%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ARI636_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 : n014.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 4.17s 1.44s
% Output : Refutation 4.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 20
% Syntax : Number of formulae : 53 ( 31 unt; 0 typ; 15 def)
% Number of atoms : 82 ( 15 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 57 ( 28 ~; 16 |; 0 &)
% ( 10 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number arithmetic : 68 ( 34 atm; 19 fun; 4 num; 11 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 : 16 ( 10 usr; 11 prp; 0-2 aty)
% Number of functors : 13 ( 10 usr; 10 con; 0-2 aty)
% Number of variables : 11 ( 11 !; 0 ?; 11 :)
% Comments :
%------------------------------------------------------------------------------
tff(func_def_0,type,
u: $real ).
tff(func_def_1,type,
v: $real ).
tff(func_def_2,type,
x: $real ).
tff(func_def_3,type,
y: $real ).
tff(func_def_4,type,
f: $real > $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,
! [X1: $real,X0: $real] :
( $greatereq(X0,X1)
=> $greatereq(f(X0),f(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f_non_decreasing) ).
tff(f2,axiom,
$less(u,v),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hypothesis) ).
tff(f3,axiom,
$greater(v,1/1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hypothesis_01) ).
tff(f4,axiom,
$lesseq(x,y),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hypothesis_02) ).
tff(f5,conjecture,
$less($sum(f(x),u),$sum($product(v,v),f(y))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conclusion) ).
tff(f6,negated_conjecture,
~ $less($sum(f(x),u),$sum($product(v,v),f(y))),
inference(negated_conjecture,[status(cth)],[f5]) ).
tff(f7,plain,
$less(1/1,v),
inference(theory_normalization,[],[f3]) ).
tff(f8,plain,
! [X1: $real,X0: $real] :
( ~ $less(X0,X1)
=> ~ $less(f(X0),f(X1)) ),
inference(theory_normalization,[],[f1]) ).
tff(f9,plain,
~ $less(y,x),
inference(theory_normalization,[],[f4]) ).
tff(f27,plain,
~ $less($sum(f(x),u),$sum($product(v,v),f(y))),
inference(flattening,[],[f6]) ).
tff(f28,plain,
! [X0: $real,X1: $real] :
( ~ $less(X1,X0)
=> ~ $less(f(X1),f(X0)) ),
inference(rectify,[],[f8]) ).
tff(f29,plain,
! [X0: $real,X1: $real] :
( $less(X1,X0)
| ~ $less(f(X1),f(X0)) ),
inference(ennf_transformation,[],[f28]) ).
tff(f30,plain,
$less(u,v),
inference(cnf_transformation,[],[f2]) ).
tff(f31,plain,
~ $less($sum(f(x),u),$sum($product(v,v),f(y))),
inference(cnf_transformation,[],[f27]) ).
tff(f32,plain,
~ $less(y,x),
inference(cnf_transformation,[],[f9]) ).
tff(f33,plain,
$less(1/1,v),
inference(cnf_transformation,[],[f7]) ).
tff(f34,plain,
! [X0: $real,X1: $real] :
( ~ $less(f(X1),f(X0))
| $less(X1,X0) ),
inference(cnf_transformation,[],[f29]) ).
tff(f36,definition,
sF0 = f(x),
introduced(definition,[new_symbols(definition,[sF0])],[function_definition]) ).
tff(f37,plain,
f(x) = sF0,
inference(reorient_equations,[],[f36]) ).
tff(f38,definition,
sF1 = $sum(sF0,u),
introduced(definition,[new_symbols(definition,[sF1])],[function_definition]) ).
tff(f39,definition,
sF2 = $product(v,v),
introduced(definition,[new_symbols(definition,[sF2])],[function_definition]) ).
tff(f40,plain,
$product(v,v) = sF2,
inference(reorient_equations,[],[f39]) ).
tff(f41,definition,
sF3 = f(y),
introduced(definition,[new_symbols(definition,[sF3])],[function_definition]) ).
tff(f42,plain,
f(y) = sF3,
inference(reorient_equations,[],[f41]) ).
tff(f43,definition,
sF4 = $sum(sF2,sF3),
introduced(definition,[new_symbols(definition,[sF4])],[function_definition]) ).
tff(f44,plain,
~ $less(sF1,sF4),
inference(definition_folding,[],[f31,f43,f42,f40,f38,f37]) ).
tff(f46,definition,
( spl5_1
<=> $less(y,x) ),
introduced(definition,[new_symbols(definition,[spl5_1])],[avatar_definition]) ).
tff(f48,plain,
( ~ $less(y,x)
| spl5_1 ),
inference(avatar_component_clause,[],[f46]) ).
tff(f49,plain,
~ spl5_1,
inference(avatar_split_clause,[],[f32,f46]) ).
tff(f51,definition,
( spl5_2
<=> $less(sF1,sF4) ),
introduced(definition,[new_symbols(definition,[spl5_2])],[avatar_definition]) ).
tff(f54,plain,
~ spl5_2,
inference(avatar_split_clause,[],[f44,f51]) ).
tff(f56,definition,
( spl5_3
<=> ( $product(v,v) = sF2 ) ),
introduced(definition,[new_symbols(definition,[spl5_3])],[avatar_definition]) ).
tff(f59,plain,
spl5_3,
inference(avatar_split_clause,[],[f40,f56]) ).
tff(f61,definition,
( spl5_4
<=> ( sF4 = $sum(sF2,sF3) ) ),
introduced(definition,[new_symbols(definition,[spl5_4])],[avatar_definition]) ).
tff(f64,plain,
spl5_4,
inference(avatar_split_clause,[],[f43,f61]) ).
tff(f66,definition,
( spl5_5
<=> ( sF1 = $sum(sF0,u) ) ),
introduced(definition,[new_symbols(definition,[spl5_5])],[avatar_definition]) ).
tff(f69,plain,
spl5_5,
inference(avatar_split_clause,[],[f38,f66]) ).
tff(f71,definition,
( spl5_6
<=> ( f(x) = sF0 ) ),
introduced(definition,[new_symbols(definition,[spl5_6])],[avatar_definition]) ).
tff(f73,plain,
( ( f(x) = sF0 )
| ~ spl5_6 ),
inference(avatar_component_clause,[],[f71]) ).
tff(f74,plain,
spl5_6,
inference(avatar_split_clause,[],[f37,f71]) ).
tff(f76,definition,
( spl5_7
<=> $less(1/1,v) ),
introduced(definition,[new_symbols(definition,[spl5_7])],[avatar_definition]) ).
tff(f79,plain,
spl5_7,
inference(avatar_split_clause,[],[f33,f76]) ).
tff(f81,definition,
( spl5_8
<=> ( f(y) = sF3 ) ),
introduced(definition,[new_symbols(definition,[spl5_8])],[avatar_definition]) ).
tff(f83,plain,
( ( f(y) = sF3 )
| ~ spl5_8 ),
inference(avatar_component_clause,[],[f81]) ).
tff(f84,plain,
spl5_8,
inference(avatar_split_clause,[],[f42,f81]) ).
tff(f86,definition,
( spl5_9
<=> $less(u,v) ),
introduced(definition,[new_symbols(definition,[spl5_9])],[avatar_definition]) ).
tff(f89,plain,
spl5_9,
inference(avatar_split_clause,[],[f30,f86]) ).
tff(f110,plain,
( ! [X0: $real] :
( ~ $less(sF3,f(X0))
| $less(y,X0) )
| ~ spl5_8 ),
inference(superposition,[],[f34,f83]) ).
tff(f214,plain,
( ~ $less(sF3,sF0)
| $less(y,x)
| ~ spl5_6
| ~ spl5_8 ),
inference(superposition,[],[f110,f73]) ).
tff(f216,plain,
( ~ $less(sF3,sF0)
| spl5_1
| ~ spl5_6
| ~ spl5_8 ),
inference(forward_subsumption_resolution,[],[f214,f48]) ).
tff(f218,definition,
( spl5_12
<=> $less(sF3,sF0) ),
introduced(definition,[new_symbols(definition,[spl5_12])],[avatar_definition]) ).
tff(f221,plain,
( ~ spl5_12
| spl5_1
| ~ spl5_6
| ~ spl5_8 ),
inference(avatar_split_clause,[],[f216,f81,f71,f46,f218]) ).
tff(f222,plain,
$false,
inference(avatar_smt_refutation,[],[f221,f89,f84,f79,f74,f69,f64,f59,f54,f49]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : ARI636_1 : TPTP v9.3.1. Released v6.3.0.
% 0.00/0.08 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.26 % Computer : n014.cluster.edu
% 0.10/0.26 % Model : x86_64 x86_64
% 0.10/0.26 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.26 % Memory : 8046.5625MB
% 0.10/0.26 % OS : Linux 6.8.0-71-generic
% 0.10/0.26 % CPULimit : 300
% 0.10/0.26 % WCLimit : 300
% 0.10/0.26 % DateTime : Mon Sep 28 20:54:15 UTC 2026
% 0.10/0.26 % CPUTime :
% 0.10/0.26 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.27/0.31 Running first-order theorem proving
% 0.27/0.32 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
% 4.17/1.44 % (2176746)Detected arithmetic, will pick strategies from an ALASCA-aware ARI schedule.
% 4.17/1.44 % (2176757)lrs+10_1_tgt=ground:sas=z3:si=on:random_seed=3223814884:i=33:rtra=on_2999 on theBenchmark for (2999ds/33Mi)
% 4.17/1.44 % (2176754)lrs+1002_4:1_to=lpo:sil=64000:si=on:br=off:random_seed=1753055051:s2a=on:i=7:rtra=on:inst=on_2999 on theBenchmark for (2999ds/7Mi)
% 4.17/1.44 % (2176754)Instruction limit reached!
% 4.17/1.44 % (2176754)------------------------------
% 4.17/1.44 % (2176754)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.17/1.44 % (2176754)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.17/1.44 % (2176754)CaDiCaL version: 2.1.3
% 4.17/1.44 % (2176754)Termination reason: Instruction limit
% 4.17/1.44 % (2176754)Termination phase: Saturation
% 4.17/1.44 % (2176754)Time elapsed: 0.009 s
% 4.17/1.44 % (2176754)Peak memory usage: 88 MB
% 4.17/1.44 % (2176754)Instructions burned: 7 (million)
% 4.17/1.44 % (2176757)First to succeed.
% 4.17/1.44 % (2176757)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2176746"
% 4.17/1.44 % (2176751)dis+1002_16:1_to=lpo:sil=64000:sas=z3:si=on:norm_ineq=on:gve=force:uwa=one_side_constant:random_seed=2501472695:i=12:doe=on:rtra=on:gtg=exists_top:ss=axioms_2999 on theBenchmark for (2999ds/12Mi)
% 4.17/1.44 % (2176752)dis+1002_1_to=kbo:sil=128000:tgt=ground:sas=z3:si=on:spb=units:tha=off:random_seed=3525067620:i=307:kws=precedence:nm=0:rtra=on_2999 on theBenchmark for (2999ds/307Mi)
% 4.17/1.44 % (2176753)dis+10_3_slsqr=1,4:to=lpo:sil=128000:thi=strong:si=on:uwa=off:s2agt=20:slsqc=1:slsq=on:random_seed=2920941412:i=201:slsql=off:asg=cautious:rtra=on:gtg=all:ss=axioms:sgt=16_2999 on theBenchmark for (2999ds/201Mi)
% 4.17/1.44 % (2176756)lrs+10_1_to=lpo:sas=z3:si=on:tha=off:random_seed=302187949:i=46:rtra=on_2999 on theBenchmark for (2999ds/46Mi)
% 4.17/1.44 % (2176755)dis+21_64_to=kbo:sil=128000:si=on:sp=weighted_frequency:uwa=alasca_can_abstract:random_seed=905124502:i=4:rtra=on_2999 on theBenchmark for (2999ds/4Mi)
% 4.17/1.44 % (2176755)Instruction limit reached!
% 4.17/1.44 % (2176755)------------------------------
% 4.17/1.44 % (2176755)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.17/1.44 % (2176755)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.17/1.44 % (2176755)CaDiCaL version: 2.1.3
% 4.17/1.44 % (2176755)Termination reason: Instruction limit
% 4.17/1.44 % (2176755)Termination phase: Saturation
% 4.17/1.44 % (2176755)Time elapsed: 0.006 s
% 4.17/1.44 % (2176755)Peak memory usage: 88 MB
% 4.17/1.44 % (2176755)Instructions burned: 5 (million)
% 4.17/1.44 % (2176751)Instruction limit reached!
% 4.17/1.44 % (2176751)------------------------------
% 4.17/1.44 % (2176751)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.17/1.44 % (2176751)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.17/1.44 % (2176751)CaDiCaL version: 2.1.3
% 4.17/1.44 % (2176751)Termination reason: Instruction limit
% 4.17/1.44 % (2176751)Termination phase: Saturation
% 4.17/1.44 % (2176751)Time elapsed: 0.044 s
% 4.17/1.44 % (2176751)Peak memory usage: 117 MB
% 4.17/1.44 % (2176751)Instructions burned: 12 (million)
% 4.17/1.44 % (2176752)Refutation not found, incomplete strategy
% 4.17/1.44 % (2176752)------------------------------
% 4.17/1.44 % (2176752)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.17/1.44 % (2176752)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.17/1.44 % (2176752)CaDiCaL version: 2.1.3
% 4.17/1.44 % (2176752)Termination reason: Refutation not found, incomplete strategy
% 4.17/1.44 % (2176752)Time elapsed: 0.058 s
% 4.17/1.44 % (2176752)Peak memory usage: 117 MB
% 4.17/1.44 % (2176752)Instructions burned: 21 (million)
% 4.17/1.44 % (2176756)Refutation not found, incomplete strategy
% 4.17/1.44 % (2176756)------------------------------
% 4.17/1.44 % (2176756)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.17/1.44 % (2176756)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.17/1.44 % (2176756)CaDiCaL version: 2.1.3
% 4.17/1.44 % (2176756)Termination reason: Refutation not found, incomplete strategy
% 4.17/1.44 % (2176756)Time elapsed: 0.044 s
% 4.17/1.44 % (2176756)Peak memory usage: 116 MB
% 4.17/1.44 % (2176756)Instructions burned: 8 (million)
% 4.17/1.44 % (2176757)Refutation found. Thanks to Tanya!
% 4.17/1.44 % SZS status Theorem for theBenchmark
% 4.17/1.44 % SZS output start Proof for theBenchmark
% See solution above
% 4.17/1.44 % (2176757)------------------------------
% 4.17/1.44 % (2176757)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.17/1.44 % (2176757)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.17/1.44 % (2176757)CaDiCaL version: 2.1.3
% 4.17/1.44 % (2176757)Termination reason: Refutation
% 4.17/1.44 % (2176757)Time elapsed: 0.049 s
% 4.17/1.44 % (2176757)Peak memory usage: 118 MB
% 4.17/1.44 % (2176757)Instructions burned: 29 (million)
% 4.17/1.44 % (2176757)------------------------------
% 4.17/1.44 % (2176757)------------------------------
% 4.17/1.44 % (2176746)Success in time 0.482 s
% 4.17/1.44 % Vampire exiting
%------------------------------------------------------------------------------