%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : DAT022_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 : n010.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 1.79s 0.72s
% Output : Refutation 2.47s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 14
% Syntax : Number of formulae : 61 ( 13 unt; 0 typ; 11 def)
% Number of atoms : 171 ( 38 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 172 ( 62 ~; 59 |; 29 &)
% ( 13 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number arithmetic : 104 ( 19 atm; 0 fun; 45 num; 40 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 : 14 ( 10 usr; 10 prp; 0-2 aty)
% Number of functors : 11 ( 8 usr; 9 con; 0-2 aty)
% Number of variables : 64 ( 55 !; 9 ?; 64 :)
% 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_9,type,
sK0: collection ).
tff(func_def_10,type,
sK1: collection ).
tff(func_def_11,type,
sK2: $int ).
tff(func_def_12,type,
sF3: collection ).
tff(func_def_13,type,
sF4: collection ).
tff(pred_def_1,type,
in: ( $int * collection ) > $o ).
tff(f4,axiom,
! [X1: collection,X0: $int,X2: $int] :
( ( ( X0 = X2 )
| in(X0,X1) )
<=> in(X0,add(X2,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax4) ).
tff(f5,axiom,
! [X1: collection,X0: $int,X2: $int] :
( in(X0,remove(X2,X1))
<=> ( ( X0 != X2 )
& in(X0,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax5) ).
tff(f6,conjecture,
! [X0: collection,X1: collection] :
( ( ( X0 = add(2,remove(7,X1)) )
& ! [X2: $int] :
( in(X2,X1)
=> $greater(X2,0) ) )
=> ! [X3: $int] :
( in(X3,X0)
=> $greater(X3,0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1) ).
tff(f7,negated_conjecture,
~ ! [X0: collection,X1: collection] :
( ( ( X0 = add(2,remove(7,X1)) )
& ! [X2: $int] :
( in(X2,X1)
=> $greater(X2,0) ) )
=> ! [X3: $int] :
( in(X3,X0)
=> $greater(X3,0) ) ),
inference(negated_conjecture,[status(cth)],[f6]) ).
tff(f8,plain,
~ ! [X0: collection,X1: collection] :
( ( ( X0 = add(2,remove(7,X1)) )
& ! [X2: $int] :
( in(X2,X1)
=> $less(0,X2) ) )
=> ! [X3: $int] :
( in(X3,X0)
=> $less(0,X3) ) ),
inference(theory_normalization,[],[f7]) ).
tff(f22,plain,
! [X0: collection,X2: $int,X1: $int] :
( ( in(X1,X0)
| ( X1 = X2 ) )
<=> in(X1,add(X2,X0)) ),
inference(rectify,[],[f4]) ).
tff(f23,plain,
! [X2: $int,X1: $int,X0: collection] :
( in(X1,remove(X2,X0))
<=> ( in(X1,X0)
& ( X1 != X2 ) ) ),
inference(rectify,[],[f5]) ).
tff(f24,plain,
? [X0: collection,X1: collection] :
( ? [X3: $int] :
( ~ $less(0,X3)
& in(X3,X0) )
& ( X0 = add(2,remove(7,X1)) )
& ! [X2: $int] :
( $less(0,X2)
| ~ in(X2,X1) ) ),
inference(ennf_transformation,[],[f8]) ).
tff(f25,plain,
? [X1: collection,X0: collection] :
( ( X0 = add(2,remove(7,X1)) )
& ! [X2: $int] :
( $less(0,X2)
| ~ in(X2,X1) )
& ? [X3: $int] :
( ~ $less(0,X3)
& in(X3,X0) ) ),
inference(flattening,[],[f24]) ).
tff(f27,plain,
! [X0: collection,X2: $int,X1: $int] :
( ( in(X1,X0)
| ( X1 = X2 )
| ~ in(X1,add(X2,X0)) )
& ( in(X1,add(X2,X0))
| ( ~ in(X1,X0)
& ( X1 != X2 ) ) ) ),
inference(nnf_transformation,[],[f22]) ).
tff(f28,plain,
! [X0: collection,X2: $int,X1: $int] :
( ( in(X1,X0)
| ( X1 = X2 )
| ~ in(X1,add(X2,X0)) )
& ( in(X1,add(X2,X0))
| ( ~ in(X1,X0)
& ( X1 != X2 ) ) ) ),
inference(flattening,[],[f27]) ).
tff(f29,plain,
! [X0: collection,X1: $int,X2: $int] :
( ( in(X2,X0)
| ( X1 = X2 )
| ~ in(X2,add(X1,X0)) )
& ( in(X2,add(X1,X0))
| ( ~ in(X2,X0)
& ( X1 != X2 ) ) ) ),
inference(rectify,[],[f28]) ).
tff(f30,plain,
! [X2: $int,X1: $int,X0: collection] :
( ( in(X1,remove(X2,X0))
| ~ in(X1,X0)
| ( X1 = X2 ) )
& ( ( in(X1,X0)
& ( X1 != X2 ) )
| ~ in(X1,remove(X2,X0)) ) ),
inference(nnf_transformation,[],[f23]) ).
tff(f31,plain,
! [X2: $int,X1: $int,X0: collection] :
( ( in(X1,remove(X2,X0))
| ~ in(X1,X0)
| ( X1 = X2 ) )
& ( ( in(X1,X0)
& ( X1 != X2 ) )
| ~ in(X1,remove(X2,X0)) ) ),
inference(flattening,[],[f30]) ).
tff(f32,plain,
! [X0: $int,X1: $int,X2: collection] :
( ( in(X1,remove(X0,X2))
| ~ in(X1,X2)
| ( X0 = X1 ) )
& ( ( in(X1,X2)
& ( X0 != X1 ) )
| ~ in(X1,remove(X0,X2)) ) ),
inference(rectify,[],[f31]) ).
tff(f33,plain,
? [X0: collection,X1: collection] :
( ( add(2,remove(7,X0)) = X1 )
& ! [X2: $int] :
( $less(0,X2)
| ~ in(X2,X0) )
& ? [X3: $int] :
( ~ $less(0,X3)
& in(X3,X1) ) ),
inference(rectify,[],[f25]) ).
tff(f34,plain,
( ( sK1 = add(2,remove(7,sK0)) )
& ! [X2: $int] :
( $less(0,X2)
| ~ in(X2,sK0) )
& ~ $less(0,sK2)
& in(sK2,sK1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X3,sK2)],[f33]) ).
tff(f39,plain,
! [X2: $int,X0: collection,X1: $int] :
( ~ in(X2,add(X1,X0))
| in(X2,X0)
| ( X1 = X2 ) ),
inference(cnf_transformation,[],[f29]) ).
tff(f42,plain,
! [X2: collection,X0: $int,X1: $int] :
( ~ in(X1,remove(X0,X2))
| in(X1,X2) ),
inference(cnf_transformation,[],[f32]) ).
tff(f44,plain,
in(sK2,sK1),
inference(cnf_transformation,[],[f34]) ).
tff(f45,plain,
~ $less(0,sK2),
inference(cnf_transformation,[],[f34]) ).
tff(f46,plain,
! [X2: $int] :
( ~ in(X2,sK0)
| $less(0,X2) ),
inference(cnf_transformation,[],[f34]) ).
tff(f47,plain,
sK1 = add(2,remove(7,sK0)),
inference(cnf_transformation,[],[f34]) ).
tff(f51,definition,
sF3 = remove(7,sK0),
introduced(definition,[new_symbols(definition,[sF3])],[function_definition]) ).
tff(f52,definition,
sF4 = add(2,sF3),
introduced(definition,[new_symbols(definition,[sF4])],[function_definition]) ).
tff(f53,plain,
add(2,sF3) = sF4,
inference(reorient_equations,[],[f52]) ).
tff(f54,plain,
sK1 = sF4,
inference(definition_folding,[],[f47,f53,f51]) ).
tff(f56,definition,
( spl5_1
<=> ( sF3 = remove(7,sK0) ) ),
introduced(definition,[new_symbols(definition,[spl5_1])],[avatar_definition]) ).
tff(f58,plain,
( ( sF3 = remove(7,sK0) )
| ~ spl5_1 ),
inference(avatar_component_clause,[],[f56]) ).
tff(f59,plain,
spl5_1,
inference(avatar_split_clause,[],[f51,f56]) ).
tff(f61,definition,
( spl5_2
<=> $less(0,sK2) ),
introduced(definition,[new_symbols(definition,[spl5_2])],[avatar_definition]) ).
tff(f63,plain,
( ~ $less(0,sK2)
| spl5_2 ),
inference(avatar_component_clause,[],[f61]) ).
tff(f64,plain,
~ spl5_2,
inference(avatar_split_clause,[],[f45,f61]) ).
tff(f66,definition,
( spl5_3
<=> ( sK1 = sF4 ) ),
introduced(definition,[new_symbols(definition,[spl5_3])],[avatar_definition]) ).
tff(f68,plain,
( ( sK1 = sF4 )
| ~ spl5_3 ),
inference(avatar_component_clause,[],[f66]) ).
tff(f69,plain,
spl5_3,
inference(avatar_split_clause,[],[f54,f66]) ).
tff(f71,definition,
( spl5_4
<=> ( add(2,sF3) = sF4 ) ),
introduced(definition,[new_symbols(definition,[spl5_4])],[avatar_definition]) ).
tff(f73,plain,
( ( add(2,sF3) = sF4 )
| ~ spl5_4 ),
inference(avatar_component_clause,[],[f71]) ).
tff(f74,plain,
spl5_4,
inference(avatar_split_clause,[],[f53,f71]) ).
tff(f76,definition,
( spl5_5
<=> in(sK2,sK1) ),
introduced(definition,[new_symbols(definition,[spl5_5])],[avatar_definition]) ).
tff(f78,plain,
( in(sK2,sK1)
| ~ spl5_5 ),
inference(avatar_component_clause,[],[f76]) ).
tff(f79,plain,
spl5_5,
inference(avatar_split_clause,[],[f44,f76]) ).
tff(f80,plain,
( in(sK2,sF4)
| ~ spl5_3
| ~ spl5_5 ),
inference(superposition,[],[f78,f68]) ).
tff(f82,definition,
( spl5_6
<=> in(sK2,sF4) ),
introduced(definition,[new_symbols(definition,[spl5_6])],[avatar_definition]) ).
tff(f84,plain,
( in(sK2,sF4)
| ~ spl5_6 ),
inference(avatar_component_clause,[],[f82]) ).
tff(f85,plain,
( spl5_6
| ~ spl5_3
| ~ spl5_5 ),
inference(avatar_split_clause,[],[f80,f76,f66,f82]) ).
tff(f119,plain,
( ! [X0: $int] :
( ~ in(X0,sF3)
| in(X0,sK0) )
| ~ spl5_1 ),
inference(superposition,[],[f42,f58]) ).
tff(f213,plain,
( ! [X0: $int] :
( ~ in(X0,sF4)
| in(X0,sF3)
| ( 2 = X0 ) )
| ~ spl5_4 ),
inference(superposition,[],[f39,f73]) ).
tff(f284,plain,
( ( 2 = sK2 )
| in(sK2,sF3)
| ~ spl5_4
| ~ spl5_6 ),
inference(resolution,[],[f213,f84]) ).
tff(f287,definition,
( spl5_9
<=> in(sK2,sF3) ),
introduced(definition,[new_symbols(definition,[spl5_9])],[avatar_definition]) ).
tff(f289,plain,
( in(sK2,sF3)
| ~ spl5_9 ),
inference(avatar_component_clause,[],[f287]) ).
tff(f291,definition,
( spl5_10
<=> ( 2 = sK2 ) ),
introduced(definition,[new_symbols(definition,[spl5_10])],[avatar_definition]) ).
tff(f294,plain,
( spl5_9
| spl5_10
| ~ spl5_4
| ~ spl5_6 ),
inference(avatar_split_clause,[],[f284,f82,f71,f291,f287]) ).
tff(f295,plain,
( in(sK2,sK0)
| ~ spl5_1
| ~ spl5_9 ),
inference(resolution,[],[f289,f119]) ).
tff(f298,definition,
( spl5_11
<=> in(sK2,sK0) ),
introduced(definition,[new_symbols(definition,[spl5_11])],[avatar_definition]) ).
tff(f300,plain,
( in(sK2,sK0)
| ~ spl5_11 ),
inference(avatar_component_clause,[],[f298]) ).
tff(f301,plain,
( spl5_11
| ~ spl5_1
| ~ spl5_9 ),
inference(avatar_split_clause,[],[f295,f287,f56,f298]) ).
tff(f303,plain,
( $less(0,sK2)
| ~ spl5_11 ),
inference(resolution,[],[f300,f46]) ).
tff(f304,plain,
( $false
| spl5_2
| ~ spl5_11 ),
inference(forward_subsumption_resolution,[],[f303,f63]) ).
tff(f305,plain,
( spl5_2
| ~ spl5_11 ),
inference(avatar_contradiction_clause,[],[f304]) ).
tff(f306,plain,
$false,
inference(avatar_smt_refutation,[],[f305,f301,f294,f85,f79,f74,f69,f64,f59]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : DAT022_1 : TPTP v9.3.1. Released v5.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.19 % Computer : n010.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 00:06:03 UTC 2026
% 0.09/0.19 % CPUTime :
% 0.09/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.23 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
% 1.79/0.72 % (2478669)Detected arithmetic, will pick strategies from an ALASCA-aware ARI schedule.
% 1.79/0.72 % (2478727)lrs+10_1_tgt=ground:sas=z3:si=on:random_seed=4130094536:i=33:rtra=on_3000 on theBenchmark for (3000ds/33Mi)
% 1.79/0.72 % (2478727)First to succeed.
% 1.79/0.72 % (2478727)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2478669"
% 1.79/0.72 % (2478725)dis+21_64_to=kbo:sil=128000:si=on:sp=weighted_frequency:uwa=alasca_can_abstract:random_seed=4010151961:i=4:rtra=on_3000 on theBenchmark for (3000ds/4Mi)
% 1.79/0.72 % (2478722)dis+1002_1_to=kbo:sil=128000:tgt=ground:sas=z3:si=on:spb=units:tha=off:random_seed=2777466379:i=307:kws=precedence:nm=0:rtra=on_3000 on theBenchmark for (3000ds/307Mi)
% 1.79/0.72 % (2478721)dis+1002_16:1_to=lpo:sil=64000:sas=z3:si=on:norm_ineq=on:gve=force:uwa=one_side_constant:random_seed=666492203:i=12:doe=on:rtra=on:gtg=exists_top:ss=axioms_3000 on theBenchmark for (3000ds/12Mi)
% 1.79/0.72 % (2478726)lrs+10_1_to=lpo:sas=z3:si=on:tha=off:random_seed=4118989438:i=46:rtra=on_3000 on theBenchmark for (3000ds/46Mi)
% 1.79/0.72 % (2478723)dis+10_3_slsqr=1,4:to=lpo:sil=128000:thi=strong:si=on:uwa=off:s2agt=20:slsqc=1:slsq=on:random_seed=1779190858:i=201:slsql=off:asg=cautious:rtra=on:gtg=all:ss=axioms:sgt=16_3000 on theBenchmark for (3000ds/201Mi)
% 1.79/0.72 % (2478724)lrs+1002_4:1_to=lpo:sil=64000:si=on:br=off:random_seed=4034579956:s2a=on:i=7:rtra=on:inst=on_3000 on theBenchmark for (3000ds/7Mi)
% 1.79/0.72 % (2478725)Instruction limit reached!
% 1.79/0.72 % (2478725)------------------------------
% 1.79/0.72 % (2478725)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 1.79/0.72 % (2478725)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.79/0.72 % (2478725)CaDiCaL version: 2.1.3
% 1.79/0.72 % (2478725)Termination reason: Instruction limit
% 1.79/0.72 % (2478725)Termination phase: Saturation
% 1.79/0.72 % (2478725)Time elapsed: 0.004 s
% 1.79/0.72 % (2478725)Peak memory usage: 88 MB
% 1.79/0.72 % (2478725)Instructions burned: 5 (million)
% 1.79/0.72 % (2478724)Instruction limit reached!
% 1.79/0.72 % (2478724)------------------------------
% 1.79/0.72 % (2478724)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 1.79/0.72 % (2478724)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.79/0.72 % (2478724)CaDiCaL version: 2.1.3
% 1.79/0.72 % (2478724)Termination reason: Instruction limit
% 1.79/0.72 % (2478724)Termination phase: Saturation
% 1.79/0.72 % (2478724)Time elapsed: 0.006 s
% 1.79/0.72 % (2478724)Peak memory usage: 88 MB
% 1.79/0.72 % (2478724)Instructions burned: 7 (million)
% 1.79/0.72 % (2478721)Instruction limit reached!
% 1.79/0.72 % (2478721)------------------------------
% 1.79/0.72 % (2478721)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 1.79/0.72 % (2478721)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.79/0.72 % (2478721)CaDiCaL version: 2.1.3
% 1.79/0.72 % (2478721)Termination reason: Instruction limit
% 1.79/0.72 % (2478721)Termination phase: Saturation
% 1.79/0.72 % (2478721)Time elapsed: 0.030 s
% 1.79/0.72 % (2478721)Peak memory usage: 115 MB
% 1.79/0.72 % (2478721)Instructions burned: 12 (million)
% 1.79/0.72 % (2478726)Also succeeded, but the first one will report.
% 1.79/0.72 % (2478722)Also succeeded, but the first one will report.
% 1.79/0.72 % (2478723)Also succeeded, but the first one will report.
% 1.79/0.72 % (2478727)Refutation found. Thanks to Tanya!
% 1.79/0.72 % SZS status Theorem for theBenchmark
% 1.79/0.72 % SZS output start Proof for theBenchmark
% See solution above
% 2.47/0.92 % (2478727)------------------------------
% 2.47/0.92 % (2478727)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.47/0.92 % (2478727)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.47/0.92 % (2478727)CaDiCaL version: 2.1.3
% 2.47/0.92 % (2478727)Termination reason: Refutation
% 2.47/0.92 % (2478727)Time elapsed: 0.026 s
% 2.47/0.92 % (2478727)Peak memory usage: 116 MB
% 2.47/0.92 % (2478727)Instructions burned: 23 (million)
% 2.47/0.92 % (2478727)------------------------------
% 2.47/0.92 % (2478727)------------------------------
% 2.47/0.92 % (2478669)Success in time 0.277 s
% 2.47/0.92 % Vampire exiting
%------------------------------------------------------------------------------