%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWX048+1 : TPTP v9.3.1. Released v9.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n010.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 01:45:45 PM UTC 2026
% Result : Theorem 3.74s 1.33s
% Output : Refutation 3.74s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 6
% Syntax : Number of formulae : 39 ( 8 unt; 2 def)
% Number of atoms : 152 ( 69 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 183 ( 70 ~; 57 |; 46 &)
% ( 6 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-3 aty)
% Number of functors : 10 ( 10 usr; 5 con; 0-3 aty)
% Number of variables : 107 ( 87 !; 20 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f49,axiom,
! [X0,X1,X2] :
( occ_succeeds(X0,X1,X2)
<=> ( ? [X3,X4] :
( X1 = cons(X3,X4)
& X0 != X3
& occ_succeeds(X0,X4,X2) )
| ? [X5,X6] :
( X1 = cons(X0,X5)
& X2 = s(X6)
& occ_succeeds(X0,X5,X6) )
| ( X1 = nil
& X2 = '0' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',id49) ).
fof(f273,axiom,
! [X0,X1,X2] :
( list_succeeds(X1)
=> ( occ(X0,X1) = X2
<=> occ_succeeds(X0,X1,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','occ/2') ).
fof(f283,axiom,
! [X0,X1,X2] :
( occ_succeeds(X0,X1,X2)
=> ( list_succeeds(X1)
& nat_succeeds(X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','lemma-(occ:types)') ).
fof(f288,conjecture,
! [X0,X1,X2] :
( ( list_succeeds(X2)
& X0 != X1 )
=> occ(X0,cons(X1,X2)) = occ(X0,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','lemma-(occ:cons:diff)') ).
fof(f289,negated_conjecture,
~ ! [X0,X1,X2] :
( ( list_succeeds(X2)
& X0 != X1 )
=> occ(X0,cons(X1,X2)) = occ(X0,X2) ),
inference(negated_conjecture,[status(cth)],[f288]) ).
fof(f291,plain,
? [X0,X1,X2] :
( occ(X0,cons(X1,X2)) != occ(X0,X2)
& list_succeeds(X2)
& X0 != X1 ),
inference(ennf_transformation,[],[f289]) ).
fof(f292,plain,
? [X0,X1,X2] :
( occ(X0,cons(X1,X2)) != occ(X0,X2)
& list_succeeds(X2)
& X0 != X1 ),
inference(flattening,[],[f291]) ).
fof(f297,plain,
! [X0,X1,X2] :
( ( occ(X0,X1) = X2
<=> occ_succeeds(X0,X1,X2) )
| ~ list_succeeds(X1) ),
inference(ennf_transformation,[],[f273]) ).
fof(f302,plain,
! [X0,X1,X2] :
( ( list_succeeds(X1)
& nat_succeeds(X2) )
| ~ occ_succeeds(X0,X1,X2) ),
inference(ennf_transformation,[],[f283]) ).
fof(f340,definition,
! [X1,X0,X2] :
( sP0(X1,X0,X2)
<=> ? [X5,X6] :
( X1 = cons(X0,X5)
& X2 = s(X6)
& occ_succeeds(X0,X5,X6) ) ),
introduced(definition,[new_symbols(definition,[sP0])],[predicate_definition_introduction]) ).
fof(f341,definition,
! [X1,X0,X2] :
( sP1(X1,X0,X2)
<=> ( ? [X3,X4] :
( X1 = cons(X3,X4)
& X0 != X3
& occ_succeeds(X0,X4,X2) )
| sP0(X1,X0,X2)
| ( X1 = nil
& X2 = '0' ) ) ),
introduced(definition,[new_symbols(definition,[sP1])],[predicate_definition_introduction]) ).
fof(f342,plain,
! [X0,X1,X2] :
( occ_succeeds(X0,X1,X2)
<=> sP1(X1,X0,X2) ),
inference(definition_folding,[],[f49,f341,f340]) ).
fof(f343,plain,
( occ(sK2,cons(sK3,sK4)) != occ(sK2,sK4)
& list_succeeds(sK4)
& sK2 != sK3 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3,sK4]),skolemize(X0,sK2),skolemize(X1,sK3),skolemize(X2,sK4)],[f292]) ).
fof(f346,plain,
! [X0,X1,X2] :
( ( ( occ(X0,X1) = X2
| ~ occ_succeeds(X0,X1,X2) )
& ( occ_succeeds(X0,X1,X2)
| occ(X0,X1) != X2 ) )
| ~ list_succeeds(X1) ),
inference(nnf_transformation,[],[f297]) ).
fof(f360,plain,
! [X1,X0,X2] :
( ( sP1(X1,X0,X2)
| ( ! [X3,X4] :
( cons(X3,X4) != X1
| X0 = X3
| ~ occ_succeeds(X0,X4,X2) )
& ~ sP0(X1,X0,X2)
& ( nil != X1
| '0' != X2 ) ) )
& ( ? [X3,X4] :
( X1 = cons(X3,X4)
& X0 != X3
& occ_succeeds(X0,X4,X2) )
| sP0(X1,X0,X2)
| ( X1 = nil
& X2 = '0' )
| ~ sP1(X1,X0,X2) ) ),
inference(nnf_transformation,[],[f341]) ).
fof(f361,plain,
! [X1,X0,X2] :
( ( sP1(X1,X0,X2)
| ( ! [X3,X4] :
( cons(X3,X4) != X1
| X0 = X3
| ~ occ_succeeds(X0,X4,X2) )
& ~ sP0(X1,X0,X2)
& ( nil != X1
| '0' != X2 ) ) )
& ( ? [X3,X4] :
( X1 = cons(X3,X4)
& X0 != X3
& occ_succeeds(X0,X4,X2) )
| sP0(X1,X0,X2)
| ( X1 = nil
& X2 = '0' )
| ~ sP1(X1,X0,X2) ) ),
inference(flattening,[],[f360]) ).
fof(f362,plain,
! [X0,X1,X2] :
( ( sP1(X0,X1,X2)
| ( ! [X3,X4] :
( cons(X3,X4) != X0
| X1 = X3
| ~ occ_succeeds(X1,X4,X2) )
& ~ sP0(X0,X1,X2)
& ( nil != X0
| '0' != X2 ) ) )
& ( ? [X5,X6] :
( cons(X5,X6) = X0
& X1 != X5
& occ_succeeds(X1,X6,X2) )
| sP0(X0,X1,X2)
| ( nil = X0
& X2 = '0' )
| ~ sP1(X0,X1,X2) ) ),
inference(rectify,[],[f361]) ).
fof(f363,plain,
! [X0,X1,X2] :
( ( sP1(X0,X1,X2)
| ( ! [X3,X4] :
( cons(X3,X4) != X0
| X1 = X3
| ~ occ_succeeds(X1,X4,X2) )
& ~ sP0(X0,X1,X2)
& ( nil != X0
| '0' != X2 ) ) )
& ( ( cons(sK16(X0,X1,X2),sK17(X0,X1,X2)) = X0
& sK16(X0,X1,X2) != X1
& occ_succeeds(X1,sK17(X0,X1,X2),X2) )
| sP0(X0,X1,X2)
| ( nil = X0
& X2 = '0' )
| ~ sP1(X0,X1,X2) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK16,sK17]),skolemize(X5,sK16(X0,X1,X2)),skolemize(X6,sK17(X0,X1,X2))],[f362]) ).
fof(f367,plain,
! [X0,X1,X2] :
( ( occ_succeeds(X0,X1,X2)
| ~ sP1(X1,X0,X2) )
& ( sP1(X1,X0,X2)
| ~ occ_succeeds(X0,X1,X2) ) ),
inference(nnf_transformation,[],[f342]) ).
fof(f372,plain,
sK2 != sK3,
inference(cnf_transformation,[],[f343]) ).
fof(f373,plain,
list_succeeds(sK4),
inference(cnf_transformation,[],[f343]) ).
fof(f374,plain,
occ(sK2,cons(sK3,sK4)) != occ(sK2,sK4),
inference(cnf_transformation,[],[f343]) ).
fof(f384,plain,
! [X2,X0,X1] :
( occ_succeeds(X0,X1,X2)
| occ(X0,X1) != X2
| ~ list_succeeds(X1) ),
inference(cnf_transformation,[],[f346]) ).
fof(f385,plain,
! [X2,X0,X1] :
( occ(X0,X1) = X2
| ~ occ_succeeds(X0,X1,X2)
| ~ list_succeeds(X1) ),
inference(cnf_transformation,[],[f346]) ).
fof(f412,plain,
! [X2,X0,X1] :
( ~ occ_succeeds(X0,X1,X2)
| list_succeeds(X1) ),
inference(cnf_transformation,[],[f302]) ).
fof(f422,plain,
! [X2,X3,X0,X1,X4] :
( sP1(X0,X1,X2)
| cons(X3,X4) != X0
| X1 = X3
| ~ occ_succeeds(X1,X4,X2) ),
inference(cnf_transformation,[],[f363]) ).
fof(f428,plain,
! [X2,X0,X1] :
( occ_succeeds(X0,X1,X2)
| ~ sP1(X1,X0,X2) ),
inference(cnf_transformation,[],[f367]) ).
fof(f459,plain,
! [X0,X1] :
( occ_succeeds(X0,X1,occ(X0,X1))
| ~ list_succeeds(X1) ),
inference(equality_resolution,[],[f384]) ).
fof(f467,plain,
! [X2,X3,X1,X4] :
( sP1(cons(X3,X4),X1,X2)
| X1 = X3
| ~ occ_succeeds(X1,X4,X2) ),
inference(equality_resolution,[],[f422]) ).
fof(f585,plain,
! [X2,X0,X1] :
( occ(X0,X1) = X2
| ~ occ_succeeds(X0,X1,X2) ),
inference(forward_subsumption_resolution,[],[f385,f412]) ).
fof(f588,plain,
! [X0] :
( occ(sK2,sK4) != X0
| ~ occ_succeeds(sK2,cons(sK3,sK4),X0) ),
inference(superposition,[],[f374,f585]) ).
fof(f594,plain,
~ occ_succeeds(sK2,cons(sK3,sK4),occ(sK2,sK4)),
inference(equality_resolution,[],[f588]) ).
fof(f601,plain,
~ sP1(cons(sK3,sK4),sK2,occ(sK2,sK4)),
inference(resolution,[],[f594,f428]) ).
fof(f605,plain,
! [X0] :
( ~ sP1(cons(sK3,sK4),sK2,X0)
| ~ occ_succeeds(sK2,sK4,X0) ),
inference(superposition,[],[f601,f585]) ).
fof(f915,plain,
! [X0] :
( sK2 = sK3
| ~ occ_succeeds(sK2,sK4,X0)
| ~ occ_succeeds(sK2,sK4,X0) ),
inference(resolution,[],[f467,f605]) ).
fof(f921,plain,
! [X0] :
( sK2 = sK3
| ~ occ_succeeds(sK2,sK4,X0) ),
inference(duplicate_literal_removal,[],[f915]) ).
fof(f922,plain,
! [X0] : ~ occ_succeeds(sK2,sK4,X0),
inference(forward_subsumption_resolution,[],[f921,f372]) ).
fof(f929,plain,
~ list_succeeds(sK4),
inference(resolution,[],[f922,f459]) ).
fof(f930,plain,
$false,
inference(forward_subsumption_resolution,[],[f929,f373]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWX048+1 : TPTP v9.3.1. Released v9.1.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.20 % Computer : n010.cluster.edu
% 0.09/0.20 % Model : x86_64 x86_64
% 0.09/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.20 % Memory : 8046.5625MB
% 0.09/0.20 % OS : Linux 6.8.0-71-generic
% 0.09/0.20 % CPULimit : 300
% 0.09/0.20 % WCLimit : 300
% 0.09/0.20 % DateTime : Mon Sep 28 14:55:17 UTC 2026
% 0.09/0.20 % CPUTime :
% 0.09/0.20 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.23 Running first-order theorem proving
% 0.09/0.23 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
% 3.74/1.33 % (1982663)Detected formulas, will run a generic FOF schedule.
% 3.74/1.33 % (1982740)lrs+11_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:lma=off:spb=units:urr=ec_only:bce=on:s2agt=64:updr=off:random_seed=2774654179:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.74/1.33 % (1982738)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=285712922:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.74/1.33 % (1982746)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1708235488:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.74/1.33 % (1982744)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=207027170:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.74/1.33 % (1982741)lrs+1010_1_anc=all:sfv=off:to=kbo:ncem=casc2026/models/loop7.pt:sil=128000:npcc=on:prc=on:sos=all:bsr=unit_only:sac=on:random_seed=3278028860:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.74/1.33 % (1982747)dis-21_1_sil=8000:lcm=predicate:random_seed=2195563869:st=5:avsq=on:i=129:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/129Mi)
% 3.74/1.33 % (1982743)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=98985861:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.74/1.33 % (1982743)Refutation not found, incomplete strategy
% 3.74/1.33 % (1982743)------------------------------
% 3.74/1.33 % (1982743)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.74/1.33 % (1982743)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.74/1.33 % (1982743)CaDiCaL version: 2.1.3
% 3.74/1.33 % (1982743)Termination reason: Refutation not found, incomplete strategy
% 3.74/1.33 % (1982743)Time elapsed: 0.004 s
% 3.74/1.33 % (1982743)Peak memory usage: 89 MB
% 3.74/1.33 % (1982743)Instructions burned: 3 (million)
% 3.74/1.33 % (1982744)First to succeed.
% 3.74/1.33 % (1982744)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-1982663"
% 3.74/1.33 % (1982747)Instruction limit reached!
% 3.74/1.33 % (1982747)------------------------------
% 3.74/1.33 % (1982747)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.74/1.33 % (1982747)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.74/1.33 % (1982747)CaDiCaL version: 2.1.3
% 3.74/1.33 % (1982747)Termination reason: Instruction limit
% 3.74/1.33 % (1982747)Termination phase: Saturation
% 3.74/1.33 % (1982747)Time elapsed: 0.079 s
% 3.74/1.33 % (1982747)Peak memory usage: 90 MB
% 3.74/1.33 % (1982747)Instructions burned: 130 (million)
% 3.74/1.33 % (1982746)Instruction limit reached!
% 3.74/1.33 % (1982746)------------------------------
% 3.74/1.33 % (1982746)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.74/1.33 % (1982746)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.74/1.33 % (1982746)CaDiCaL version: 2.1.3
% 3.74/1.33 % (1982746)Termination reason: Instruction limit
% 3.74/1.33 % (1982746)Termination phase: Saturation
% 3.74/1.33 % (1982746)Time elapsed: 0.124 s
% 3.74/1.33 % (1982746)Peak memory usage: 90 MB
% 3.74/1.33 % (1982746)Instructions burned: 139 (million)
% 3.74/1.33 % (1982807)lrs+10_1_sil=8000:sp=occurrence:random_seed=804684455:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 3.74/1.33 % (1982744)Refutation found. Thanks to Tanya!
% 3.74/1.33 % SZS status Theorem for theBenchmark
% 3.74/1.33 % SZS output start Proof for theBenchmark
% See solution above
% 3.74/1.33 % (1982744)------------------------------
% 3.74/1.33 % (1982744)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.74/1.33 % (1982744)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.74/1.33 % (1982744)CaDiCaL version: 2.1.3
% 3.74/1.33 % (1982744)Termination reason: Refutation
% 3.74/1.33 % (1982744)Time elapsed: 0.015 s
% 3.74/1.33 % (1982744)Peak memory usage: 88 MB
% 3.74/1.33 % (1982744)Instructions burned: 20 (million)
% 3.74/1.33 % (1982744)------------------------------
% 3.74/1.33 % (1982744)------------------------------
% 3.74/1.33 % (1982663)Success in time 0.454 s
% 3.74/1.33 % Vampire exiting
%------------------------------------------------------------------------------