%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SWX048+1 : TPTP v9.3.1. Released v9.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 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 01:46:24 PM UTC 2026
% Result : Theorem 3.22s 0.74s
% Output : Refutation 3.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 5
% Syntax : Number of formulae : 38 ( 10 unt; 1 def)
% Number of atoms : 96 ( 39 equ)
% Maximal formula atoms : 9 ( 2 avg)
% Number of connectives : 91 ( 33 ~; 37 |; 13 &)
% ( 4 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 2 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 81 ( 0 sgn 71 !; 10 ?)
% 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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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(f616,plain,
! [X0,X1,X2] :
( ( occ(X0,X1) = X2
<=> occ_succeeds(X0,X1,X2) )
| ~ list_succeeds(X1) ),
inference(ennf_transformation,[],[f273]) ).
fof(f632,plain,
! [X0,X1,X2] :
( ( list_succeeds(X1)
& nat_succeeds(X2) )
| ~ occ_succeeds(X0,X1,X2) ),
inference(ennf_transformation,[],[f283]) ).
fof(f637,plain,
? [X0,X1,X2] :
( occ(X0,cons(X1,X2)) != occ(X0,X2)
& list_succeeds(X2)
& X0 != X1 ),
inference(ennf_transformation,[],[f289]) ).
fof(f638,plain,
? [X0,X1,X2] :
( occ(X0,cons(X1,X2)) != occ(X0,X2)
& list_succeeds(X2)
& X0 != X1 ),
inference(flattening,[],[f637]) ).
fof(f696,plain,
! [X2,X3,X0,X1,X4] :
( ~ occ_succeeds(X0,X4,X2)
| X0 = X3
| cons(X3,X4) != X1
| occ_succeeds(X0,X1,X2) ),
inference(cnf_transformation,[],[f49]) ).
fof(f1202,plain,
! [X2,X0,X1] :
( ~ list_succeeds(X1)
| ~ occ_succeeds(X0,X1,X2)
| occ(X0,X1) = X2 ),
inference(cnf_transformation,[],[f616]) ).
fof(f1203,plain,
! [X2,X0,X1] :
( ~ list_succeeds(X1)
| occ_succeeds(X0,X1,X2)
| occ(X0,X1) != X2 ),
inference(cnf_transformation,[],[f616]) ).
fof(f1215,plain,
! [X2,X0,X1] :
( ~ occ_succeeds(X0,X1,X2)
| list_succeeds(X1) ),
inference(cnf_transformation,[],[f632]) ).
fof(f1224,plain,
sK132 != sK133,
inference(cnf_transformation,[],[f638]) ).
fof(f1225,plain,
list_succeeds(sK134),
inference(cnf_transformation,[],[f638]) ).
fof(f1226,plain,
occ(sK132,cons(sK133,sK134)) != occ(sK132,sK134),
inference(cnf_transformation,[],[f638]) ).
fof(f1231,plain,
! [X2,X3,X0,X4] :
( ~ occ_succeeds(X0,X4,X2)
| X0 = X3
| occ_succeeds(X0,cons(X3,X4),X2) ),
inference(equality_resolution,[],[f696]) ).
fof(f1342,plain,
! [X0,X1] :
( ~ list_succeeds(X1)
| occ_succeeds(X0,X1,occ(X0,X1)) ),
inference(equality_resolution,[],[f1203]) ).
fof(f1404,plain,
! [X2,X3,X0,X4] :
( ~ occ_succeeds(X0,cons(X3,X4),X2)
| X0 = X3
| occ_succeeds(X0,X4,X2) ),
inference(consistent_polarity_flipping,[],[f1231]) ).
fof(f1770,plain,
! [X0,X1] :
( ~ occ_succeeds(X0,X1,occ(X0,X1))
| list_succeeds(X1) ),
inference(consistent_polarity_flipping,[],[f1342]) ).
fof(f1771,plain,
! [X2,X0,X1] :
( list_succeeds(X1)
| occ_succeeds(X0,X1,X2)
| occ(X0,X1) = X2 ),
inference(consistent_polarity_flipping,[],[f1202]) ).
fof(f1781,plain,
! [X2,X0,X1] :
( ~ list_succeeds(X1)
| occ_succeeds(X0,X1,X2) ),
inference(consistent_polarity_flipping,[],[f1215]) ).
fof(f1790,plain,
~ list_succeeds(sK134),
inference(consistent_polarity_flipping,[],[f1225]) ).
fof(f1792,definition,
( spl135_1
<=> ! [X9,X7,X8] :
( list_succeeds(X7)
| occ(X8,cons(X9,X7)) = occ(X8,X7)
| X8 = X9 ) ),
introduced(definition,[new_symbols(definition,[spl135_1])],[avatar_definition]) ).
fof(f1793,plain,
( ! [X8,X9,X7] :
( list_succeeds(X7)
| occ(X8,cons(X9,X7)) = occ(X8,X7)
| X8 = X9 )
| ~ spl135_1 ),
inference(avatar_component_clause,[],[f1792]) ).
fof(f3096,plain,
! [X2,X0,X1] :
( occ_succeeds(X0,X1,X2)
| occ(X0,X1) = X2 ),
inference(forward_subsumption_resolution,[],[f1771,f1781]) ).
fof(f3651,plain,
! [X2,X3,X0,X1] :
( occ_succeeds(X0,X2,X3)
| X0 = X1
| occ(X0,cons(X1,X2)) = X3 ),
inference(resolution,[],[f1404,f3096]) ).
fof(f15824,plain,
! [X2,X0,X1] :
( X0 = X1
| occ(X0,cons(X1,X2)) = occ(X0,X2)
| list_succeeds(X2) ),
inference(resolution,[],[f3651,f1770]) ).
fof(f15837,plain,
spl135_1,
inference(avatar_split_clause,[],[f15824,f1792]) ).
fof(f15860,plain,
( ! [X0,X1] :
( occ(X0,sK134) = occ(X0,cons(X1,sK134))
| X0 = X1 )
| ~ spl135_1 ),
inference(resolution,[],[f1793,f1790]) ).
fof(f16188,plain,
( occ(sK132,sK134) != occ(sK132,sK134)
| sK132 = sK133
| ~ spl135_1 ),
inference(superposition,[],[f1226,f15860]) ).
fof(f16192,plain,
( sK132 = sK133
| ~ spl135_1 ),
inference(trivial_inequality_removal,[],[f16188]) ).
fof(f16193,plain,
( $false
| ~ spl135_1 ),
inference(forward_subsumption_resolution,[],[f16192,f1224]) ).
fof(f16194,plain,
~ spl135_1,
inference(avatar_contradiction_clause,[],[f16193]) ).
cnf(s622,plain,
spl135_1,
inference(sat_conversion,[],[f15837]) ).
cnf(s705,plain,
~ spl135_1,
inference(sat_conversion,[],[f16194]) ).
cnf(s706,plain,
$false,
inference(rat,[],[s622,s705]) ).
fof(f16195,plain,
$false,
inference(avatar_sat_refutation,[],[s706]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWX048+1 : TPTP v9.3.1. Released v9.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.19 % Computer : n020.cluster.edu
% 0.09/0.19 % Model : x86_64 x86_64
% 0.09/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.19 % Memory : 8046.5625MB
% 0.09/0.19 % OS : Linux 6.8.0-71-generic
% 0.09/0.19 % CPULimit : 300
% 0.09/0.19 % WCLimit : 300
% 0.09/0.19 % DateTime : Mon Sep 28 14:55:49 UTC 2026
% 0.09/0.19 % CPUTime :
% 0.09/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.22 Running first-order model finding
% 0.09/0.22 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.22/0.74 % (221417)Will run a generic schedule for satisfiability detection.
% 3.22/0.74 % (221422)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1029633174_2999 on theBenchmark for (2999ds/0Mi)
% 3.22/0.74 % (221423)% WARNING: option uhcvi not known.
% 3.22/0.74 % (221423)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2574834294:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 3.22/0.74 % (221426)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=588942619:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 3.22/0.74 % (221424)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2045177278:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 3.22/0.74 % (221425)dis+10_1_sil=32000:sp=arity:random_seed=2493348431:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 3.22/0.74 % (221427)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1627542241:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 3.22/0.74 % (221428)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2211963149:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 3.22/0.74 % TRYING [1]
% 3.22/0.74 % TRYING [2]
% 3.22/0.74 % TRYING [3]
% 3.22/0.74 % TRYING [4]
% 3.22/0.74 % (221425)Instruction limit reached!
% 3.22/0.74 % (221425)------------------------------
% 3.22/0.74 % (221425)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.22/0.74 % (221425)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.22/0.74 % (221425)CaDiCaL version: 2.1.3
% 3.22/0.74 % (221425)Termination reason: Instruction limit
% 3.22/0.74 % (221425)Termination phase: Saturation
% 3.22/0.74 % (221425)Time elapsed: 0.067 s
% 3.22/0.74 % (221425)Peak memory usage: 13 MB
% 3.22/0.74 % (221425)Instructions burned: 103 (million)
% 3.22/0.74 % (221426)Instruction limit reached!
% 3.22/0.74 % (221426)------------------------------
% 3.22/0.74 % (221426)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.22/0.74 % (221426)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.22/0.74 % (221426)CaDiCaL version: 2.1.3
% 3.22/0.74 % (221426)Termination reason: Instruction limit
% 3.22/0.74 % (221426)Termination phase: Saturation
% 3.22/0.74 % (221426)Time elapsed: 0.070 s
% 3.22/0.74 % (221426)Peak memory usage: 14 MB
% 3.22/0.74 % (221426)Instructions burned: 117 (million)
% 3.22/0.74 % (221427)Instruction limit reached!
% 3.22/0.74 % (221427)------------------------------
% 3.22/0.74 % (221427)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.22/0.74 % (221427)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.22/0.74 % (221427)CaDiCaL version: 2.1.3
% 3.22/0.74 % (221427)Termination reason: Instruction limit
% 3.22/0.74 % (221427)Termination phase: Saturation
% 3.22/0.74 % (221427)Time elapsed: 0.071 s
% 3.22/0.74 % (221427)Peak memory usage: 13 MB
% 3.22/0.74 % (221427)Instructions burned: 131 (million)
% 3.22/0.74 % (221436)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=3373778399:i=714:nm=2_2998 on theBenchmark for (2998ds/714Mi)
% 3.22/0.74 % (221437)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=2368024056:i=131:bd=preordered:fsd=on_2998 on theBenchmark for (2998ds/131Mi)
% 3.22/0.74 % (221438)dis+11_32_anc=none:slsqr=2,1:sil=64000:sas=cadical:lma=off:lsd=50:s2agt=8:slsqc=1:kmz=on:newcnf=on:slsq=on:random_seed=2183506584:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2998 on theBenchmark for (2998ds/684Mi)
% 3.22/0.74 % (221428)Instruction limit reached!
% 3.22/0.74 % (221428)------------------------------
% 3.22/0.74 % (221428)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.22/0.74 % (221428)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.22/0.74 % (221428)CaDiCaL version: 2.1.3
% 3.22/0.74 % (221428)Termination reason: Instruction limit
% 3.22/0.74 % (221428)Termination phase: Saturation
% 3.22/0.74 % (221428)Time elapsed: 0.094 s
% 3.22/0.74 % (221428)Peak memory usage: 15 MB
% 3.22/0.74 % (221428)Instructions burned: 160 (million)
% 3.22/0.74 % (221442)ott-21_1_sil=16000:fs=off:random_seed=3829855916:i=180:av=off:fsr=off_2998 on theBenchmark for (2998ds/180Mi)
% 3.22/0.74 % TRYING [1]
% 3.22/0.74 % TRYING [2]
% 3.22/0.74 % TRYING [3]
% 3.22/0.74 % (221437)Instruction limit reached!
% 3.22/0.74 % (221437)------------------------------
% 3.22/0.74 % (221437)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.22/0.74 % (221437)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.22/0.74 % (221437)CaDiCaL version: 2.1.3
% 3.22/0.74 % (221437)Termination reason: Instruction limit
% 3.22/0.74 % (221437)Termination phase: Saturation
% 3.22/0.74 % (221437)Time elapsed: 0.074 s
% 3.22/0.74 % (221437)Peak memory usage: 13 MB
% 3.22/0.74 % (221437)Instructions burned: 131 (million)
% 3.22/0.74 % TRYING [5]
% 3.22/0.74 % (221444)dis+10_4_sil=64000:sp=reverse_arity:bsr=on:sac=on:cn=on:random_seed=983081571:i=477:bd=all_2997 on theBenchmark for (2997ds/477Mi)
% 3.22/0.74 % (221442)Instruction limit reached!
% 3.22/0.74 % (221442)------------------------------
% 3.22/0.74 % (221442)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.22/0.74 % (221442)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.22/0.74 % (221442)CaDiCaL version: 2.1.3
% 3.22/0.74 % (221442)Termination reason: Instruction limit
% 3.22/0.74 % (221442)Termination phase: Saturation
% 3.22/0.74 % (221442)Time elapsed: 0.084 s
% 3.22/0.74 % (221442)Peak memory usage: 13 MB
% 3.22/0.74 % (221442)Instructions burned: 182 (million)
% 3.22/0.74 % TRYING [4]
% 3.22/0.74 % (221446)fmb+10_1_sil=64000:erd=off:updr=off:random_seed=809092918:fmbsr=1.3:i=865:ins=25_2997 on theBenchmark for (2997ds/865Mi)
% 3.22/0.74 % TRYING [1]
% 3.22/0.74 % TRYING [2]
% 3.22/0.74 % TRYING [3]
% 3.22/0.74 % (221436)Instruction limit reached!
% 3.22/0.74 % (221436)------------------------------
% 3.22/0.74 % (221436)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.22/0.74 % (221436)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.22/0.74 % (221436)CaDiCaL version: 2.1.3
% 3.22/0.74 % (221436)Termination reason: Instruction limit
% 3.22/0.74 % (221436)Termination phase: Finite model building constraint generation
% 3.22/0.74 % (221436)Time elapsed: 0.278 s
% 3.22/0.74 % (221436)Peak memory usage: 42 MB
% 3.22/0.74 % (221436)Instructions burned: 715 (million)
% 3.22/0.74 % (221448)ott+10_1_to=lpo:sil=64000:tgt=full:sp=arity:spb=goal_then_units:random_seed=3469446126:i=1179_2995 on theBenchmark for (2995ds/1179Mi)
% 3.22/0.74 % (221423) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-221417-221423"...
% 3.22/0.74 % (221423)...printing done.
% 3.22/0.74 % (221423)Refutation found. Thanks to Tanya!
% 3.22/0.74 % SZS status Theorem for theBenchmark
% 3.22/0.74 % SZS output start Proof for theBenchmark
% See solution above
% 3.22/0.74 % (221423)------------------------------
% 3.22/0.74 % (221423)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.22/0.74 % (221423)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.22/0.74 % (221423)CaDiCaL version: 2.1.3
% 3.22/0.74 % (221423)Termination reason: Refutation
% 3.22/0.74 % (221423)Time elapsed: 0.449 s
% 3.22/0.74 % (221423)Peak memory usage: 19 MB
% 3.22/0.74 % (221423)Instructions burned: 726 (million)
% 3.22/0.74 % (221417)Success in time 0.502 s
% 3.22/0.74 % Vampire exiting
%------------------------------------------------------------------------------