%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SWC252+1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n005.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 01:05:16 PM UTC 2026
% Result : Theorem 0.19s 0.27s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 5
% Syntax : Number of formulae : 46 ( 14 unt; 0 def)
% Number of atoms : 203 ( 64 equ)
% Maximal formula atoms : 21 ( 4 avg)
% Number of connectives : 252 ( 95 ~; 87 |; 55 &)
% ( 0 <=>; 15 =>; 0 <=; 0 <~>)
% Maximal formula depth : 24 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 6 con; 0-3 aty)
% Number of variables : 72 ( 54 !; 18 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f17,axiom,
ssList(nil),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax17) ).
fof(f28,axiom,
! [X0] :
( ssList(X0)
=> app(nil,X0) = X0 ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax28) ).
fof(f38,axiom,
! [X0] :
( ssItem(X0)
=> ~ memberP(nil,X0) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax38) ).
fof(f84,axiom,
! [X0] :
( ssList(X0)
=> app(X0,nil) = X0 ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax84) ).
fof(f96,conjecture,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( X1 != X3
| X0 != X2
| nil = X0
| ? [X4] :
( ssItem(X4)
& ? [X5] :
( ssList(X5)
& ? [X6] :
( ssList(X6)
& app(app(X5,cons(X4,nil)),X6) = X0
& ! [X7] :
( ssItem(X7)
=> ( ~ memberP(X5,X7)
| ~ memberP(X6,X7)
| ~ lt(X4,X7)
| leq(X4,X7) ) ) ) ) )
| ( ! [X8] :
( ssItem(X8)
=> ( cons(X8,nil) != X2
| ~ memberP(X3,X8) ) )
& ( nil != X3
| nil != X2 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1) ).
fof(f97,negated_conjecture,
~ ! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( X1 != X3
| X0 != X2
| nil = X0
| ? [X4] :
( ssItem(X4)
& ? [X5] :
( ssList(X5)
& ? [X6] :
( ssList(X6)
& app(app(X5,cons(X4,nil)),X6) = X0
& ! [X7] :
( ssItem(X7)
=> ( ~ memberP(X5,X7)
| ~ memberP(X6,X7)
| ~ lt(X4,X7)
| leq(X4,X7) ) ) ) ) )
| ( ! [X8] :
( ssItem(X8)
=> ( cons(X8,nil) != X2
| ~ memberP(X3,X8) ) )
& ( nil != X3
| nil != X2 ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f96]) ).
fof(f134,plain,
! [X0] :
( app(nil,X0) = X0
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f28]) ).
fof(f148,plain,
! [X0] :
( ~ memberP(nil,X0)
| ~ ssItem(X0) ),
inference(ennf_transformation,[],[f38]) ).
fof(f201,plain,
! [X0] :
( app(X0,nil) = X0
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f84]) ).
fof(f221,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( X1 = X3
& X0 = X2
& nil != X0
& ! [X4] :
( ~ ssItem(X4)
| ! [X5] :
( ~ ssList(X5)
| ! [X6] :
( ~ ssList(X6)
| app(app(X5,cons(X4,nil)),X6) != X0
| ? [X7] :
( memberP(X5,X7)
& memberP(X6,X7)
& lt(X4,X7)
& ~ leq(X4,X7)
& ssItem(X7) ) ) ) )
& ( ? [X8] :
( cons(X8,nil) = X2
& memberP(X3,X8)
& ssItem(X8) )
| ( nil = X3
& nil = X2 ) )
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) ),
inference(ennf_transformation,[],[f97]) ).
fof(f222,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( X1 = X3
& X0 = X2
& nil != X0
& ! [X4] :
( ~ ssItem(X4)
| ! [X5] :
( ~ ssList(X5)
| ! [X6] :
( ~ ssList(X6)
| app(app(X5,cons(X4,nil)),X6) != X0
| ? [X7] :
( memberP(X5,X7)
& memberP(X6,X7)
& lt(X4,X7)
& ~ leq(X4,X7)
& ssItem(X7) ) ) ) )
& ( ? [X8] :
( cons(X8,nil) = X2
& memberP(X3,X8)
& ssItem(X8) )
| ( nil = X3
& nil = X2 ) )
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) ),
inference(flattening,[],[f221]) ).
fof(f296,plain,
( sK54 = sK56
& sK53 = sK55
& nil != sK53
& ! [X4] :
( ~ ssItem(X4)
| ! [X5] :
( ~ ssList(X5)
| ! [X6] :
( ~ ssList(X6)
| app(app(X5,cons(X4,nil)),X6) != sK53
| ( memberP(X5,sK57(X4,X5,X6))
& memberP(X6,sK57(X4,X5,X6))
& lt(X4,sK57(X4,X5,X6))
& ~ leq(X4,sK57(X4,X5,X6))
& ssItem(sK57(X4,X5,X6)) ) ) ) )
& ( ( sK55 = cons(sK58,nil)
& memberP(sK56,sK58)
& ssItem(sK58) )
| ( nil = sK56
& nil = sK55 ) )
& ssList(sK56)
& ssList(sK55)
& ssList(sK54)
& ssList(sK53) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK53,sK54,sK55,sK56,sK57,sK58]),skolemize(X0,sK53),skolemize(X1,sK54),skolemize(X2,sK55),skolemize(X3,sK56),skolemize(X7,sK57(X4,X5,X6)),skolemize(X8,sK58)],[f222]) ).
fof(f389,plain,
ssList(nil),
inference(cnf_transformation,[],[f17]) ).
fof(f403,plain,
! [X0] :
( ~ ssList(X0)
| app(nil,X0) = X0 ),
inference(cnf_transformation,[],[f134]) ).
fof(f419,plain,
! [X0] :
( ~ memberP(nil,X0)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f148]) ).
fof(f482,plain,
! [X0] :
( ~ ssList(X0)
| app(X0,nil) = X0 ),
inference(cnf_transformation,[],[f201]) ).
fof(f498,plain,
ssList(sK55),
inference(cnf_transformation,[],[f296]) ).
fof(f500,plain,
( ssItem(sK58)
| nil = sK55 ),
inference(cnf_transformation,[],[f296]) ).
fof(f504,plain,
( sK55 = cons(sK58,nil)
| nil = sK55 ),
inference(cnf_transformation,[],[f296]) ).
fof(f506,plain,
! [X6,X4,X5] :
( ~ ssItem(X4)
| ~ ssList(X5)
| ~ ssList(X6)
| app(app(X5,cons(X4,nil)),X6) != sK53
| ssItem(sK57(X4,X5,X6)) ),
inference(cnf_transformation,[],[f296]) ).
fof(f510,plain,
! [X6,X4,X5] :
( ~ ssItem(X4)
| ~ ssList(X5)
| ~ ssList(X6)
| app(app(X5,cons(X4,nil)),X6) != sK53
| memberP(X5,sK57(X4,X5,X6)) ),
inference(cnf_transformation,[],[f296]) ).
fof(f511,plain,
nil != sK53,
inference(cnf_transformation,[],[f296]) ).
fof(f512,plain,
sK53 = sK55,
inference(cnf_transformation,[],[f296]) ).
fof(f514,plain,
nil != sK55,
inference(definition_unfolding,[],[f511,f512]) ).
fof(f515,plain,
! [X6,X4,X5] :
( app(app(X5,cons(X4,nil)),X6) != sK55
| ~ ssList(X5)
| ~ ssList(X6)
| ~ ssItem(X4)
| memberP(X5,sK57(X4,X5,X6)) ),
inference(definition_unfolding,[],[f510,f512]) ).
fof(f519,plain,
! [X6,X4,X5] :
( app(app(X5,cons(X4,nil)),X6) != sK55
| ~ ssList(X5)
| ~ ssList(X6)
| ~ ssItem(X4)
| ssItem(sK57(X4,X5,X6)) ),
inference(definition_unfolding,[],[f506,f512]) ).
fof(f576,plain,
ssItem(sK58),
inference(forward_subsumption_resolution,[],[f500,f514]) ).
fof(f608,plain,
sK55 = cons(sK58,nil),
inference(forward_subsumption_resolution,[],[f504,f514]) ).
fof(f1012,plain,
sK55 = app(nil,sK55),
inference(resolution,[],[f403,f498]) ).
fof(f1060,plain,
sK55 = app(sK55,nil),
inference(resolution,[],[f482,f498]) ).
fof(f1100,plain,
! [X0,X1] :
( sK55 != app(app(X0,sK55),X1)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ ssItem(sK58)
| ssItem(sK57(sK58,X0,X1)) ),
inference(superposition,[],[f519,f608]) ).
fof(f1103,plain,
! [X0,X1] :
( sK55 != app(app(X0,sK55),X1)
| ~ ssList(X0)
| ~ ssList(X1)
| ssItem(sK57(sK58,X0,X1)) ),
inference(forward_subsumption_resolution,[],[f1100,f576]) ).
fof(f1107,plain,
! [X0,X1] :
( sK55 != app(app(X0,sK55),X1)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ ssItem(sK58)
| memberP(X0,sK57(sK58,X0,X1)) ),
inference(superposition,[],[f515,f608]) ).
fof(f1110,plain,
! [X0,X1] :
( sK55 != app(app(X0,sK55),X1)
| ~ ssList(X0)
| ~ ssList(X1)
| memberP(X0,sK57(sK58,X0,X1)) ),
inference(forward_subsumption_resolution,[],[f1107,f576]) ).
fof(f1127,plain,
! [X0] :
( sK55 != app(sK55,X0)
| ~ ssList(nil)
| ~ ssList(X0)
| ssItem(sK57(sK58,nil,X0)) ),
inference(superposition,[],[f1103,f1012]) ).
fof(f1128,plain,
! [X0] :
( sK55 != app(sK55,X0)
| ~ ssList(X0)
| ssItem(sK57(sK58,nil,X0)) ),
inference(forward_subsumption_resolution,[],[f1127,f389]) ).
fof(f1137,plain,
! [X0] :
( sK55 != app(sK55,X0)
| ~ ssList(nil)
| ~ ssList(X0)
| memberP(nil,sK57(sK58,nil,X0)) ),
inference(superposition,[],[f1110,f1012]) ).
fof(f1138,plain,
! [X0] :
( sK55 != app(sK55,X0)
| ~ ssList(X0)
| memberP(nil,sK57(sK58,nil,X0)) ),
inference(forward_subsumption_resolution,[],[f1137,f389]) ).
fof(f1150,plain,
( sK55 != sK55
| ~ ssList(nil)
| ssItem(sK57(sK58,nil,nil)) ),
inference(superposition,[],[f1128,f1060]) ).
fof(f1151,plain,
( ~ ssList(nil)
| ssItem(sK57(sK58,nil,nil)) ),
inference(trivial_inequality_removal,[],[f1150]) ).
fof(f1152,plain,
ssItem(sK57(sK58,nil,nil)),
inference(forward_subsumption_resolution,[],[f1151,f389]) ).
fof(f1156,plain,
( sK55 != sK55
| ~ ssList(nil)
| memberP(nil,sK57(sK58,nil,nil)) ),
inference(superposition,[],[f1138,f1060]) ).
fof(f1157,plain,
( ~ ssList(nil)
| memberP(nil,sK57(sK58,nil,nil)) ),
inference(trivial_inequality_removal,[],[f1156]) ).
fof(f1158,plain,
memberP(nil,sK57(sK58,nil,nil)),
inference(forward_subsumption_resolution,[],[f1157,f389]) ).
fof(f1164,plain,
~ ssItem(sK57(sK58,nil,nil)),
inference(resolution,[],[f1158,f419]) ).
fof(f1165,plain,
$false,
inference(forward_subsumption_resolution,[],[f1164,f1152]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC252+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.07/0.18 % Computer : n005.cluster.edu
% 0.07/0.18 % Model : x86_64 x86_64
% 0.07/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.18 % Memory : 8046.5625MB
% 0.07/0.18 % OS : Linux 6.8.0-71-generic
% 0.07/0.18 % CPULimit : 300
% 0.07/0.18 % WCLimit : 300
% 0.07/0.19 % DateTime : Mon Sep 28 08:41:32 UTC 2026
% 0.07/0.19 % CPUTime :
% 0.07/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.07/0.22 Running first-order model finding
% 0.07/0.22 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.27 % (647095)Will run a generic schedule for satisfiability detection.
% 0.19/0.27 % (647102)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1267493681:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.19/0.27 % (647101)% WARNING: option uhcvi not known.
% 0.19/0.27 % (647100)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2627181921_2999 on theBenchmark for (2999ds/0Mi)
% 0.19/0.27 % (647101)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=576232757:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.19/0.27 % (647103)dis+10_1_sil=32000:sp=arity:random_seed=2130817314:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.19/0.27 % (647104)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=270385389:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.19/0.27 % (647105)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=612871001:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.19/0.27 % (647106)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=1717374777:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.19/0.27 % (647102) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-647095-647102"...
% 0.19/0.27 % (647102)...printing done.
% 0.19/0.27 % (647102)Refutation found. Thanks to Tanya!
% 0.19/0.27 % SZS status Theorem for theBenchmark
% 0.19/0.27 % SZS output start Proof for theBenchmark
% See solution above
% 0.19/0.28 % (647102)------------------------------
% 0.19/0.28 % (647102)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.28 % (647102)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.28 % (647102)CaDiCaL version: 2.1.3
% 0.19/0.28 % (647102)Termination reason: Refutation
% 0.19/0.28 % (647102)Time elapsed: 0.014 s
% 0.19/0.28 % (647102)Peak memory usage: 12 MB
% 0.19/0.28 % (647102)Instructions burned: 34 (million)
% 0.19/0.28 % (647095)Success in time 0.045 s
% 0.19/0.28 % Vampire exiting
%------------------------------------------------------------------------------