%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : DAT024_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 : n003.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 09:47:07 AM UTC 2026
% Result : Theorem 0.19s 1.31s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 8
% Syntax : Number of formulae : 28 ( 9 unt; 0 typ; 6 def)
% Number of atoms : 79 ( 4 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 87 ( 36 ~; 14 |; 22 &)
% ( 6 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number arithmetic : 80 ( 22 atm; 0 fun; 41 num; 17 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 : 11 ( 7 usr; 7 prp; 0-2 aty)
% Number of functors : 8 ( 5 usr; 6 con; 0-2 aty)
% Number of variables : 23 ( 17 !; 6 ?; 23 :)
% Comments :
%------------------------------------------------------------------------------
tff(type_def_5,type,
collection: $tType ).
tff(func_def_0,type,
empty: collection ).
tff(func_def_1,type,
add: ( $int * collection ) > collection ).
tff(func_def_2,type,
remove: ( $int * collection ) > collection ).
tff(func_def_8,type,
sK0: collection ).
tff(func_def_9,type,
sK1: $int ).
tff(pred_def_1,type,
in: ( $int * collection ) > $o ).
tff(f6,conjecture,
! [X0: collection] :
( ( ~ in(1,X0)
& ~ in(0,X0)
& ! [X1: $int] :
( in(X1,X0)
=> $greatereq(X1,0) ) )
=> ! [X2: $int] :
( in(X2,X0)
=> $greatereq(X2,2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1) ).
tff(f7,negated_conjecture,
~ ! [X0: collection] :
( ( ~ in(1,X0)
& ~ in(0,X0)
& ! [X1: $int] :
( in(X1,X0)
=> $greatereq(X1,0) ) )
=> ! [X2: $int] :
( in(X2,X0)
=> $greatereq(X2,2) ) ),
inference(negated_conjecture,[status(cth)],[f6]) ).
tff(f8,plain,
~ ! [X0: collection] :
( ( ~ in(1,X0)
& ~ in(0,X0)
& ! [X1: $int] :
( in(X1,X0)
=> ~ $less(X1,0) ) )
=> ! [X2: $int] :
( in(X2,X0)
=> ~ $less(X2,2) ) ),
inference(theory_normalization,[],[f7]) ).
tff(f16,plain,
! [X0: $int,X1: $int] :
( $less(X1,X0)
| $less(X0,X1)
| ( X0 = X1 ) ),
introduced(definition,[],[tha_order_totality]) ).
tff(f23,plain,
? [X0: collection] :
( ? [X2: $int] :
( in(X2,X0)
& $less(X2,2) )
& ~ in(1,X0)
& ~ in(0,X0)
& ! [X1: $int] :
( ~ $less(X1,0)
| ~ in(X1,X0) ) ),
inference(ennf_transformation,[],[f8]) ).
tff(f24,plain,
? [X0: collection] :
( ~ in(0,X0)
& ? [X2: $int] :
( in(X2,X0)
& $less(X2,2) )
& ! [X1: $int] :
( ~ $less(X1,0)
| ~ in(X1,X0) )
& ~ in(1,X0) ),
inference(flattening,[],[f23]) ).
tff(f31,plain,
? [X0: collection] :
( ~ in(0,X0)
& ? [X1: $int] :
( in(X1,X0)
& $less(X1,2) )
& ! [X2: $int] :
( ~ $less(X2,0)
| ~ in(X2,X0) )
& ~ in(1,X0) ),
inference(rectify,[],[f24]) ).
tff(f32,plain,
( ~ in(0,sK0)
& in(sK1,sK0)
& $less(sK1,2)
& ! [X2: $int] :
( ~ $less(X2,0)
| ~ in(X2,sK0) )
& ~ in(1,sK0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f31]) ).
tff(f42,plain,
~ in(1,sK0),
inference(cnf_transformation,[],[f32]) ).
tff(f43,plain,
! [X2: $int] :
( ~ $less(X2,0)
| ~ in(X2,sK0) ),
inference(cnf_transformation,[],[f32]) ).
tff(f44,plain,
$less(sK1,2),
inference(cnf_transformation,[],[f32]) ).
tff(f45,plain,
in(sK1,sK0),
inference(cnf_transformation,[],[f32]) ).
tff(f46,plain,
~ in(0,sK0),
inference(cnf_transformation,[],[f32]) ).
tff(f50,definition,
( spl2_1
<=> in(1,sK0) ),
introduced(definition,[new_symbols(definition,[spl2_1])],[avatar_definition]) ).
tff(f53,plain,
~ spl2_1,
inference(avatar_split_clause,[],[f42,f50]) ).
tff(f55,definition,
( spl2_2
<=> in(0,sK0) ),
introduced(definition,[new_symbols(definition,[spl2_2])],[avatar_definition]) ).
tff(f58,plain,
~ spl2_2,
inference(avatar_split_clause,[],[f46,f55]) ).
tff(f60,definition,
( spl2_3
<=> in(sK1,sK0) ),
introduced(definition,[new_symbols(definition,[spl2_3])],[avatar_definition]) ).
tff(f62,plain,
( in(sK1,sK0)
| ~ spl2_3 ),
inference(avatar_component_clause,[],[f60]) ).
tff(f63,plain,
spl2_3,
inference(avatar_split_clause,[],[f45,f60]) ).
tff(f65,definition,
( spl2_4
<=> $less(sK1,2) ),
introduced(definition,[new_symbols(definition,[spl2_4])],[avatar_definition]) ).
tff(f68,plain,
spl2_4,
inference(avatar_split_clause,[],[f44,f65]) ).
tff(f98,plain,
! [X0: $int] :
( ~ in(X0,sK0)
| $less(0,X0)
| ( 0 = X0 ) ),
inference(resolution,[],[f16,f43]) ).
tff(f102,plain,
( ( 0 = sK1 )
| $less(0,sK1)
| ~ spl2_3 ),
inference(resolution,[],[f98,f62]) ).
tff(f104,definition,
( spl2_5
<=> $less(0,sK1) ),
introduced(definition,[new_symbols(definition,[spl2_5])],[avatar_definition]) ).
tff(f108,definition,
( spl2_6
<=> ( 0 = sK1 ) ),
introduced(definition,[new_symbols(definition,[spl2_6])],[avatar_definition]) ).
tff(f111,plain,
( spl2_5
| spl2_6
| ~ spl2_3 ),
inference(avatar_split_clause,[],[f102,f60,f108,f104]) ).
tff(f112,plain,
$false,
inference(avatar_smt_refutation,[],[f111,f68,f63,f58,f53]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : DAT024_1 : TPTP v9.3.1. Released v5.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.18 % Computer : n003.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 00:07:28 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
% 0.19/1.31 % (2153091)Detected arithmetic, will pick strategies from an ALASCA-aware ARI schedule.
% 0.19/1.31 % (2153100)dis+21_64_to=kbo:sil=128000:si=on:sp=weighted_frequency:uwa=alasca_can_abstract:random_seed=1259875110:i=4:rtra=on_2999 on theBenchmark for (2999ds/4Mi)
% 0.19/1.31 % (2153100)Instruction limit reached!
% 0.19/1.31 % (2153100)------------------------------
% 0.19/1.31 % (2153100)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.19/1.31 % (2153100)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/1.31 % (2153100)CaDiCaL version: 2.1.3
% 0.19/1.31 % (2153100)Termination reason: Instruction limit
% 0.19/1.31 % (2153100)Termination phase: Saturation
% 0.19/1.31 % (2153100)Time elapsed: 0.003 s
% 0.19/1.31 % (2153100)Peak memory usage: 89 MB
% 0.19/1.31 % (2153100)Instructions burned: 7 (million)
% 0.19/1.31 % (2153101)lrs+10_1_to=lpo:sas=z3:si=on:tha=off:random_seed=2194612184:i=46:rtra=on_2999 on theBenchmark for (2999ds/46Mi)
% 0.19/1.31 % (2153099)lrs+1002_4:1_to=lpo:sil=64000:si=on:br=off:random_seed=3319224396:s2a=on:i=7:rtra=on:inst=on_2999 on theBenchmark for (2999ds/7Mi)
% 0.19/1.31 % (2153097)dis+1002_1_to=kbo:sil=128000:tgt=ground:sas=z3:si=on:spb=units:tha=off:random_seed=446331967:i=307:kws=precedence:nm=0:rtra=on_2999 on theBenchmark for (2999ds/307Mi)
% 0.19/1.31 % (2153096)dis+1002_16:1_to=lpo:sil=64000:sas=z3:si=on:norm_ineq=on:gve=force:uwa=one_side_constant:random_seed=1250454238:i=12:doe=on:rtra=on:gtg=exists_top:ss=axioms_2999 on theBenchmark for (2999ds/12Mi)
% 0.19/1.31 % (2153102)lrs+10_1_tgt=ground:sas=z3:si=on:random_seed=4138373639:i=33:rtra=on_2999 on theBenchmark for (2999ds/33Mi)
% 0.19/1.31 % (2153098)dis+10_3_slsqr=1,4:to=lpo:sil=128000:thi=strong:si=on:uwa=off:s2agt=20:slsqc=1:slsq=on:random_seed=847830954:i=201:slsql=off:asg=cautious:rtra=on:gtg=all:ss=axioms:sgt=16_2999 on theBenchmark for (2999ds/201Mi)
% 0.19/1.31 % (2153099)Instruction limit reached!
% 0.19/1.31 % (2153099)------------------------------
% 0.19/1.31 % (2153099)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.19/1.31 % (2153099)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/1.31 % (2153099)CaDiCaL version: 2.1.3
% 0.19/1.31 % (2153099)Termination reason: Instruction limit
% 0.19/1.31 % (2153099)Termination phase: Saturation
% 0.19/1.31 % (2153099)Time elapsed: 0.007 s
% 0.19/1.31 % (2153099)Peak memory usage: 88 MB
% 0.19/1.31 % (2153099)Instructions burned: 8 (million)
% 0.19/1.31 % (2153101)Refutation not found, incomplete strategy
% 0.19/1.31 % (2153101)------------------------------
% 0.19/1.31 % (2153101)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.19/1.31 % (2153101)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/1.31 % (2153101)CaDiCaL version: 2.1.3
% 0.19/1.31 % (2153101)Termination reason: Refutation not found, incomplete strategy
% 0.19/1.31 % (2153101)Time elapsed: 0.030 s
% 0.19/1.31 % (2153101)Peak memory usage: 115 MB
% 0.19/1.31 % (2153101)Instructions burned: 7 (million)
% 0.19/1.31 % (2153097)Refutation not found, incomplete strategy
% 0.19/1.31 % (2153097)------------------------------
% 0.19/1.31 % (2153097)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.19/1.31 % (2153097)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/1.31 % (2153097)CaDiCaL version: 2.1.3
% 0.19/1.31 % (2153097)Termination reason: Refutation not found, incomplete strategy
% 0.19/1.31 % (2153097)Time elapsed: 0.030 s
% 0.19/1.31 % (2153097)Peak memory usage: 115 MB
% 0.19/1.31 % (2153097)Instructions burned: 7 (million)
% 0.19/1.31 % (2153096)Instruction limit reached!
% 0.19/1.31 % (2153096)------------------------------
% 0.19/1.31 % (2153096)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.19/1.31 % (2153096)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/1.31 % (2153096)CaDiCaL version: 2.1.3
% 0.19/1.31 % (2153096)Termination reason: Instruction limit
% 0.19/1.31 % (2153096)Termination phase: Saturation
% 0.19/1.31 % (2153096)Time elapsed: 0.032 s
% 0.19/1.31 % (2153096)Peak memory usage: 114 MB
% 0.19/1.31 % (2153096)Instructions burned: 13 (million)
% 0.19/1.31 % (2153102)First to succeed.
% 0.19/1.31 % (2153102)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2153091"
% 0.19/1.31 % (2153104)dis+11_3_anc=none:drc=ordering:si=on:urr=ec_only:bce=on:tha=off:sac=on:random_seed=58152580:st=5:i=14:sd=10:rtra=on:ss=axioms:rawr=on_2998 on theBenchmark for (2998ds/14Mi)
% 0.19/1.31 % (2153104)Refutation not found, incomplete strategy
% 0.19/1.31 % (2153104)------------------------------
% 0.19/1.31 % (2153104)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.19/1.31 % (2153104)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/1.31 % (2153104)CaDiCaL version: 2.1.3
% 0.19/1.31 % (2153104)Termination reason: Refutation not found, incomplete strategy
% 0.19/1.31 % (2153104)Time elapsed: 0.001 s
% 0.19/1.31 % (2153104)Peak memory usage: 89 MB
% 0.19/1.31 % (2153104)Instructions burned: 1 (million)
% 0.19/1.31 % (2153098)Instruction limit reached!
% 0.19/1.31 % (2153098)------------------------------
% 0.19/1.31 % (2153098)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.19/1.31 % (2153098)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/1.31 % (2153098)CaDiCaL version: 2.1.3
% 0.19/1.31 % (2153098)Termination reason: Instruction limit
% 0.19/1.31 % (2153098)Termination phase: Saturation
% 0.19/1.31 % (2153098)Time elapsed: 0.137 s
% 0.19/1.31 % (2153098)Peak memory usage: 116 MB
% 0.19/1.31 % (2153098)Instructions burned: 203 (million)
% 0.19/1.31 % (2153111)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=3906708663:i=29:thsqd=64:nm=0:thsqc=8:rtra=on:thsq=on:ev=off_2998 on theBenchmark for (2998ds/29Mi)
% 0.19/1.31 % (2153111)Instruction limit reached!
% 0.19/1.31 % (2153111)------------------------------
% 0.19/1.31 % (2153111)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.19/1.31 % (2153111)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/1.31 % (2153111)CaDiCaL version: 2.1.3
% 0.19/1.31 % (2153111)Termination reason: Instruction limit
% 0.19/1.31 % (2153111)Termination phase: Saturation
% 0.19/1.31 % (2153111)Time elapsed: 0.019 s
% 0.19/1.31 % (2153111)Peak memory usage: 88 MB
% 0.19/1.31 % (2153111)Instructions burned: 29 (million)
% 0.19/1.31 % (2153112)ott+21_1024_to=lakbo:sil=128000:bsd=on:si=on:alasca=on:uwa=alasca_main:nwc=0.5:random_seed=2157825920:cond=on:i=16:fgj=on:ep=RS:asg=force:nm=10:rtra=on:rawr=on_2997 on theBenchmark for (2997ds/16Mi)
% 0.19/1.31 % (2153112)Refutation not found, incomplete strategy
% 0.19/1.31 % (2153112)------------------------------
% 0.19/1.31 % (2153112)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.19/1.31 % (2153112)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/1.31 % (2153112)CaDiCaL version: 2.1.3
% 0.19/1.31 % (2153112)Termination reason: Refutation not found, incomplete strategy
% 0.19/1.31 % (2153112)Time elapsed: 0.006 s
% 0.19/1.31 % (2153112)Peak memory usage: 90 MB
% 0.19/1.31 % (2153112)Instructions burned: 8 (million)
% 0.19/1.31 % (2153104)------------------------------
% 0.19/1.31 % (2153104)------------------------------
% 0.19/1.31 % (2153097)------------------------------
% 0.19/1.31 % (2153097)------------------------------
% 0.19/1.31 % (2153101)------------------------------
% 0.19/1.31 % (2153101)------------------------------
% 0.19/1.31 % (2153102)Refutation found. Thanks to Tanya!
% 0.19/1.31 % SZS status Theorem for theBenchmark
% 0.19/1.31 % SZS output start Proof for theBenchmark
% See solution above
% 0.19/1.31 % (2153102)------------------------------
% 0.19/1.31 % (2153102)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.19/1.31 % (2153102)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/1.31 % (2153102)CaDiCaL version: 2.1.3
% 0.19/1.31 % (2153102)Termination reason: Refutation
% 0.19/1.31 % (2153102)Time elapsed: 0.034 s
% 0.19/1.31 % (2153102)Peak memory usage: 116 MB
% 0.19/1.31 % (2153102)Instructions burned: 12 (million)
% 0.19/1.31 % (2153102)------------------------------
% 0.19/1.31 % (2153102)------------------------------
% 0.19/1.31 % (2153091)Success in time 0.457 s
% 0.19/1.31 % Vampire exiting
%------------------------------------------------------------------------------