%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : DAT104_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 : n004.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 09:47:18 AM UTC 2026
% Result : Theorem 1.56s 0.98s
% Output : Refutation 2.94s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 7
% Syntax : Number of formulae : 53 ( 13 unt; 0 typ; 2 def)
% Number of atoms : 154 ( 37 equ)
% Maximal formula atoms : 12 ( 2 avg)
% Number of connectives : 169 ( 68 ~; 67 |; 26 &)
% ( 4 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number arithmetic : 169 ( 34 atm; 23 fun; 73 num; 39 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 : 14 ( 8 usr; 6 con; 0-2 aty)
% Number of variables : 80 ( 0 sgn 70 !; 10 ?; 80 :)
% 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_9,type,
sK0: ( $int * list ) > $int ).
tff(func_def_10,type,
sK1: ( $int * list ) > list ).
tff(func_def_12,type,
'$inst2': $int ).
tff(func_def_13,type,
'$inst3': $int ).
tff(pred_def_1,type,
inRange: ( $int * list ) > $o ).
tff(f4,axiom,
! [X1: list,X0: $int] : ( cons(X0,X1) != nil ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l4) ).
tff(f5,negated_conjecture,
! [X0: $int,X1: list] :
( ( ( X1 = nil )
| ? [X2: $int,X3: list] :
( $less(X2,X0)
& $lesseq(0,X2)
& ( X1 = cons(X2,X3) )
& inRange(X0,X3) ) )
<=> inRange(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',inRange) ).
tff(f6,conjecture,
~ ! [X1: list,X0: $int] :
( inRange(X0,X1)
=> inRange($difference(X0,1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c) ).
tff(f7,negated_conjecture,
~ ~ ! [X1: list,X0: $int] :
( inRange(X0,X1)
=> inRange($difference(X0,1),X1) ),
inference(negated_conjecture,[status(cth)],[f6]) ).
tff(f8,plain,
! [X1: list,X0: $int] :
( inRange(X0,X1)
=> inRange($sum(X0,$uminus(1)),X1) ),
inference(theory_normalization,[],[f7]) ).
tff(f9,plain,
! [X0: $int,X1: list] :
( inRange(X0,X1)
<=> ( ? [X2: $int,X3: list] :
( inRange(X0,X3)
& ~ $less(X2,0)
& ( X1 = cons(X2,X3) )
& $less(X2,X0) )
| ( X1 = nil ) ) ),
inference(theory_normalization,[],[f5]) ).
tff(f10,plain,
! [X0: $int,X1: $int] : ( $sum(X1,X0) = $sum(X0,X1) ),
introduced(definition,[],[tha_commutativity]) ).
tff(f14,plain,
! [X0: $int] : ( 0 = $sum(X0,$uminus(X0)) ),
introduced(definition,[],[tha_inverse_op_unit]) ).
tff(f22,plain,
! [X0: list,X1: $int] :
( inRange(X1,X0)
=> inRange($sum(X1,$uminus(1)),X0) ),
inference(rectify,[],[f8]) ).
tff(f24,plain,
! [X1: $int,X0: list] :
( ~ inRange(X1,X0)
| inRange($sum(X1,$uminus(1)),X0) ),
inference(ennf_transformation,[],[f22]) ).
tff(f25,plain,
! [X0: $int,X1: list] :
( ~ inRange(X0,X1)
| inRange($sum(X0,$uminus(1)),X1) ),
inference(rectify,[],[f24]) ).
tff(f26,plain,
! [X0: $int,X1: list] :
( ( inRange(X0,X1)
| ( ! [X2: $int,X3: list] :
( ~ inRange(X0,X3)
| $less(X2,0)
| ( cons(X2,X3) != X1 )
| ~ $less(X2,X0) )
& ( nil != X1 ) ) )
& ( ? [X2: $int,X3: list] :
( inRange(X0,X3)
& ~ $less(X2,0)
& ( X1 = cons(X2,X3) )
& $less(X2,X0) )
| ( X1 = nil )
| ~ inRange(X0,X1) ) ),
inference(nnf_transformation,[],[f9]) ).
tff(f27,plain,
! [X0: $int,X1: list] :
( ( inRange(X0,X1)
| ( ! [X2: $int,X3: list] :
( ~ inRange(X0,X3)
| $less(X2,0)
| ( cons(X2,X3) != X1 )
| ~ $less(X2,X0) )
& ( nil != X1 ) ) )
& ( ? [X2: $int,X3: list] :
( inRange(X0,X3)
& ~ $less(X2,0)
& ( X1 = cons(X2,X3) )
& $less(X2,X0) )
| ( X1 = nil )
| ~ inRange(X0,X1) ) ),
inference(flattening,[],[f26]) ).
tff(f28,plain,
! [X0: $int,X1: list] :
( ( inRange(X0,X1)
| ( ! [X2: $int,X3: list] :
( ~ inRange(X0,X3)
| $less(X2,0)
| ( cons(X2,X3) != X1 )
| ~ $less(X2,X0) )
& ( nil != X1 ) ) )
& ( ? [X4: $int,X5: list] :
( inRange(X0,X5)
& ~ $less(X4,0)
& ( cons(X4,X5) = X1 )
& $less(X4,X0) )
| ( X1 = nil )
| ~ inRange(X0,X1) ) ),
inference(rectify,[],[f27]) ).
tff(f29,plain,
! [X0: $int,X1: list] :
( ( inRange(X0,X1)
| ( ! [X2: $int,X3: list] :
( ~ inRange(X0,X3)
| $less(X2,0)
| ( cons(X2,X3) != X1 )
| ~ $less(X2,X0) )
& ( nil != X1 ) ) )
& ( ( inRange(X0,sK1(X0,X1))
& ~ $less(sK0(X0,X1),0)
& ( cons(sK0(X0,X1),sK1(X0,X1)) = X1 )
& $less(sK0(X0,X1),X0) )
| ( X1 = nil )
| ~ inRange(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X4,sK0(X0,X1)),skolemize(X5,sK1(X0,X1))],[f28]) ).
tff(f30,plain,
! [X0: list,X1: $int] : ( nil != cons(X1,X0) ),
inference(rectify,[],[f4]) ).
tff(f34,plain,
! [X0: $int,X1: list] :
( inRange($sum(X0,$uminus(1)),X1)
| ~ inRange(X0,X1) ),
inference(cnf_transformation,[],[f25]) ).
tff(f35,plain,
! [X0: $int,X1: list] :
( ~ inRange(X0,X1)
| $less(sK0(X0,X1),X0)
| ( nil = X1 ) ),
inference(cnf_transformation,[],[f29]) ).
tff(f37,plain,
! [X0: $int,X1: list] :
( ~ $less(sK0(X0,X1),0)
| ( nil = X1 )
| ~ inRange(X0,X1) ),
inference(cnf_transformation,[],[f29]) ).
tff(f39,plain,
! [X0: $int,X1: list] :
( inRange(X0,X1)
| ( nil != X1 ) ),
inference(cnf_transformation,[],[f29]) ).
tff(f40,plain,
! [X2: $int,X3: list,X0: $int,X1: list] :
( inRange(X0,X1)
| ~ inRange(X0,X3)
| $less(X2,0)
| ( cons(X2,X3) != X1 )
| ~ $less(X2,X0) ),
inference(cnf_transformation,[],[f29]) ).
tff(f41,plain,
! [X0: list,X1: $int] : ( nil != cons(X1,X0) ),
inference(cnf_transformation,[],[f30]) ).
tff(f42,plain,
! [X2: $int,X3: list,X0: $int] :
( inRange(X0,cons(X2,X3))
| ~ $less(X2,X0)
| $less(X2,0)
| ~ inRange(X0,X3) ),
inference(equality_resolution,[],[f40]) ).
tff(f43,plain,
! [X0: $int] : inRange(X0,nil),
inference(equality_resolution,[],[f39]) ).
tff(f44,plain,
! [X0: $int,X1: list] :
( inRange($sum(X0,-1),X1)
| ~ inRange(X0,X1) ),
inference(evaluation,[],[f34]) ).
tff(f46,plain,
! [X0: $int,X1: list] :
( ~ inRange(X0,X1)
| $less(sK0($sum(X0,-1),X1),$sum(X0,-1))
| ( nil = X1 ) ),
inference(resolution,[],[f35,f44]) ).
tff(f48,plain,
! [X3: list] :
( inRange(1,cons(0,X3))
| ~ $less(0,1)
| $less(0,0)
| ~ inRange(1,X3) ),
inference(instantiation,[],[f42]) ).
tff(f49,plain,
! [X3: list] :
( inRange(1,cons(0,X3))
| ~ inRange(1,X3) ),
inference(interpreted_simplification,[],[f48]) ).
tff(f61,plain,
! [X0: list] :
( ~ inRange(1,X0)
| ( nil = cons(0,X0) )
| $less(sK0($sum(1,-1),cons(0,X0)),$sum(1,-1)) ),
inference(resolution,[],[f46,f49]) ).
tff(f62,plain,
! [X0: list] :
( ~ inRange(1,X0)
| ( nil = cons(0,X0) )
| $less(sK0(0,cons(0,X0)),0) ),
inference(evaluation,[],[f61]) ).
tff(f68,definition,
( spl4_1
<=> ( nil = cons(0,nil) ) ),
introduced(definition,[new_symbols(definition,[spl4_1])],[avatar_definition]) ).
tff(f70,plain,
( ( nil = cons(0,nil) )
| ~ spl4_1 ),
inference(avatar_component_clause,[],[f68]) ).
tff(f77,plain,
( $less(sK0(0,cons(0,nil)),0)
| ( nil = cons(0,nil) ) ),
inference(resolution,[],[f62,f43]) ).
tff(f81,definition,
( spl4_3
<=> $less(sK0(0,cons(0,nil)),0) ),
introduced(definition,[new_symbols(definition,[spl4_3])],[avatar_definition]) ).
tff(f83,plain,
( $less(sK0(0,cons(0,nil)),0)
| ~ spl4_3 ),
inference(avatar_component_clause,[],[f81]) ).
tff(f84,plain,
( spl4_1
| spl4_3 ),
inference(avatar_split_clause,[],[f77,f81,f68]) ).
tff(f109,plain,
( ( nil != nil )
| ~ spl4_1 ),
inference(superposition,[],[f41,f70]) ).
tff(f110,plain,
( $false
| ~ spl4_1 ),
inference(trivial_inequality_removal,[],[f109]) ).
tff(f111,plain,
~ spl4_1,
inference(avatar_contradiction_clause,[],[f110]) ).
tff(f113,plain,
( ( nil = cons(0,nil) )
| ~ inRange(0,cons(0,nil))
| ~ spl4_3 ),
inference(resolution,[],[f83,f37]) ).
tff(f114,plain,
( ~ inRange(0,cons(0,nil))
| ~ spl4_3 ),
inference(forward_subsumption_resolution,[],[f113,f41]) ).
tff(f144,plain,
! [X0: $int,X1: list] :
( inRange($sum(-1,X0),X1)
| ~ inRange(X0,X1) ),
inference(superposition,[],[f44,f10]) ).
tff(f154,plain,
! [X0: list] :
( inRange(0,X0)
| ~ inRange($uminus(-1),X0) ),
inference(superposition,[],[f144,f14]) ).
tff(f157,plain,
! [X0: list] :
( ~ inRange(1,X0)
| inRange(0,X0) ),
inference(evaluation,[],[f154]) ).
tff(f165,plain,
! [X0: list] :
( ~ inRange(1,X0)
| inRange(0,cons(0,X0)) ),
inference(resolution,[],[f157,f49]) ).
tff(f175,plain,
inRange(0,cons(0,nil)),
inference(resolution,[],[f165,f43]) ).
tff(f178,plain,
( $false
| ~ spl4_3 ),
inference(forward_subsumption_resolution,[],[f175,f114]) ).
tff(f179,plain,
~ spl4_3,
inference(avatar_contradiction_clause,[],[f178]) ).
cnf(s2,plain,
( spl4_1
| spl4_3 ),
inference(sat_conversion,[],[f84]) ).
cnf(s3,plain,
~ spl4_1,
inference(sat_conversion,[],[f111]) ).
cnf(s4,plain,
~ spl4_3,
inference(sat_conversion,[],[f179]) ).
cnf(s5,plain,
$false,
inference(rat,[],[s2,s4,s3]) ).
tff(f180,plain,
$false,
inference(avatar_sat_refutation,[],[s5]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : DAT104_1 : TPTP v9.3.1. Released v6.1.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.18 % Computer : n004.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 00:08:22 UTC 2026
% 0.09/0.19 % CPUTime :
% 0.09/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.22 Running first-order theorem proving
% 0.09/0.22 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
% 1.56/0.98 % (918074)Detected arithmetic, will pick strategies from an ALASCA-aware ARI schedule.
% 1.56/0.98 % (918081)dis+10_3_slsqr=1,4:to=lpo:sil=128000:thi=strong:si=on:uwa=off:s2agt=20:slsqc=1:slsq=on:random_seed=203529785:i=201:slsql=off:asg=cautious:rtra=on:gtg=all:ss=axioms:sgt=16_2999 on theBenchmark for (2999ds/201Mi)
% 1.56/0.98 % (918081)First to succeed.
% 1.56/0.98 % (918081)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-918074"
% 1.56/0.98 % (918080)dis+1002_1_to=kbo:sil=128000:tgt=ground:sas=z3:si=on:spb=units:tha=off:random_seed=4007874186:i=307:kws=precedence:nm=0:rtra=on_2999 on theBenchmark for (2999ds/307Mi)
% 1.56/0.98 % (918083)dis+21_64_to=kbo:sil=128000:si=on:sp=weighted_frequency:uwa=alasca_can_abstract:random_seed=2218781764:i=4:rtra=on_2999 on theBenchmark for (2999ds/4Mi)
% 1.56/0.98 % (918082)lrs+1002_4:1_to=lpo:sil=64000:si=on:br=off:random_seed=882495416:s2a=on:i=7:rtra=on:inst=on_2999 on theBenchmark for (2999ds/7Mi)
% 1.56/0.98 % (918084)lrs+10_1_to=lpo:sas=z3:si=on:tha=off:random_seed=1528283426:i=46:rtra=on_2999 on theBenchmark for (2999ds/46Mi)
% 1.56/0.98 % (918079)dis+1002_16:1_to=lpo:sil=64000:sas=z3:si=on:norm_ineq=on:gve=force:uwa=one_side_constant:random_seed=2760525453:i=12:doe=on:rtra=on:gtg=exists_top:ss=axioms_2999 on theBenchmark for (2999ds/12Mi)
% 1.56/0.98 % (918085)lrs+10_1_tgt=ground:sas=z3:si=on:random_seed=620933682:i=33:rtra=on_2999 on theBenchmark for (2999ds/33Mi)
% 1.56/0.98 % (918083)Instruction limit reached!
% 1.56/0.98 % (918083)------------------------------
% 1.56/0.98 % (918083)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 1.56/0.98 % (918083)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.56/0.98 % (918083)CaDiCaL version: 2.1.3
% 1.56/0.98 % (918083)Termination reason: Instruction limit
% 1.56/0.98 % (918083)Termination phase: Saturation
% 1.56/0.98 % (918083)Time elapsed: 0.004 s
% 1.56/0.98 % (918083)Peak memory usage: 88 MB
% 1.56/0.98 % (918083)Instructions burned: 5 (million)
% 1.56/0.98 % (918082)Instruction limit reached!
% 1.56/0.98 % (918082)------------------------------
% 1.56/0.98 % (918082)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 1.56/0.98 % (918082)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.56/0.98 % (918082)CaDiCaL version: 2.1.3
% 1.56/0.98 % (918082)Termination reason: Instruction limit
% 1.56/0.98 % (918082)Termination phase: Saturation
% 1.56/0.98 % (918082)Time elapsed: 0.007 s
% 1.56/0.98 % (918082)Peak memory usage: 88 MB
% 1.56/0.98 % (918082)Instructions burned: 8 (million)
% 1.56/0.98 % (918079)Instruction limit reached!
% 1.56/0.98 % (918079)------------------------------
% 1.56/0.98 % (918079)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 1.56/0.98 % (918079)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.56/0.98 % (918079)CaDiCaL version: 2.1.3
% 1.56/0.98 % (918079)Termination reason: Instruction limit
% 1.56/0.98 % (918079)Termination phase: Saturation
% 1.56/0.98 % (918079)Time elapsed: 0.030 s
% 1.56/0.98 % (918079)Peak memory usage: 111 MB
% 1.56/0.98 % (918079)Instructions burned: 13 (million)
% 1.56/0.98 % (918085)Instruction limit reached!
% 1.56/0.98 % (918085)------------------------------
% 1.56/0.98 % (918085)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 1.56/0.98 % (918085)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.56/0.98 % (918085)CaDiCaL version: 2.1.3
% 1.56/0.98 % (918085)Termination reason: Instruction limit
% 1.56/0.98 % (918085)Termination phase: Saturation
% 1.56/0.98 % (918085)Time elapsed: 0.046 s
% 1.56/0.98 % (918085)Peak memory usage: 115 MB
% 1.56/0.98 % (918085)Instructions burned: 34 (million)
% 1.56/0.98 % (918084)Instruction limit reached!
% 1.56/0.98 % (918084)------------------------------
% 1.56/0.98 % (918084)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 1.56/0.98 % (918084)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.56/0.98 % (918084)CaDiCaL version: 2.1.3
% 1.56/0.98 % (918084)Termination reason: Instruction limit
% 1.56/0.98 % (918084)Termination phase: Saturation
% 1.56/0.98 % (918084)Time elapsed: 0.047 s
% 1.56/0.98 % (918084)Peak memory usage: 111 MB
% 1.56/0.98 % (918084)Instructions burned: 47 (million)
% 1.56/0.98 % (918081)Refutation found. Thanks to Tanya!
% 1.56/0.98 % SZS status Theorem for theBenchmark
% 1.56/0.98 % SZS output start Proof for theBenchmark
% See solution above
% 2.94/1.17 % (918081)------------------------------
% 2.94/1.17 % (918081)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.94/1.17 % (918081)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.94/1.17 % (918081)CaDiCaL version: 2.1.3
% 2.94/1.17 % (918081)Termination reason: Refutation
% 2.94/1.17 % (918081)Time elapsed: 0.025 s
% 2.94/1.17 % (918081)Peak memory usage: 117 MB
% 2.94/1.17 % (918081)Instructions burned: 19 (million)
% 2.94/1.17 % (918081)------------------------------
% 2.94/1.17 % (918081)------------------------------
% 2.94/1.17 % (918074)Success in time 0.324 s
% 2.94/1.17 % Vampire exiting
%------------------------------------------------------------------------------