 ( 9 usr; 8 con; 0-2 aty)
% Number of variables : 9 ( 9 !; 0 ?; 9 :)
% Comments :
%------------------------------------------------------------------------------
tff(func_def_0,type,
x: $real ).
tff(func_def_1,type,
y: $real ).
tff(func_def_2,type,
u: $real ).
tff(func_def_3,type,
v: $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,X1: $real] :
( $greatereq(X0,X1)
=> $greatereq(f(X0),f(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f_non_decreasing) ).
tff(f2,axiom,
$less(u,v),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hypothesis) ).
tff(f3,axiom,
$lesseq(x,y),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hypothesis_01) ).
tff(f4,conjecture,
$less($sum(u,f(x)),$sum(v,f(y))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conclusion) ).
tff(f5,negated_conjecture,
~ $less($sum(u,f(x)),$sum(v,f(y))),
inference(negated_conjecture,[status(cth)],[f4]) ).
tff(f6,plain,
! [X0: $real,X1: $real] :
( ~ $less(X0,X1)
=> ~ $less(f(X0),f(X1)) ),
inference(theory_normalization,[],[f1]) ).
tff(f7,plain,
~ $less(y,x),
inference(theory_normalization,[],[f3]) ).
tff(f19,plain,
~ $less($sum(u,f(x)),$sum(v,f(y))),
inference(flattening,[],[f5]) ).
tff(f20,plain,
! [X0: $real,X1: $real] :
( $less(X0,X1)
| ~ $less(f(X0),f(X1)) ),
inference(ennf_transformation,[],[f6]) ).
tff(f21,plain,
~ $less(y,x),
inference(cnf_transformation,[],[f7]) ).
tff(f22,plain,
$less(u,v),
inference(cnf_transformation,[],[f2]) ).
tff(f23,plain,
! [X0: $real,X1: $real] :
( ~ $less(f(X0),f(X1))
| $less(X0,X1) ),
inference(cnf_transformation,[],[f20]) ).
tff(f24,plain,
~ $less($sum(u,f(x)),$sum(v,f(y))),
inference(cnf_transformation,[],[f19]) ).
tff(f25,definition,
sF0 = f(x),
introduced(definition,[new_symbols(definition,[sF0])],[function_definition]) ).
tff(f26,plain,
f(x) = sF0,
inference(reorient_equations,[],[f25]) ).
tff(f27,definition,
sF1 = $sum(u,sF0),
introduced(definition,[new_symbols(definition,[sF1])],[function_definition]) ).
tff(f28,plain,
$sum(u,sF0) = sF1,
inference(reorient_equations,[],[f27]) ).
tff(f29,definition,
sF2 = f(y),
introduced(definition,[new_symbols(definition,[sF2])],[function_definition]) ).
tff(f30,plain,
f(y) = sF2,
inference(reorient_equations,[],[f29]) ).
tff(f31,definition,
sF3 = $sum(v,sF2),
introduced(definition,[new_symbols(definition,[sF3])],[function_definition]) ).
tff(f32,plain,
~ $less(sF1,sF3),
inference(definition_folding,[],[f24,f31,f30,f28,f26]) ).
tff(f34,definition,
( spl4_1
<=> ( f(y) = sF2 ) ),
introduced(definition,[new_symbols(definition,[spl4_1])],[avatar_definition]) ).
tff(f36,plain,
( ( f(y) = sF2 )
| ~ spl4_1 ),
inference(avatar_component_clause,[],[f34]) ).
tff(f37,plain,
spl4_1,
inference(avatar_split_clause,[],[f30,f34]) ).
tff(f39,definition,
( spl4_2
<=> $less(u,v) ),
introduced(definition,[new_symbols(definition,[spl4_2])],[avatar_definition]) ).
tff(f42,plain,
spl4_2,
inference(avatar_split_clause,[],[f22,f39]) ).
tff(f44,definition,
( spl4_3
<=> ( $sum(u,sF0) = sF1 ) ),
introduced(definition,[new_symbols(definition,[spl4_3])],[avatar_definition]) ).
tff(f47,plain,
spl4_3,
inference(avatar_split_clause,[],[f28,f44]) ).
tff(f49,definition,
( spl4_4
<=> $less(sF1,sF3) ),
introduced(definition,[new_symbols(definition,[spl4_4])],[avatar_definition]) ).
tff(f52,plain,
~ spl4_4,
inference(avatar_split_clause,[],[f32,f49]) ).
tff(f54,definition,
( spl4_5
<=> ( sF3 = $sum(v,sF2) ) ),
introduced(definition,[new_symbols(definition,[spl4_5])],[avatar_definition]) ).
tff(f57,plain,
spl4_5,
inference(avatar_split_clause,[],[f31,f54]) ).
tff(f59,definition,
( spl4_6
<=> $less(y,x) ),
introduced(definition,[new_symbols(definition,[spl4_6])],[avatar_definition]) ).
tff(f61,plain,
( ~ $less(y,x)
| spl4_6 ),
inference(avatar_component_clause,[],[f59]) ).
tff(f62,plain,
~ spl4_6,
inference(avatar_split_clause,[],[f21,f59]) ).
tff(f64,definition,
( spl4_7
<=> ( f(x) = sF0 ) ),
introduced(definition,[new_symbols(definition,[spl4_7])],[avatar_definition]) ).
tff(f66,plain,
( ( f(x) = sF0 )
| ~ spl4_7 ),
inference(avatar_component_clause,[],[f64]) ).
tff(f67,plain,
spl4_7,
inference(avatar_split_clause,[],[f26,f64]) ).
tff(f83,plain,
( ! [X0: $real] :
( ~ $less(sF2,f(X0))
| $less(y,X0) )
| ~ spl4_1 ),
inference(superposition,[],[f23,f36]) ).
tff(f117,plain,
( ~ $less(sF2,sF0)
| $less(y,x)
| ~ spl4_1
| ~ spl4_7 ),
inference(superposition,[],[f83,f66]) ).
tff(f118,plain,
( ~ $less(sF2,sF0)
| ~ spl4_1
| spl4_6
| ~ spl4_7 ),
inference(forward_subsumption_resolution,[],[f117,f61]) ).
tff(f120,definition,
( spl4_9
<=> $less(sF2,sF0) ),
introduced(definition,[new_symbols(definition,[spl4_9])],[avatar_definition]) ).
tff(f123,plain,
( ~ spl4_9
| ~ spl4_1
| spl4_6
| ~ spl4_7 ),
inference(avatar_split_clause,[],[f118,f64,f59,f34,f120]) ).
tff(f124,plain,
$false,
inference(avatar_smt_refutation,[],[f123,f67,f62,f57,f52,f47,f42,f37]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : ARI632_1 : TPTP v9.3.1. Released v6.3.0.
% 0.00/0.03 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.00/0.10 % Computer : n012.cluster.edu
% 0.00/0.10 % Model : x86_64 x86_64
% 0.00/0.10 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.00/0.10 % Memory : 8046.5625MB
% 0.00/0.10 % OS : Linux 6.8.0-71-generic
% 0.00/0.10 % CPULimit : 300
% 0.00/0.10 % WCLimit : 300
% 0.00/0.10 % DateTime : Mon Sep 28 20:53:49 UTC 2026
% 0.00/0.10 % CPUTime :
% 0.00/0.10 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.12 Running first-order theorem proving
% 0.08/0.12 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
% 1.98/0.64 % (3752179)Detected arithmetic, will pick strategies from an ALASCA-aware ARI schedule.
% 1.98/0.64 % (3752186)dis+10_3_slsqr=1,4:to=lpo:sil=128000:thi=strong:si=on:uwa=off:s2agt=20:slsqc=1:slsq=on:random_seed=2603176270:i=201:slsql=off:asg=cautious:rtra=on:gtg=all:ss=axioms:sgt=16_2999 on theBenchmark for (2999ds/201Mi)
% 1.98/0.64 % (3752189)lrs+10_1_to=lpo:sas=z3:si=on:tha=off:random_seed=2575034983:i=46:rtra=on_2999 on theBenchmark for (2999ds/46Mi)
% 1.98/0.64 % (3752190)lrs+10_1_tgt=ground:sas=z3:si=on:random_seed=1070796888:i=33:rtra=on_2999 on theBenchmark for (2999ds/33Mi)
% 1.98/0.64 % (3752185)dis+1002_1_to=kbo:sil=128000:tgt=ground:sas=z3:si=on:spb=units:tha=off:random_seed=838762041:i=307:kws=precedence:nm=0:rtra=on_2999 on theBenchmark for (2999ds/307Mi)
% 1.98/0.64 % (3752187)lrs+1002_4:1_to=lpo:sil=64000:si=on:br=off:random_seed=1377354148:s2a=on:i=7:rtra=on:inst=on_2999 on theBenchmark for (2999ds/7Mi)
% 1.98/0.64 % (3752184)dis+1002_16:1_to=lpo:sil=64000:sas=z3:si=on:norm_ineq=on:gve=force:uwa=one_side_constant:random_seed=1341581529:i=12:doe=on:rtra=on:gtg=exists_top:ss=axioms_2999 on theBenchmark for (2999ds/12Mi)
% 1.98/0.64 % (3752188)dis+21_64_to=kbo:sil=128000:si=on:sp=weighted_frequency:uwa=alasca_can_abstract:random_seed=2566425986:i=4:rtra=on_2999 on theBenchmark for (2999ds/4Mi)
% 1.98/0.64 % (3752188)Instruction limit reached!
% 1.98/0.64 % (3752188)------------------------------
% 1.98/0.64 % (3752188)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 1.98/0.64 % (3752188)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.98/0.64 % (3752188)CaDiCaL version: 2.1.3
% 1.98/0.64 % (3752188)Termination reason: Instruction limit
% 1.98/0.64 % (3752188)Termination phase: Saturation
% 1.98/0.64 % (3752188)Time elapsed: 0.002 s
% 1.98/0.64 % (3752188)Peak memory usage: 88 MB
% 1.98/0.64 % (3752188)Instructions burned: 5 (million)
% 1.98/0.64 % (3752187)Instruction limit reached!
% 1.98/0.64 % (3752187)------------------------------
% 1.98/0.64 % (3752187)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 1.98/0.64 % (3752187)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.98/0.64 % (3752187)CaDiCaL version: 2.1.3
% 1.98/0.64 % (3752187)Termination reason: Instruction limit
% 1.98/0.64 % (3752187)Termination phase: Saturation
% 1.98/0.64 % (3752187)Time elapsed: 0.003 s
% 1.98/0.64 % (3752187)Peak memory usage: 88 MB
% 1.98/0.64 % (3752187)Instructions burned: 8 (million)
% 1.98/0.64 % (3752189)Refutation not found, incomplete strategy
% 1.98/0.64 % (3752189)------------------------------
% 1.98/0.64 % (3752189)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 1.98/0.64 % (3752189)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.98/0.64 % (3752189)CaDiCaL version: 2.1.3
% 1.98/0.64 % (3752189)Termination reason: Refutation not found, incomplete strategy
% 1.98/0.64 % (3752189)Time elapsed: 0.019 s
% 1.98/0.64 % (3752189)Peak memory usage: 114 MB
% 1.98/0.64 % (3752189)Instructions burned: 6 (million)
% 1.98/0.64 % (3752184)Instruction limit reached!
% 1.98/0.64 % (3752184)------------------------------
% 1.98/0.64 % (3752184)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 1.98/0.64 % (3752184)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.98/0.64 % (3752184)CaDiCaL version: 2.1.3
% 1.98/0.64 % (3752184)Termination reason: Instruction limit
% 1.98/0.64 % (3752184)Termination phase: Saturation
% 1.98/0.64 % (3752184)Time elapsed: 0.019 s
% 1.98/0.64 % (3752184)Peak memory usage: 114 MB
% 1.98/0.64 % (3752184)Instructions burned: 14 (million)
% 1.98/0.64 % (3752185)Refutation not found, incomplete strategy
% 1.98/0.64 % (3752185)------------------------------
% 1.98/0.64 % (3752185)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 1.98/0.64 % (3752185)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.98/0.64 % (3752185)CaDiCaL version: 2.1.3
% 1.98/0.64 % (3752185)Termination reason: Refutation not found, incomplete strategy
% 1.98/0.64 % (3752185)Time elapsed: 0.019 s
% 1.98/0.64 % (3752185)Peak memory usage: 115 MB
% 1.98/0.64 % (3752185)Instructions burned: 9 (million)
% 1.98/0.64 % (3752190)First to succeed.
% 1.98/0.64 % (3752190)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3752179"
% 1.98/0.64 % (3752186)Instruction limit reached!
% 1.98/0.64 % (3752186)------------------------------
% 1.98/0.64 % (3752186)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.47/0.74 % (3752186)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.47/0.74 % (3752186)CaDiCaL version: 2.1.3
% 2.47/0.74 % (3752186)Termination reason: Instruction limit
% 2.47/0.74 % (3752186)Termination phase: Saturation
% 2.47/0.74 % (3752186)Time elapsed: 0.089 s
% 2.47/0.74 % (3752186)Peak memory usage: 117 MB
% 2.47/0.74 % (3752186)Instructions burned: 203 (million)
% 2.47/0.74 % (3752198)dis+11_3_anc=none:drc=ordering:si=on:urr=ec_only:bce=on:tha=off:sac=on:random_seed=1772353700:st=5:i=14:sd=10:rtra=on:ss=axioms:rawr=on_2998 on theBenchmark for (2998ds/14Mi)
% 2.47/0.74 % (3752199)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=2865072285:i=29:thsqd=64:nm=0:thsqc=8:rtra=on:thsq=on:ev=off_2998 on theBenchmark for (2998ds/29Mi)
% 2.47/0.74 % (3752198)Refutation not found, incomplete strategy
% 2.47/0.74 % (3752198)------------------------------
% 2.47/0.74 % (3752198)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.47/0.74 % (3752198)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.47/0.74 % (3752198)CaDiCaL version: 2.1.3
% 2.47/0.74 % (3752198)Termination reason: Refutation not found, incomplete strategy
% 2.47/0.74 % (3752198)Time elapsed: 0.001 s
% 2.47/0.74 % (3752198)Peak memory usage: 88 MB
% 2.47/0.74 % (3752199)Instruction limit reached!
% 2.47/0.74 % (3752199)------------------------------
% 2.47/0.74 % (3752199)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.47/0.74 % (3752199)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.47/0.74 % (3752199)CaDiCaL version: 2.1.3
% 2.47/0.74 % (3752199)Termination reason: Instruction limit
% 2.47/0.74 % (3752199)Termination phase: Saturation
% 2.47/0.74 % (3752199)Time elapsed: 0.009 s
% 2.47/0.74 % (3752199)Peak memory usage: 88 MB
% 2.47/0.74 % (3752199)Instructions burned: 30 (million)
% 2.47/0.74 % (3752200)ott+21_1024_to=lakbo:sil=128000:bsd=on:si=on:alasca=on:uwa=alasca_main:nwc=0.5:random_seed=3392722296:cond=on:i=16:fgj=on:ep=RS:asg=force:nm=10:rtra=on:rawr=on_2998 on theBenchmark for (2998ds/16Mi)
% 2.47/0.74 % (3752200)Instruction limit reached!
% 2.47/0.74 % (3752200)------------------------------
% 2.47/0.74 % (3752200)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.47/0.74 % (3752200)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.47/0.74 % (3752200)CaDiCaL version: 2.1.3
% 2.47/0.74 % (3752200)Termination reason: Instruction limit
% 2.47/0.74 % (3752200)Termination phase: Saturation
% 2.47/0.74 % (3752200)Time elapsed: 0.005 s
% 2.47/0.74 % (3752200)Peak memory usage: 90 MB
% 2.47/0.74 % (3752200)Instructions burned: 18 (million)
% 2.47/0.74 % (3752185)------------------------------
% 2.47/0.74 % (3752185)------------------------------
% 2.47/0.74 % (3752189)------------------------------
% 2.47/0.74 % (3752189)------------------------------
% 2.47/0.74 % (3752190)Refutation found. Thanks to Tanya!
% 2.47/0.74 % SZS status Theorem for theBenchmark
% 2.47/0.74 % SZS output start Proof for theBenchmark
% See solution above
% 2.47/0.74 % (3752190)------------------------------
% 2.47/0.74 % (3752190)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.47/0.74 % (3752190)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.47/0.74 % (3752190)CaDiCaL version: 2.1.3
% 2.47/0.74 % (3752190)Termination reason: Refutation
% 2.47/0.74 % (3752190)Time elapsed: 0.022 s
% 2.47/0.74 % (3752190)Peak memory usage: 116 MB
% 2.47/0.74 % (3752190)Instructions burned: 15 (million)
% 2.47/0.74 % (3752190)------------------------------
% 2.47/0.74 % (3752190)------------------------------
% 2.47/0.74 % (3752179)Success in time 0.324 s
% 2.47/0.74 % Vampire exiting
%------------------------------------------------------------------------------