%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : DAT079_1 : TPTP v9.3.1. Released v6.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n017.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 09:47:15 AM UTC 2026
% Result : Theorem 3.96s 1.37s
% Output : Refutation 3.96s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 9
% Syntax : Number of formulae : 40 ( 16 unt; 0 typ; 7 def)
% Number of atoms : 109 ( 44 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 114 ( 45 ~; 43 |; 20 &)
% ( 6 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number arithmetic : 67 ( 0 atm; 0 fun; 33 num; 34 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 : 8 ( 6 usr; 5 prp; 0-2 aty)
% Number of functors : 19 ( 16 usr; 7 con; 0-2 aty)
% Number of variables : 65 ( 45 !; 20 ?; 65 :)
% Comments :
%------------------------------------------------------------------------------
tff(type_def_5,type,
list: $tType ).
tff(func_def_0,type,
nil: list ).
tff(func_def_1,type,
cons: ( $int * list ) > list ).
tff(func_def_2,type,
head: list > $int ).
tff(func_def_3,type,
tail: list > list ).
tff(func_def_5,type,
length: list > $int ).
tff(func_def_8,type,
count: ( $int * list ) > $int ).
tff(func_def_9,type,
append: ( list * list ) > list ).
tff(func_def_12,type,
sK0: ( $int * list ) > $int ).
tff(func_def_13,type,
sK1: ( $int * list ) > list ).
tff(func_def_14,type,
sK2: ( list * $int ) > $int ).
tff(func_def_15,type,
sK3: ( list * $int ) > list ).
tff(func_def_16,type,
sK4: ( list * $int ) > list ).
tff(func_def_17,type,
sK5: ( list * $int ) > $int ).
tff(func_def_18,type,
sF6: list ).
tff(func_def_19,type,
sF7: list ).
tff(func_def_20,type,
sF8: list ).
tff(pred_def_1,type,
in: ( $int * list ) > $o ).
tff(pred_def_2,type,
inRange: ( $int * list ) > $o ).
tff(f5,axiom,
! [X1: list,X0: $int] :
( in(X0,X1)
<=> ( ? [X2: $int,X3: list] :
( ( X1 = cons(X2,X3) )
& ( X0 = X2 ) )
| ? [X2: $int,X3: list] :
( ( X1 = cons(X2,X3) )
& in(X0,X3) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',in_conv) ).
tff(f15,conjecture,
in(2,cons(1,cons(2,cons(3,nil)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c) ).
tff(f16,negated_conjecture,
~ in(2,cons(1,cons(2,cons(3,nil)))),
inference(negated_conjecture,[status(cth)],[f15]) ).
tff(f19,plain,
~ in(2,cons(1,cons(2,cons(3,nil)))),
inference(flattening,[],[f16]) ).
tff(f25,plain,
! [X0: list,X1: $int] :
( ( ? [X4: $int,X5: list] :
( ( cons(X4,X5) = X0 )
& in(X1,X5) )
| ? [X3: list,X2: $int] :
( ( cons(X2,X3) = X0 )
& ( X1 = X2 ) ) )
<=> in(X1,X0) ),
inference(rectify,[],[f5]) ).
tff(f37,plain,
! [X0: list,X1: $int] :
( ( ? [X4: $int,X5: list] :
( ( cons(X4,X5) = X0 )
& in(X1,X5) )
| ? [X3: list,X2: $int] :
( ( cons(X2,X3) = X0 )
& ( X1 = X2 ) )
| ~ in(X1,X0) )
& ( in(X1,X0)
| ( ! [X4: $int,X5: list] :
( ( cons(X4,X5) != X0 )
| ~ in(X1,X5) )
& ! [X3: list,X2: $int] :
( ( cons(X2,X3) != X0 )
| ( X1 != X2 ) ) ) ) ),
inference(nnf_transformation,[],[f25]) ).
tff(f38,plain,
! [X0: list,X1: $int] :
( ( ? [X4: $int,X5: list] :
( ( cons(X4,X5) = X0 )
& in(X1,X5) )
| ? [X3: list,X2: $int] :
( ( cons(X2,X3) = X0 )
& ( X1 = X2 ) )
| ~ in(X1,X0) )
& ( in(X1,X0)
| ( ! [X4: $int,X5: list] :
( ( cons(X4,X5) != X0 )
| ~ in(X1,X5) )
& ! [X3: list,X2: $int] :
( ( cons(X2,X3) != X0 )
| ( X1 != X2 ) ) ) ) ),
inference(flattening,[],[f37]) ).
tff(f39,plain,
! [X0: list,X1: $int] :
( ( ? [X2: $int,X3: list] :
( ( cons(X2,X3) = X0 )
& in(X1,X3) )
| ? [X4: list,X5: $int] :
( ( cons(X5,X4) = X0 )
& ( X1 = X5 ) )
| ~ in(X1,X0) )
& ( in(X1,X0)
| ( ! [X6: $int,X7: list] :
( ( cons(X6,X7) != X0 )
| ~ in(X1,X7) )
& ! [X8: list,X9: $int] :
( ( cons(X9,X8) != X0 )
| ( X1 != X9 ) ) ) ) ),
inference(rectify,[],[f38]) ).
tff(f40,plain,
! [X0: list,X1: $int] :
( ( ( ( cons(sK2(X0,X1),sK3(X0,X1)) = X0 )
& in(X1,sK3(X0,X1)) )
| ( ( cons(sK5(X0,X1),sK4(X0,X1)) = X0 )
& ( sK5(X0,X1) = X1 ) )
| ~ in(X1,X0) )
& ( in(X1,X0)
| ( ! [X6: $int,X7: list] :
( ( cons(X6,X7) != X0 )
| ~ in(X1,X7) )
& ! [X8: list,X9: $int] :
( ( cons(X9,X8) != X0 )
| ( X1 != X9 ) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3,sK4,sK5]),skolemize(X2,sK2(X0,X1)),skolemize(X3,sK3(X0,X1)),skolemize(X4,sK4(X0,X1)),skolemize(X5,sK5(X0,X1))],[f39]) ).
tff(f56,plain,
! [X0: list,X1: $int,X8: list,X9: $int] :
( in(X1,X0)
| ( cons(X9,X8) != X0 )
| ( X1 != X9 ) ),
inference(cnf_transformation,[],[f40]) ).
tff(f57,plain,
! [X0: list,X1: $int,X6: $int,X7: list] :
( in(X1,X0)
| ( cons(X6,X7) != X0 )
| ~ in(X1,X7) ),
inference(cnf_transformation,[],[f40]) ).
tff(f64,plain,
~ in(2,cons(1,cons(2,cons(3,nil)))),
inference(cnf_transformation,[],[f19]) ).
tff(f71,plain,
! [X1: $int,X6: $int,X7: list] :
( in(X1,cons(X6,X7))
| ~ in(X1,X7) ),
inference(equality_resolution,[],[f57]) ).
tff(f72,plain,
! [X1: $int,X8: list,X9: $int] :
( in(X1,cons(X9,X8))
| ( X1 != X9 ) ),
inference(equality_resolution,[],[f56]) ).
tff(f73,plain,
! [X8: list,X9: $int] : in(X9,cons(X9,X8)),
inference(equality_resolution,[],[f72]) ).
tff(f74,definition,
sF6 = cons(3,nil),
introduced(definition,[new_symbols(definition,[sF6])],[function_definition]) ).
tff(f75,plain,
cons(3,nil) = sF6,
inference(reorient_equations,[],[f74]) ).
tff(f76,definition,
sF7 = cons(2,sF6),
introduced(definition,[new_symbols(definition,[sF7])],[function_definition]) ).
tff(f77,plain,
cons(2,sF6) = sF7,
inference(reorient_equations,[],[f76]) ).
tff(f78,definition,
sF8 = cons(1,sF7),
introduced(definition,[new_symbols(definition,[sF8])],[function_definition]) ).
tff(f79,plain,
cons(1,sF7) = sF8,
inference(reorient_equations,[],[f78]) ).
tff(f80,plain,
~ in(2,sF8),
inference(definition_folding,[],[f64,f79,f77,f75]) ).
tff(f82,definition,
( spl9_1
<=> ( cons(2,sF6) = sF7 ) ),
introduced(definition,[new_symbols(definition,[spl9_1])],[avatar_definition]) ).
tff(f84,plain,
( ( cons(2,sF6) = sF7 )
| ~ spl9_1 ),
inference(avatar_component_clause,[],[f82]) ).
tff(f85,plain,
spl9_1,
inference(avatar_split_clause,[],[f77,f82]) ).
tff(f87,definition,
( spl9_2
<=> ( cons(1,sF7) = sF8 ) ),
introduced(definition,[new_symbols(definition,[spl9_2])],[avatar_definition]) ).
tff(f89,plain,
( ( cons(1,sF7) = sF8 )
| ~ spl9_2 ),
inference(avatar_component_clause,[],[f87]) ).
tff(f90,plain,
spl9_2,
inference(avatar_split_clause,[],[f79,f87]) ).
tff(f97,definition,
( spl9_4
<=> in(2,sF8) ),
introduced(definition,[new_symbols(definition,[spl9_4])],[avatar_definition]) ).
tff(f99,plain,
( ~ in(2,sF8)
| spl9_4 ),
inference(avatar_component_clause,[],[f97]) ).
tff(f100,plain,
~ spl9_4,
inference(avatar_split_clause,[],[f80,f97]) ).
tff(f106,plain,
( in(2,sF7)
| ~ spl9_1 ),
inference(superposition,[],[f73,f84]) ).
tff(f114,definition,
( spl9_7
<=> in(2,sF7) ),
introduced(definition,[new_symbols(definition,[spl9_7])],[avatar_definition]) ).
tff(f116,plain,
( in(2,sF7)
| ~ spl9_7 ),
inference(avatar_component_clause,[],[f114]) ).
tff(f117,plain,
( spl9_7
| ~ spl9_1 ),
inference(avatar_split_clause,[],[f106,f82,f114]) ).
tff(f166,plain,
( ! [X0: $int] :
( in(X0,sF8)
| ~ in(X0,sF7) )
| ~ spl9_2 ),
inference(superposition,[],[f71,f89]) ).
tff(f193,plain,
( ~ in(2,sF7)
| ~ spl9_2
| spl9_4 ),
inference(resolution,[],[f166,f99]) ).
tff(f194,plain,
( $false
| ~ spl9_2
| spl9_4
| ~ spl9_7 ),
inference(forward_subsumption_resolution,[],[f193,f116]) ).
tff(f195,plain,
( ~ spl9_2
| spl9_4
| ~ spl9_7 ),
inference(avatar_contradiction_clause,[],[f194]) ).
tff(f196,plain,
$false,
inference(avatar_smt_refutation,[],[f195,f117,f100,f90,f85]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : DAT079_1 : TPTP v9.3.1. Released v6.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.19 % Computer : n017.cluster.edu
% 0.07/0.19 % Model : x86_64 x86_64
% 0.07/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.19 % Memory : 8046.5625MB
% 0.07/0.19 % OS : Linux 6.8.0-71-generic
% 0.07/0.19 % CPULimit : 300
% 0.07/0.19 % WCLimit : 300
% 0.07/0.19 % DateTime : Tue Sep 29 00:03:21 UTC 2026
% 0.07/0.19 % CPUTime :
% 0.07/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.23 Running first-order theorem proving
% 0.07/0.23 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
% 3.96/1.37 % (4150437)Detected arithmetic, will pick strategies from an ALASCA-aware ARI schedule.
% 3.96/1.37 % (4150530)dis+1002_16:1_to=lpo:sil=64000:sas=z3:si=on:norm_ineq=on:gve=force:uwa=one_side_constant:random_seed=964932008:i=12:doe=on:rtra=on:gtg=exists_top:ss=axioms_2999 on theBenchmark for (2999ds/12Mi)
% 3.96/1.37 % (4150530)Instruction limit reached!
% 3.96/1.37 % (4150530)------------------------------
% 3.96/1.37 % (4150530)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.96/1.37 % (4150530)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.96/1.37 % (4150530)CaDiCaL version: 2.1.3
% 3.96/1.37 % (4150530)Termination reason: Instruction limit
% 3.96/1.37 % (4150530)Termination phase: Saturation
% 3.96/1.37 % (4150530)Time elapsed: 0.020 s
% 3.96/1.37 % (4150530)Peak memory usage: 115 MB
% 3.96/1.37 % (4150530)Instructions burned: 13 (million)
% 3.96/1.37 % (4150542)lrs+10_1_tgt=ground:sas=z3:si=on:random_seed=2971138717:i=33:rtra=on_2999 on theBenchmark for (2999ds/33Mi)
% 3.96/1.37 % (4150537)lrs+1002_4:1_to=lpo:sil=64000:si=on:br=off:random_seed=2807217956:s2a=on:i=7:rtra=on:inst=on_2999 on theBenchmark for (2999ds/7Mi)
% 3.96/1.37 % (4150538)dis+21_64_to=kbo:sil=128000:si=on:sp=weighted_frequency:uwa=alasca_can_abstract:random_seed=607641959:i=4:rtra=on_2999 on theBenchmark for (2999ds/4Mi)
% 3.96/1.37 % (4150532)dis+1002_1_to=kbo:sil=128000:tgt=ground:sas=z3:si=on:spb=units:tha=off:random_seed=3869211232:i=307:kws=precedence:nm=0:rtra=on_2999 on theBenchmark for (2999ds/307Mi)
% 3.96/1.37 % (4150534)dis+10_3_slsqr=1,4:to=lpo:sil=128000:thi=strong:si=on:uwa=off:s2agt=20:slsqc=1:slsq=on:random_seed=75633922:i=201:slsql=off:asg=cautious:rtra=on:gtg=all:ss=axioms:sgt=16_2999 on theBenchmark for (2999ds/201Mi)
% 3.96/1.37 % (4150538)Instruction limit reached!
% 3.96/1.37 % (4150538)------------------------------
% 3.96/1.37 % (4150538)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.96/1.37 % (4150538)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.96/1.37 % (4150538)CaDiCaL version: 2.1.3
% 3.96/1.37 % (4150538)Termination reason: Instruction limit
% 3.96/1.37 % (4150538)Termination phase: Saturation
% 3.96/1.37 % (4150538)Time elapsed: 0.004 s
% 3.96/1.37 % (4150538)Peak memory usage: 88 MB
% 3.96/1.37 % (4150538)Instructions burned: 5 (million)
% 3.96/1.37 % (4150537)Instruction limit reached!
% 3.96/1.37 % (4150537)------------------------------
% 3.96/1.37 % (4150537)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.96/1.37 % (4150537)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.96/1.37 % (4150537)CaDiCaL version: 2.1.3
% 3.96/1.37 % (4150537)Termination reason: Instruction limit
% 3.96/1.37 % (4150537)Termination phase: Saturation
% 3.96/1.37 % (4150537)Time elapsed: 0.005 s
% 3.96/1.37 % (4150537)Peak memory usage: 88 MB
% 3.96/1.37 % (4150537)Instructions burned: 7 (million)
% 3.96/1.37 % (4150540)lrs+10_1_to=lpo:sas=z3:si=on:tha=off:random_seed=1086670115:i=46:rtra=on_2999 on theBenchmark for (2999ds/46Mi)
% 3.96/1.37 % (4150532)First to succeed.
% 3.96/1.37 % (4150532)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-4150437"
% 3.96/1.37 % (4150542)Also succeeded, but the first one will report.
% 3.96/1.37 % (4150540)Also succeeded, but the first one will report.
% 3.96/1.37 % (4150534)Also succeeded, but the first one will report.
% 3.96/1.37 % (4150577)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=1966503499:i=29:thsqd=64:nm=0:thsqc=8:rtra=on:thsq=on:ev=off_2998 on theBenchmark for (2998ds/29Mi)
% 3.96/1.37 % (4150578)ott+21_1024_to=lakbo:sil=128000:bsd=on:si=on:alasca=on:uwa=alasca_main:nwc=0.5:random_seed=232643874:cond=on:i=16:fgj=on:ep=RS:asg=force:nm=10:rtra=on:rawr=on_2998 on theBenchmark for (2998ds/16Mi)
% 3.96/1.37 % (4150577)Also succeeded, but the first one will report.
% 3.96/1.37 % (4150578)Instruction limit reached!
% 3.96/1.37 % (4150578)------------------------------
% 3.96/1.37 % (4150578)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.96/1.37 % (4150578)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.96/1.37 % (4150578)CaDiCaL version: 2.1.3
% 3.96/1.37 % (4150578)Termination reason: Instruction limit
% 3.96/1.37 % (4150578)Termination phase: Saturation
% 3.96/1.37 % (4150578)Time elapsed: 0.013 s
% 3.96/1.37 % (4150578)Peak memory usage: 90 MB
% 3.96/1.37 % (4150578)Instructions burned: 17 (million)
% 3.96/1.37 % (4150568)dis+11_3_anc=none:drc=ordering:si=on:urr=ec_only:bce=on:tha=off:sac=on:random_seed=2655681001:st=5:i=14:sd=10:rtra=on:ss=axioms:rawr=on_2998 on theBenchmark for (2998ds/14Mi)
% 3.96/1.37 % (4150568)Also succeeded, but the first one will report.
% 3.96/1.37 % (4150532)Refutation found. Thanks to Tanya!
% 3.96/1.37 % SZS status Theorem for theBenchmark
% 3.96/1.37 % SZS output start Proof for theBenchmark
% See solution above
% 3.96/1.37 % (4150532)------------------------------
% 3.96/1.37 % (4150532)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.96/1.37 % (4150532)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.96/1.37 % (4150532)CaDiCaL version: 2.1.3
% 3.96/1.37 % (4150532)Termination reason: Refutation
% 3.96/1.37 % (4150532)Time elapsed: 0.040 s
% 3.96/1.37 % (4150532)Peak memory usage: 116 MB
% 3.96/1.37 % (4150532)Instructions burned: 20 (million)
% 3.96/1.37 % (4150532)------------------------------
% 3.96/1.37 % (4150532)------------------------------
% 3.96/1.37 % (4150437)Success in time 0.474 s
% 3.96/1.37 % Vampire exiting
%------------------------------------------------------------------------------