%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : DAT031_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 09:47:08 AM UTC 2026
% Result : Theorem 5.54s 1.62s
% Output : Refutation 5.54s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 4
% Syntax : Number of formulae : 27 ( 5 unt; 0 typ; 2 def)
% Number of atoms : 76 ( 17 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 76 ( 27 ~; 28 |; 14 &)
% ( 4 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number arithmetic : 81 ( 14 atm; 0 fun; 45 num; 22 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 : 7 ( 3 usr; 3 prp; 0-2 aty)
% Number of functors : 9 ( 4 usr; 7 con; 0-2 aty)
% Number of variables : 34 ( 30 !; 4 ?; 34 :)
% 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(pred_def_1,type,
in: ( $int * collection ) > $o ).
tff(f4,axiom,
! [X1: collection,X0: $int,X2: $int] :
( in(X0,add(X2,X1))
<=> ( ( X0 = X2 )
| in(X0,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax4) ).
tff(f6,conjecture,
! [X0: collection] :
( ( X0 = add(10,add(30,add(50,empty))) )
=> ? [X1: $int] :
( $lesseq(20,X1)
& $lesseq(X1,40)
& in(X1,X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1) ).
tff(f7,negated_conjecture,
~ ! [X0: collection] :
( ( X0 = add(10,add(30,add(50,empty))) )
=> ? [X1: $int] :
( $lesseq(20,X1)
& $lesseq(X1,40)
& in(X1,X0) ) ),
inference(negated_conjecture,[status(cth)],[f6]) ).
tff(f8,plain,
~ ! [X0: collection] :
( ( X0 = add(10,add(30,add(50,empty))) )
=> ? [X1: $int] :
( ~ $less(40,X1)
& in(X1,X0)
& ~ $less(X1,20) ) ),
inference(theory_normalization,[],[f7]) ).
tff(f11,plain,
! [X2: $int,X0: collection,X1: $int] :
( in(X1,add(X2,X0))
<=> ( ( X1 = X2 )
| in(X1,X0) ) ),
inference(rectify,[],[f4]) ).
tff(f12,plain,
? [X0: collection] :
( ! [X1: $int] :
( ~ in(X1,X0)
| $less(X1,20)
| $less(40,X1) )
& ( X0 = add(10,add(30,add(50,empty))) ) ),
inference(ennf_transformation,[],[f8]) ).
tff(f15,plain,
( ! [X1: $int] :
( ~ in(X1,sK0)
| $less(X1,20)
| $less(40,X1) )
& ( add(10,add(30,add(50,empty))) = sK0 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[f12]) ).
tff(f17,plain,
! [X2: $int,X0: collection,X1: $int] :
( ( in(X1,add(X2,X0))
| ( ( X1 != X2 )
& ~ in(X1,X0) ) )
& ( ( X1 = X2 )
| in(X1,X0)
| ~ in(X1,add(X2,X0)) ) ),
inference(nnf_transformation,[],[f11]) ).
tff(f18,plain,
! [X2: $int,X0: collection,X1: $int] :
( ( in(X1,add(X2,X0))
| ( ( X1 != X2 )
& ~ in(X1,X0) ) )
& ( ( X1 = X2 )
| in(X1,X0)
| ~ in(X1,add(X2,X0)) ) ),
inference(flattening,[],[f17]) ).
tff(f19,plain,
! [X0: $int,X1: collection,X2: $int] :
( ( in(X2,add(X0,X1))
| ( ( X0 != X2 )
& ~ in(X2,X1) ) )
& ( ( X0 = X2 )
| in(X2,X1)
| ~ in(X2,add(X0,X1)) ) ),
inference(rectify,[],[f18]) ).
tff(f25,plain,
add(10,add(30,add(50,empty))) = sK0,
inference(cnf_transformation,[],[f15]) ).
tff(f26,plain,
! [X1: $int] :
( ~ in(X1,sK0)
| $less(X1,20)
| $less(40,X1) ),
inference(cnf_transformation,[],[f15]) ).
tff(f29,plain,
! [X2: $int,X0: $int,X1: collection] :
( in(X2,add(X0,X1))
| ~ in(X2,X1) ),
inference(cnf_transformation,[],[f19]) ).
tff(f30,plain,
! [X2: $int,X0: $int,X1: collection] :
( in(X2,add(X0,X1))
| ( X0 != X2 ) ),
inference(cnf_transformation,[],[f19]) ).
tff(f32,plain,
! [X2: $int,X1: collection] : in(X2,add(X2,X1)),
inference(equality_resolution,[],[f30]) ).
tff(f34,definition,
( spl1_1
<=> ( add(10,add(30,add(50,empty))) = sK0 ) ),
introduced(definition,[new_symbols(definition,[spl1_1])],[avatar_definition]) ).
tff(f36,plain,
( ( add(10,add(30,add(50,empty))) = sK0 )
| ~ spl1_1 ),
inference(avatar_component_clause,[],[f34]) ).
tff(f37,plain,
spl1_1,
inference(avatar_split_clause,[],[f25,f34]) ).
tff(f45,plain,
( ! [X0: $int] :
( ~ in(X0,add(30,add(50,empty)))
| in(X0,sK0) )
| ~ spl1_1 ),
inference(superposition,[],[f29,f36]) ).
tff(f46,plain,
( in(30,sK0)
| ~ spl1_1 ),
inference(resolution,[],[f45,f32]) ).
tff(f49,definition,
( spl1_3
<=> in(30,sK0) ),
introduced(definition,[new_symbols(definition,[spl1_3])],[avatar_definition]) ).
tff(f51,plain,
( in(30,sK0)
| ~ spl1_3 ),
inference(avatar_component_clause,[],[f49]) ).
tff(f52,plain,
( spl1_3
| ~ spl1_1 ),
inference(avatar_split_clause,[],[f46,f34,f49]) ).
tff(f55,plain,
( $less(30,20)
| $less(40,30)
| ~ spl1_3 ),
inference(resolution,[],[f51,f26]) ).
tff(f56,plain,
( $false
| ~ spl1_3 ),
inference(evaluation,[],[f55]) ).
tff(f57,plain,
~ spl1_3,
inference(avatar_contradiction_clause,[],[f56]) ).
tff(f58,plain,
$false,
inference(avatar_smt_refutation,[],[f57,f52,f37]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : DAT031_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 00:08:37 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
% 5.54/1.62 % (908935)Detected arithmetic, will pick strategies from an ALASCA-aware ARI schedule.
% 5.54/1.62 % (909085)dis+1002_1_to=kbo:sil=128000:tgt=ground:sas=z3:si=on:spb=units:tha=off:random_seed=1946899562:i=307:kws=precedence:nm=0:rtra=on_2999 on theBenchmark for (2999ds/307Mi)
% 5.54/1.62 % (909078)dis+1002_16:1_to=lpo:sil=64000:sas=z3:si=on:norm_ineq=on:gve=force:uwa=one_side_constant:random_seed=2269362848:i=12:doe=on:rtra=on:gtg=exists_top:ss=axioms_2999 on theBenchmark for (2999ds/12Mi)
% 5.54/1.62 % (909085)Refutation not found, incomplete strategy
% 5.54/1.62 % (909085)------------------------------
% 5.54/1.62 % (909085)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.54/1.62 % (909085)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.54/1.62 % (909085)CaDiCaL version: 2.1.3
% 5.54/1.62 % (909085)Termination reason: Refutation not found, incomplete strategy
% 5.54/1.62 % (909085)Time elapsed: 0.026 s
% 5.54/1.62 % (909085)Peak memory usage: 115 MB
% 5.54/1.62 % (909085)Instructions burned: 10 (million)
% 5.54/1.62 % (909090)lrs+10_1_to=lpo:sas=z3:si=on:tha=off:random_seed=44202116:i=46:rtra=on_2999 on theBenchmark for (2999ds/46Mi)
% 5.54/1.62 % (909088)lrs+1002_4:1_to=lpo:sil=64000:si=on:br=off:random_seed=1348909134:s2a=on:i=7:rtra=on:inst=on_2999 on theBenchmark for (2999ds/7Mi)
% 5.54/1.62 % (909088)Instruction limit reached!
% 5.54/1.62 % (909088)------------------------------
% 5.54/1.62 % (909088)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.54/1.62 % (909088)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.54/1.62 % (909088)CaDiCaL version: 2.1.3
% 5.54/1.62 % (909088)Termination reason: Instruction limit
% 5.54/1.62 % (909088)Termination phase: Saturation
% 5.54/1.62 % (909088)Time elapsed: 0.006 s
% 5.54/1.62 % (909088)Peak memory usage: 88 MB
% 5.54/1.62 % (909088)Instructions burned: 7 (million)
% 5.54/1.62 % (909087)dis+10_3_slsqr=1,4:to=lpo:sil=128000:thi=strong:si=on:uwa=off:s2agt=20:slsqc=1:slsq=on:random_seed=3305413769:i=201:slsql=off:asg=cautious:rtra=on:gtg=all:ss=axioms:sgt=16_2999 on theBenchmark for (2999ds/201Mi)
% 5.54/1.62 % (909091)lrs+10_1_tgt=ground:sas=z3:si=on:random_seed=1422929902:i=33:rtra=on_2999 on theBenchmark for (2999ds/33Mi)
% 5.54/1.62 % (909078)Refutation not found, incomplete strategy
% 5.54/1.62 % (909078)------------------------------
% 5.54/1.62 % (909078)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.54/1.62 % (909078)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.54/1.62 % (909078)CaDiCaL version: 2.1.3
% 5.54/1.62 % (909078)Termination reason: Refutation not found, incomplete strategy
% 5.54/1.62 % (909078)Time elapsed: 0.045 s
% 5.54/1.62 % (909078)Peak memory usage: 116 MB
% 5.54/1.62 % (909078)Instructions burned: 9 (million)
% 5.54/1.62 % (909090)First to succeed.
% 5.54/1.62 % (909090)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-908935"
% 5.54/1.62 % (909089)dis+21_64_to=kbo:sil=128000:si=on:sp=weighted_frequency:uwa=alasca_can_abstract:random_seed=3730567066:i=4:rtra=on_2999 on theBenchmark for (2999ds/4Mi)
% 5.54/1.62 % (909089)Instruction limit reached!
% 5.54/1.62 % (909089)------------------------------
% 5.54/1.62 % (909089)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.54/1.62 % (909089)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.54/1.62 % (909089)CaDiCaL version: 2.1.3
% 5.54/1.62 % (909089)Termination reason: Instruction limit
% 5.54/1.62 % (909089)Termination phase: Saturation
% 5.54/1.62 % (909089)Time elapsed: 0.007 s
% 5.54/1.62 % (909089)Peak memory usage: 89 MB
% 5.54/1.62 % (909089)Instructions burned: 5 (million)
% 5.54/1.62 % (909087)Also succeeded, but the first one will report.
% 5.54/1.62 % (909091)Also succeeded, but the first one will report.
% 5.54/1.62 % (909085)------------------------------
% 5.54/1.62 % (909085)------------------------------
% 5.54/1.62 % (909113)dis+11_3_anc=none:drc=ordering:si=on:urr=ec_only:bce=on:tha=off:sac=on:random_seed=3593370174:st=5:i=14:sd=10:rtra=on:ss=axioms:rawr=on_2997 on theBenchmark for (2997ds/14Mi)
% 5.54/1.62 % (909113)Also succeeded, but the first one will report.
% 5.54/1.62 % (909118)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=829920869:i=29:thsqd=64:nm=0:thsqc=8:rtra=on:thsq=on:ev=off_2997 on theBenchmark for (2997ds/29Mi)
% 5.54/1.62 % (909118)Instruction limit reached!
% 5.54/1.62 % (909118)------------------------------
% 5.54/1.62 % (909118)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.54/1.62 % (909118)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.54/1.62 % (909118)CaDiCaL version: 2.1.3
% 5.54/1.62 % (909118)Termination reason: Instruction limit
% 5.54/1.62 % (909118)Termination phase: Saturation
% 5.54/1.62 % (909118)Time elapsed: 0.035 s
% 5.54/1.62 % (909118)Peak memory usage: 88 MB
% 5.54/1.62 % (909118)Instructions burned: 29 (million)
% 5.54/1.62 % (909120)ott+21_1024_to=lakbo:sil=128000:bsd=on:si=on:alasca=on:uwa=alasca_main:nwc=0.5:random_seed=15031432:cond=on:i=16:fgj=on:ep=RS:asg=force:nm=10:rtra=on:rawr=on_2995 on theBenchmark for (2995ds/16Mi)
% 5.54/1.62 % (909120)Refutation not found, incomplete strategy
% 5.54/1.62 % (909120)------------------------------
% 5.54/1.62 % (909120)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.54/1.62 % (909120)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.54/1.62 % (909120)CaDiCaL version: 2.1.3
% 5.54/1.62 % (909120)Termination reason: Refutation not found, incomplete strategy
% 5.54/1.62 % (909120)Time elapsed: 0.005 s
% 5.54/1.62 % (909120)Peak memory usage: 90 MB
% 5.54/1.62 % (909120)Instructions burned: 7 (million)
% 5.54/1.62 % (909078)------------------------------
% 5.54/1.62 % (909078)------------------------------
% 5.54/1.62 % (909090)Refutation found. Thanks to Tanya!
% 5.54/1.62 % SZS status Theorem for theBenchmark
% 5.54/1.62 % SZS output start Proof for theBenchmark
% See solution above
% 5.54/1.62 % (909090)------------------------------
% 5.54/1.62 % (909090)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.54/1.62 % (909090)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.54/1.62 % (909090)CaDiCaL version: 2.1.3
% 5.54/1.62 % (909090)Termination reason: Refutation
% 5.54/1.62 % (909090)Time elapsed: 0.048 s
% 5.54/1.62 % (909090)Peak memory usage: 116 MB
% 5.54/1.62 % (909090)Instructions burned: 11 (million)
% 5.54/1.62 % (909090)------------------------------
% 5.54/1.62 % (909090)------------------------------
% 5.54/1.62 % (908935)Success in time 0.688 s
% 5.54/1.62 % Vampire exiting
%------------------------------------------------------------------------------