%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ARI639_1 : TPTP v9.3.1. Released v6.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n020.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 09:33:33 AM UTC 2026
% Result : Theorem 2.59s 1.02s
% Output : Refutation 2.59s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 29
% Syntax : Number of formulae : 69 ( 55 unt; 0 typ; 22 def)
% Number of atoms : 83 ( 28 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 22 ( 8 ~; 0 |; 0 &)
% ( 14 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 3 ( 1 avg)
% Maximal term depth : 7 ( 2 avg)
% Number arithmetic : 155 ( 26 atm; 71 fun; 56 num; 2 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 : 19 ( 14 usr; 15 prp; 0-2 aty)
% Number of functors : 22 ( 13 usr; 19 con; 0-2 aty)
% Number of variables : 2 ( 2 !; 0 ?; 2 :)
% Comments :
%------------------------------------------------------------------------------
tff(func_def_0,type,
eps: $real ).
tff(func_def_1,type,
c: $real ).
tff(func_def_2,type,
k: $real ).
tff(func_def_3,type,
x: $real ).
tff(func_def_4,type,
n: $real ).
tff(func_def_13,type,
sF0: $real ).
tff(func_def_14,type,
sF1: $real ).
tff(func_def_15,type,
sF2: $real ).
tff(func_def_16,type,
sF3: $real ).
tff(func_def_17,type,
sF4: $real ).
tff(func_def_18,type,
sF5: $real ).
tff(func_def_19,type,
sF6: $real ).
tff(func_def_20,type,
sF7: $real ).
tff(f1,axiom,
$greatereq(n,0/1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hypothesis) ).
tff(f2,axiom,
$less(n,$product($quotient(1/1,2/1),$product(k,x))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hypothesis_01) ).
tff(f3,axiom,
$greater(c,0/1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hypothesis_02) ).
tff(f4,axiom,
$greater(eps,0/1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hypothesis_03) ).
tff(f5,axiom,
$less(eps,1/1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hypothesis_04) ).
tff(f6,conjecture,
$less($product($sum($product($quotient(1/1,3/1),$product($quotient(1/1,$sum(3/1,c)),eps)),1/1),n),$product(k,x)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conclusion) ).
tff(f7,negated_conjecture,
~ $less($product($sum($product($quotient(1/1,3/1),$product($quotient(1/1,$sum(3/1,c)),eps)),1/1),n),$product(k,x)),
inference(negated_conjecture,[status(cth)],[f6]) ).
tff(f8,plain,
$less(0/1,eps),
inference(theory_normalization,[],[f4]) ).
tff(f9,plain,
$less(0/1,c),
inference(theory_normalization,[],[f3]) ).
tff(f10,plain,
~ $less(n,0/1),
inference(theory_normalization,[],[f1]) ).
tff(f22,plain,
! [X0: $real,X1: $real] : ( $product(X1,X0) = $product(X0,X1) ),
introduced(definition,[],[tha_commutativity]) ).
tff(f30,plain,
~ $less($product($sum($product($quotient(1/1,3/1),$product($quotient(1/1,$sum(3/1,c)),eps)),1/1),n),$product(k,x)),
inference(flattening,[],[f7]) ).
tff(f31,plain,
~ $less(n,0/1),
inference(cnf_transformation,[],[f10]) ).
tff(f32,plain,
~ $less($product($sum($product($quotient(1/1,3/1),$product($quotient(1/1,$sum(3/1,c)),eps)),1/1),n),$product(k,x)),
inference(cnf_transformation,[],[f30]) ).
tff(f33,plain,
$less(n,$product($quotient(1/1,2/1),$product(k,x))),
inference(cnf_transformation,[],[f2]) ).
tff(f34,plain,
$less(0/1,c),
inference(cnf_transformation,[],[f9]) ).
tff(f35,plain,
$less(eps,1/1),
inference(cnf_transformation,[],[f5]) ).
tff(f36,plain,
$less(0/1,eps),
inference(cnf_transformation,[],[f8]) ).
tff(f38,definition,
sF0 = $quotient(1/1,3/1),
introduced(definition,[new_symbols(definition,[sF0])],[function_definition]) ).
tff(f39,plain,
$quotient(1/1,3/1) = sF0,
inference(reorient_equations,[],[f38]) ).
tff(f40,definition,
sF1 = $sum(3/1,c),
introduced(definition,[new_symbols(definition,[sF1])],[function_definition]) ).
tff(f41,plain,
$sum(3/1,c) = sF1,
inference(reorient_equations,[],[f40]) ).
tff(f42,definition,
sF2 = $quotient(1/1,sF1),
introduced(definition,[new_symbols(definition,[sF2])],[function_definition]) ).
tff(f43,definition,
sF3 = $product(sF2,eps),
introduced(definition,[new_symbols(definition,[sF3])],[function_definition]) ).
tff(f44,definition,
sF4 = $product(sF0,sF3),
introduced(definition,[new_symbols(definition,[sF4])],[function_definition]) ).
tff(f45,plain,
$product(sF0,sF3) = sF4,
inference(reorient_equations,[],[f44]) ).
tff(f46,definition,
sF5 = $sum(sF4,1/1),
introduced(definition,[new_symbols(definition,[sF5])],[function_definition]) ).
tff(f47,plain,
$sum(sF4,1/1) = sF5,
inference(reorient_equations,[],[f46]) ).
tff(f48,definition,
sF6 = $product(sF5,n),
introduced(definition,[new_symbols(definition,[sF6])],[function_definition]) ).
tff(f49,plain,
$product(sF5,n) = sF6,
inference(reorient_equations,[],[f48]) ).
tff(f50,definition,
sF7 = $product(k,x),
introduced(definition,[new_symbols(definition,[sF7])],[function_definition]) ).
tff(f51,plain,
$product(k,x) = sF7,
inference(reorient_equations,[],[f50]) ).
tff(f52,plain,
~ $less(sF6,sF7),
inference(definition_folding,[],[f32,f51,f49,f47,f45,f43,f42,f41,f39]) ).
tff(f53,plain,
$less(n,$product(1/2,$product(k,x))),
inference(evaluation,[],[f33]) ).
tff(f54,plain,
1/3 = sF0,
inference(evaluation,[],[f39]) ).
tff(f56,definition,
( spl8_1
<=> $less(sF6,sF7) ),
introduced(definition,[new_symbols(definition,[spl8_1])],[avatar_definition]) ).
tff(f59,plain,
~ spl8_1,
inference(avatar_split_clause,[],[f52,f56]) ).
tff(f61,definition,
( spl8_2
<=> $less(n,0/1) ),
introduced(definition,[new_symbols(definition,[spl8_2])],[avatar_definition]) ).
tff(f64,plain,
~ spl8_2,
inference(avatar_split_clause,[],[f31,f61]) ).
tff(f66,definition,
( spl8_3
<=> $less(0/1,eps) ),
introduced(definition,[new_symbols(definition,[spl8_3])],[avatar_definition]) ).
tff(f69,plain,
spl8_3,
inference(avatar_split_clause,[],[f36,f66]) ).
tff(f71,definition,
( spl8_4
<=> ( sF2 = $quotient(1/1,sF1) ) ),
introduced(definition,[new_symbols(definition,[spl8_4])],[avatar_definition]) ).
tff(f74,plain,
spl8_4,
inference(avatar_split_clause,[],[f42,f71]) ).
tff(f76,definition,
( spl8_5
<=> $less(eps,1/1) ),
introduced(definition,[new_symbols(definition,[spl8_5])],[avatar_definition]) ).
tff(f79,plain,
spl8_5,
inference(avatar_split_clause,[],[f35,f76]) ).
tff(f81,definition,
( spl8_6
<=> $less(0/1,c) ),
introduced(definition,[new_symbols(definition,[spl8_6])],[avatar_definition]) ).
tff(f84,plain,
spl8_6,
inference(avatar_split_clause,[],[f34,f81]) ).
tff(f86,definition,
( spl8_7
<=> ( $sum(sF4,1/1) = sF5 ) ),
introduced(definition,[new_symbols(definition,[spl8_7])],[avatar_definition]) ).
tff(f89,plain,
spl8_7,
inference(avatar_split_clause,[],[f47,f86]) ).
tff(f90,plain,
$less(n,$product(1/2,$product(x,k))),
inference(forward_demodulation,[],[f53,f22]) ).
tff(f91,plain,
$product(eps,sF2) = sF3,
inference(forward_demodulation,[],[f43,f22]) ).
tff(f92,plain,
sF4 = $product(sF3,sF0),
inference(forward_demodulation,[],[f45,f22]) ).
tff(f94,definition,
( spl8_8
<=> ( 1/3 = sF0 ) ),
introduced(definition,[new_symbols(definition,[spl8_8])],[avatar_definition]) ).
tff(f97,plain,
spl8_8,
inference(avatar_split_clause,[],[f54,f94]) ).
tff(f98,plain,
sF7 = $product(x,k),
inference(forward_demodulation,[],[f51,f22]) ).
tff(f99,plain,
sF6 = $product(n,sF5),
inference(forward_demodulation,[],[f49,f22]) ).
tff(f101,definition,
( spl8_9
<=> ( $sum(3/1,c) = sF1 ) ),
introduced(definition,[new_symbols(definition,[spl8_9])],[avatar_definition]) ).
tff(f104,plain,
spl8_9,
inference(avatar_split_clause,[],[f41,f101]) ).
tff(f106,definition,
( spl8_10
<=> $less(n,$product(1/2,$product(x,k))) ),
introduced(definition,[new_symbols(definition,[spl8_10])],[avatar_definition]) ).
tff(f109,plain,
spl8_10,
inference(avatar_split_clause,[],[f90,f106]) ).
tff(f111,definition,
( spl8_11
<=> ( $product(eps,sF2) = sF3 ) ),
introduced(definition,[new_symbols(definition,[spl8_11])],[avatar_definition]) ).
tff(f114,plain,
spl8_11,
inference(avatar_split_clause,[],[f91,f111]) ).
tff(f116,definition,
( spl8_12
<=> ( sF4 = $product(sF3,sF0) ) ),
introduced(definition,[new_symbols(definition,[spl8_12])],[avatar_definition]) ).
tff(f119,plain,
spl8_12,
inference(avatar_split_clause,[],[f92,f116]) ).
tff(f121,definition,
( spl8_13
<=> ( sF7 = $product(x,k) ) ),
introduced(definition,[new_symbols(definition,[spl8_13])],[avatar_definition]) ).
tff(f124,plain,
spl8_13,
inference(avatar_split_clause,[],[f98,f121]) ).
tff(f126,definition,
( spl8_14
<=> ( sF6 = $product(n,sF5) ) ),
introduced(definition,[new_symbols(definition,[spl8_14])],[avatar_definition]) ).
tff(f129,plain,
spl8_14,
inference(avatar_split_clause,[],[f99,f126]) ).
tff(f130,plain,
$false,
inference(avatar_smt_refutation,[],[f129,f124,f119,f114,f109,f104,f97,f89,f84,f79,f74,f69,f64,f59]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ARI639_1 : TPTP v9.3.1. Released v6.3.0.
% 0.00/0.04 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.06/0.19 % Computer : n020.cluster.edu
% 0.06/0.19 % Model : x86_64 x86_64
% 0.06/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.19 % Memory : 8046.5625MB
% 0.06/0.19 % OS : Linux 6.8.0-71-generic
% 0.06/0.19 % CPULimit : 300
% 0.06/0.19 % WCLimit : 300
% 0.06/0.19 % DateTime : Mon Sep 28 20:55:19 UTC 2026
% 0.06/0.19 % CPUTime :
% 0.06/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.06/0.22 Running first-order theorem proving
% 0.06/0.22 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
% 2.59/1.02 % (545430)Detected arithmetic, will pick strategies from an ALASCA-aware ARI schedule.
% 2.59/1.02 % (545458)lrs+10_1_tgt=ground:sas=z3:si=on:random_seed=8250659:i=33:rtra=on_2999 on theBenchmark for (2999ds/33Mi)
% 2.59/1.02 % (545458)First to succeed.
% 2.59/1.02 % (545458)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-545430"
% 2.59/1.02 % (545454)dis+10_3_slsqr=1,4:to=lpo:sil=128000:thi=strong:si=on:uwa=off:s2agt=20:slsqc=1:slsq=on:random_seed=3244698606:i=201:slsql=off:asg=cautious:rtra=on:gtg=all:ss=axioms:sgt=16_2999 on theBenchmark for (2999ds/201Mi)
% 2.59/1.02 % (545452)dis+1002_1_to=kbo:sil=128000:tgt=ground:sas=z3:si=on:spb=units:tha=off:random_seed=3011233515:i=307:kws=precedence:nm=0:rtra=on_2999 on theBenchmark for (2999ds/307Mi)
% 2.59/1.02 % (545451)dis+1002_16:1_to=lpo:sil=64000:sas=z3:si=on:norm_ineq=on:gve=force:uwa=one_side_constant:random_seed=2044615094:i=12:doe=on:rtra=on:gtg=exists_top:ss=axioms_2999 on theBenchmark for (2999ds/12Mi)
% 2.59/1.02 % (545457)lrs+10_1_to=lpo:sas=z3:si=on:tha=off:random_seed=3856054609:i=46:rtra=on_2999 on theBenchmark for (2999ds/46Mi)
% 2.59/1.02 % (545455)lrs+1002_4:1_to=lpo:sil=64000:si=on:br=off:random_seed=3867895127:s2a=on:i=7:rtra=on:inst=on_2999 on theBenchmark for (2999ds/7Mi)
% 2.59/1.02 % (545455)Instruction limit reached!
% 2.59/1.02 % (545455)------------------------------
% 2.59/1.02 % (545455)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.59/1.02 % (545455)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.59/1.02 % (545455)CaDiCaL version: 2.1.3
% 2.59/1.02 % (545455)Termination reason: Instruction limit
% 2.59/1.02 % (545455)Termination phase: Saturation
% 2.59/1.02 % (545455)Time elapsed: 0.004 s
% 2.59/1.02 % (545455)Peak memory usage: 88 MB
% 2.59/1.02 % (545455)Instructions burned: 7 (million)
% 2.59/1.02 % (545451)Instruction limit reached!
% 2.59/1.02 % (545451)------------------------------
% 2.59/1.02 % (545451)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.59/1.02 % (545451)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.59/1.02 % (545451)CaDiCaL version: 2.1.3
% 2.59/1.02 % (545451)Termination reason: Instruction limit
% 2.59/1.02 % (545451)Termination phase: Saturation
% 2.59/1.02 % (545451)Time elapsed: 0.031 s
% 2.59/1.02 % (545451)Peak memory usage: 116 MB
% 2.59/1.02 % (545451)Instructions burned: 13 (million)
% 2.59/1.02 % (545456)dis+21_64_to=kbo:sil=128000:si=on:sp=weighted_frequency:uwa=alasca_can_abstract:random_seed=594071057:i=4:rtra=on_2999 on theBenchmark for (2999ds/4Mi)
% 2.59/1.02 % (545457)Also succeeded, but the first one will report.
% 2.59/1.02 % (545456)Instruction limit reached!
% 2.59/1.02 % (545456)------------------------------
% 2.59/1.02 % (545456)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.59/1.02 % (545456)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.59/1.02 % (545456)CaDiCaL version: 2.1.3
% 2.59/1.02 % (545456)Termination reason: Instruction limit
% 2.59/1.02 % (545456)Termination phase: Saturation
% 2.59/1.02 % (545456)Time elapsed: 0.003 s
% 2.59/1.02 % (545456)Peak memory usage: 88 MB
% 2.59/1.02 % (545456)Instructions burned: 5 (million)
% 2.59/1.02 % (545452)Also succeeded, but the first one will report.
% 2.59/1.02 % (545458)Refutation found. Thanks to Tanya!
% 2.59/1.02 % SZS status Theorem for theBenchmark
% 2.59/1.02 % SZS output start Proof for theBenchmark
% See solution above
% 2.59/1.02 % (545458)------------------------------
% 2.59/1.02 % (545458)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.59/1.02 % (545458)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.59/1.02 % (545458)CaDiCaL version: 2.1.3
% 2.59/1.02 % (545458)Termination reason: Refutation
% 2.59/1.02 % (545458)Time elapsed: 0.033 s
% 2.59/1.02 % (545458)Peak memory usage: 118 MB
% 2.59/1.02 % (545458)Instructions burned: 30 (million)
% 2.59/1.02 % (545458)------------------------------
% 2.59/1.02 % (545458)------------------------------
% 2.59/1.02 % (545430)Success in time 0.321 s
% 2.59/1.02 % Vampire exiting
%------------------------------------------------------------------------------