%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : DAT001_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 : n015.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 09:47:04 AM UTC 2026
% Result : Theorem 2.06s 1.42s
% Output : Refutation 4.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 21
% Syntax : Number of formulae : 75 ( 21 unt; 0 typ; 18 def)
% Number of atoms : 177 ( 17 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 190 ( 88 ~; 85 |; 2 &)
% ( 13 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 6 ( 1 avg)
% Number arithmetic : 102 ( 21 atm; 0 fun; 56 num; 25 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 : 17 ( 14 usr; 14 prp; 0-2 aty)
% Number of functors : 12 ( 7 usr; 11 con; 0-2 aty)
% Number of variables : 31 ( 31 !; 0 ?; 31 :)
% Comments :
%------------------------------------------------------------------------------
tff(type_def_5,type,
list: $tType ).
tff(func_def_0,type,
nil: list ).
tff(func_def_1,type,
mycons: ( $int * list ) > list ).
tff(func_def_10,type,
sF0: list ).
tff(func_def_11,type,
sF1: list ).
tff(func_def_12,type,
sF2: list ).
tff(func_def_13,type,
sF3: list ).
tff(func_def_14,type,
sF4: list ).
tff(pred_def_1,type,
sorted: list > $o ).
tff(f2,axiom,
! [X0: $int] : sorted(mycons(X0,nil)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',single_is_sorted) ).
tff(f3,axiom,
! [X2: list,X0: $int,X1: $int] :
( ( sorted(mycons(X1,X2))
& $less(X0,X1) )
=> sorted(mycons(X0,mycons(X1,X2))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',recursive_sort) ).
tff(f4,conjecture,
sorted(mycons(1,mycons(2,mycons(4,mycons(7,mycons(100,nil)))))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',check_list) ).
tff(f5,negated_conjecture,
~ sorted(mycons(1,mycons(2,mycons(4,mycons(7,mycons(100,nil)))))),
inference(negated_conjecture,[status(cth)],[f4]) ).
tff(f18,plain,
~ sorted(mycons(1,mycons(2,mycons(4,mycons(7,mycons(100,nil)))))),
inference(flattening,[],[f5]) ).
tff(f19,plain,
! [X2: $int,X1: $int,X0: list] :
( ( sorted(mycons(X2,X0))
& $less(X1,X2) )
=> sorted(mycons(X1,mycons(X2,X0))) ),
inference(rectify,[],[f3]) ).
tff(f20,plain,
! [X2: $int,X1: $int,X0: list] :
( sorted(mycons(X1,mycons(X2,X0)))
| ~ sorted(mycons(X2,X0))
| ~ $less(X1,X2) ),
inference(ennf_transformation,[],[f19]) ).
tff(f21,plain,
! [X1: $int,X0: list,X2: $int] :
( ~ sorted(mycons(X2,X0))
| ~ $less(X1,X2)
| sorted(mycons(X1,mycons(X2,X0))) ),
inference(flattening,[],[f20]) ).
tff(f22,plain,
! [X0: $int,X1: list,X2: $int] :
( ~ sorted(mycons(X2,X1))
| ~ $less(X0,X2)
| sorted(mycons(X0,mycons(X2,X1))) ),
inference(rectify,[],[f21]) ).
tff(f23,plain,
! [X2: $int,X0: $int,X1: list] :
( sorted(mycons(X0,mycons(X2,X1)))
| ~ sorted(mycons(X2,X1))
| ~ $less(X0,X2) ),
inference(cnf_transformation,[],[f22]) ).
tff(f25,plain,
! [X0: $int] : sorted(mycons(X0,nil)),
inference(cnf_transformation,[],[f2]) ).
tff(f26,plain,
~ sorted(mycons(1,mycons(2,mycons(4,mycons(7,mycons(100,nil)))))),
inference(cnf_transformation,[],[f18]) ).
tff(f27,definition,
sF0 = mycons(100,nil),
introduced(definition,[new_symbols(definition,[sF0])],[function_definition]) ).
tff(f28,plain,
mycons(100,nil) = sF0,
inference(reorient_equations,[],[f27]) ).
tff(f29,definition,
sF1 = mycons(7,sF0),
introduced(definition,[new_symbols(definition,[sF1])],[function_definition]) ).
tff(f30,definition,
sF2 = mycons(4,sF1),
introduced(definition,[new_symbols(definition,[sF2])],[function_definition]) ).
tff(f31,definition,
sF3 = mycons(2,sF2),
introduced(definition,[new_symbols(definition,[sF3])],[function_definition]) ).
tff(f32,definition,
sF4 = mycons(1,sF3),
introduced(definition,[new_symbols(definition,[sF4])],[function_definition]) ).
tff(f33,plain,
mycons(1,sF3) = sF4,
inference(reorient_equations,[],[f32]) ).
tff(f34,plain,
~ sorted(sF4),
inference(definition_folding,[],[f26,f33,f31,f30,f29,f28]) ).
tff(f36,definition,
( spl5_1
<=> ( sF1 = mycons(7,sF0) ) ),
introduced(definition,[new_symbols(definition,[spl5_1])],[avatar_definition]) ).
tff(f38,plain,
( ( sF1 = mycons(7,sF0) )
| ~ spl5_1 ),
inference(avatar_component_clause,[],[f36]) ).
tff(f39,plain,
spl5_1,
inference(avatar_split_clause,[],[f29,f36]) ).
tff(f41,definition,
( spl5_2
<=> ( sF3 = mycons(2,sF2) ) ),
introduced(definition,[new_symbols(definition,[spl5_2])],[avatar_definition]) ).
tff(f43,plain,
( ( sF3 = mycons(2,sF2) )
| ~ spl5_2 ),
inference(avatar_component_clause,[],[f41]) ).
tff(f44,plain,
spl5_2,
inference(avatar_split_clause,[],[f31,f41]) ).
tff(f46,definition,
( spl5_3
<=> ( sF2 = mycons(4,sF1) ) ),
introduced(definition,[new_symbols(definition,[spl5_3])],[avatar_definition]) ).
tff(f48,plain,
( ( sF2 = mycons(4,sF1) )
| ~ spl5_3 ),
inference(avatar_component_clause,[],[f46]) ).
tff(f49,plain,
spl5_3,
inference(avatar_split_clause,[],[f30,f46]) ).
tff(f51,definition,
( spl5_4
<=> ( mycons(100,nil) = sF0 ) ),
introduced(definition,[new_symbols(definition,[spl5_4])],[avatar_definition]) ).
tff(f53,plain,
( ( mycons(100,nil) = sF0 )
| ~ spl5_4 ),
inference(avatar_component_clause,[],[f51]) ).
tff(f54,plain,
spl5_4,
inference(avatar_split_clause,[],[f28,f51]) ).
tff(f56,definition,
( spl5_5
<=> sorted(sF4) ),
introduced(definition,[new_symbols(definition,[spl5_5])],[avatar_definition]) ).
tff(f58,plain,
( ~ sorted(sF4)
| spl5_5 ),
inference(avatar_component_clause,[],[f56]) ).
tff(f59,plain,
~ spl5_5,
inference(avatar_split_clause,[],[f34,f56]) ).
tff(f61,definition,
( spl5_6
<=> ( mycons(1,sF3) = sF4 ) ),
introduced(definition,[new_symbols(definition,[spl5_6])],[avatar_definition]) ).
tff(f63,plain,
( ( mycons(1,sF3) = sF4 )
| ~ spl5_6 ),
inference(avatar_component_clause,[],[f61]) ).
tff(f64,plain,
spl5_6,
inference(avatar_split_clause,[],[f33,f61]) ).
tff(f70,plain,
( sorted(sF0)
| ~ spl5_4 ),
inference(superposition,[],[f25,f53]) ).
tff(f72,definition,
( spl5_8
<=> sorted(sF0) ),
introduced(definition,[new_symbols(definition,[spl5_8])],[avatar_definition]) ).
tff(f74,plain,
( sorted(sF0)
| ~ spl5_8 ),
inference(avatar_component_clause,[],[f72]) ).
tff(f75,plain,
( spl5_8
| ~ spl5_4 ),
inference(avatar_split_clause,[],[f70,f51,f72]) ).
tff(f180,plain,
( ! [X0: $int] :
( sorted(mycons(X0,sF3))
| ~ $less(X0,2)
| ~ sorted(sF3) )
| ~ spl5_2 ),
inference(superposition,[],[f23,f43]) ).
tff(f181,plain,
( ! [X0: $int] :
( sorted(mycons(X0,sF2))
| ~ $less(X0,4)
| ~ sorted(sF2) )
| ~ spl5_3 ),
inference(superposition,[],[f23,f48]) ).
tff(f182,plain,
( ! [X0: $int] :
( sorted(mycons(X0,sF1))
| ~ sorted(sF1)
| ~ $less(X0,7) )
| ~ spl5_1 ),
inference(superposition,[],[f23,f38]) ).
tff(f183,plain,
( ! [X0: $int] :
( ~ $less(X0,100)
| ~ sorted(sF0)
| sorted(mycons(X0,sF0)) )
| ~ spl5_4 ),
inference(superposition,[],[f23,f53]) ).
tff(f184,plain,
( ! [X0: $int] :
( sorted(mycons(X0,sF0))
| ~ $less(X0,100) )
| ~ spl5_4
| ~ spl5_8 ),
inference(forward_subsumption_resolution,[],[f183,f74]) ).
tff(f186,definition,
( spl5_9
<=> sorted(sF1) ),
introduced(definition,[new_symbols(definition,[spl5_9])],[avatar_definition]) ).
tff(f190,definition,
( spl5_10
<=> ! [X0: $int] :
( sorted(mycons(X0,sF1))
| ~ $less(X0,7) ) ),
introduced(definition,[new_symbols(definition,[spl5_10])],[avatar_definition]) ).
tff(f191,plain,
( ! [X0: $int] :
( sorted(mycons(X0,sF1))
| ~ $less(X0,7) )
| ~ spl5_10 ),
inference(avatar_component_clause,[],[f190]) ).
tff(f192,plain,
( ~ spl5_9
| spl5_10
| ~ spl5_1 ),
inference(avatar_split_clause,[],[f182,f36,f190,f186]) ).
tff(f194,definition,
( spl5_11
<=> ! [X0: $int] :
( sorted(mycons(X0,sF2))
| ~ $less(X0,4) ) ),
introduced(definition,[new_symbols(definition,[spl5_11])],[avatar_definition]) ).
tff(f195,plain,
( ! [X0: $int] :
( sorted(mycons(X0,sF2))
| ~ $less(X0,4) )
| ~ spl5_11 ),
inference(avatar_component_clause,[],[f194]) ).
tff(f197,definition,
( spl5_12
<=> sorted(sF2) ),
introduced(definition,[new_symbols(definition,[spl5_12])],[avatar_definition]) ).
tff(f200,plain,
( spl5_11
| ~ spl5_12
| ~ spl5_3 ),
inference(avatar_split_clause,[],[f181,f46,f197,f194]) ).
tff(f202,definition,
( spl5_13
<=> sorted(sF3) ),
introduced(definition,[new_symbols(definition,[spl5_13])],[avatar_definition]) ).
tff(f204,plain,
( ~ sorted(sF3)
| spl5_13 ),
inference(avatar_component_clause,[],[f202]) ).
tff(f206,definition,
( spl5_14
<=> ! [X0: $int] :
( sorted(mycons(X0,sF3))
| ~ $less(X0,2) ) ),
introduced(definition,[new_symbols(definition,[spl5_14])],[avatar_definition]) ).
tff(f207,plain,
( ! [X0: $int] :
( sorted(mycons(X0,sF3))
| ~ $less(X0,2) )
| ~ spl5_14 ),
inference(avatar_component_clause,[],[f206]) ).
tff(f208,plain,
( ~ spl5_13
| spl5_14
| ~ spl5_2 ),
inference(avatar_split_clause,[],[f180,f41,f206,f202]) ).
tff(f209,plain,
( sorted(sF1)
| ~ $less(7,100)
| ~ spl5_1
| ~ spl5_4
| ~ spl5_8 ),
inference(superposition,[],[f184,f38]) ).
tff(f210,plain,
( sorted(sF1)
| ~ spl5_1
| ~ spl5_4
| ~ spl5_8 ),
inference(evaluation,[],[f209]) ).
tff(f213,plain,
( spl5_9
| ~ spl5_1
| ~ spl5_4
| ~ spl5_8 ),
inference(avatar_split_clause,[],[f210,f72,f51,f36,f186]) ).
tff(f214,plain,
( ~ $less(4,7)
| sorted(sF2)
| ~ spl5_3
| ~ spl5_10 ),
inference(superposition,[],[f191,f48]) ).
tff(f215,plain,
( sorted(sF2)
| ~ spl5_3
| ~ spl5_10 ),
inference(evaluation,[],[f214]) ).
tff(f218,plain,
( spl5_12
| ~ spl5_3
| ~ spl5_10 ),
inference(avatar_split_clause,[],[f215,f190,f46,f197]) ).
tff(f219,plain,
( sorted(sF3)
| ~ $less(2,4)
| ~ spl5_2
| ~ spl5_11 ),
inference(superposition,[],[f195,f43]) ).
tff(f220,plain,
( sorted(sF3)
| ~ spl5_2
| ~ spl5_11 ),
inference(evaluation,[],[f219]) ).
tff(f221,plain,
( $false
| ~ spl5_2
| ~ spl5_11
| spl5_13 ),
inference(forward_subsumption_resolution,[],[f220,f204]) ).
tff(f222,plain,
( ~ spl5_2
| ~ spl5_11
| spl5_13 ),
inference(avatar_contradiction_clause,[],[f221]) ).
tff(f223,plain,
( sorted(sF4)
| ~ $less(1,2)
| ~ spl5_6
| ~ spl5_14 ),
inference(superposition,[],[f207,f63]) ).
tff(f224,plain,
( sorted(sF4)
| ~ spl5_6
| ~ spl5_14 ),
inference(evaluation,[],[f223]) ).
tff(f225,plain,
( $false
| spl5_5
| ~ spl5_6
| ~ spl5_14 ),
inference(forward_subsumption_resolution,[],[f224,f58]) ).
tff(f226,plain,
( spl5_5
| ~ spl5_6
| ~ spl5_14 ),
inference(avatar_contradiction_clause,[],[f225]) ).
tff(f227,plain,
$false,
inference(avatar_smt_refutation,[],[f226,f222,f218,f213,f208,f200,f192,f75,f64,f59,f54,f49,f44,f39]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : DAT001_1 : TPTP v9.3.1. Released v5.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.19 % Computer : n015.cluster.edu
% 0.10/0.19 % Model : x86_64 x86_64
% 0.10/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.19 % Memory : 8046.5625MB
% 0.10/0.19 % OS : Linux 6.8.0-71-generic
% 0.10/0.19 % CPULimit : 300
% 0.10/0.19 % WCLimit : 300
% 0.10/0.19 % DateTime : Tue Sep 29 00:08:17 UTC 2026
% 0.10/0.19 % CPUTime :
% 0.10/0.20 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.25 Running first-order theorem proving
% 0.10/0.25 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
% 2.06/1.42 % (3162578)Detected arithmetic, will pick strategies from an ALASCA-aware ARI schedule.
% 2.06/1.42 % (3162623)lrs+10_1_tgt=ground:sas=z3:si=on:random_seed=1389448868:i=33:rtra=on_2999 on theBenchmark for (2999ds/33Mi)
% 2.06/1.42 % (3162623)First to succeed.
% 2.06/1.42 % (3162623)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3162578"
% 2.06/1.42 % (3162621)dis+21_64_to=kbo:sil=128000:si=on:sp=weighted_frequency:uwa=alasca_can_abstract:random_seed=4106274011:i=4:rtra=on_2999 on theBenchmark for (2999ds/4Mi)
% 2.06/1.42 % (3162620)lrs+1002_4:1_to=lpo:sil=64000:si=on:br=off:random_seed=2543120026:s2a=on:i=7:rtra=on:inst=on_2999 on theBenchmark for (2999ds/7Mi)
% 2.06/1.42 % (3162622)lrs+10_1_to=lpo:sas=z3:si=on:tha=off:random_seed=2731824668:i=46:rtra=on_2999 on theBenchmark for (2999ds/46Mi)
% 2.06/1.42 % (3162618)dis+1002_1_to=kbo:sil=128000:tgt=ground:sas=z3:si=on:spb=units:tha=off:random_seed=1792699010:i=307:kws=precedence:nm=0:rtra=on_2999 on theBenchmark for (2999ds/307Mi)
% 2.06/1.42 % (3162617)dis+1002_16:1_to=lpo:sil=64000:sas=z3:si=on:norm_ineq=on:gve=force:uwa=one_side_constant:random_seed=2908305716:i=12:doe=on:rtra=on:gtg=exists_top:ss=axioms_2999 on theBenchmark for (2999ds/12Mi)
% 2.06/1.42 % (3162619)dis+10_3_slsqr=1,4:to=lpo:sil=128000:thi=strong:si=on:uwa=off:s2agt=20:slsqc=1:slsq=on:random_seed=3884114454:i=201:slsql=off:asg=cautious:rtra=on:gtg=all:ss=axioms:sgt=16_2999 on theBenchmark for (2999ds/201Mi)
% 2.06/1.42 % (3162621)Instruction limit reached!
% 2.06/1.42 % (3162621)------------------------------
% 2.06/1.42 % (3162621)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.06/1.42 % (3162621)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.06/1.42 % (3162621)CaDiCaL version: 2.1.3
% 2.06/1.42 % (3162621)Termination reason: Instruction limit
% 2.06/1.42 % (3162621)Termination phase: Saturation
% 2.06/1.42 % (3162621)Time elapsed: 0.006 s
% 2.06/1.42 % (3162621)Peak memory usage: 88 MB
% 2.06/1.42 % (3162621)Instructions burned: 4 (million)
% 2.06/1.42 % (3162620)Instruction limit reached!
% 2.06/1.42 % (3162620)------------------------------
% 2.06/1.42 % (3162620)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.06/1.42 % (3162620)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.06/1.42 % (3162620)CaDiCaL version: 2.1.3
% 2.06/1.42 % (3162620)Termination reason: Instruction limit
% 2.06/1.42 % (3162620)Termination phase: Saturation
% 2.06/1.42 % (3162620)Time elapsed: 0.009 s
% 2.06/1.42 % (3162620)Peak memory usage: 88 MB
% 2.06/1.42 % (3162620)Instructions burned: 7 (million)
% 2.06/1.42 % (3162617)Refutation not found, incomplete strategy
% 2.06/1.42 % (3162617)------------------------------
% 2.06/1.42 % (3162617)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.06/1.42 % (3162617)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.06/1.42 % (3162617)CaDiCaL version: 2.1.3
% 2.06/1.42 % (3162617)Termination reason: Refutation not found, incomplete strategy
% 2.06/1.42 % (3162617)Time elapsed: 0.046 s
% 2.06/1.42 % (3162617)Peak memory usage: 115 MB
% 2.06/1.42 % (3162617)Instructions burned: 11 (million)
% 2.06/1.42 % (3162622)Also succeeded, but the first one will report.
% 2.06/1.42 % (3162618)Also succeeded, but the first one will report.
% 2.06/1.42 % (3162619)Also succeeded, but the first one will report.
% 2.06/1.42 % (3162623)Refutation found. Thanks to Tanya!
% 2.06/1.42 % SZS status Theorem for theBenchmark
% 2.06/1.42 % SZS output start Proof for theBenchmark
% See solution above
% 4.26/1.59 % (3162623)------------------------------
% 4.26/1.59 % (3162623)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.26/1.59 % (3162623)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.26/1.59 % (3162623)CaDiCaL version: 2.1.3
% 4.26/1.59 % (3162623)Termination reason: Refutation
% 4.26/1.59 % (3162623)Time elapsed: 0.036 s
% 4.26/1.59 % (3162623)Peak memory usage: 116 MB
% 4.26/1.59 % (3162623)Instructions burned: 23 (million)
% 4.26/1.59 % (3162623)------------------------------
% 4.26/1.59 % (3162623)------------------------------
% 4.26/1.59 % (3162578)Success in time 0.494 s
% 4.26/1.59 % Vampire exiting
%------------------------------------------------------------------------------