%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : DAT030_1 : TPTP v9.3.1. Released v5.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n014.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 09:47:08 AM UTC 2026
% Result : Theorem 0.21s 1.30s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 6
% Syntax : Number of formulae : 30 ( 5 unt; 0 typ; 5 def)
% Number of atoms : 97 ( 10 equ)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 94 ( 27 ~; 19 |; 27 &)
% ( 5 <=>; 16 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number arithmetic : 94 ( 23 atm; 10 fun; 23 num; 38 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 : 10 ( 6 usr; 6 prp; 0-2 aty)
% Number of functors : 11 ( 8 usr; 6 con; 0-2 aty)
% Number of variables : 50 ( 32 !; 18 ?; 50 :)
% 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_7,type,
sK0: collection ).
tff(func_def_8,type,
sK1: collection ).
tff(func_def_9,type,
sK2: $int > $int ).
tff(func_def_10,type,
sK3: $int > $int ).
tff(func_def_11,type,
sK4: $int ).
tff(pred_def_1,type,
in: ( $int * collection ) > $o ).
tff(f6,conjecture,
! [X0: collection,X1: collection] :
( ( ! [X2: $int] :
( in(X2,X1)
=> $greater(X2,0) )
& ! [X3: $int] :
( in(X3,X0)
=> ? [X5: $int,X4: $int] :
( ( X3 = $sum(X4,X5) )
& in(X4,X1)
& in(X5,X1) ) ) )
=> ! [X6: $int] :
( in(X6,X0)
=> $greater(X6,1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1) ).
tff(f7,negated_conjecture,
~ ! [X0: collection,X1: collection] :
( ( ! [X2: $int] :
( in(X2,X1)
=> $greater(X2,0) )
& ! [X3: $int] :
( in(X3,X0)
=> ? [X5: $int,X4: $int] :
( ( X3 = $sum(X4,X5) )
& in(X4,X1)
& in(X5,X1) ) ) )
=> ! [X6: $int] :
( in(X6,X0)
=> $greater(X6,1) ) ),
inference(negated_conjecture,[status(cth)],[f6]) ).
tff(f8,plain,
~ ! [X0: collection,X1: collection] :
( ( ! [X2: $int] :
( in(X2,X1)
=> $less(0,X2) )
& ! [X3: $int] :
( in(X3,X0)
=> ? [X5: $int,X4: $int] :
( ( X3 = $sum(X4,X5) )
& in(X4,X1)
& in(X5,X1) ) ) )
=> ! [X6: $int] :
( in(X6,X0)
=> $less(1,X6) ) ),
inference(theory_normalization,[],[f7]) ).
tff(f24,plain,
~ ! [X1: collection,X0: collection] :
( ( ! [X2: $int] :
( in(X2,X1)
=> $less(0,X2) )
& ! [X3: $int] :
( in(X3,X0)
=> ? [X4: $int,X5: $int] :
( ( $sum(X5,X4) = X3 )
& in(X5,X1)
& in(X4,X1) ) ) )
=> ! [X6: $int] :
( in(X6,X0)
=> $less(1,X6) ) ),
inference(rectify,[],[f8]) ).
tff(f25,plain,
? [X1: collection,X0: collection] :
( ? [X6: $int] :
( ~ $less(1,X6)
& in(X6,X0) )
& ! [X2: $int] :
( $less(0,X2)
| ~ in(X2,X1) )
& ! [X3: $int] :
( ? [X4: $int,X5: $int] :
( ( $sum(X5,X4) = X3 )
& in(X5,X1)
& in(X4,X1) )
| ~ in(X3,X0) ) ),
inference(ennf_transformation,[],[f24]) ).
tff(f26,plain,
? [X0: collection,X1: collection] :
( ! [X2: $int] :
( $less(0,X2)
| ~ in(X2,X1) )
& ! [X3: $int] :
( ? [X4: $int,X5: $int] :
( ( $sum(X5,X4) = X3 )
& in(X5,X1)
& in(X4,X1) )
| ~ in(X3,X0) )
& ? [X6: $int] :
( ~ $less(1,X6)
& in(X6,X0) ) ),
inference(flattening,[],[f25]) ).
tff(f34,plain,
( ! [X2: $int] :
( $less(0,X2)
| ~ in(X2,sK1) )
& ! [X3: $int] :
( ( ( $sum(sK3(X3),sK2(X3)) = X3 )
& in(sK3(X3),sK1)
& in(sK2(X3),sK1) )
| ~ in(X3,sK0) )
& ~ $less(1,sK4)
& in(sK4,sK0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X4,sK2(X3)),skolemize(X5,sK3(X3)),skolemize(X6,sK4)],[f26]) ).
tff(f44,plain,
in(sK4,sK0),
inference(cnf_transformation,[],[f34]) ).
tff(f45,plain,
~ $less(1,sK4),
inference(cnf_transformation,[],[f34]) ).
tff(f46,plain,
! [X3: $int] :
( in(sK2(X3),sK1)
| ~ in(X3,sK0) ),
inference(cnf_transformation,[],[f34]) ).
tff(f47,plain,
! [X3: $int] :
( in(sK3(X3),sK1)
| ~ in(X3,sK0) ),
inference(cnf_transformation,[],[f34]) ).
tff(f48,plain,
! [X3: $int] :
( ~ in(X3,sK0)
| ( $sum(sK3(X3),sK2(X3)) = X3 ) ),
inference(cnf_transformation,[],[f34]) ).
tff(f49,plain,
! [X2: $int] :
( ~ in(X2,sK1)
| $less(0,X2) ),
inference(cnf_transformation,[],[f34]) ).
tff(f53,definition,
( spl5_1
<=> in(sK4,sK0) ),
introduced(definition,[new_symbols(definition,[spl5_1])],[avatar_definition]) ).
tff(f55,plain,
( in(sK4,sK0)
| ~ spl5_1 ),
inference(avatar_component_clause,[],[f53]) ).
tff(f56,plain,
spl5_1,
inference(avatar_split_clause,[],[f44,f53]) ).
tff(f58,definition,
( spl5_2
<=> $less(1,sK4) ),
introduced(definition,[new_symbols(definition,[spl5_2])],[avatar_definition]) ).
tff(f61,plain,
~ spl5_2,
inference(avatar_split_clause,[],[f45,f58]) ).
tff(f62,plain,
! [X0: $int] :
( ~ in(X0,sK0)
| $less(0,sK2(X0)) ),
inference(resolution,[],[f46,f49]) ).
tff(f63,plain,
! [X0: $int] :
( ~ in(X0,sK0)
| $less(0,sK3(X0)) ),
inference(resolution,[],[f47,f49]) ).
tff(f64,plain,
( ( sK4 = $sum(sK3(sK4),sK2(sK4)) )
| ~ spl5_1 ),
inference(resolution,[],[f48,f55]) ).
tff(f66,definition,
( spl5_3
<=> ( sK4 = $sum(sK3(sK4),sK2(sK4)) ) ),
introduced(definition,[new_symbols(definition,[spl5_3])],[avatar_definition]) ).
tff(f69,plain,
( spl5_3
| ~ spl5_1 ),
inference(avatar_split_clause,[],[f64,f53,f66]) ).
tff(f70,plain,
( $less(0,sK2(sK4))
| ~ spl5_1 ),
inference(resolution,[],[f62,f55]) ).
tff(f72,definition,
( spl5_4
<=> $less(0,sK2(sK4)) ),
introduced(definition,[new_symbols(definition,[spl5_4])],[avatar_definition]) ).
tff(f75,plain,
( spl5_4
| ~ spl5_1 ),
inference(avatar_split_clause,[],[f70,f53,f72]) ).
tff(f76,plain,
( $less(0,sK3(sK4))
| ~ spl5_1 ),
inference(resolution,[],[f63,f55]) ).
tff(f78,definition,
( spl5_5
<=> $less(0,sK3(sK4)) ),
introduced(definition,[new_symbols(definition,[spl5_5])],[avatar_definition]) ).
tff(f81,plain,
( spl5_5
| ~ spl5_1 ),
inference(avatar_split_clause,[],[f76,f53,f78]) ).
tff(f82,plain,
$false,
inference(avatar_smt_refutation,[],[f81,f75,f69,f61,f56]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : DAT030_1 : TPTP v9.3.1. Released v5.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.19 % Computer : n014.cluster.edu
% 0.11/0.19 % Model : x86_64 x86_64
% 0.11/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.19 % Memory : 8046.5625MB
% 0.11/0.19 % OS : Linux 6.8.0-71-generic
% 0.11/0.19 % CPULimit : 300
% 0.11/0.19 % WCLimit : 300
% 0.11/0.19 % DateTime : Tue Sep 29 00:05:46 UTC 2026
% 0.11/0.19 % CPUTime :
% 0.11/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.22 Running first-order theorem proving
% 0.11/0.22 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.06/1.11 % (2301930)Detected arithmetic, will pick strategies from an ALASCA-aware ARI schedule.
% 3.06/1.11 % (2301936)dis+1002_1_to=kbo:sil=128000:tgt=ground:sas=z3:si=on:spb=units:tha=off:random_seed=3400351155:i=307:kws=precedence:nm=0:rtra=on_2999 on theBenchmark for (2999ds/307Mi)
% 3.06/1.11 % (2301936)Refutation not found, incomplete strategy
% 3.06/1.11 % (2301936)------------------------------
% 3.06/1.11 % (2301936)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.06/1.11 % (2301936)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.06/1.11 % (2301936)CaDiCaL version: 2.1.3
% 3.06/1.11 % (2301936)Termination reason: Refutation not found, incomplete strategy
% 3.06/1.11 % (2301936)Time elapsed: 0.019 s
% 3.06/1.11 % (2301936)Peak memory usage: 115 MB
% 3.06/1.11 % (2301936)Instructions burned: 7 (million)
% 3.06/1.11 % (2301940)lrs+10_1_to=lpo:sas=z3:si=on:tha=off:random_seed=3382524106:i=46:rtra=on_2999 on theBenchmark for (2999ds/46Mi)
% 3.06/1.11 % (2301941)lrs+10_1_tgt=ground:sas=z3:si=on:random_seed=1608330427:i=33:rtra=on_2999 on theBenchmark for (2999ds/33Mi)
% 3.06/1.11 % (2301935)dis+1002_16:1_to=lpo:sil=64000:sas=z3:si=on:norm_ineq=on:gve=force:uwa=one_side_constant:random_seed=786838696:i=12:doe=on:rtra=on:gtg=exists_top:ss=axioms_2999 on theBenchmark for (2999ds/12Mi)
% 3.06/1.11 % (2301939)dis+21_64_to=kbo:sil=128000:si=on:sp=weighted_frequency:uwa=alasca_can_abstract:random_seed=1852925952:i=4:rtra=on_2999 on theBenchmark for (2999ds/4Mi)
% 3.06/1.11 % (2301937)dis+10_3_slsqr=1,4:to=lpo:sil=128000:thi=strong:si=on:uwa=off:s2agt=20:slsqc=1:slsq=on:random_seed=457608936:i=201:slsql=off:asg=cautious:rtra=on:gtg=all:ss=axioms:sgt=16_2999 on theBenchmark for (2999ds/201Mi)
% 3.06/1.11 % (2301938)lrs+1002_4:1_to=lpo:sil=64000:si=on:br=off:random_seed=4066404774:s2a=on:i=7:rtra=on:inst=on_2999 on theBenchmark for (2999ds/7Mi)
% 3.06/1.11 % (2301939)Instruction limit reached!
% 3.06/1.11 % (2301939)------------------------------
% 3.06/1.11 % (2301939)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.06/1.11 % (2301939)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.06/1.11 % (2301939)CaDiCaL version: 2.1.3
% 3.06/1.11 % (2301939)Termination reason: Instruction limit
% 3.06/1.11 % (2301939)Termination phase: Saturation
% 3.06/1.11 % (2301939)Time elapsed: 0.004 s
% 3.06/1.11 % (2301939)Peak memory usage: 88 MB
% 3.06/1.11 % (2301939)Instructions burned: 5 (million)
% 3.06/1.11 % (2301938)Instruction limit reached!
% 3.06/1.11 % (2301938)------------------------------
% 3.06/1.11 % (2301938)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.06/1.11 % (2301938)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.06/1.11 % (2301938)CaDiCaL version: 2.1.3
% 3.06/1.11 % (2301938)Termination reason: Instruction limit
% 3.06/1.11 % (2301938)Termination phase: Saturation
% 3.06/1.11 % (2301938)Time elapsed: 0.006 s
% 3.06/1.11 % (2301938)Peak memory usage: 88 MB
% 3.06/1.11 % (2301938)Instructions burned: 8 (million)
% 3.06/1.11 % (2301935)Instruction limit reached!
% 3.06/1.11 % (2301935)------------------------------
% 3.06/1.11 % (2301935)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.06/1.11 % (2301935)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.06/1.11 % (2301935)CaDiCaL version: 2.1.3
% 3.06/1.11 % (2301935)Termination reason: Instruction limit
% 3.06/1.11 % (2301935)Termination phase: Saturation
% 3.06/1.11 % (2301935)Time elapsed: 0.031 s
% 3.06/1.11 % (2301935)Peak memory usage: 115 MB
% 3.06/1.11 % (2301935)Instructions burned: 12 (million)
% 3.06/1.11 % (2301940)Also succeeded, but the first one will report.
% 3.06/1.11 % (2301941)First to succeed.
% 3.06/1.11 % (2301941)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2301930"
% 3.06/1.11 % (2301949)dis+11_3_anc=none:drc=ordering:si=on:urr=ec_only:bce=on:tha=off:sac=on:random_seed=251547833:st=5:i=14:sd=10:rtra=on:ss=axioms:rawr=on_2998 on theBenchmark for (2998ds/14Mi)
% 3.06/1.11 % (2301950)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=2672571840:i=29:thsqd=64:nm=0:thsqc=8:rtra=on:thsq=on:ev=off_2998 on theBenchmark for (2998ds/29Mi)
% 3.06/1.11 % (2301949)Refutation not found, incomplete strategy
% 3.06/1.11 % (2301949)------------------------------
% 3.06/1.11 % (2301949)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.06/1.11 % (2301949)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/1.30 % (2301949)CaDiCaL version: 2.1.3
% 0.21/1.30 % (2301949)Termination reason: Refutation not found, incomplete strategy
% 0.21/1.30 % (2301949)Time elapsed: 0.002 s
% 0.21/1.30 % (2301949)Peak memory usage: 89 MB
% 0.21/1.30 % (2301949)Instructions burned: 1 (million)
% 0.21/1.30 % (2301936)------------------------------
% 0.21/1.30 % (2301936)------------------------------
% 0.21/1.30 % (2301937)Also succeeded, but the first one will report.
% 0.21/1.30 % (2301950)Instruction limit reached!
% 0.21/1.30 % (2301950)------------------------------
% 0.21/1.30 % (2301950)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.21/1.30 % (2301950)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/1.30 % (2301950)CaDiCaL version: 2.1.3
% 0.21/1.30 % (2301950)Termination reason: Instruction limit
% 0.21/1.30 % (2301950)Termination phase: Saturation
% 0.21/1.30 % (2301950)Time elapsed: 0.020 s
% 0.21/1.30 % (2301950)Peak memory usage: 88 MB
% 0.21/1.30 % (2301950)Instructions burned: 29 (million)
% 0.21/1.30 % (2301951)ott+21_1024_to=lakbo:sil=128000:bsd=on:si=on:alasca=on:uwa=alasca_main:nwc=0.5:random_seed=1496784893: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 % (2301951)Refutation not found, incomplete strategy
% 0.21/1.30 % (2301951)------------------------------
% 0.21/1.30 % (2301951)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.21/1.30 % (2301951)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/1.30 % (2301951)CaDiCaL version: 2.1.3
% 0.21/1.30 % (2301951)Termination reason: Refutation not found, incomplete strategy
% 0.21/1.30 % (2301951)Time elapsed: 0.008 s
% 0.21/1.30 % (2301951)Peak memory usage: 90 MB
% 0.21/1.30 % (2301951)Instructions burned: 11 (million)
% 0.21/1.30 % (2301954)dis+1011_1_prc=on:drc=off:si=on:sac=on:random_seed=3300312942:i=24:canc=force:rtra=on_2997 on theBenchmark for (2997ds/24Mi)
% 0.21/1.30 % (2301954)Instruction limit reached!
% 0.21/1.30 % (2301954)------------------------------
% 0.21/1.30 % (2301954)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.21/1.30 % (2301954)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/1.30 % (2301954)CaDiCaL version: 2.1.3
% 0.21/1.30 % (2301954)Termination reason: Instruction limit
% 0.21/1.30 % (2301954)Termination phase: Saturation
% 0.21/1.30 % (2301954)Time elapsed: 0.010 s
% 0.21/1.30 % (2301954)Peak memory usage: 89 MB
% 0.21/1.30 % (2301954)Instructions burned: 25 (million)
% 0.21/1.30 % (2301955)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=1165152314:i=27:canc=cautious:fsr=off:rtra=on_2996 on theBenchmark for (2996ds/27Mi)
% 0.21/1.30 % (2301941)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 % (2301941)------------------------------
% 0.21/1.30 % (2301941)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.21/1.30 % (2301941)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/1.30 % (2301941)CaDiCaL version: 2.1.3
% 0.21/1.30 % (2301941)Termination reason: Refutation
% 0.21/1.30 % (2301941)Time elapsed: 0.034 s
% 0.21/1.30 % (2301941)Peak memory usage: 116 MB
% 0.21/1.30 % (2301941)Instructions burned: 12 (million)
% 0.21/1.30 % (2301941)------------------------------
% 0.21/1.30 % (2301941)------------------------------
% 0.21/1.30 % (2301930)Success in time 0.456 s
% 0.21/1.30 % Vampire exiting
%------------------------------------------------------------------------------