%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ARI735_1 : TPTP v9.3.1. Released v6.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n009.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 09:33:46 AM UTC 2026
% Result : Theorem 4.32s 1.39s
% Output : Refutation 4.32s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 8
% Syntax : Number of formulae : 26 ( 13 unt; 0 typ; 7 def)
% Number of atoms : 59 ( 25 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 58 ( 25 ~; 4 |; 13 &)
% ( 5 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number arithmetic : 97 ( 20 atm; 19 fun; 44 num; 14 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 : 10 ( 5 usr; 7 prp; 0-2 aty)
% Number of functors : 9 ( 3 usr; 6 con; 0-2 aty)
% Number of variables : 14 ( 8 !; 6 ?; 14 :)
% Comments :
%------------------------------------------------------------------------------
tff(func_def_5,type,
sK0: $int ).
tff(func_def_6,type,
sF1: $int ).
tff(func_def_7,type,
sF2: $int ).
tff(f1,conjecture,
! [X0: $int] :
( $greatereq(X0,0)
=> ( ( ( X0 = 0 )
=> $true )
& ( ( X0 != 0 )
=> ? [X1: $int] :
( ( X1 = $difference(X0,1) )
& $greatereq(X1,0) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',formula) ).
tff(f2,negated_conjecture,
~ ! [X0: $int] :
( $greatereq(X0,0)
=> ( ( ( X0 = 0 )
=> $true )
& ( ( X0 != 0 )
=> ? [X1: $int] :
( ( X1 = $difference(X0,1) )
& $greatereq(X1,0) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
tff(f3,plain,
~ ! [X0: $int] :
( ~ $less(X0,0)
=> ( ( ( X0 = 0 )
=> $true )
& ( ( X0 != 0 )
=> ? [X1: $int] :
( ( $sum(X0,$uminus(1)) = X1 )
& ~ $less(X1,0) ) ) ) ),
inference(theory_normalization,[],[f2]) ).
tff(f4,plain,
~ ! [X0: $int] :
( ~ $less(X0,0)
=> ( ( X0 != 0 )
=> ? [X1: $int] :
( ( $sum(X0,$uminus(1)) = X1 )
& ~ $less(X1,0) ) ) ),
inference(true_and_false_elimination,[],[f3]) ).
tff(f5,plain,
? [X0: $int] :
( ! [X1: $int] :
( $less(X1,0)
| ( $sum(X0,$uminus(1)) != X1 ) )
& ( X0 != 0 )
& ~ $less(X0,0) ),
inference(ennf_transformation,[],[f4]) ).
tff(f6,plain,
? [X0: $int] :
( ~ $less(X0,0)
& ! [X1: $int] :
( $less(X1,0)
| ( $sum(X0,$uminus(1)) != X1 ) )
& ( X0 != 0 ) ),
inference(flattening,[],[f5]) ).
tff(f7,plain,
( ~ $less(sK0,0)
& ! [X1: $int] :
( $less(X1,0)
| ( $sum(sK0,$uminus(1)) != X1 ) )
& ( 0 != sK0 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[f6]) ).
tff(f8,plain,
0 != sK0,
inference(cnf_transformation,[],[f7]) ).
tff(f9,plain,
! [X1: $int] :
( $less(X1,0)
| ( $sum(sK0,$uminus(1)) != X1 ) ),
inference(cnf_transformation,[],[f7]) ).
tff(f10,plain,
~ $less(sK0,0),
inference(cnf_transformation,[],[f7]) ).
tff(f11,plain,
$less($sum(sK0,$uminus(1)),0),
inference(equality_resolution,[],[f9]) ).
tff(f12,definition,
sF1 = $uminus(1),
introduced(definition,[new_symbols(definition,[sF1])],[function_definition]) ).
tff(f13,definition,
sF2 = $sum(sK0,sF1),
introduced(definition,[new_symbols(definition,[sF2])],[function_definition]) ).
tff(f14,plain,
$less(sF2,0),
inference(definition_folding,[],[f11,f13,f12]) ).
tff(f15,plain,
-1 = sF1,
inference(evaluation,[],[f12]) ).
tff(f17,definition,
( spl3_1
<=> $less(sF2,0) ),
introduced(definition,[new_symbols(definition,[spl3_1])],[avatar_definition]) ).
tff(f20,plain,
spl3_1,
inference(avatar_split_clause,[],[f14,f17]) ).
tff(f22,definition,
( spl3_2
<=> ( -1 = sF1 ) ),
introduced(definition,[new_symbols(definition,[spl3_2])],[avatar_definition]) ).
tff(f25,plain,
spl3_2,
inference(avatar_split_clause,[],[f15,f22]) ).
tff(f27,definition,
( spl3_3
<=> ( 0 = sK0 ) ),
introduced(definition,[new_symbols(definition,[spl3_3])],[avatar_definition]) ).
tff(f30,plain,
~ spl3_3,
inference(avatar_split_clause,[],[f8,f27]) ).
tff(f32,definition,
( spl3_4
<=> $less(sK0,0) ),
introduced(definition,[new_symbols(definition,[spl3_4])],[avatar_definition]) ).
tff(f35,plain,
~ spl3_4,
inference(avatar_split_clause,[],[f10,f32]) ).
tff(f37,definition,
( spl3_5
<=> ( sF2 = $sum(sK0,sF1) ) ),
introduced(definition,[new_symbols(definition,[spl3_5])],[avatar_definition]) ).
tff(f40,plain,
spl3_5,
inference(avatar_split_clause,[],[f13,f37]) ).
tff(f41,plain,
$false,
inference(avatar_smt_refutation,[],[f40,f35,f30,f25,f20]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ARI735_1 : TPTP v9.3.1. Released v6.4.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.19 % Computer : n009.cluster.edu
% 0.09/0.19 % Model : x86_64 x86_64
% 0.09/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.19 % Memory : 8046.5625MB
% 0.09/0.19 % OS : Linux 6.8.0-71-generic
% 0.09/0.20 % CPULimit : 300
% 0.09/0.20 % WCLimit : 300
% 0.09/0.20 % DateTime : Mon Sep 28 21:01:45 UTC 2026
% 0.09/0.20 % CPUTime :
% 0.09/0.20 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.23 Running first-order theorem proving
% 0.09/0.24 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
% 4.32/1.39 % (3471825)Detected arithmetic, will pick strategies from an ALASCA-aware ARI schedule.
% 4.32/1.39 % (3471962)dis+10_3_slsqr=1,4:to=lpo:sil=128000:thi=strong:si=on:uwa=off:s2agt=20:slsqc=1:slsq=on:random_seed=1380078756:i=201:slsql=off:asg=cautious:rtra=on:gtg=all:ss=axioms:sgt=16_2999 on theBenchmark for (2999ds/201Mi)
% 4.32/1.39 % (3471961)dis+1002_1_to=kbo:sil=128000:tgt=ground:sas=z3:si=on:spb=units:tha=off:random_seed=2391005301:i=307:kws=precedence:nm=0:rtra=on_2999 on theBenchmark for (2999ds/307Mi)
% 4.32/1.39 % (3471964)dis+21_64_to=kbo:sil=128000:si=on:sp=weighted_frequency:uwa=alasca_can_abstract:random_seed=2201782625:i=4:rtra=on_2999 on theBenchmark for (2999ds/4Mi)
% 4.32/1.39 % (3471963)lrs+1002_4:1_to=lpo:sil=64000:si=on:br=off:random_seed=600690862:s2a=on:i=7:rtra=on:inst=on_2999 on theBenchmark for (2999ds/7Mi)
% 4.32/1.39 % (3471964)Instruction limit reached!
% 4.32/1.39 % (3471964)------------------------------
% 4.32/1.39 % (3471964)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.32/1.39 % (3471964)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.32/1.39 % (3471964)CaDiCaL version: 2.1.3
% 4.32/1.39 % (3471964)Termination reason: Instruction limit
% 4.32/1.39 % (3471964)Termination phase: Saturation
% 4.32/1.39 % (3471964)Time elapsed: 0.004 s
% 4.32/1.39 % (3471964)Peak memory usage: 88 MB
% 4.32/1.39 % (3471964)Instructions burned: 5 (million)
% 4.32/1.39 % (3471963)Instruction limit reached!
% 4.32/1.39 % (3471963)------------------------------
% 4.32/1.39 % (3471963)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.32/1.39 % (3471963)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.32/1.39 % (3471963)CaDiCaL version: 2.1.3
% 4.32/1.39 % (3471963)Termination reason: Instruction limit
% 4.32/1.39 % (3471963)Termination phase: Saturation
% 4.32/1.39 % (3471963)Time elapsed: 0.005 s
% 4.32/1.39 % (3471963)Peak memory usage: 88 MB
% 4.32/1.39 % (3471963)Instructions burned: 8 (million)
% 4.32/1.39 % (3471960)dis+1002_16:1_to=lpo:sil=64000:sas=z3:si=on:norm_ineq=on:gve=force:uwa=one_side_constant:random_seed=27363274:i=12:doe=on:rtra=on:gtg=exists_top:ss=axioms_2999 on theBenchmark for (2999ds/12Mi)
% 4.32/1.39 % (3471966)lrs+10_1_tgt=ground:sas=z3:si=on:random_seed=3363499908:i=33:rtra=on_2999 on theBenchmark for (2999ds/33Mi)
% 4.32/1.39 % (3471965)lrs+10_1_to=lpo:sas=z3:si=on:tha=off:random_seed=3875436502:i=46:rtra=on_2999 on theBenchmark for (2999ds/46Mi)
% 4.32/1.39 % (3471961)First to succeed.
% 4.32/1.39 % (3471961)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3471825"
% 4.32/1.39 % (3471965)Also succeeded, but the first one will report.
% 4.32/1.39 % (3471960)Also succeeded, but the first one will report.
% 4.32/1.39 % (3471966)Also succeeded, but the first one will report.
% 4.32/1.39 % (3471962)Also succeeded, but the first one will report.
% 4.32/1.39 % (3471972)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=3265377497:i=29:thsqd=64:nm=0:thsqc=8:rtra=on:thsq=on:ev=off_2998 on theBenchmark for (2998ds/29Mi)
% 4.32/1.39 % (3471971)dis+11_3_anc=none:drc=ordering:si=on:urr=ec_only:bce=on:tha=off:sac=on:random_seed=3361883669:st=5:i=14:sd=10:rtra=on:ss=axioms:rawr=on_2998 on theBenchmark for (2998ds/14Mi)
% 4.32/1.39 % (3471971)Refutation not found, incomplete strategy
% 4.32/1.39 % (3471971)------------------------------
% 4.32/1.39 % (3471971)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.32/1.39 % (3471971)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.32/1.39 % (3471971)CaDiCaL version: 2.1.3
% 4.32/1.39 % (3471971)Termination reason: Refutation not found, incomplete strategy
% 4.32/1.39 % (3471971)Time elapsed: 0.002 s
% 4.32/1.39 % (3471971)Peak memory usage: 88 MB
% 4.32/1.39 % (3471972)Instruction limit reached!
% 4.32/1.39 % (3471972)------------------------------
% 4.32/1.39 % (3471972)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.32/1.39 % (3471972)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.32/1.39 % (3471972)CaDiCaL version: 2.1.3
% 4.32/1.39 % (3471972)Termination reason: Instruction limit
% 4.32/1.39 % (3471972)Termination phase: Saturation
% 4.32/1.39 % (3471972)Time elapsed: 0.030 s
% 4.32/1.39 % (3471972)Peak memory usage: 88 MB
% 4.32/1.39 % (3471972)Instructions burned: 29 (million)
% 4.32/1.39 % (3471961)Refutation found. Thanks to Tanya!
% 4.32/1.39 % SZS status Theorem for theBenchmark
% 4.32/1.39 % SZS output start Proof for theBenchmark
% See solution above
% 4.32/1.39 % (3471961)------------------------------
% 4.32/1.39 % (3471961)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.32/1.39 % (3471961)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.32/1.39 % (3471961)CaDiCaL version: 2.1.3
% 4.32/1.39 % (3471961)Termination reason: Refutation
% 4.32/1.39 % (3471961)Time elapsed: 0.032 s
% 4.32/1.39 % (3471961)Peak memory usage: 115 MB
% 4.32/1.39 % (3471961)Instructions burned: 9 (million)
% 4.32/1.39 % (3471961)------------------------------
% 4.32/1.39 % (3471961)------------------------------
% 4.32/1.39 % (3471825)Success in time 0.544 s
% 4.32/1.39 % Vampire exiting
%------------------------------------------------------------------------------