%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ARI628_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 : n011.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 09:33:31 AM UTC 2026
% Result : Theorem 4.09s 1.61s
% Output : Refutation 4.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 22
% Syntax : Number of formulae : 51 ( 40 unt; 0 typ; 16 def)
% Number of atoms : 62 ( 15 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 22 ( 11 ~; 0 |; 0 &)
% ( 11 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 2 ( 1 avg)
% Maximal term depth : 4 ( 1 avg)
% Number arithmetic : 77 ( 24 atm; 35 fun; 18 num; 0 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 : 17 ( 11 usr; 12 prp; 0-2 aty)
% Number of functors : 13 ( 9 usr; 12 con; 0-2 aty)
% Number of variables : 0 ( 0 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(func_def_0,type,
y: $real ).
tff(func_def_1,type,
x: $real ).
tff(func_def_2,type,
v: $real ).
tff(func_def_3,type,
u: $real ).
tff(func_def_10,type,
sF0: $real ).
tff(func_def_11,type,
sF1: $real ).
tff(func_def_12,type,
sF2: $real ).
tff(func_def_13,type,
sF3: $real ).
tff(func_def_14,type,
sF4: $real ).
tff(f1,axiom,
$greater(u,0/1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hypothesis_00) ).
tff(f2,axiom,
$less(u,v),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hypothesis_01) ).
tff(f3,axiom,
$less(v,1/1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hypothesis_02) ).
tff(f4,axiom,
$greatereq(x,2/1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hypothesis_03) ).
tff(f5,axiom,
$lesseq(x,y),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hypothesis_04) ).
tff(f6,conjecture,
$less($product($product(2/1,$product(u,u)),x),$product($product(y,y),v)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conclusion) ).
tff(f7,negated_conjecture,
~ $less($product($product(2/1,$product(u,u)),x),$product($product(y,y),v)),
inference(negated_conjecture,[status(cth)],[f6]) ).
tff(f8,plain,
~ $less(y,x),
inference(theory_normalization,[],[f5]) ).
tff(f9,plain,
$less(0/1,u),
inference(theory_normalization,[],[f1]) ).
tff(f10,plain,
~ $less(x,2/1),
inference(theory_normalization,[],[f4]) ).
tff(f28,plain,
~ $less($product($product(2/1,$product(u,u)),x),$product($product(y,y),v)),
inference(flattening,[],[f7]) ).
tff(f29,plain,
~ $less(x,2/1),
inference(cnf_transformation,[],[f10]) ).
tff(f30,plain,
$less(v,1/1),
inference(cnf_transformation,[],[f3]) ).
tff(f31,plain,
~ $less(y,x),
inference(cnf_transformation,[],[f8]) ).
tff(f32,plain,
$less(u,v),
inference(cnf_transformation,[],[f2]) ).
tff(f33,plain,
$less(0/1,u),
inference(cnf_transformation,[],[f9]) ).
tff(f34,plain,
~ $less($product($product(2/1,$product(u,u)),x),$product($product(y,y),v)),
inference(cnf_transformation,[],[f28]) ).
tff(f36,definition,
sF0 = $product(u,u),
introduced(definition,[new_symbols(definition,[sF0])],[function_definition]) ).
tff(f37,plain,
$product(u,u) = sF0,
inference(reorient_equations,[],[f36]) ).
tff(f38,definition,
sF1 = $product(2/1,sF0),
introduced(definition,[new_symbols(definition,[sF1])],[function_definition]) ).
tff(f39,plain,
$product(2/1,sF0) = sF1,
inference(reorient_equations,[],[f38]) ).
tff(f40,definition,
sF2 = $product(sF1,x),
introduced(definition,[new_symbols(definition,[sF2])],[function_definition]) ).
tff(f41,plain,
$product(sF1,x) = sF2,
inference(reorient_equations,[],[f40]) ).
tff(f42,definition,
sF3 = $product(y,y),
introduced(definition,[new_symbols(definition,[sF3])],[function_definition]) ).
tff(f43,plain,
$product(y,y) = sF3,
inference(reorient_equations,[],[f42]) ).
tff(f44,definition,
sF4 = $product(sF3,v),
introduced(definition,[new_symbols(definition,[sF4])],[function_definition]) ).
tff(f45,plain,
$product(sF3,v) = sF4,
inference(reorient_equations,[],[f44]) ).
tff(f46,plain,
~ $less(sF2,sF4),
inference(definition_folding,[],[f34,f45,f43,f41,f39,f37]) ).
tff(f48,definition,
( spl5_1
<=> ( $product(2/1,sF0) = sF1 ) ),
introduced(definition,[new_symbols(definition,[spl5_1])],[avatar_definition]) ).
tff(f51,plain,
spl5_1,
inference(avatar_split_clause,[],[f39,f48]) ).
tff(f53,definition,
( spl5_2
<=> $less(sF2,sF4) ),
introduced(definition,[new_symbols(definition,[spl5_2])],[avatar_definition]) ).
tff(f56,plain,
~ spl5_2,
inference(avatar_split_clause,[],[f46,f53]) ).
tff(f58,definition,
( spl5_3
<=> ( $product(y,y) = sF3 ) ),
introduced(definition,[new_symbols(definition,[spl5_3])],[avatar_definition]) ).
tff(f61,plain,
spl5_3,
inference(avatar_split_clause,[],[f43,f58]) ).
tff(f63,definition,
( spl5_4
<=> $less(y,x) ),
introduced(definition,[new_symbols(definition,[spl5_4])],[avatar_definition]) ).
tff(f66,plain,
~ spl5_4,
inference(avatar_split_clause,[],[f31,f63]) ).
tff(f68,definition,
( spl5_5
<=> ( $product(sF1,x) = sF2 ) ),
introduced(definition,[new_symbols(definition,[spl5_5])],[avatar_definition]) ).
tff(f71,plain,
spl5_5,
inference(avatar_split_clause,[],[f41,f68]) ).
tff(f73,definition,
( spl5_6
<=> ( $product(sF3,v) = sF4 ) ),
introduced(definition,[new_symbols(definition,[spl5_6])],[avatar_definition]) ).
tff(f76,plain,
spl5_6,
inference(avatar_split_clause,[],[f45,f73]) ).
tff(f78,definition,
( spl5_7
<=> $less(0/1,u) ),
introduced(definition,[new_symbols(definition,[spl5_7])],[avatar_definition]) ).
tff(f81,plain,
spl5_7,
inference(avatar_split_clause,[],[f33,f78]) ).
tff(f83,definition,
( spl5_8
<=> $less(x,2/1) ),
introduced(definition,[new_symbols(definition,[spl5_8])],[avatar_definition]) ).
tff(f86,plain,
~ spl5_8,
inference(avatar_split_clause,[],[f29,f83]) ).
tff(f88,definition,
( spl5_9
<=> $less(u,v) ),
introduced(definition,[new_symbols(definition,[spl5_9])],[avatar_definition]) ).
tff(f91,plain,
spl5_9,
inference(avatar_split_clause,[],[f32,f88]) ).
tff(f93,definition,
( spl5_10
<=> $less(v,1/1) ),
introduced(definition,[new_symbols(definition,[spl5_10])],[avatar_definition]) ).
tff(f96,plain,
spl5_10,
inference(avatar_split_clause,[],[f30,f93]) ).
tff(f98,definition,
( spl5_11
<=> ( $product(u,u) = sF0 ) ),
introduced(definition,[new_symbols(definition,[spl5_11])],[avatar_definition]) ).
tff(f101,plain,
spl5_11,
inference(avatar_split_clause,[],[f37,f98]) ).
tff(f102,plain,
$false,
inference(avatar_smt_refutation,[],[f101,f96,f91,f86,f81,f76,f71,f66,f61,f56,f51]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : ARI628_1 : TPTP v9.3.1. Released v6.3.0.
% 0.00/0.07 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.26 % Computer : n011.cluster.edu
% 0.11/0.26 % Model : x86_64 x86_64
% 0.11/0.26 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.26 % Memory : 8046.5625MB
% 0.11/0.26 % OS : Linux 6.8.0-71-generic
% 0.11/0.26 % CPULimit : 300
% 0.11/0.26 % WCLimit : 300
% 0.11/0.26 % DateTime : Mon Sep 28 20:54:16 UTC 2026
% 0.11/0.27 % CPUTime :
% 0.11/0.27 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.27/0.32 Running first-order theorem proving
% 0.27/0.32 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
% 4.09/1.61 % (3774382)Detected arithmetic, will pick strategies from an ALASCA-aware ARI schedule.
% 4.09/1.61 % (3774393)lrs+1002_4:1_to=lpo:sil=64000:si=on:br=off:random_seed=4289967790:s2a=on:i=7:rtra=on:inst=on_2999 on theBenchmark for (2999ds/7Mi)
% 4.09/1.61 % (3774396)lrs+10_1_tgt=ground:sas=z3:si=on:random_seed=1228149419:i=33:rtra=on_2999 on theBenchmark for (2999ds/33Mi)
% 4.09/1.61 % (3774393)Instruction limit reached!
% 4.09/1.61 % (3774393)------------------------------
% 4.09/1.61 % (3774393)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.09/1.61 % (3774393)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.09/1.61 % (3774393)CaDiCaL version: 2.1.3
% 4.09/1.61 % (3774393)Termination reason: Instruction limit
% 4.09/1.61 % (3774393)Termination phase: Saturation
% 4.09/1.61 % (3774393)Time elapsed: 0.005 s
% 4.09/1.61 % (3774393)Peak memory usage: 88 MB
% 4.09/1.61 % (3774393)Instructions burned: 8 (million)
% 4.09/1.61 % (3774396)First to succeed.
% 4.09/1.61 % (3774396)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3774382"
% 4.09/1.61 % (3774395)lrs+10_1_to=lpo:sas=z3:si=on:tha=off:random_seed=3575875419:i=46:rtra=on_2999 on theBenchmark for (2999ds/46Mi)
% 4.09/1.61 % (3774394)dis+21_64_to=kbo:sil=128000:si=on:sp=weighted_frequency:uwa=alasca_can_abstract:random_seed=1072202491:i=4:rtra=on_2999 on theBenchmark for (2999ds/4Mi)
% 4.09/1.61 % (3774390)dis+1002_16:1_to=lpo:sil=64000:sas=z3:si=on:norm_ineq=on:gve=force:uwa=one_side_constant:random_seed=2236554771:i=12:doe=on:rtra=on:gtg=exists_top:ss=axioms_2999 on theBenchmark for (2999ds/12Mi)
% 4.09/1.61 % (3774392)dis+10_3_slsqr=1,4:to=lpo:sil=128000:thi=strong:si=on:uwa=off:s2agt=20:slsqc=1:slsq=on:random_seed=3487688225:i=201:slsql=off:asg=cautious:rtra=on:gtg=all:ss=axioms:sgt=16_2999 on theBenchmark for (2999ds/201Mi)
% 4.09/1.61 % (3774394)Instruction limit reached!
% 4.09/1.61 % (3774394)------------------------------
% 4.09/1.61 % (3774394)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.09/1.61 % (3774394)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.09/1.61 % (3774394)CaDiCaL version: 2.1.3
% 4.09/1.61 % (3774394)Termination reason: Instruction limit
% 4.09/1.61 % (3774394)Termination phase: Saturation
% 4.09/1.61 % (3774394)Time elapsed: 0.005 s
% 4.09/1.61 % (3774394)Peak memory usage: 88 MB
% 4.09/1.61 % (3774394)Instructions burned: 4 (million)
% 4.09/1.61 % (3774390)Instruction limit reached!
% 4.09/1.61 % (3774390)------------------------------
% 4.09/1.61 % (3774390)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.09/1.61 % (3774390)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.09/1.61 % (3774390)CaDiCaL version: 2.1.3
% 4.09/1.61 % (3774390)Termination reason: Instruction limit
% 4.09/1.61 % (3774390)Termination phase: Saturation
% 4.09/1.61 % (3774390)Time elapsed: 0.043 s
% 4.09/1.61 % (3774390)Peak memory usage: 117 MB
% 4.09/1.61 % (3774390)Instructions burned: 12 (million)
% 4.09/1.61 % (3774395)Also succeeded, but the first one will report.
% 4.09/1.61 % (3774391)dis+1002_1_to=kbo:sil=128000:tgt=ground:sas=z3:si=on:spb=units:tha=off:random_seed=2413520222:i=307:kws=precedence:nm=0:rtra=on_2999 on theBenchmark for (2999ds/307Mi)
% 4.09/1.61 % (3774391)Also succeeded, but the first one will report.
% 4.09/1.61 % (3774399)dis+11_3_anc=none:drc=ordering:si=on:urr=ec_only:bce=on:tha=off:sac=on:random_seed=2134062026:st=5:i=14:sd=10:rtra=on:ss=axioms:rawr=on_2998 on theBenchmark for (2998ds/14Mi)
% 4.09/1.61 % (3774399)Refutation not found, incomplete strategy
% 4.09/1.61 % (3774399)------------------------------
% 4.09/1.61 % (3774399)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.09/1.61 % (3774399)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.09/1.61 % (3774399)CaDiCaL version: 2.1.3
% 4.09/1.61 % (3774399)Termination reason: Refutation not found, incomplete strategy
% 4.09/1.61 % (3774399)Time elapsed: 0.002 s
% 4.09/1.61 % (3774399)Peak memory usage: 88 MB
% 4.09/1.61 % (3774404)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=960104798:i=29:thsqd=64:nm=0:thsqc=8:rtra=on:thsq=on:ev=off_2997 on theBenchmark for (2997ds/29Mi)
% 4.09/1.61 % (3774404)Instruction limit reached!
% 4.09/1.61 % (3774404)------------------------------
% 4.09/1.61 % (3774404)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.09/1.61 % (3774404)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.09/1.61 % (3774404)CaDiCaL version: 2.1.3
% 4.09/1.61 % (3774404)Termination reason: Instruction limit
% 4.09/1.61 % (3774404)Termination phase: Saturation
% 4.09/1.61 % (3774404)Time elapsed: 0.034 s
% 4.09/1.61 % (3774404)Peak memory usage: 88 MB
% 4.09/1.61 % (3774404)Instructions burned: 30 (million)
% 4.09/1.61 % (3774392)Instruction limit reached!
% 4.09/1.61 % (3774392)------------------------------
% 4.09/1.61 % (3774392)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.09/1.61 % (3774392)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.09/1.61 % (3774392)CaDiCaL version: 2.1.3
% 4.09/1.61 % (3774392)Termination reason: Instruction limit
% 4.09/1.61 % (3774392)Termination phase: Saturation
% 4.09/1.61 % (3774392)Time elapsed: 0.221 s
% 4.09/1.61 % (3774392)Peak memory usage: 117 MB
% 4.09/1.61 % (3774392)Instructions burned: 201 (million)
% 4.09/1.61 % (3774396)Refutation found. Thanks to Tanya!
% 4.09/1.61 % SZS status Theorem for theBenchmark
% 4.09/1.61 % SZS output start Proof for theBenchmark
% See solution above
% 4.09/1.61 % (3774396)------------------------------
% 4.09/1.61 % (3774396)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.09/1.61 % (3774396)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.09/1.61 % (3774396)CaDiCaL version: 2.1.3
% 4.09/1.61 % (3774396)Termination reason: Refutation
% 4.09/1.61 % (3774396)Time elapsed: 0.044 s
% 4.09/1.61 % (3774396)Peak memory usage: 118 MB
% 4.09/1.61 % (3774396)Instructions burned: 22 (million)
% 4.09/1.61 % (3774396)------------------------------
% 4.09/1.61 % (3774396)------------------------------
% 4.09/1.61 % (3774382)Success in time 0.45 s
% 4.09/1.61 % Vampire exiting
%------------------------------------------------------------------------------