%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : DAT066_1 : TPTP v9.3.1. Released v5.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n026.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 09:47:13 AM UTC 2026
% Result : Theorem 2.68s 1.06s
% Output : Refutation 2.68s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 4
% Syntax : Number of formulae : 21 ( 6 unt; 0 typ; 2 def)
% Number of atoms : 38 ( 24 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 32 ( 15 ~; 11 |; 2 &)
% ( 2 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 4 ( 2 avg)
% Number arithmetic : 41 ( 0 atm; 13 fun; 13 num; 15 var)
% Number of types : 3 ( 1 usr; 1 ari; 0 dat; 0 cdt)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 5 ( 3 usr; 3 prp; 0-2 aty)
% Number of functors : 11 ( 9 usr; 5 con; 0-2 aty)
% Number of variables : 23 ( 20 !; 3 ?; 23 :)
% Comments :
%------------------------------------------------------------------------------
tff(type_def_5,type,
heap: $tType ).
tff(func_def_0,type,
empty: heap ).
tff(func_def_1,type,
toop: heap > $int ).
tff(func_def_2,type,
sel: ( heap * $int ) > $int ).
tff(func_def_3,type,
length: heap > $int ).
tff(func_def_4,type,
app: ( heap * $int ) > heap ).
tff(func_def_5,type,
get: heap > heap ).
tff(func_def_9,type,
sK0: $int ).
tff(func_def_10,type,
sK1: $int ).
tff(func_def_11,type,
sK2: heap ).
tff(pred_def_1,type,
lsls: ( heap * heap ) > $o ).
tff(f2,axiom,
! [X1: $int,X0: heap,X2: $int] :
( ( X1 = $sum(1,length(X0)) )
=> ( sel(app(X0,X2),X1) = X2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax_2) ).
tff(f15,conjecture,
! [X2: heap,X0: $int,X1: $int] :
( ( sel(app(X2,X0),X1) = X0 )
| ( X1 != $sum(1,length(X2)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',th_1) ).
tff(f16,negated_conjecture,
~ ! [X2: heap,X0: $int,X1: $int] :
( ( sel(app(X2,X0),X1) = X0 )
| ( X1 != $sum(1,length(X2)) ) ),
inference(negated_conjecture,[status(cth)],[f15]) ).
tff(f22,plain,
! [X2: $int,X0: $int,X1: heap] :
( ( $sum(1,length(X1)) = X0 )
=> ( sel(app(X1,X2),X0) = X2 ) ),
inference(rectify,[],[f2]) ).
tff(f26,plain,
! [X0: $int,X1: heap,X2: $int] :
( ( $sum(1,length(X1)) != X0 )
| ( sel(app(X1,X2),X0) = X2 ) ),
inference(ennf_transformation,[],[f22]) ).
tff(f27,plain,
? [X0: $int,X1: $int,X2: heap] :
( ( $sum(1,length(X2)) = X1 )
& ( sel(app(X2,X0),X1) != X0 ) ),
inference(ennf_transformation,[],[f16]) ).
tff(f31,plain,
( ( $sum(1,length(sK2)) = sK1 )
& ( sK0 != sel(app(sK2,sK0),sK1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f27]) ).
tff(f40,plain,
! [X2: $int,X0: $int,X1: heap] :
( ( $sum(1,length(X1)) != X0 )
| ( sel(app(X1,X2),X0) = X2 ) ),
inference(cnf_transformation,[],[f26]) ).
tff(f45,plain,
sK0 != sel(app(sK2,sK0),sK1),
inference(cnf_transformation,[],[f31]) ).
tff(f46,plain,
$sum(1,length(sK2)) = sK1,
inference(cnf_transformation,[],[f31]) ).
tff(f58,plain,
! [X2: $int,X1: heap] : ( sel(app(X1,X2),$sum(1,length(X1))) = X2 ),
inference(equality_resolution,[],[f40]) ).
tff(f62,definition,
( spl3_1
<=> ( $sum(1,length(sK2)) = sK1 ) ),
introduced(definition,[new_symbols(definition,[spl3_1])],[avatar_definition]) ).
tff(f64,plain,
( ( $sum(1,length(sK2)) = sK1 )
| ~ spl3_1 ),
inference(avatar_component_clause,[],[f62]) ).
tff(f65,plain,
spl3_1,
inference(avatar_split_clause,[],[f46,f62]) ).
tff(f72,definition,
( spl3_3
<=> ( sK0 = sel(app(sK2,sK0),sK1) ) ),
introduced(definition,[new_symbols(definition,[spl3_3])],[avatar_definition]) ).
tff(f74,plain,
( ( sK0 != sel(app(sK2,sK0),sK1) )
| spl3_3 ),
inference(avatar_component_clause,[],[f72]) ).
tff(f75,plain,
~ spl3_3,
inference(avatar_split_clause,[],[f45,f72]) ).
tff(f76,plain,
( ( sK0 != sel(app(sK2,sK0),$sum(1,length(sK2))) )
| ~ spl3_1
| spl3_3 ),
inference(superposition,[],[f74,f64]) ).
tff(f77,plain,
( $false
| ~ spl3_1
| spl3_3 ),
inference(forward_subsumption_resolution,[],[f76,f58]) ).
tff(f78,plain,
( ~ spl3_1
| spl3_3 ),
inference(avatar_contradiction_clause,[],[f77]) ).
tff(f79,plain,
$false,
inference(avatar_smt_refutation,[],[f78,f75,f65]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : DAT066_1 : TPTP v9.3.1. Released v5.5.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.18 % Computer : n026.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 : Tue Sep 29 00:10:27 UTC 2026
% 0.09/0.19 % CPUTime :
% 0.09/0.19 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
% 2.68/1.06 % (216706)Detected arithmetic, will pick strategies from an ALASCA-aware ARI schedule.
% 2.68/1.06 % (216716)lrs+10_1_to=lpo:sas=z3:si=on:tha=off:random_seed=858534925:i=46:rtra=on_2999 on theBenchmark for (2999ds/46Mi)
% 2.68/1.06 % (216716)First to succeed.
% 2.68/1.06 % (216716)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-216706"
% 2.68/1.06 % (216712)dis+1002_1_to=kbo:sil=128000:tgt=ground:sas=z3:si=on:spb=units:tha=off:random_seed=3554593543:i=307:kws=precedence:nm=0:rtra=on_2999 on theBenchmark for (2999ds/307Mi)
% 2.68/1.06 % (216711)dis+1002_16:1_to=lpo:sil=64000:sas=z3:si=on:norm_ineq=on:gve=force:uwa=one_side_constant:random_seed=1035760567:i=12:doe=on:rtra=on:gtg=exists_top:ss=axioms_2999 on theBenchmark for (2999ds/12Mi)
% 2.68/1.06 % (216713)dis+10_3_slsqr=1,4:to=lpo:sil=128000:thi=strong:si=on:uwa=off:s2agt=20:slsqc=1:slsq=on:random_seed=888694392:i=201:slsql=off:asg=cautious:rtra=on:gtg=all:ss=axioms:sgt=16_2999 on theBenchmark for (2999ds/201Mi)
% 2.68/1.06 % (216717)lrs+10_1_tgt=ground:sas=z3:si=on:random_seed=2189025245:i=33:rtra=on_2999 on theBenchmark for (2999ds/33Mi)
% 2.68/1.06 % (216715)dis+21_64_to=kbo:sil=128000:si=on:sp=weighted_frequency:uwa=alasca_can_abstract:random_seed=101380964:i=4:rtra=on_2999 on theBenchmark for (2999ds/4Mi)
% 2.68/1.06 % (216714)lrs+1002_4:1_to=lpo:sil=64000:si=on:br=off:random_seed=876804284:s2a=on:i=7:rtra=on:inst=on_2999 on theBenchmark for (2999ds/7Mi)
% 2.68/1.06 % (216715)Instruction limit reached!
% 2.68/1.06 % (216715)------------------------------
% 2.68/1.06 % (216715)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.68/1.06 % (216715)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.68/1.06 % (216715)CaDiCaL version: 2.1.3
% 2.68/1.06 % (216715)Termination reason: Instruction limit
% 2.68/1.06 % (216715)Termination phase: Saturation
% 2.68/1.06 % (216715)Time elapsed: 0.004 s
% 2.68/1.06 % (216715)Peak memory usage: 88 MB
% 2.68/1.06 % (216715)Instructions burned: 5 (million)
% 2.68/1.06 % (216714)Also succeeded, but the first one will report.
% 2.68/1.06 % (216712)Also succeeded, but the first one will report.
% 2.68/1.06 % (216711)Instruction limit reached!
% 2.68/1.06 % (216711)------------------------------
% 2.68/1.06 % (216711)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.68/1.06 % (216711)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.68/1.06 % (216711)CaDiCaL version: 2.1.3
% 2.68/1.06 % (216711)Termination reason: Instruction limit
% 2.68/1.06 % (216711)Termination phase: Saturation
% 2.68/1.06 % (216711)Time elapsed: 0.032 s
% 2.68/1.06 % (216711)Peak memory usage: 115 MB
% 2.68/1.06 % (216711)Instructions burned: 12 (million)
% 2.68/1.06 % (216713)Also succeeded, but the first one will report.
% 2.68/1.06 % (216717)Also succeeded, but the first one will report.
% 2.68/1.06 % (216716)Refutation found. Thanks to Tanya!
% 2.68/1.06 % SZS status Theorem for theBenchmark
% 2.68/1.06 % SZS output start Proof for theBenchmark
% See solution above
% 2.68/1.06 % (216716)------------------------------
% 2.68/1.06 % (216716)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.68/1.06 % (216716)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.68/1.06 % (216716)CaDiCaL version: 2.1.3
% 2.68/1.06 % (216716)Termination reason: Refutation
% 2.68/1.06 % (216716)Time elapsed: 0.021 s
% 2.68/1.06 % (216716)Peak memory usage: 116 MB
% 2.68/1.06 % (216716)Instructions burned: 10 (million)
% 2.68/1.06 % (216716)------------------------------
% 2.68/1.06 % (216716)------------------------------
% 2.68/1.06 % (216706)Success in time 0.302 s
% 2.68/1.06 % Vampire exiting
%------------------------------------------------------------------------------