%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ARI630_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 : n001.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 2.83s 1.11s
% Output : Refutation 2.83s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 20
% Syntax : Number of formulae : 45 ( 35 unt; 0 typ; 17 def)
% Number of atoms : 55 ( 20 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 16 ( 6 ~; 0 |; 0 &)
% ( 10 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 2 ( 1 avg)
% Maximal term depth : 5 ( 2 avg)
% Number arithmetic : 119 ( 14 atm; 55 fun; 50 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 : 14 ( 10 usr; 11 prp; 0-2 aty)
% Number of functors : 15 ( 8 usr; 11 con; 0-2 aty)
% Number of variables : 0 ( 0 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(func_def_0,type,
x: $real ).
tff(func_def_7,type,
sF0: $real ).
tff(func_def_8,type,
sF1: $real ).
tff(func_def_9,type,
sF2: $real ).
tff(func_def_10,type,
sF3: $real ).
tff(func_def_11,type,
sF4: $real ).
tff(func_def_12,type,
sF5: $real ).
tff(func_def_13,type,
sF6: $real ).
tff(f1,axiom,
$greater(x,0/1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hypothesis_00) ).
tff(f2,axiom,
$less(x,1/1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hypothesis_01) ).
tff(f3,conjecture,
$greater($quotient(1/1,$sum($product(-1/1,x),1/1)),$quotient(1/1,$sum($product(-1/1,$product(x,x)),1/1))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conclusion) ).
tff(f4,negated_conjecture,
~ $greater($quotient(1/1,$sum($product(-1/1,x),1/1)),$quotient(1/1,$sum($product(-1/1,$product(x,x)),1/1))),
inference(negated_conjecture,[status(cth)],[f3]) ).
tff(f5,plain,
~ $less($quotient(1/1,$sum($product(-1/1,$product(x,x)),1/1)),$quotient(1/1,$sum($product(-1/1,x),1/1))),
inference(theory_normalization,[],[f4]) ).
tff(f6,plain,
$less(0/1,x),
inference(theory_normalization,[],[f1]) ).
tff(f7,plain,
~ $less($quotient(1/1,$sum($product(-1/1,$product(x,x)),1/1)),$quotient(1/1,$sum($product(-1/1,x),1/1))),
inference(flattening,[],[f5]) ).
tff(f8,plain,
$less(x,1/1),
inference(cnf_transformation,[],[f2]) ).
tff(f9,plain,
~ $less($quotient(1/1,$sum($product(-1/1,$product(x,x)),1/1)),$quotient(1/1,$sum($product(-1/1,x),1/1))),
inference(cnf_transformation,[],[f7]) ).
tff(f10,plain,
$less(0/1,x),
inference(cnf_transformation,[],[f6]) ).
tff(f11,definition,
sF0 = $product(x,x),
introduced(definition,[new_symbols(definition,[sF0])],[function_definition]) ).
tff(f12,plain,
$product(x,x) = sF0,
inference(reorient_equations,[],[f11]) ).
tff(f13,definition,
sF1 = $product(-1/1,sF0),
introduced(definition,[new_symbols(definition,[sF1])],[function_definition]) ).
tff(f14,definition,
sF2 = $sum(sF1,1/1),
introduced(definition,[new_symbols(definition,[sF2])],[function_definition]) ).
tff(f15,plain,
$sum(sF1,1/1) = sF2,
inference(reorient_equations,[],[f14]) ).
tff(f16,definition,
sF3 = $quotient(1/1,sF2),
introduced(definition,[new_symbols(definition,[sF3])],[function_definition]) ).
tff(f17,plain,
$quotient(1/1,sF2) = sF3,
inference(reorient_equations,[],[f16]) ).
tff(f18,definition,
sF4 = $product(-1/1,x),
introduced(definition,[new_symbols(definition,[sF4])],[function_definition]) ).
tff(f19,plain,
$product(-1/1,x) = sF4,
inference(reorient_equations,[],[f18]) ).
tff(f20,definition,
sF5 = $sum(sF4,1/1),
introduced(definition,[new_symbols(definition,[sF5])],[function_definition]) ).
tff(f21,definition,
sF6 = $quotient(1/1,sF5),
introduced(definition,[new_symbols(definition,[sF6])],[function_definition]) ).
tff(f22,plain,
~ $less(sF3,sF6),
inference(definition_folding,[],[f9,f21,f20,f19,f17,f15,f13,f12]) ).
tff(f23,plain,
sF4 = $uminus(x),
inference(evaluation,[],[f19]) ).
tff(f24,plain,
sF1 = $uminus(sF0),
inference(evaluation,[],[f13]) ).
tff(f26,definition,
( spl7_1
<=> ( sF5 = $sum(sF4,1/1) ) ),
introduced(definition,[new_symbols(definition,[spl7_1])],[avatar_definition]) ).
tff(f29,plain,
spl7_1,
inference(avatar_split_clause,[],[f20,f26]) ).
tff(f31,definition,
( spl7_2
<=> ( $product(x,x) = sF0 ) ),
introduced(definition,[new_symbols(definition,[spl7_2])],[avatar_definition]) ).
tff(f34,plain,
spl7_2,
inference(avatar_split_clause,[],[f12,f31]) ).
tff(f36,definition,
( spl7_3
<=> $less(x,1/1) ),
introduced(definition,[new_symbols(definition,[spl7_3])],[avatar_definition]) ).
tff(f39,plain,
spl7_3,
inference(avatar_split_clause,[],[f8,f36]) ).
tff(f41,definition,
( spl7_4
<=> $less(0/1,x) ),
introduced(definition,[new_symbols(definition,[spl7_4])],[avatar_definition]) ).
tff(f44,plain,
spl7_4,
inference(avatar_split_clause,[],[f10,f41]) ).
tff(f46,definition,
( spl7_5
<=> $less(sF3,sF6) ),
introduced(definition,[new_symbols(definition,[spl7_5])],[avatar_definition]) ).
tff(f49,plain,
~ spl7_5,
inference(avatar_split_clause,[],[f22,f46]) ).
tff(f51,definition,
( spl7_6
<=> ( sF4 = $uminus(x) ) ),
introduced(definition,[new_symbols(definition,[spl7_6])],[avatar_definition]) ).
tff(f54,plain,
spl7_6,
inference(avatar_split_clause,[],[f23,f51]) ).
tff(f56,definition,
( spl7_7
<=> ( sF1 = $uminus(sF0) ) ),
introduced(definition,[new_symbols(definition,[spl7_7])],[avatar_definition]) ).
tff(f59,plain,
spl7_7,
inference(avatar_split_clause,[],[f24,f56]) ).
tff(f61,definition,
( spl7_8
<=> ( $quotient(1/1,sF2) = sF3 ) ),
introduced(definition,[new_symbols(definition,[spl7_8])],[avatar_definition]) ).
tff(f64,plain,
spl7_8,
inference(avatar_split_clause,[],[f17,f61]) ).
tff(f66,definition,
( spl7_9
<=> ( sF6 = $quotient(1/1,sF5) ) ),
introduced(definition,[new_symbols(definition,[spl7_9])],[avatar_definition]) ).
tff(f69,plain,
spl7_9,
inference(avatar_split_clause,[],[f21,f66]) ).
tff(f71,definition,
( spl7_10
<=> ( $sum(sF1,1/1) = sF2 ) ),
introduced(definition,[new_symbols(definition,[spl7_10])],[avatar_definition]) ).
tff(f74,plain,
spl7_10,
inference(avatar_split_clause,[],[f15,f71]) ).
tff(f75,plain,
$false,
inference(avatar_smt_refutation,[],[f74,f69,f64,f59,f54,f49,f44,f39,f34,f29]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ARI630_1 : TPTP v9.3.1. Released v6.3.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.19 % Computer : n001.cluster.edu
% 0.08/0.19 % Model : x86_64 x86_64
% 0.08/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.19 % Memory : 8046.5625MB
% 0.08/0.19 % OS : Linux 6.8.0-71-generic
% 0.08/0.19 % CPULimit : 300
% 0.08/0.19 % WCLimit : 300
% 0.08/0.19 % DateTime : Mon Sep 28 21:00:04 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.22 Running first-order theorem proving
% 0.08/0.22 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
% 2.83/1.11 % (737093)Detected arithmetic, will pick strategies from an ALASCA-aware ARI schedule.
% 2.83/1.11 % (737212)dis+1002_1_to=kbo:sil=128000:tgt=ground:sas=z3:si=on:spb=units:tha=off:random_seed=1628286358:i=307:kws=precedence:nm=0:rtra=on_2999 on theBenchmark for (2999ds/307Mi)
% 2.83/1.11 % (737212)First to succeed.
% 2.83/1.11 % (737212)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-737093"
% 2.83/1.11 % (737215)dis+21_64_to=kbo:sil=128000:si=on:sp=weighted_frequency:uwa=alasca_can_abstract:random_seed=2999043136:i=4:rtra=on_2999 on theBenchmark for (2999ds/4Mi)
% 2.83/1.11 % (737214)lrs+1002_4:1_to=lpo:sil=64000:si=on:br=off:random_seed=2701022466:s2a=on:i=7:rtra=on:inst=on_2999 on theBenchmark for (2999ds/7Mi)
% 2.83/1.11 % (737217)lrs+10_1_tgt=ground:sas=z3:si=on:random_seed=1243206729:i=33:rtra=on_2999 on theBenchmark for (2999ds/33Mi)
% 2.83/1.11 % (737213)dis+10_3_slsqr=1,4:to=lpo:sil=128000:thi=strong:si=on:uwa=off:s2agt=20:slsqc=1:slsq=on:random_seed=403314746:i=201:slsql=off:asg=cautious:rtra=on:gtg=all:ss=axioms:sgt=16_2999 on theBenchmark for (2999ds/201Mi)
% 2.83/1.11 % (737211)dis+1002_16:1_to=lpo:sil=64000:sas=z3:si=on:norm_ineq=on:gve=force:uwa=one_side_constant:random_seed=2625480583:i=12:doe=on:rtra=on:gtg=exists_top:ss=axioms_2999 on theBenchmark for (2999ds/12Mi)
% 2.83/1.11 % (737216)lrs+10_1_to=lpo:sas=z3:si=on:tha=off:random_seed=967531229:i=46:rtra=on_2999 on theBenchmark for (2999ds/46Mi)
% 2.83/1.11 % (737215)Instruction limit reached!
% 2.83/1.11 % (737215)------------------------------
% 2.83/1.11 % (737215)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.83/1.11 % (737215)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.83/1.11 % (737215)CaDiCaL version: 2.1.3
% 2.83/1.11 % (737215)Termination reason: Instruction limit
% 2.83/1.11 % (737215)Termination phase: Saturation
% 2.83/1.11 % (737215)Time elapsed: 0.003 s
% 2.83/1.11 % (737215)Peak memory usage: 88 MB
% 2.83/1.11 % (737215)Instructions burned: 4 (million)
% 2.83/1.11 % (737214)Instruction limit reached!
% 2.83/1.11 % (737214)------------------------------
% 2.83/1.11 % (737214)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.83/1.11 % (737214)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.83/1.11 % (737214)CaDiCaL version: 2.1.3
% 2.83/1.11 % (737214)Termination reason: Instruction limit
% 2.83/1.11 % (737214)Termination phase: Saturation
% 2.83/1.11 % (737214)Time elapsed: 0.004 s
% 2.83/1.11 % (737214)Peak memory usage: 88 MB
% 2.83/1.11 % (737214)Instructions burned: 7 (million)
% 2.83/1.11 % (737211)Instruction limit reached!
% 2.83/1.11 % (737211)------------------------------
% 2.83/1.11 % (737211)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.83/1.11 % (737211)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.83/1.11 % (737211)CaDiCaL version: 2.1.3
% 2.83/1.11 % (737211)Termination reason: Instruction limit
% 2.83/1.11 % (737211)Termination phase: Saturation
% 2.83/1.11 % (737211)Time elapsed: 0.032 s
% 2.83/1.11 % (737211)Peak memory usage: 117 MB
% 2.83/1.11 % (737211)Instructions burned: 13 (million)
% 2.83/1.11 % (737216)Also succeeded, but the first one will report.
% 2.83/1.11 % (737217)Also succeeded, but the first one will report.
% 2.83/1.11 % (737212)Refutation found. Thanks to Tanya!
% 2.83/1.11 % SZS status Theorem for theBenchmark
% 2.83/1.11 % SZS output start Proof for theBenchmark
% See solution above
% 2.83/1.11 % (737212)------------------------------
% 2.83/1.11 % (737212)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.83/1.11 % (737212)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.83/1.11 % (737212)CaDiCaL version: 2.1.3
% 2.83/1.11 % (737212)Termination reason: Refutation
% 2.83/1.11 % (737212)Time elapsed: 0.027 s
% 2.83/1.11 % (737212)Peak memory usage: 118 MB
% 2.83/1.11 % (737212)Instructions burned: 24 (million)
% 2.83/1.11 % (737212)------------------------------
% 2.83/1.11 % (737212)------------------------------
% 2.83/1.11 % (737093)Success in time 0.326 s
% 2.83/1.11 % Vampire exiting
%------------------------------------------------------------------------------