%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : DAT098_1 : TPTP v9.3.1. Released v6.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n020.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 09:47:17 AM UTC 2026
% Result : Theorem 3.73s 1.30s
% Output : Refutation 3.73s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 2
% Syntax : Number of formulae : 21 ( 9 unt; 0 typ; 0 def)
% Number of atoms : 89 ( 22 equ)
% Maximal formula atoms : 12 ( 4 avg)
% Number of connectives : 111 ( 43 ~; 40 |; 26 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number arithmetic : 103 ( 30 atm; 0 fun; 52 num; 21 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 : 5 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 8 usr; 8 con; 0-2 aty)
% Number of variables : 40 ( 30 !; 10 ?; 40 :)
% 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_11,type,
sK0: ( $int * list ) > list ).
tff(func_def_12,type,
sK1: ( $int * list ) > $int ).
tff(func_def_13,type,
'$inst2': $int ).
tff(func_def_14,type,
'$inst3': $int ).
tff(pred_def_1,type,
inRange: ( $int * list ) > $o ).
tff(f5,negated_conjecture,
! [X0: $int,X1: list] :
( ( ? [X2: $int,X3: list] :
( $lesseq(0,X2)
& ( X1 = cons(X2,X3) )
& inRange(X0,X3)
& $less(X2,X0) )
| ( X1 = nil ) )
<=> inRange(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inRange) ).
tff(f6,conjecture,
inRange(4,cons(1,cons(3,cons(2,nil)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c) ).
tff(f7,negated_conjecture,
~ inRange(4,cons(1,cons(3,cons(2,nil)))),
inference(negated_conjecture,[status(cth)],[f6]) ).
tff(f8,plain,
! [X0: $int,X1: list] :
( inRange(X0,X1)
<=> ( ? [X3: list,X2: $int] :
( ( X1 = cons(X2,X3) )
& inRange(X0,X3)
& ~ $less(X2,0)
& $less(X2,X0) )
| ( X1 = nil ) ) ),
inference(theory_normalization,[],[f5]) ).
tff(f21,plain,
~ inRange(4,cons(1,cons(3,cons(2,nil)))),
inference(flattening,[],[f7]) ).
tff(f25,plain,
! [X0: $int,X1: list] :
( ( inRange(X0,X1)
| ( ! [X3: list,X2: $int] :
( ( cons(X2,X3) != X1 )
| ~ inRange(X0,X3)
| $less(X2,0)
| ~ $less(X2,X0) )
& ( nil != X1 ) ) )
& ( ? [X3: list,X2: $int] :
( ( X1 = cons(X2,X3) )
& inRange(X0,X3)
& ~ $less(X2,0)
& $less(X2,X0) )
| ( X1 = nil )
| ~ inRange(X0,X1) ) ),
inference(nnf_transformation,[],[f8]) ).
tff(f26,plain,
! [X0: $int,X1: list] :
( ( inRange(X0,X1)
| ( ! [X3: list,X2: $int] :
( ( cons(X2,X3) != X1 )
| ~ inRange(X0,X3)
| $less(X2,0)
| ~ $less(X2,X0) )
& ( nil != X1 ) ) )
& ( ? [X3: list,X2: $int] :
( ( X1 = cons(X2,X3) )
& inRange(X0,X3)
& ~ $less(X2,0)
& $less(X2,X0) )
| ( X1 = nil )
| ~ inRange(X0,X1) ) ),
inference(flattening,[],[f25]) ).
tff(f27,plain,
! [X0: $int,X1: list] :
( ( inRange(X0,X1)
| ( ! [X2: list,X3: $int] :
( ( cons(X3,X2) != X1 )
| ~ inRange(X0,X2)
| $less(X3,0)
| ~ $less(X3,X0) )
& ( nil != X1 ) ) )
& ( ? [X4: list,X5: $int] :
( ( cons(X5,X4) = X1 )
& inRange(X0,X4)
& ~ $less(X5,0)
& $less(X5,X0) )
| ( X1 = nil )
| ~ inRange(X0,X1) ) ),
inference(rectify,[],[f26]) ).
tff(f28,plain,
! [X0: $int,X1: list] :
( ( inRange(X0,X1)
| ( ! [X2: list,X3: $int] :
( ( cons(X3,X2) != X1 )
| ~ inRange(X0,X2)
| $less(X3,0)
| ~ $less(X3,X0) )
& ( nil != X1 ) ) )
& ( ( ( cons(sK1(X0,X1),sK0(X0,X1)) = X1 )
& inRange(X0,sK0(X0,X1))
& ~ $less(sK1(X0,X1),0)
& $less(sK1(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))],[f27]) ).
tff(f29,plain,
~ inRange(4,cons(1,cons(3,cons(2,nil)))),
inference(cnf_transformation,[],[f21]) ).
tff(f37,plain,
! [X0: $int,X1: list] :
( inRange(X0,X1)
| ( nil != X1 ) ),
inference(cnf_transformation,[],[f28]) ).
tff(f38,plain,
! [X2: list,X3: $int,X0: $int,X1: list] :
( inRange(X0,X1)
| ( cons(X3,X2) != X1 )
| ~ inRange(X0,X2)
| $less(X3,0)
| ~ $less(X3,X0) ),
inference(cnf_transformation,[],[f28]) ).
tff(f40,plain,
! [X2: list,X3: $int,X0: $int] :
( inRange(X0,cons(X3,X2))
| ~ inRange(X0,X2)
| ~ $less(X3,X0)
| $less(X3,0) ),
inference(equality_resolution,[],[f38]) ).
tff(f41,plain,
! [X0: $int] : inRange(X0,nil),
inference(equality_resolution,[],[f37]) ).
tff(f46,plain,
( $less(1,0)
| ~ inRange(4,cons(3,cons(2,nil)))
| ~ $less(1,4) ),
inference(resolution,[],[f40,f29]) ).
tff(f48,plain,
~ inRange(4,cons(3,cons(2,nil))),
inference(evaluation,[],[f46]) ).
tff(f49,plain,
( $less(3,0)
| ~ $less(3,4)
| ~ inRange(4,cons(2,nil)) ),
inference(resolution,[],[f48,f40]) ).
tff(f50,plain,
~ inRange(4,cons(2,nil)),
inference(evaluation,[],[f49]) ).
tff(f51,plain,
( $less(2,0)
| ~ $less(2,4)
| ~ inRange(4,nil) ),
inference(resolution,[],[f50,f40]) ).
tff(f52,plain,
~ inRange(4,nil),
inference(evaluation,[],[f51]) ).
tff(f53,plain,
$false,
inference(forward_subsumption_resolution,[],[f52,f41]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : DAT098_1 : TPTP v9.3.1. Released v6.1.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.18 % Computer : n020.cluster.edu
% 0.10/0.18 % Model : x86_64 x86_64
% 0.10/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.18 % Memory : 8046.5625MB
% 0.10/0.18 % OS : Linux 6.8.0-71-generic
% 0.10/0.18 % CPULimit : 300
% 0.10/0.18 % WCLimit : 300
% 0.10/0.18 % DateTime : Tue Sep 29 00:09:20 UTC 2026
% 0.10/0.19 % CPUTime :
% 0.10/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.22 Running first-order theorem proving
% 0.10/0.22 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
% 3.73/1.29 % (702535)Detected arithmetic, will pick strategies from an ALASCA-aware ARI schedule.
% 3.73/1.29 % (702601)lrs+1002_4:1_to=lpo:sil=64000:si=on:br=off:random_seed=942365021:s2a=on:i=7:rtra=on:inst=on_2999 on theBenchmark for (2999ds/7Mi)
% 3.73/1.29 % (702601)Instruction limit reached!
% 3.73/1.29 % (702601)------------------------------
% 3.73/1.29 % (702601)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.73/1.29 % (702601)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.73/1.29 % (702601)CaDiCaL version: 2.1.3
% 3.73/1.29 % (702601)Termination reason: Instruction limit
% 3.73/1.29 % (702601)Termination phase: Saturation
% 3.73/1.29 % (702601)Time elapsed: 0.003 s
% 3.73/1.29 % (702601)Peak memory usage: 88 MB
% 3.73/1.29 % (702601)Instructions burned: 7 (million)
% 3.73/1.29 % (702604)lrs+10_1_tgt=ground:sas=z3:si=on:random_seed=338570329:i=33:rtra=on_2999 on theBenchmark for (2999ds/33Mi)
% 3.73/1.29 % (702598)dis+1002_16:1_to=lpo:sil=64000:sas=z3:si=on:norm_ineq=on:gve=force:uwa=one_side_constant:random_seed=916067927:i=12:doe=on:rtra=on:gtg=exists_top:ss=axioms_2999 on theBenchmark for (2999ds/12Mi)
% 3.73/1.29 % (702600)dis+10_3_slsqr=1,4:to=lpo:sil=128000:thi=strong:si=on:uwa=off:s2agt=20:slsqc=1:slsq=on:random_seed=514404899:i=201:slsql=off:asg=cautious:rtra=on:gtg=all:ss=axioms:sgt=16_2999 on theBenchmark for (2999ds/201Mi)
% 3.73/1.29 % (702602)dis+21_64_to=kbo:sil=128000:si=on:sp=weighted_frequency:uwa=alasca_can_abstract:random_seed=2508516728:i=4:rtra=on_2999 on theBenchmark for (2999ds/4Mi)
% 3.73/1.29 % (702599)dis+1002_1_to=kbo:sil=128000:tgt=ground:sas=z3:si=on:spb=units:tha=off:random_seed=4126954249:i=307:kws=precedence:nm=0:rtra=on_2999 on theBenchmark for (2999ds/307Mi)
% 3.73/1.29 % (702603)lrs+10_1_to=lpo:sas=z3:si=on:tha=off:random_seed=3307167260:i=46:rtra=on_2999 on theBenchmark for (2999ds/46Mi)
% 3.73/1.29 % (702602)Instruction limit reached!
% 3.73/1.29 % (702602)------------------------------
% 3.73/1.29 % (702602)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.73/1.29 % (702602)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.73/1.29 % (702602)CaDiCaL version: 2.1.3
% 3.73/1.29 % (702602)Termination reason: Instruction limit
% 3.73/1.29 % (702602)Termination phase: Saturation
% 3.73/1.29 % (702602)Time elapsed: 0.004 s
% 3.73/1.29 % (702602)Peak memory usage: 89 MB
% 3.73/1.29 % (702602)Instructions burned: 6 (million)
% 3.73/1.29 % (702600)First to succeed.
% 3.73/1.29 % (702598)Instruction limit reached!
% 3.73/1.29 % (702598)------------------------------
% 3.73/1.29 % (702598)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.73/1.29 % (702598)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.73/1.29 % (702598)CaDiCaL version: 2.1.3
% 3.73/1.29 % (702598)Termination reason: Instruction limit
% 3.73/1.29 % (702598)Termination phase: Saturation
% 3.73/1.29 % (702598)Time elapsed: 0.031 s
% 3.73/1.29 % (702598)Peak memory usage: 115 MB
% 3.73/1.29 % (702598)Instructions burned: 13 (million)
% 3.73/1.29 % (702600)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-702535"
% 3.73/1.29 % (702603)Also succeeded, but the first one will report.
% 3.73/1.29 % (702606)dis+11_3_anc=none:drc=ordering:si=on:urr=ec_only:bce=on:tha=off:sac=on:random_seed=3979991539:st=5:i=14:sd=10:rtra=on:ss=axioms:rawr=on_2998 on theBenchmark for (2998ds/14Mi)
% 3.73/1.30 % (702604)Instruction limit reached!
% 3.73/1.30 % (702604)------------------------------
% 3.73/1.30 % (702604)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.73/1.30 % (702604)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.73/1.30 % (702604)CaDiCaL version: 2.1.3
% 3.73/1.30 % (702604)Termination reason: Instruction limit
% 3.73/1.30 % (702604)Termination phase: Saturation
% 3.73/1.30 % (702604)Time elapsed: 0.047 s
% 3.73/1.30 % (702604)Peak memory usage: 115 MB
% 3.73/1.30 % (702604)Instructions burned: 33 (million)
% 3.73/1.30 % (702606)Instruction limit reached!
% 3.73/1.30 % (702606)------------------------------
% 3.73/1.30 % (702606)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.73/1.30 % (702606)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.73/1.30 % (702606)CaDiCaL version: 2.1.3
% 3.73/1.30 % (702606)Termination reason: Instruction limit
% 3.73/1.30 % (702606)Termination phase: Saturation
% 3.73/1.30 % (702606)Time elapsed: 0.005 s
% 3.73/1.30 % (702606)Peak memory usage: 88 MB
% 3.73/1.30 % (702606)Instructions burned: 19 (million)
% 3.73/1.30 % (702616)dis+1011_1_prc=on:drc=off:si=on:sac=on:random_seed=1926988127:i=24:canc=force:rtra=on_2998 on theBenchmark for (2998ds/24Mi)
% 3.73/1.30 % (702616)Instruction limit reached!
% 3.73/1.30 % (702616)------------------------------
% 3.73/1.30 % (702616)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.73/1.30 % (702616)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.73/1.30 % (702616)CaDiCaL version: 2.1.3
% 3.73/1.30 % (702616)Termination reason: Instruction limit
% 3.73/1.30 % (702616)Termination phase: Saturation
% 3.73/1.30 % (702616)Time elapsed: 0.009 s
% 3.73/1.30 % (702616)Peak memory usage: 89 MB
% 3.73/1.30 % (702616)Instructions burned: 24 (million)
% 3.73/1.30 % (702613)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=2690612314:i=29:thsqd=64:nm=0:thsqc=8:rtra=on:thsq=on:ev=off_2998 on theBenchmark for (2998ds/29Mi)
% 3.73/1.30 % (702613)Instruction limit reached!
% 3.73/1.30 % (702613)------------------------------
% 3.73/1.30 % (702613)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.73/1.30 % (702613)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.73/1.30 % (702613)CaDiCaL version: 2.1.3
% 3.73/1.30 % (702613)Termination reason: Instruction limit
% 3.73/1.30 % (702613)Termination phase: Saturation
% 3.73/1.30 % (702613)Time elapsed: 0.020 s
% 3.73/1.30 % (702613)Peak memory usage: 88 MB
% 3.73/1.30 % (702613)Instructions burned: 29 (million)
% 3.73/1.30 % (702614)ott+21_1024_to=lakbo:sil=128000:bsd=on:si=on:alasca=on:uwa=alasca_main:nwc=0.5:random_seed=1516621368:cond=on:i=16:fgj=on:ep=RS:asg=force:nm=10:rtra=on:rawr=on_2998 on theBenchmark for (2998ds/16Mi)
% 3.73/1.30 % (702617)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=45769657:i=27:canc=cautious:fsr=off:rtra=on_2998 on theBenchmark for (2998ds/27Mi)
% 3.73/1.30 % (702617)Refutation not found, incomplete strategy
% 3.73/1.30 % (702617)------------------------------
% 3.73/1.30 % (702617)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.73/1.30 % (702617)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.73/1.30 % (702617)CaDiCaL version: 2.1.3
% 3.73/1.30 % (702617)Termination reason: Refutation not found, incomplete strategy
% 3.73/1.30 % (702617)Time elapsed: 0.002 s
% 3.73/1.30 % (702617)Peak memory usage: 89 MB
% 3.73/1.30 % (702617)Instructions burned: 1 (million)
% 3.73/1.30 % (702614)Also succeeded, but the first one will report.
% 3.73/1.30 % (702599)Instruction limit reached!
% 3.73/1.30 % (702599)------------------------------
% 3.73/1.30 % (702599)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.73/1.30 % (702599)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.73/1.30 % (702599)CaDiCaL version: 2.1.3
% 3.73/1.30 % (702599)Termination reason: Instruction limit
% 3.73/1.30 % (702599)Termination phase: Saturation
% 3.73/1.30 % (702599)Time elapsed: 0.208 s
% 3.73/1.30 % (702599)Peak memory usage: 116 MB
% 3.73/1.30 % (702599)Instructions burned: 309 (million)
% 3.73/1.30 % (702620)dis+1002_24_to=kbo:sil=128000:si=on:random_seed=469853406:i=85:gtgl=4:rtra=on:gtg=exists_sym_2997 on theBenchmark for (2997ds/85Mi)
% 3.73/1.30 % (702620)Also succeeded, but the first one will report.
% 3.73/1.30 % (702600)Refutation found. Thanks to Tanya!
% 3.73/1.30 % SZS status Theorem for theBenchmark
% 3.73/1.30 % SZS output start Proof for theBenchmark
% See solution above
% 3.73/1.30 % (702600)------------------------------
% 3.73/1.30 % (702600)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.73/1.30 % (702600)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.73/1.30 % (702600)CaDiCaL version: 2.1.3
% 3.73/1.30 % (702600)Termination reason: Refutation
% 3.73/1.30 % (702600)Time elapsed: 0.031 s
% 3.73/1.30 % (702600)Peak memory usage: 116 MB
% 3.73/1.30 % (702600)Instructions burned: 9 (million)
% 3.73/1.30 % (702600)------------------------------
% 3.73/1.30 % (702600)------------------------------
% 3.73/1.30 % (702535)Success in time 0.441 s
% 3.73/1.30 % Vampire exiting
%------------------------------------------------------------------------------