%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ARI687_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 : 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 09:33:39 AM UTC 2026
% Result : Theorem 1.95s 0.74s
% Output : Refutation 2.61s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 25
% Syntax : Number of formulae : 63 ( 52 unt; 0 typ; 19 def)
% Number of atoms : 74 ( 51 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 16 ( 5 ~; 0 |; 0 &)
% ( 11 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 1 avg)
% Maximal term depth : 11 ( 3 avg)
% Number of FOOLs : 1 ( 1 fml; 0 var)
% Number arithmetic : 620 ( 0 atm; 461 fun; 152 num; 7 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 ( 11 usr; 12 prp; 0-2 aty)
% Number of functors : 20 ( 10 usr; 16 con; 0-2 aty)
% Number of variables : 7 ( 7 !; 0 ?; 7 :)
% Comments :
%------------------------------------------------------------------------------
tff(func_def_0,type,
x: $int ).
tff(func_def_1,type,
y: $int ).
tff(func_def_14,type,
sF0: $int ).
tff(func_def_15,type,
sF1: $int ).
tff(func_def_16,type,
sF2: $int ).
tff(func_def_17,type,
sF3: $int ).
tff(func_def_18,type,
sF4: $int ).
tff(func_def_19,type,
sF5: $int ).
tff(func_def_20,type,
sF6: $int ).
tff(func_def_21,type,
sF7: $int ).
tff(f1,axiom,
$sum($sum($sum($product($product($product(x,x),x),y),$product($product(x,x),y)),$product($product($product(3,x),x),x)),$product($product(2,x),x)) = 0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',eq1) ).
tff(f2,axiom,
$sum($sum($sum($sum($difference($sum($product($product($product($product(2,x),x),x),y),$product(-1,$product(x,y))),y),$product($product($product(6,x),x),x)),$product(-1,$product($product(2,x),x))),$product(-1,$product(3,x))),3) = 0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',eq2) ).
tff(f4,conjecture,
$sum($product(2,$product($product(x,x),x)),$product(-1,$sum($product(5,x),$product(5,$product(x,x))))) = 0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj) ).
tff(f5,negated_conjecture,
( ( ~ $sum($product(2,$product($product(x,x),x)),$product(-1,$sum($product(5,x),$product(5,$product(x,x))))) ) = 0 ),
inference(negated_conjecture,[status(cth)],[f4]) ).
tff(f7,plain,
0 = $sum($sum($sum($sum($sum($sum($product($product($product($product(2,x),x),x),y),$product(-1,$product(x,y))),$uminus(y)),$product($product($product(6,x),x),x)),$product(-1,$product($product(2,x),x))),$product(-1,$product(3,x))),3),
inference(theory_normalization,[],[f2]) ).
tff(f8,plain,
! [X0: $int,X1: $int] : ( $sum(X1,X0) = $sum(X0,X1) ),
introduced(definition,[],[tha_commutativity]) ).
tff(f19,plain,
! [X0: $int,X1: $int] : ( $product(X0,X1) = $product(X1,X0) ),
introduced(definition,[],[tha_commutativity]) ).
tff(f20,plain,
! [X2: $int,X0: $int,X1: $int] : ( $product(X0,$product(X1,X2)) = $product($product(X0,X1),X2) ),
introduced(definition,[],[tha_associativity]) ).
tff(f26,plain,
0 != $sum($product(2,$product($product(x,x),x)),$product(-1,$sum($product(5,x),$product(5,$product(x,x))))),
inference(flattening,[],[f5]) ).
tff(f27,plain,
0 != $sum($product(2,$product($product(x,x),x)),$product(-1,$sum($product(5,x),$product(5,$product(x,x))))),
inference(cnf_transformation,[],[f26]) ).
tff(f29,plain,
$sum($sum($sum($product($product($product(x,x),x),y),$product($product(x,x),y)),$product($product($product(3,x),x),x)),$product($product(2,x),x)) = 0,
inference(cnf_transformation,[],[f1]) ).
tff(f30,plain,
0 = $sum($sum($sum($sum($sum($sum($product($product($product($product(2,x),x),x),y),$product(-1,$product(x,y))),$uminus(y)),$product($product($product(6,x),x),x)),$product(-1,$product($product(2,x),x))),$product(-1,$product(3,x))),3),
inference(cnf_transformation,[],[f7]) ).
tff(f32,definition,
sF0 = $product(x,x),
introduced(definition,[new_symbols(definition,[sF0])],[function_definition]) ).
tff(f33,plain,
$product(x,x) = sF0,
inference(reorient_equations,[],[f32]) ).
tff(f34,definition,
sF1 = $product(sF0,x),
introduced(definition,[new_symbols(definition,[sF1])],[function_definition]) ).
tff(f35,definition,
sF2 = $product(2,sF1),
introduced(definition,[new_symbols(definition,[sF2])],[function_definition]) ).
tff(f36,plain,
$product(2,sF1) = sF2,
inference(reorient_equations,[],[f35]) ).
tff(f37,definition,
sF3 = $product(5,x),
introduced(definition,[new_symbols(definition,[sF3])],[function_definition]) ).
tff(f38,plain,
$product(5,x) = sF3,
inference(reorient_equations,[],[f37]) ).
tff(f39,definition,
sF4 = $product(5,sF0),
introduced(definition,[new_symbols(definition,[sF4])],[function_definition]) ).
tff(f40,plain,
$product(5,sF0) = sF4,
inference(reorient_equations,[],[f39]) ).
tff(f41,definition,
sF5 = $sum(sF3,sF4),
introduced(definition,[new_symbols(definition,[sF5])],[function_definition]) ).
tff(f42,definition,
sF6 = $product(-1,sF5),
introduced(definition,[new_symbols(definition,[sF6])],[function_definition]) ).
tff(f43,definition,
sF7 = $sum(sF2,sF6),
introduced(definition,[new_symbols(definition,[sF7])],[function_definition]) ).
tff(f44,plain,
0 != sF7,
inference(definition_folding,[],[f27,f43,f42,f41,f40,f33,f38,f36,f34,f33]) ).
tff(f45,plain,
sF6 = $uminus(sF5),
inference(evaluation,[],[f42]) ).
tff(f47,plain,
0 = $sum($sum($sum($sum($sum($sum($product($product($product($product(2,x),x),x),y),$uminus($product(x,y))),$uminus(y)),$product($product($product(6,x),x),x)),$uminus($product($product(2,x),x))),$uminus($product(3,x))),3),
inference(evaluation,[],[f30]) ).
tff(f49,definition,
( spl8_1
<=> ( $sum($sum($sum($product($product($product(x,x),x),y),$product($product(x,x),y)),$product($product($product(3,x),x),x)),$product($product(2,x),x)) = 0 ) ),
introduced(definition,[new_symbols(definition,[spl8_1])],[avatar_definition]) ).
tff(f52,plain,
spl8_1,
inference(avatar_split_clause,[],[f29,f49]) ).
tff(f54,definition,
( spl8_2
<=> ( $product(5,sF0) = sF4 ) ),
introduced(definition,[new_symbols(definition,[spl8_2])],[avatar_definition]) ).
tff(f57,plain,
spl8_2,
inference(avatar_split_clause,[],[f40,f54]) ).
tff(f59,definition,
( spl8_3
<=> ( 0 = sF7 ) ),
introduced(definition,[new_symbols(definition,[spl8_3])],[avatar_definition]) ).
tff(f62,plain,
~ spl8_3,
inference(avatar_split_clause,[],[f44,f59]) ).
tff(f64,definition,
( spl8_4
<=> ( $product(2,sF1) = sF2 ) ),
introduced(definition,[new_symbols(definition,[spl8_4])],[avatar_definition]) ).
tff(f67,plain,
spl8_4,
inference(avatar_split_clause,[],[f36,f64]) ).
tff(f69,definition,
( spl8_5
<=> ( sF6 = $uminus(sF5) ) ),
introduced(definition,[new_symbols(definition,[spl8_5])],[avatar_definition]) ).
tff(f72,plain,
spl8_5,
inference(avatar_split_clause,[],[f45,f69]) ).
tff(f75,definition,
( spl8_6
<=> ( $product(5,x) = sF3 ) ),
introduced(definition,[new_symbols(definition,[spl8_6])],[avatar_definition]) ).
tff(f78,plain,
spl8_6,
inference(avatar_split_clause,[],[f38,f75]) ).
tff(f80,definition,
( spl8_7
<=> ( sF7 = $sum(sF2,sF6) ) ),
introduced(definition,[new_symbols(definition,[spl8_7])],[avatar_definition]) ).
tff(f83,plain,
spl8_7,
inference(avatar_split_clause,[],[f43,f80]) ).
tff(f85,definition,
( spl8_8
<=> ( sF5 = $sum(sF3,sF4) ) ),
introduced(definition,[new_symbols(definition,[spl8_8])],[avatar_definition]) ).
tff(f88,plain,
spl8_8,
inference(avatar_split_clause,[],[f41,f85]) ).
tff(f90,definition,
( spl8_9
<=> ( $product(x,x) = sF0 ) ),
introduced(definition,[new_symbols(definition,[spl8_9])],[avatar_definition]) ).
tff(f93,plain,
spl8_9,
inference(avatar_split_clause,[],[f33,f90]) ).
tff(f94,plain,
$product(x,sF0) = sF1,
inference(forward_demodulation,[],[f34,f19]) ).
tff(f95,plain,
0 = $sum(3,$sum($sum($sum($sum($sum($product($product($product($product(2,x),x),x),y),$uminus($product(x,y))),$uminus(y)),$product($product($product(6,x),x),x)),$uminus($product($product(2,x),x))),$uminus($product(3,x)))),
inference(forward_demodulation,[],[f47,f8]) ).
tff(f98,definition,
( spl8_10
<=> ( $product(x,sF0) = sF1 ) ),
introduced(definition,[new_symbols(definition,[spl8_10])],[avatar_definition]) ).
tff(f101,plain,
spl8_10,
inference(avatar_split_clause,[],[f94,f98]) ).
tff(f102,plain,
0 = $sum(3,$sum($uminus($product(3,x)),$sum($sum($sum($sum($product($product($product($product(2,x),x),x),y),$uminus($product(x,y))),$uminus(y)),$product($product($product(6,x),x),x)),$uminus($product($product(2,x),x))))),
inference(forward_demodulation,[],[f95,f8]) ).
tff(f104,plain,
0 = $sum(3,$sum($uminus($product(3,x)),$sum($uminus($product($product(2,x),x)),$sum($sum($sum($product($product($product($product(2,x),x),x),y),$uminus($product(x,y))),$uminus(y)),$product($product($product(6,x),x),x))))),
inference(forward_demodulation,[],[f102,f8]) ).
tff(f106,plain,
0 = $sum(3,$sum($uminus($product(3,x)),$sum($uminus($product($product(2,x),x)),$sum($product($product($product(6,x),x),x),$sum($sum($product($product($product($product(2,x),x),x),y),$uminus($product(x,y))),$uminus(y)))))),
inference(forward_demodulation,[],[f104,f8]) ).
tff(f108,plain,
0 = $sum(3,$sum($uminus($product(3,x)),$sum($uminus($product($product(2,x),x)),$sum($product($product($product(6,x),x),x),$sum($uminus(y),$sum($product($product($product($product(2,x),x),x),y),$uminus($product(x,y)))))))),
inference(forward_demodulation,[],[f106,f8]) ).
tff(f110,plain,
0 = $sum(3,$sum($uminus($product(3,x)),$sum($uminus($product($product(2,x),x)),$sum($product($product($product(6,x),x),x),$sum($uminus(y),$sum($uminus($product(x,y)),$product($product($product($product(2,x),x),x),y))))))),
inference(forward_demodulation,[],[f108,f8]) ).
tff(f112,plain,
0 = $sum(3,$sum($uminus($product(3,x)),$sum($uminus($product($product(2,x),x)),$sum($product($product($product(6,x),x),x),$sum($uminus(y),$sum($uminus($product(x,y)),$product($product($product(2,x),x),$product(x,y)))))))),
inference(forward_demodulation,[],[f110,f20]) ).
tff(f114,plain,
0 = $sum(3,$sum($uminus($product(3,x)),$sum($uminus($product($product(2,x),x)),$sum($product($product($product(6,x),x),x),$sum($uminus(y),$sum($uminus($product(x,y)),$product($product(2,x),$product(x,$product(x,y))))))))),
inference(forward_demodulation,[],[f112,f20]) ).
tff(f116,plain,
0 = $sum(3,$sum($uminus($product(3,x)),$sum($uminus($product($product(2,x),x)),$sum($product($product($product(6,x),x),x),$sum($uminus(y),$sum($uminus($product(x,y)),$product(2,$product(x,$product(x,$product(x,y)))))))))),
inference(forward_demodulation,[],[f114,f20]) ).
tff(f118,plain,
0 = $sum(3,$sum($uminus($product(3,x)),$sum($uminus($product($product(2,x),x)),$sum($product($product(6,x),$product(x,x)),$sum($uminus(y),$sum($uminus($product(x,y)),$product(2,$product(x,$product(x,$product(x,y)))))))))),
inference(forward_demodulation,[],[f116,f20]) ).
tff(f124,plain,
0 = $sum(3,$sum($uminus($product(3,x)),$sum($uminus($product($product(2,x),x)),$sum($product(6,$product(x,$product(x,x))),$sum($uminus(y),$sum($uminus($product(x,y)),$product(2,$product(x,$product(x,$product(x,y)))))))))),
inference(forward_demodulation,[],[f118,f20]) ).
tff(f125,plain,
0 = $sum(3,$sum($uminus($product(3,x)),$sum($uminus($product(2,$product(x,x))),$sum($product(6,$product(x,$product(x,x))),$sum($uminus(y),$sum($uminus($product(x,y)),$product(2,$product(x,$product(x,$product(x,y)))))))))),
inference(forward_demodulation,[],[f124,f20]) ).
tff(f127,definition,
( spl8_12
<=> ( 0 = $sum(3,$sum($uminus($product(3,x)),$sum($uminus($product(2,$product(x,x))),$sum($product(6,$product(x,$product(x,x))),$sum($uminus(y),$sum($uminus($product(x,y)),$product(2,$product(x,$product(x,$product(x,y)))))))))) ) ),
introduced(definition,[new_symbols(definition,[spl8_12])],[avatar_definition]) ).
tff(f130,plain,
spl8_12,
inference(avatar_split_clause,[],[f125,f127]) ).
tff(f131,plain,
$false,
inference(avatar_smt_refutation,[],[f130,f101,f93,f88,f83,f78,f72,f67,f62,f57,f52]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ARI687_1 : TPTP v9.3.1. Released v6.3.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.18 % Computer : n020.cluster.edu
% 0.09/0.18 % Model : x86_64 x86_64
% 0.09/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.18 % Memory : 8046.5625MB
% 0.09/0.18 % OS : Linux 6.8.0-71-generic
% 0.09/0.18 % CPULimit : 300
% 0.09/0.18 % WCLimit : 300
% 0.09/0.18 % DateTime : Mon Sep 28 20:58:30 UTC 2026
% 0.09/0.18 % CPUTime :
% 0.09/0.18 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.22 Running first-order theorem proving
% 0.09/0.22 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
% 1.95/0.74 % (548922)Detected arithmetic, will pick strategies from an ALASCA-aware ARI schedule.
% 1.95/0.74 % (548991)lrs+10_1_tgt=ground:sas=z3:si=on:random_seed=2458770196:i=33:rtra=on_2999 on theBenchmark for (2999ds/33Mi)
% 1.95/0.74 % (548991)First to succeed.
% 1.95/0.74 % (548991)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-548922"
% 1.95/0.74 % (548988)lrs+1002_4:1_to=lpo:sil=64000:si=on:br=off:random_seed=857491476:s2a=on:i=7:rtra=on:inst=on_2999 on theBenchmark for (2999ds/7Mi)
% 1.95/0.74 % (548987)dis+10_3_slsqr=1,4:to=lpo:sil=128000:thi=strong:si=on:uwa=off:s2agt=20:slsqc=1:slsq=on:random_seed=2955880024:i=201:slsql=off:asg=cautious:rtra=on:gtg=all:ss=axioms:sgt=16_2999 on theBenchmark for (2999ds/201Mi)
% 1.95/0.74 % (548985)dis+1002_16:1_to=lpo:sil=64000:sas=z3:si=on:norm_ineq=on:gve=force:uwa=one_side_constant:random_seed=968665384:i=12:doe=on:rtra=on:gtg=exists_top:ss=axioms_2999 on theBenchmark for (2999ds/12Mi)
% 1.95/0.74 % (548990)lrs+10_1_to=lpo:sas=z3:si=on:tha=off:random_seed=2859060678:i=46:rtra=on_2999 on theBenchmark for (2999ds/46Mi)
% 1.95/0.74 % (548986)dis+1002_1_to=kbo:sil=128000:tgt=ground:sas=z3:si=on:spb=units:tha=off:random_seed=1215444117:i=307:kws=precedence:nm=0:rtra=on_2999 on theBenchmark for (2999ds/307Mi)
% 1.95/0.74 % (548989)dis+21_64_to=kbo:sil=128000:si=on:sp=weighted_frequency:uwa=alasca_can_abstract:random_seed=4039212383:i=4:rtra=on_2999 on theBenchmark for (2999ds/4Mi)
% 1.95/0.74 % (548989)Instruction limit reached!
% 1.95/0.74 % (548989)------------------------------
% 1.95/0.74 % (548989)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 1.95/0.74 % (548989)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.95/0.74 % (548989)CaDiCaL version: 2.1.3
% 1.95/0.74 % (548989)Termination reason: Instruction limit
% 1.95/0.74 % (548989)Termination phase: Saturation
% 1.95/0.74 % (548989)Time elapsed: 0.003 s
% 1.95/0.74 % (548989)Peak memory usage: 88 MB
% 1.95/0.74 % (548989)Instructions burned: 4 (million)
% 1.95/0.74 % (548988)Instruction limit reached!
% 1.95/0.74 % (548988)------------------------------
% 1.95/0.74 % (548988)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 1.95/0.74 % (548988)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.95/0.74 % (548988)CaDiCaL version: 2.1.3
% 1.95/0.74 % (548988)Termination reason: Instruction limit
% 1.95/0.74 % (548988)Termination phase: Saturation
% 1.95/0.74 % (548988)Time elapsed: 0.004 s
% 1.95/0.74 % (548988)Peak memory usage: 88 MB
% 1.95/0.74 % (548988)Instructions burned: 7 (million)
% 1.95/0.74 % (548985)Refutation not found, incomplete strategy
% 1.95/0.74 % (548985)------------------------------
% 1.95/0.74 % (548985)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 1.95/0.74 % (548985)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.95/0.74 % (548985)CaDiCaL version: 2.1.3
% 1.95/0.74 % (548985)Termination reason: Refutation not found, incomplete strategy
% 1.95/0.74 % (548985)Time elapsed: 0.032 s
% 1.95/0.74 % (548985)Peak memory usage: 117 MB
% 1.95/0.74 % (548985)Instructions burned: 9 (million)
% 1.95/0.74 % (548990)Also succeeded, but the first one will report.
% 1.95/0.74 % (548986)Also succeeded, but the first one will report.
% 1.95/0.74 % (548987)Instruction limit reached!
% 1.95/0.74 % (548987)------------------------------
% 1.95/0.74 % (548987)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 1.95/0.74 % (548987)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.95/0.74 % (548987)CaDiCaL version: 2.1.3
% 1.95/0.74 % (548987)Termination reason: Instruction limit
% 1.95/0.74 % (548987)Termination phase: Saturation
% 1.95/0.74 % (548987)Time elapsed: 0.138 s
% 1.95/0.74 % (548987)Peak memory usage: 117 MB
% 1.95/0.74 % (548987)Instructions burned: 202 (million)
% 1.95/0.74 % (548991)Refutation found. Thanks to Tanya!
% 1.95/0.74 % SZS status Theorem for theBenchmark
% 1.95/0.74 % SZS output start Proof for theBenchmark
% See solution above
% 2.61/0.93 % (548991)------------------------------
% 2.61/0.93 % (548991)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.61/0.93 % (548991)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.61/0.93 % (548991)CaDiCaL version: 2.1.3
% 2.61/0.93 % (548991)Termination reason: Refutation
% 2.61/0.93 % (548991)Time elapsed: 0.024 s
% 2.61/0.93 % (548991)Peak memory usage: 117 MB
% 2.61/0.93 % (548991)Instructions burned: 21 (million)
% 2.61/0.93 % (548991)------------------------------
% 2.61/0.93 % (548991)------------------------------
% 2.61/0.93 % (548922)Success in time 0.311 s
% 2.61/0.93 % Vampire exiting
%------------------------------------------------------------------------------