%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : DAT009_1 : TPTP v9.3.1. Released v5.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n002.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 09:47:05 AM UTC 2026
% Result : Theorem 0.21s 1.30s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 7
% Syntax : Number of formulae : 34 ( 10 unt; 0 typ; 4 def)
% Number of atoms : 70 ( 30 equ)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 53 ( 17 ~; 16 |; 12 &)
% ( 4 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number arithmetic : 92 ( 21 atm; 13 fun; 13 num; 45 var)
% Number of types : 2 ( 1 usr; 1 ari; 0 dat; 0 cdt)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 8 ( 4 usr; 5 prp; 0-2 aty)
% Number of functors : 8 ( 6 usr; 5 con; 0-3 aty)
% Number of variables : 67 ( 55 !; 12 ?; 67 :)
% Comments :
%------------------------------------------------------------------------------
tff(type_def_5,type,
array: $tType ).
tff(func_def_0,type,
read: ( array * $int ) > $int ).
tff(func_def_1,type,
write: ( array * $int * $int ) > array ).
tff(func_def_4,type,
sK0: array ).
tff(func_def_5,type,
sK1: $int ).
tff(func_def_6,type,
sK2: array ).
tff(func_def_7,type,
sK3: $int ).
tff(f1,axiom,
! [X0: array,X2: $int,X1: $int] : ( read(write(X0,X1,X2),X1) = X2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax1) ).
tff(f2,axiom,
! [X1: $int,X3: $int,X0: array,X2: $int] :
( ( X1 = X2 )
| ( read(write(X0,X1,X3),X2) = read(X0,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax2) ).
tff(f3,conjecture,
! [X0: array,X2: $int,X1: array] :
( ( ( X0 = write(X1,X2,$sum(X2,3)) )
& ! [X3: $int] : $greater(read(X1,X3),X3) )
=> ! [X4: $int] : $greater(read(X0,X4),X4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1) ).
tff(f4,negated_conjecture,
~ ! [X0: array,X2: $int,X1: array] :
( ( ( X0 = write(X1,X2,$sum(X2,3)) )
& ! [X3: $int] : $greater(read(X1,X3),X3) )
=> ! [X4: $int] : $greater(read(X0,X4),X4) ),
inference(negated_conjecture,[status(cth)],[f3]) ).
tff(f5,plain,
~ ! [X0: array,X2: $int,X1: array] :
( ( ( X0 = write(X1,X2,$sum(X2,3)) )
& ! [X3: $int] : $less(X3,read(X1,X3)) )
=> ! [X4: $int] : $less(X4,read(X0,X4)) ),
inference(theory_normalization,[],[f4]) ).
tff(f6,plain,
~ ! [X0: array,X1: $int,X2: array] :
( ( ( write(X2,X1,$sum(X1,3)) = X0 )
& ! [X3: $int] : $less(X3,read(X2,X3)) )
=> ! [X4: $int] : $less(X4,read(X0,X4)) ),
inference(rectify,[],[f5]) ).
tff(f7,plain,
! [X3: $int,X0: $int,X2: array,X1: $int] :
( ( X0 = X3 )
| ( read(X2,X3) = read(write(X2,X0,X1),X3) ) ),
inference(rectify,[],[f2]) ).
tff(f8,plain,
! [X2: $int,X1: $int,X0: array] : ( read(write(X0,X2,X1),X2) = X1 ),
inference(rectify,[],[f1]) ).
tff(f9,plain,
? [X0: array,X1: $int,X2: array] :
( ? [X4: $int] : ~ $less(X4,read(X0,X4))
& ( write(X2,X1,$sum(X1,3)) = X0 )
& ! [X3: $int] : $less(X3,read(X2,X3)) ),
inference(ennf_transformation,[],[f6]) ).
tff(f10,plain,
? [X2: array,X1: $int,X0: array] :
( ( write(X2,X1,$sum(X1,3)) = X0 )
& ? [X4: $int] : ~ $less(X4,read(X0,X4))
& ! [X3: $int] : $less(X3,read(X2,X3)) ),
inference(flattening,[],[f9]) ).
tff(f11,plain,
! [X0: $int,X1: $int,X2: array] : ( read(write(X2,X0,X1),X0) = X1 ),
inference(rectify,[],[f8]) ).
tff(f12,plain,
! [X0: $int,X1: $int,X2: array,X3: $int] :
( ( X0 = X1 )
| ( read(write(X2,X1,X3),X0) = read(X2,X0) ) ),
inference(rectify,[],[f7]) ).
tff(f13,plain,
? [X0: array,X1: $int,X2: array] :
( ( write(X0,X1,$sum(X1,3)) = X2 )
& ? [X3: $int] : ~ $less(X3,read(X2,X3))
& ! [X4: $int] : $less(X4,read(X0,X4)) ),
inference(rectify,[],[f10]) ).
tff(f14,plain,
( ( sK2 = write(sK0,sK1,$sum(sK1,3)) )
& ~ $less(sK3,read(sK2,sK3))
& ! [X4: $int] : $less(X4,read(sK0,X4)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3)],[f13]) ).
tff(f15,plain,
! [X2: array,X0: $int,X1: $int] : ( read(write(X2,X0,X1),X0) = X1 ),
inference(cnf_transformation,[],[f11]) ).
tff(f16,plain,
! [X2: array,X3: $int,X0: $int,X1: $int] :
( ( read(write(X2,X1,X3),X0) = read(X2,X0) )
| ( X0 = X1 ) ),
inference(cnf_transformation,[],[f12]) ).
tff(f17,plain,
! [X4: $int] : $less(X4,read(sK0,X4)),
inference(cnf_transformation,[],[f14]) ).
tff(f18,plain,
~ $less(sK3,read(sK2,sK3)),
inference(cnf_transformation,[],[f14]) ).
tff(f19,plain,
sK2 = write(sK0,sK1,$sum(sK1,3)),
inference(cnf_transformation,[],[f14]) ).
tff(f21,definition,
( spl4_1
<=> $less(sK3,read(sK2,sK3)) ),
introduced(definition,[new_symbols(definition,[spl4_1])],[avatar_definition]) ).
tff(f23,plain,
( ~ $less(sK3,read(sK2,sK3))
| spl4_1 ),
inference(avatar_component_clause,[],[f21]) ).
tff(f24,plain,
~ spl4_1,
inference(avatar_split_clause,[],[f18,f21]) ).
tff(f26,definition,
( spl4_2
<=> ( sK2 = write(sK0,sK1,$sum(sK1,3)) ) ),
introduced(definition,[new_symbols(definition,[spl4_2])],[avatar_definition]) ).
tff(f28,plain,
( ( sK2 = write(sK0,sK1,$sum(sK1,3)) )
| ~ spl4_2 ),
inference(avatar_component_clause,[],[f26]) ).
tff(f29,plain,
spl4_2,
inference(avatar_split_clause,[],[f19,f26]) ).
tff(f30,plain,
( ( $sum(sK1,3) = read(sK2,sK1) )
| ~ spl4_2 ),
inference(superposition,[],[f15,f28]) ).
tff(f32,definition,
( spl4_3
<=> ( $sum(sK1,3) = read(sK2,sK1) ) ),
introduced(definition,[new_symbols(definition,[spl4_3])],[avatar_definition]) ).
tff(f35,plain,
( spl4_3
| ~ spl4_2 ),
inference(avatar_split_clause,[],[f30,f26,f32]) ).
tff(f36,plain,
( ! [X0: $int] :
( ( read(sK2,X0) = read(sK0,X0) )
| ( sK1 = X0 ) )
| ~ spl4_2 ),
inference(superposition,[],[f16,f28]) ).
tff(f37,plain,
( ! [X0: $int] :
( $less(X0,read(sK2,X0))
| ( sK1 = X0 ) )
| ~ spl4_2 ),
inference(superposition,[],[f17,f36]) ).
tff(f38,plain,
( ( sK1 = sK3 )
| spl4_1
| ~ spl4_2 ),
inference(resolution,[],[f37,f23]) ).
tff(f40,definition,
( spl4_4
<=> ( sK1 = sK3 ) ),
introduced(definition,[new_symbols(definition,[spl4_4])],[avatar_definition]) ).
tff(f43,plain,
( spl4_4
| spl4_1
| ~ spl4_2 ),
inference(avatar_split_clause,[],[f38,f26,f21,f40]) ).
tff(f44,plain,
$false,
inference(avatar_smt_refutation,[],[f43,f35,f29,f24]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : DAT009_1 : TPTP v9.3.1. Released v5.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.19 % Computer : n002.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
% 0.09/0.19 % CPULimit : 300
% 0.09/0.19 % WCLimit : 300
% 0.09/0.19 % DateTime : Tue Sep 29 00:07:53 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
% 0.09/0.23 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
% 3.01/1.11 % (906803)Detected arithmetic, will pick strategies from an ALASCA-aware ARI schedule.
% 3.01/1.11 % (906814)lrs+10_1_tgt=ground:sas=z3:si=on:random_seed=1790648980:i=33:rtra=on_2999 on theBenchmark for (2999ds/33Mi)
% 3.01/1.11 % (906814)Instruction limit reached!
% 3.01/1.11 % (906814)------------------------------
% 3.01/1.11 % (906814)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.01/1.11 % (906814)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.01/1.11 % (906814)CaDiCaL version: 2.1.3
% 3.01/1.11 % (906814)Termination reason: Instruction limit
% 3.01/1.11 % (906814)Termination phase: Saturation
% 3.01/1.11 % (906814)Time elapsed: 0.029 s
% 3.01/1.11 % (906814)Peak memory usage: 116 MB
% 3.01/1.11 % (906814)Instructions burned: 34 (million)
% 3.01/1.11 % (906808)dis+1002_16:1_to=lpo:sil=64000:sas=z3:si=on:norm_ineq=on:gve=force:uwa=one_side_constant:random_seed=2337098446:i=12:doe=on:rtra=on:gtg=exists_top:ss=axioms_2999 on theBenchmark for (2999ds/12Mi)
% 3.01/1.11 % (906813)lrs+10_1_to=lpo:sas=z3:si=on:tha=off:random_seed=2809167385:i=46:rtra=on_2999 on theBenchmark for (2999ds/46Mi)
% 3.01/1.11 % (906810)dis+10_3_slsqr=1,4:to=lpo:sil=128000:thi=strong:si=on:uwa=off:s2agt=20:slsqc=1:slsq=on:random_seed=1884226943:i=201:slsql=off:asg=cautious:rtra=on:gtg=all:ss=axioms:sgt=16_2999 on theBenchmark for (2999ds/201Mi)
% 3.01/1.11 % (906811)lrs+1002_4:1_to=lpo:sil=64000:si=on:br=off:random_seed=2692636787:s2a=on:i=7:rtra=on:inst=on_2999 on theBenchmark for (2999ds/7Mi)
% 3.01/1.11 % (906812)dis+21_64_to=kbo:sil=128000:si=on:sp=weighted_frequency:uwa=alasca_can_abstract:random_seed=2328335105:i=4:rtra=on_2999 on theBenchmark for (2999ds/4Mi)
% 3.01/1.11 % (906809)dis+1002_1_to=kbo:sil=128000:tgt=ground:sas=z3:si=on:spb=units:tha=off:random_seed=334385690:i=307:kws=precedence:nm=0:rtra=on_2999 on theBenchmark for (2999ds/307Mi)
% 3.01/1.11 % (906812)Instruction limit reached!
% 3.01/1.11 % (906812)------------------------------
% 3.01/1.11 % (906812)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.01/1.11 % (906812)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.01/1.11 % (906812)CaDiCaL version: 2.1.3
% 3.01/1.11 % (906812)Termination reason: Instruction limit
% 3.01/1.11 % (906812)Termination phase: Saturation
% 3.01/1.11 % (906812)Time elapsed: 0.004 s
% 3.01/1.11 % (906812)Peak memory usage: 88 MB
% 3.01/1.11 % (906812)Instructions burned: 5 (million)
% 3.01/1.11 % (906811)Instruction limit reached!
% 3.01/1.11 % (906811)------------------------------
% 3.01/1.11 % (906811)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.01/1.11 % (906811)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.01/1.11 % (906811)CaDiCaL version: 2.1.3
% 3.01/1.11 % (906811)Termination reason: Instruction limit
% 3.01/1.11 % (906811)Termination phase: Saturation
% 3.01/1.11 % (906811)Time elapsed: 0.005 s
% 3.01/1.11 % (906811)Peak memory usage: 88 MB
% 3.01/1.11 % (906811)Instructions burned: 7 (million)
% 3.01/1.11 % (906808)Instruction limit reached!
% 3.01/1.11 % (906808)------------------------------
% 3.01/1.11 % (906808)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.01/1.11 % (906808)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.01/1.11 % (906808)CaDiCaL version: 2.1.3
% 3.01/1.11 % (906808)Termination reason: Instruction limit
% 3.01/1.11 % (906808)Termination phase: Saturation
% 3.01/1.11 % (906808)Time elapsed: 0.032 s
% 3.01/1.11 % (906808)Peak memory usage: 115 MB
% 3.01/1.11 % (906808)Instructions burned: 12 (million)
% 3.01/1.11 % (906813)First to succeed.
% 3.01/1.11 % (906809)Also succeeded, but the first one will report.
% 3.01/1.11 % (906813)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-906803"
% 3.01/1.11 % (906817)dis+11_3_anc=none:drc=ordering:si=on:urr=ec_only:bce=on:tha=off:sac=on:random_seed=3597427854:st=5:i=14:sd=10:rtra=on:ss=axioms:rawr=on_2998 on theBenchmark for (2998ds/14Mi)
% 3.01/1.11 % (906817)Refutation not found, incomplete strategy
% 3.01/1.11 % (906817)------------------------------
% 3.01/1.11 % (906817)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.01/1.11 % (906817)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.01/1.11 % (906817)CaDiCaL version: 2.1.3
% 3.01/1.11 % (906817)Termination reason: Refutation not found, incomplete strategy
% 3.01/1.11 % (906817)Time elapsed: 0.001 s
% 3.01/1.11 % (906817)Peak memory usage: 89 MB
% 3.01/1.11 % (906817)Instructions burned: 1 (million)
% 0.21/1.30 % (906824)ott+21_1024_to=lakbo:sil=128000:bsd=on:si=on:alasca=on:uwa=alasca_main:nwc=0.5:random_seed=746589233:cond=on:i=16:fgj=on:ep=RS:asg=force:nm=10:rtra=on:rawr=on_2998 on theBenchmark for (2998ds/16Mi)
% 0.21/1.30 % (906824)Refutation not found, incomplete strategy
% 0.21/1.30 % (906824)------------------------------
% 0.21/1.30 % (906824)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.21/1.30 % (906824)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/1.30 % (906824)CaDiCaL version: 2.1.3
% 0.21/1.30 % (906824)Termination reason: Refutation not found, incomplete strategy
% 0.21/1.30 % (906824)Time elapsed: 0.006 s
% 0.21/1.30 % (906824)Peak memory usage: 90 MB
% 0.21/1.30 % (906824)Instructions burned: 7 (million)
% 0.21/1.30 % (906823)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=918447978:i=29:thsqd=64:nm=0:thsqc=8:rtra=on:thsq=on:ev=off_2998 on theBenchmark for (2998ds/29Mi)
% 0.21/1.30 % (906825)dis+1011_1_prc=on:drc=off:si=on:sac=on:random_seed=978774745:i=24:canc=force:rtra=on_2998 on theBenchmark for (2998ds/24Mi)
% 0.21/1.30 % (906823)Instruction limit reached!
% 0.21/1.30 % (906823)------------------------------
% 0.21/1.30 % (906823)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.21/1.30 % (906823)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/1.30 % (906823)CaDiCaL version: 2.1.3
% 0.21/1.30 % (906823)Termination reason: Instruction limit
% 0.21/1.30 % (906823)Termination phase: Saturation
% 0.21/1.30 % (906823)Time elapsed: 0.020 s
% 0.21/1.30 % (906823)Peak memory usage: 88 MB
% 0.21/1.30 % (906823)Instructions burned: 29 (million)
% 0.21/1.30 % (906810)Instruction limit reached!
% 0.21/1.30 % (906810)------------------------------
% 0.21/1.30 % (906810)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.21/1.30 % (906810)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/1.30 % (906810)CaDiCaL version: 2.1.3
% 0.21/1.30 % (906810)Termination reason: Instruction limit
% 0.21/1.30 % (906810)Termination phase: Saturation
% 0.21/1.30 % (906810)Time elapsed: 0.166 s
% 0.21/1.30 % (906810)Peak memory usage: 118 MB
% 0.21/1.30 % (906810)Instructions burned: 201 (million)
% 0.21/1.30 % (906825)Also succeeded, but the first one will report.
% 0.21/1.30 % (906817)------------------------------
% 0.21/1.30 % (906817)------------------------------
% 0.21/1.30 % (906830)ott+1010_8_to=lpo:sil=128000:si=on:norm_ineq=on:sp=unary_frequency:sos=on:gve=cautious:spb=goal_then_units:uwa=alasca_main_floor:tha=some:random_seed=3605351281:i=27:canc=cautious:fsr=off:rtra=on_2996 on theBenchmark for (2996ds/27Mi)
% 0.21/1.30 % (906813)Refutation found. Thanks to Tanya!
% 0.21/1.30 % SZS status Theorem for theBenchmark
% 0.21/1.30 % SZS output start Proof for theBenchmark
% See solution above
% 0.21/1.30 % (906813)------------------------------
% 0.21/1.30 % (906813)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.21/1.30 % (906813)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/1.30 % (906813)CaDiCaL version: 2.1.3
% 0.21/1.30 % (906813)Termination reason: Refutation
% 0.21/1.30 % (906813)Time elapsed: 0.034 s
% 0.21/1.30 % (906813)Peak memory usage: 116 MB
% 0.21/1.30 % (906813)Instructions burned: 12 (million)
% 0.21/1.30 % (906813)------------------------------
% 0.21/1.30 % (906813)------------------------------
% 0.21/1.30 % (906803)Success in time 0.442 s
% 0.21/1.30 % Vampire exiting
%------------------------------------------------------------------------------