%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWV019-1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n009.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 01:07:55 PM UTC 2026
% Result : Unsatisfiable 3.48s 1.25s
% Output : Refutation 3.48s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 21
% Syntax : Number of formulae : 76 ( 22 unt; 11 def)
% Number of atoms : 159 ( 3 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 150 ( 67 ~; 72 |; 0 &)
% ( 11 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 15 ( 13 usr; 11 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 6 con; 0-2 aty)
% Number of variables : 12 ( 0 sgn 12 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] :
( in_array_bounds(array,X0)
| less_than(upper_bound,X0)
| less_than(X0,lower_bound) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',in_bounds) ).
fof(f2,axiom,
! [X0,X1] :
( ~ less_than(successor(X0),successor(X1))
| less_than(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',predecessor_less) ).
fof(f3,axiom,
! [X2,X0,X1] :
( less_than(X0,X2)
| ~ less_than(X1,X2)
| ~ less_than(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',transitivity_of_less) ).
fof(f4,axiom,
! [X0] : less_than(X0,successor(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',successor_greater) ).
fof(f5,axiom,
( ~ in_array_bounds(array,index_of_maximal)
| maximal_value = array_value_at(array,index_of_maximal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',this_is_maximal) ).
fof(f6,axiom,
less_than(index_of_maximal,an_index),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',maximal_before_somewhere) ).
fof(f7,axiom,
~ less_than(an_index,lower_bound),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',somewhere_above_lower_bound) ).
fof(f8,axiom,
~ less_than(upper_bound,an_index),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',somewhere_below_upper_bound) ).
fof(f9,axiom,
~ less_than(index_of_maximal,lower_bound),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',maximal_above_lower_bound) ).
fof(f10,negated_conjecture,
( ~ in_array_bounds(array,an_index)
| less_than(successor(an_index),lower_bound)
| less_than(successor(upper_bound),successor(an_index))
| less_than(index_of_maximal,lower_bound)
| ~ less_than(index_of_maximal,successor(an_index))
| ~ in_array_bounds(array,index_of_maximal)
| maximal_value != array_value_at(array,index_of_maximal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this) ).
fof(f11,definition,
! [X0,X1] :
( sQ0_eqProxy(X0,X1)
<=> X0 = X1 ),
introduced(definition,[new_symbols(definition,[sQ0_eqProxy])],[equality_proxy_definition]) ).
fof(f12,plain,
( ~ in_array_bounds(array,index_of_maximal)
| sQ0_eqProxy(maximal_value,array_value_at(array,index_of_maximal)) ),
inference(equality_proxy_replacement,[],[f5,f11]) ).
fof(f13,plain,
( ~ in_array_bounds(array,an_index)
| less_than(successor(an_index),lower_bound)
| less_than(successor(upper_bound),successor(an_index))
| less_than(index_of_maximal,lower_bound)
| ~ less_than(index_of_maximal,successor(an_index))
| ~ in_array_bounds(array,index_of_maximal)
| ~ sQ0_eqProxy(maximal_value,array_value_at(array,index_of_maximal)) ),
inference(equality_proxy_replacement,[],[f10,f11]) ).
fof(f17,definition,
( spl1_1
<=> sQ0_eqProxy(maximal_value,array_value_at(array,index_of_maximal)) ),
introduced(definition,[new_symbols(definition,[spl1_1])],[avatar_definition]) ).
fof(f20,definition,
( spl1_2
<=> in_array_bounds(array,index_of_maximal) ),
introduced(definition,[new_symbols(definition,[spl1_2])],[avatar_definition]) ).
fof(f21,plain,
( ~ in_array_bounds(array,index_of_maximal)
| spl1_2 ),
inference(avatar_component_clause,[],[f20]) ).
fof(f23,definition,
( spl1_3
<=> less_than(index_of_maximal,successor(an_index)) ),
introduced(definition,[new_symbols(definition,[spl1_3])],[avatar_definition]) ).
fof(f24,plain,
( ~ less_than(index_of_maximal,successor(an_index))
| spl1_3 ),
inference(avatar_component_clause,[],[f23]) ).
fof(f26,definition,
( spl1_4
<=> less_than(index_of_maximal,lower_bound) ),
introduced(definition,[new_symbols(definition,[spl1_4])],[avatar_definition]) ).
fof(f27,plain,
( less_than(index_of_maximal,lower_bound)
| ~ spl1_4 ),
inference(avatar_component_clause,[],[f26]) ).
fof(f29,definition,
( spl1_5
<=> less_than(successor(upper_bound),successor(an_index)) ),
introduced(definition,[new_symbols(definition,[spl1_5])],[avatar_definition]) ).
fof(f30,plain,
( less_than(successor(upper_bound),successor(an_index))
| ~ spl1_5 ),
inference(avatar_component_clause,[],[f29]) ).
fof(f32,definition,
( spl1_6
<=> less_than(successor(an_index),lower_bound) ),
introduced(definition,[new_symbols(definition,[spl1_6])],[avatar_definition]) ).
fof(f33,plain,
( less_than(successor(an_index),lower_bound)
| ~ spl1_6 ),
inference(avatar_component_clause,[],[f32]) ).
fof(f35,definition,
( spl1_7
<=> in_array_bounds(array,an_index) ),
introduced(definition,[new_symbols(definition,[spl1_7])],[avatar_definition]) ).
fof(f36,plain,
( ~ in_array_bounds(array,an_index)
| spl1_7 ),
inference(avatar_component_clause,[],[f35]) ).
fof(f37,plain,
( ~ spl1_1
| ~ spl1_2
| ~ spl1_3
| spl1_4
| spl1_5
| spl1_6
| ~ spl1_7 ),
inference(avatar_split_clause,[],[f13,f35,f32,f29,f26,f23,f20,f17]) ).
fof(f39,plain,
( spl1_1
| ~ spl1_2 ),
inference(avatar_split_clause,[],[f12,f20,f17]) ).
fof(f41,plain,
( less_than(upper_bound,index_of_maximal)
| less_than(index_of_maximal,lower_bound)
| spl1_2 ),
inference(resolution,[],[f1,f21]) ).
fof(f43,definition,
( spl1_8
<=> less_than(upper_bound,index_of_maximal) ),
introduced(definition,[new_symbols(definition,[spl1_8])],[avatar_definition]) ).
fof(f44,plain,
( less_than(upper_bound,index_of_maximal)
| ~ spl1_8 ),
inference(avatar_component_clause,[],[f43]) ).
fof(f45,plain,
( spl1_4
| spl1_8
| spl1_2 ),
inference(avatar_split_clause,[],[f41,f20,f43,f26]) ).
fof(f46,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f27,f9]) ).
fof(f47,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f46]) ).
fof(f48,plain,
! [X0] :
( ~ less_than(X0,an_index)
| ~ less_than(upper_bound,X0) ),
inference(resolution,[],[f3,f8]) ).
fof(f50,plain,
! [X0] :
( ~ less_than(X0,lower_bound)
| ~ less_than(index_of_maximal,X0) ),
inference(resolution,[],[f3,f9]) ).
fof(f53,plain,
( ~ less_than(index_of_maximal,an_index)
| ~ spl1_8 ),
inference(resolution,[],[f48,f44]) ).
fof(f55,plain,
( $false
| ~ spl1_8 ),
inference(resolution,[],[f53,f6]) ).
fof(f57,plain,
~ spl1_8,
inference(avatar_contradiction_clause,[],[f55]) ).
fof(f58,plain,
( ! [X0] :
( ~ less_than(X0,successor(an_index))
| ~ less_than(index_of_maximal,X0) )
| spl1_3 ),
inference(resolution,[],[f24,f3]) ).
fof(f61,plain,
( ~ less_than(index_of_maximal,an_index)
| spl1_3 ),
inference(resolution,[],[f58,f4]) ).
fof(f63,plain,
( $false
| spl1_3 ),
inference(resolution,[],[f61,f6]) ).
fof(f65,plain,
spl1_3,
inference(avatar_contradiction_clause,[],[f63]) ).
fof(f68,definition,
( spl1_9
<=> less_than(an_index,lower_bound) ),
introduced(definition,[new_symbols(definition,[spl1_9])],[avatar_definition]) ).
fof(f69,plain,
( less_than(an_index,lower_bound)
| ~ spl1_9 ),
inference(avatar_component_clause,[],[f68]) ).
fof(f71,definition,
( spl1_10
<=> less_than(upper_bound,an_index) ),
introduced(definition,[new_symbols(definition,[spl1_10])],[avatar_definition]) ).
fof(f72,plain,
( less_than(upper_bound,an_index)
| ~ spl1_10 ),
inference(avatar_component_clause,[],[f71]) ).
fof(f74,plain,
( less_than(upper_bound,an_index)
| ~ spl1_5 ),
inference(resolution,[],[f30,f2]) ).
fof(f75,plain,
( spl1_10
| ~ spl1_5 ),
inference(avatar_split_clause,[],[f74,f29,f71]) ).
fof(f76,plain,
( $false
| ~ spl1_10 ),
inference(resolution,[],[f72,f8]) ).
fof(f78,plain,
~ spl1_10,
inference(avatar_contradiction_clause,[],[f76]) ).
fof(f79,plain,
( less_than(upper_bound,an_index)
| less_than(an_index,lower_bound)
| spl1_7 ),
inference(resolution,[],[f36,f1]) ).
fof(f80,plain,
( spl1_9
| spl1_10
| spl1_7 ),
inference(avatar_split_clause,[],[f79,f35,f71,f68]) ).
fof(f81,plain,
( $false
| ~ spl1_9 ),
inference(resolution,[],[f69,f7]) ).
fof(f83,plain,
~ spl1_9,
inference(avatar_contradiction_clause,[],[f81]) ).
fof(f84,plain,
( ~ less_than(index_of_maximal,successor(an_index))
| ~ spl1_6 ),
inference(resolution,[],[f33,f50]) ).
fof(f85,plain,
( ~ spl1_3
| ~ spl1_6 ),
inference(avatar_split_clause,[],[f84,f32,f23]) ).
cnf(s1,plain,
( ~ spl1_1
| ~ spl1_2
| ~ spl1_3
| spl1_4
| spl1_5
| spl1_6
| ~ spl1_7 ),
inference(sat_conversion,[],[f37]) ).
cnf(s2,plain,
( spl1_1
| ~ spl1_2 ),
inference(sat_conversion,[],[f39]) ).
cnf(s3,plain,
( spl1_2
| spl1_4
| spl1_8 ),
inference(sat_conversion,[],[f45]) ).
cnf(s4,plain,
~ spl1_4,
inference(sat_conversion,[],[f47]) ).
cnf(s5,plain,
~ spl1_8,
inference(sat_conversion,[],[f57]) ).
cnf(s6,plain,
spl1_3,
inference(sat_conversion,[],[f65]) ).
cnf(s8,plain,
( ~ spl1_5
| spl1_10 ),
inference(sat_conversion,[],[f75]) ).
cnf(s9,plain,
~ spl1_10,
inference(sat_conversion,[],[f78]) ).
cnf(s10,plain,
( spl1_7
| spl1_9
| spl1_10 ),
inference(sat_conversion,[],[f80]) ).
cnf(s11,plain,
~ spl1_9,
inference(sat_conversion,[],[f83]) ).
cnf(s12,plain,
( ~ spl1_3
| ~ spl1_6 ),
inference(sat_conversion,[],[f85]) ).
cnf(s13,plain,
( spl1_7
| spl1_10 ),
inference(rat,[],[s10,s11]) ).
cnf(s14,plain,
spl1_7,
inference(rat,[],[s13,s9]) ).
cnf(s15,plain,
~ spl1_5,
inference(rat,[],[s8,s9]) ).
cnf(s16,plain,
~ spl1_6,
inference(rat,[],[s12,s6]) ).
cnf(s17,plain,
spl1_2,
inference(rat,[],[s3,s5,s4]) ).
cnf(s18,plain,
spl1_1,
inference(rat,[],[s2,s17]) ).
cnf(s19,plain,
$false,
inference(rat,[],[s1,s14,s16,s15,s4,s6,s17,s18]) ).
fof(f86,plain,
$false,
inference(avatar_sat_refutation,[],[s19]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWV019-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.17 % Computer : n009.cluster.edu
% 0.07/0.17 % Model : x86_64 x86_64
% 0.07/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.17 % Memory : 8046.5625MB
% 0.07/0.17 % OS : Linux 6.8.0-71-generic
% 0.07/0.17 % CPULimit : 300
% 0.07/0.17 % WCLimit : 300
% 0.07/0.17 % DateTime : Mon Sep 28 09:43:30 UTC 2026
% 0.07/0.17 % CPUTime :
% 0.07/0.17 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.21 Running first-order theorem proving
% 0.07/0.21 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
% 3.48/1.25 % (2923672)Input is clausal, will run a generic CNF schedule.
% 3.48/1.25 % (2923678)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=full:npcc=on:drc=off:sp=weighted_frequency:spb=goal:fd=preordered:foolp=on:random_seed=3312682742:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 3.48/1.25 % (2923684)dis-21_1_sil=8000:lcm=predicate:random_seed=2477105831:st=5:avsq=on:i=117:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/117Mi)
% 3.48/1.25 % (2923684)First to succeed.
% 3.48/1.25 % (2923684)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2923672"
% 3.48/1.25 % (2923681)lrs+10_1_sil=8000:sp=occurrence:random_seed=2407065245:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 3.48/1.25 % (2923679)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=3307031567:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 3.48/1.25 % (2923683)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3044388024:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 3.48/1.25 % (2923682)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=1353808357:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 3.48/1.25 % (2923680)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=1379631157:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 3.48/1.25 % (2923681)Also succeeded, but the first one will report.
% 3.48/1.25 % (2923682)Also succeeded, but the first one will report.
% 3.48/1.25 % (2923683)Also succeeded, but the first one will report.
% 3.48/1.25 % (2923684)Refutation found. Thanks to Tanya!
% 3.48/1.25 % SZS status Unsatisfiable for theBenchmark
% 3.48/1.25 % SZS output start Proof for theBenchmark
% See solution above
% 3.48/1.25 % (2923684)------------------------------
% 3.48/1.25 % (2923684)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.48/1.25 % (2923684)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.48/1.25 % (2923684)CaDiCaL version: 2.1.3
% 3.48/1.25 % (2923684)Termination reason: Refutation
% 3.48/1.25 % (2923684)Time elapsed: 0.003 s
% 3.48/1.25 % (2923684)Peak memory usage: 89 MB
% 3.48/1.25 % (2923684)Instructions burned: 2 (million)
% 3.48/1.25 % (2923684)------------------------------
% 3.48/1.25 % (2923684)------------------------------
% 3.48/1.25 % (2923672)Success in time 0.406 s
% 3.48/1.25 % Vampire exiting
%------------------------------------------------------------------------------