%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SWC039+1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n008.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 01:04:24 PM UTC 2026
% Result : Theorem 0.17s 0.50s
% Output : Refutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 9
% Syntax : Number of formulae : 77 ( 18 unt; 6 def)
% Number of atoms : 258 ( 80 equ)
% Maximal formula atoms : 21 ( 3 avg)
% Number of connectives : 270 ( 89 ~; 113 |; 42 &)
% ( 8 <=>; 18 =>; 0 <=; 0 <~>)
% Maximal formula depth : 23 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 12 ( 10 usr; 7 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 7 con; 0-2 aty)
% Number of variables : 60 ( 0 sgn 42 !; 18 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f26,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ssList(app(X0,X1)) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax26) ).
fof(f83,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ( nil = app(X0,X1)
<=> ( nil = X1
& nil = X0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax83) ).
fof(f96,conjecture,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( nil != X1
| X1 != X3
| X0 != X2
| nil = X0
| ( ! [X4] :
( ssItem(X4)
=> ! [X5] :
( ssList(X5)
=> ! [X6] :
( ssList(X6)
=> ( cons(X4,nil) != X2
| app(app(X5,X2),X6) != X3
| ? [X7] :
( ssItem(X7)
& memberP(X5,X7)
& lt(X4,X7) )
| ? [X8] :
( ssItem(X8)
& memberP(X6,X8)
& lt(X8,X4) ) ) ) ) )
& ( nil != X3
| nil != X2 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1) ).
fof(f97,negated_conjecture,
~ ! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( nil != X1
| X1 != X3
| X0 != X2
| nil = X0
| ( ! [X4] :
( ssItem(X4)
=> ! [X5] :
( ssList(X5)
=> ! [X6] :
( ssList(X6)
=> ( cons(X4,nil) != X2
| app(app(X5,X2),X6) != X3
| ? [X7] :
( ssItem(X7)
& memberP(X5,X7)
& lt(X4,X7) )
| ? [X8] :
( ssItem(X8)
& memberP(X6,X8)
& lt(X8,X4) ) ) ) ) )
& ( nil != X3
| nil != X2 ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f96]) ).
fof(f132,plain,
! [X0] :
( ! [X1] :
( ssList(app(X0,X1))
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f26]) ).
fof(f200,plain,
! [X0] :
( ! [X1] :
( ( nil = app(X0,X1)
<=> ( nil = X1
& nil = X0 ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f83]) ).
fof(f221,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( nil = X1
& X1 = X3
& X0 = X2
& nil != X0
& ( ? [X4] :
( ? [X5] :
( ? [X6] :
( cons(X4,nil) = X2
& app(app(X5,X2),X6) = X3
& ! [X7] :
( ~ ssItem(X7)
| ~ memberP(X5,X7)
| ~ lt(X4,X7) )
& ! [X8] :
( ~ ssItem(X8)
| ~ memberP(X6,X8)
| ~ lt(X8,X4) )
& ssList(X6) )
& ssList(X5) )
& ssItem(X4) )
| ( nil = X3
& nil = X2 ) )
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) ),
inference(ennf_transformation,[],[f97]) ).
fof(f222,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( nil = X1
& X1 = X3
& X0 = X2
& nil != X0
& ( ? [X4] :
( ? [X5] :
( ? [X6] :
( cons(X4,nil) = X2
& app(app(X5,X2),X6) = X3
& ! [X7] :
( ~ ssItem(X7)
| ~ memberP(X5,X7)
| ~ lt(X4,X7) )
& ! [X8] :
( ~ ssItem(X8)
| ~ memberP(X6,X8)
| ~ lt(X8,X4) )
& ssList(X6) )
& ssList(X5) )
& ssItem(X4) )
| ( nil = X3
& nil = X2 ) )
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) ),
inference(flattening,[],[f221]) ).
fof(f318,plain,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssList(X1)
| ssList(app(X0,X1)) ),
inference(cnf_transformation,[],[f132]) ).
fof(f394,plain,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssList(X1)
| nil = X0
| nil != app(X0,X1) ),
inference(cnf_transformation,[],[f200]) ).
fof(f395,plain,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssList(X1)
| nil = X1
| nil != app(X0,X1) ),
inference(cnf_transformation,[],[f200]) ).
fof(f418,plain,
( nil = sK49
| ssList(sK53) ),
inference(cnf_transformation,[],[f222]) ).
fof(f419,plain,
( nil = sK49
| sK50 = app(app(sK52,sK49),sK53) ),
inference(cnf_transformation,[],[f222]) ).
fof(f421,plain,
( nil = sK49
| ssList(sK52) ),
inference(cnf_transformation,[],[f222]) ).
fof(f426,plain,
nil != sK47,
inference(cnf_transformation,[],[f222]) ).
fof(f427,plain,
sK47 = sK49,
inference(cnf_transformation,[],[f222]) ).
fof(f428,plain,
sK48 = sK50,
inference(cnf_transformation,[],[f222]) ).
fof(f429,plain,
nil = sK48,
inference(cnf_transformation,[],[f222]) ).
fof(f432,plain,
ssList(sK47),
inference(cnf_transformation,[],[f222]) ).
fof(f433,plain,
nil = sK50,
inference(definition_unfolding,[],[f429,f428]) ).
fof(f485,plain,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssList(X1)
| sK50 = X1
| app(X0,X1) != sK50 ),
inference(definition_unfolding,[],[f395,f433,f433]) ).
fof(f486,plain,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssList(X1)
| sK50 = X0
| app(X0,X1) != sK50 ),
inference(definition_unfolding,[],[f394,f433,f433]) ).
fof(f490,plain,
ssList(sK49),
inference(definition_unfolding,[],[f432,f427]) ).
fof(f492,plain,
sK49 != sK50,
inference(definition_unfolding,[],[f426,f433,f427]) ).
fof(f496,plain,
( sK49 = sK50
| ssList(sK52) ),
inference(definition_unfolding,[],[f421,f433]) ).
fof(f498,plain,
( sK49 = sK50
| sK50 = app(app(sK52,sK49),sK53) ),
inference(definition_unfolding,[],[f419,f433]) ).
fof(f499,plain,
( sK49 = sK50
| ssList(sK53) ),
inference(definition_unfolding,[],[f418,f433]) ).
fof(f622,plain,
! [X0,X1] :
( ~ ssList(app(X0,X1))
| ssList(X1)
| ssList(X0) ),
inference(consistent_polarity_flipping,[],[f318]) ).
fof(f683,plain,
! [X0,X1] :
( app(X0,X1) != sK50
| ssList(X1)
| sK50 = X1
| ssList(X0) ),
inference(consistent_polarity_flipping,[],[f485]) ).
fof(f684,plain,
! [X0,X1] :
( app(X0,X1) != sK50
| ssList(X1)
| sK50 = X0
| ssList(X0) ),
inference(consistent_polarity_flipping,[],[f486]) ).
fof(f695,plain,
~ ssList(sK49),
inference(consistent_polarity_flipping,[],[f490]) ).
fof(f700,plain,
( sK49 = sK50
| ~ ssList(sK52) ),
inference(consistent_polarity_flipping,[],[f496]) ).
fof(f701,plain,
( sK49 = sK50
| ~ ssList(sK53) ),
inference(consistent_polarity_flipping,[],[f499]) ).
fof(f718,definition,
( spl54_2
<=> sK49 = sK50 ),
introduced(definition,[new_symbols(definition,[spl54_2])],[avatar_definition]) ).
fof(f719,plain,
( sK49 != sK50
| spl54_2 ),
inference(avatar_component_clause,[],[f718]) ).
fof(f727,definition,
( spl54_4
<=> ssList(sK53) ),
introduced(definition,[new_symbols(definition,[spl54_4])],[avatar_definition]) ).
fof(f729,plain,
( ~ ssList(sK53)
| spl54_4 ),
inference(avatar_component_clause,[],[f727]) ).
fof(f730,plain,
( ~ spl54_4
| spl54_2 ),
inference(avatar_split_clause,[],[f701,f718,f727]) ).
fof(f732,definition,
( spl54_5
<=> sK50 = app(app(sK52,sK49),sK53) ),
introduced(definition,[new_symbols(definition,[spl54_5])],[avatar_definition]) ).
fof(f734,plain,
( sK50 = app(app(sK52,sK49),sK53)
| ~ spl54_5 ),
inference(avatar_component_clause,[],[f732]) ).
fof(f735,plain,
( spl54_5
| spl54_2 ),
inference(avatar_split_clause,[],[f498,f718,f732]) ).
fof(f742,definition,
( spl54_7
<=> ssList(sK52) ),
introduced(definition,[new_symbols(definition,[spl54_7])],[avatar_definition]) ).
fof(f744,plain,
( ~ ssList(sK52)
| spl54_7 ),
inference(avatar_component_clause,[],[f742]) ).
fof(f745,plain,
( ~ spl54_7
| spl54_2 ),
inference(avatar_split_clause,[],[f700,f718,f742]) ).
fof(f751,plain,
~ spl54_2,
inference(avatar_split_clause,[],[f492,f718]) ).
fof(f914,definition,
( spl54_26
<=> ssList(app(sK52,sK49)) ),
introduced(definition,[new_symbols(definition,[spl54_26])],[avatar_definition]) ).
fof(f916,plain,
( ssList(app(sK52,sK49))
| ~ spl54_26 ),
inference(avatar_component_clause,[],[f914]) ).
fof(f918,plain,
( sK50 != sK50
| ssList(sK53)
| sK50 = app(sK52,sK49)
| ssList(app(sK52,sK49))
| ~ spl54_5 ),
inference(superposition,[],[f684,f734]) ).
fof(f919,plain,
( ssList(sK53)
| sK50 = app(sK52,sK49)
| ssList(app(sK52,sK49))
| ~ spl54_5 ),
inference(trivial_inequality_removal,[],[f918]) ).
fof(f920,plain,
( sK50 = app(sK52,sK49)
| ssList(app(sK52,sK49))
| spl54_4
| ~ spl54_5 ),
inference(forward_subsumption_resolution,[],[f919,f729]) ).
fof(f922,definition,
( spl54_27
<=> sK50 = app(sK52,sK49) ),
introduced(definition,[new_symbols(definition,[spl54_27])],[avatar_definition]) ).
fof(f924,plain,
( sK50 = app(sK52,sK49)
| ~ spl54_27 ),
inference(avatar_component_clause,[],[f922]) ).
fof(f925,plain,
( spl54_26
| spl54_27
| spl54_4
| ~ spl54_5 ),
inference(avatar_split_clause,[],[f920,f732,f727,f922,f914]) ).
fof(f1168,plain,
( sK50 != sK50
| ssList(sK49)
| sK49 = sK50
| ssList(sK52)
| ~ spl54_27 ),
inference(superposition,[],[f683,f924]) ).
fof(f1169,plain,
( ssList(sK49)
| sK49 = sK50
| ssList(sK52)
| ~ spl54_27 ),
inference(trivial_inequality_removal,[],[f1168]) ).
fof(f1171,plain,
( sK49 = sK50
| ssList(sK52)
| ~ spl54_27 ),
inference(forward_subsumption_resolution,[],[f1169,f695]) ).
fof(f1174,plain,
( ssList(sK52)
| spl54_2
| ~ spl54_27 ),
inference(forward_subsumption_resolution,[],[f1171,f719]) ).
fof(f1176,plain,
( $false
| spl54_2
| spl54_7
| ~ spl54_27 ),
inference(forward_subsumption_resolution,[],[f1174,f744]) ).
fof(f1177,plain,
( spl54_2
| spl54_7
| ~ spl54_27 ),
inference(avatar_contradiction_clause,[],[f1176]) ).
fof(f1354,plain,
( ssList(sK49)
| ssList(sK52)
| ~ spl54_26 ),
inference(resolution,[],[f622,f916]) ).
fof(f1372,plain,
( ssList(sK52)
| ~ spl54_26 ),
inference(forward_subsumption_resolution,[],[f1354,f695]) ).
fof(f1373,plain,
( $false
| spl54_7
| ~ spl54_26 ),
inference(forward_subsumption_resolution,[],[f1372,f744]) ).
fof(f1374,plain,
( spl54_7
| ~ spl54_26 ),
inference(avatar_contradiction_clause,[],[f1373]) ).
cnf(s3,plain,
( spl54_2
| ~ spl54_4 ),
inference(sat_conversion,[],[f730]) ).
cnf(s4,plain,
( spl54_2
| spl54_5 ),
inference(sat_conversion,[],[f735]) ).
cnf(s6,plain,
( spl54_2
| ~ spl54_7 ),
inference(sat_conversion,[],[f745]) ).
cnf(s8,plain,
~ spl54_2,
inference(sat_conversion,[],[f751]) ).
cnf(s29,plain,
( spl54_4
| ~ spl54_5
| spl54_26
| spl54_27 ),
inference(sat_conversion,[],[f925]) ).
cnf(s42,plain,
( spl54_2
| spl54_7
| ~ spl54_27 ),
inference(sat_conversion,[],[f1177]) ).
cnf(s49,plain,
( spl54_7
| ~ spl54_26 ),
inference(sat_conversion,[],[f1374]) ).
cnf(s55,plain,
~ spl54_7,
inference(rat,[],[s6,s8]) ).
cnf(s56,plain,
~ spl54_26,
inference(rat,[],[s49,s55]) ).
cnf(s57,plain,
~ spl54_27,
inference(rat,[],[s42,s8,s55]) ).
cnf(s65,plain,
spl54_5,
inference(rat,[],[s4,s8]) ).
cnf(s66,plain,
spl54_4,
inference(rat,[],[s29,s57,s56,s65]) ).
cnf(s67,plain,
$false,
inference(rat,[],[s3,s66,s8]) ).
fof(f1375,plain,
$false,
inference(avatar_sat_refutation,[],[s67]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC039+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.12/0.38 % Computer : n008.cluster.edu
% 0.12/0.38 % Model : x86_64 x86_64
% 0.12/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.38 % Memory : 8046.5625MB
% 0.12/0.38 % OS : Linux 6.8.0-71-generic
% 0.12/0.38 % CPULimit : 300
% 0.12/0.38 % WCLimit : 300
% 0.12/0.38 % DateTime : Mon Sep 28 07:34:24 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.39 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.12/0.42 Running first-order model finding
% 0.12/0.42 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
% 0.17/0.50 % (2080906)Will run a generic schedule for satisfiability detection.
% 0.17/0.50 % (2080911)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2282745754_2999 on theBenchmark for (2999ds/0Mi)
% 0.17/0.50 % (2080912)% WARNING: option uhcvi not known.
% 0.17/0.50 % (2080912)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=187884091:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.17/0.50 % (2080913)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1064925672:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.17/0.50 % (2080914)dis+10_1_sil=32000:sp=arity:random_seed=2446946401:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.17/0.50 % (2080915)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1123586873:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.17/0.50 % TRYING [1]
% 0.17/0.50 % (2080916)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=4235898387:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.17/0.50 % (2080917)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=1775743897:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.17/0.50 % TRYING [2]
% 0.17/0.50 % TRYING [3]
% 0.17/0.50 % TRYING [4]
% 0.17/0.50 % (2080912) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2080906-2080912"...
% 0.17/0.50 % (2080912)...printing done.
% 0.17/0.50 % (2080912)Refutation found. Thanks to Tanya!
% 0.17/0.50 % SZS status Theorem for theBenchmark
% 0.17/0.50 % SZS output start Proof for theBenchmark
% See solution above
% 0.17/0.50 % (2080912)------------------------------
% 0.17/0.50 % (2080912)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.17/0.50 % (2080912)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.17/0.50 % (2080912)CaDiCaL version: 2.1.3
% 0.17/0.50 % (2080912)Termination reason: Refutation
% 0.17/0.50 % (2080912)Time elapsed: 0.024 s
% 0.17/0.50 % (2080912)Peak memory usage: 13 MB
% 0.17/0.50 % (2080912)Instructions burned: 36 (million)
% 0.17/0.50 % (2080906)Success in time 0.074 s
% 0.17/0.50 % Vampire exiting
%------------------------------------------------------------------------------