%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SWC279+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 : n003.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 01:05:22 PM UTC 2026
% Result : Theorem 0.21s 0.27s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 5
% Syntax : Number of formulae : 60 ( 13 unt; 4 def)
% Number of atoms : 263 ( 27 equ)
% Maximal formula atoms : 24 ( 4 avg)
% Number of connectives : 328 ( 125 ~; 122 |; 61 &)
% ( 4 <=>; 16 =>; 0 <=; 0 <~>)
% Maximal formula depth : 23 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 10 ( 8 usr; 5 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 9 con; 0-2 aty)
% Number of variables : 70 ( 0 sgn 46 !; 24 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f96,conjecture,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( X1 != X3
| X0 != X2
| ? [X4] :
( ssItem(X4)
& ? [X5] :
( ssList(X5)
& ? [X6] :
( ssList(X6)
& app(app(X5,cons(X4,nil)),X6) = X2
& ? [X7] :
( ssItem(X7)
& ( ( ~ leq(X4,X7)
& memberP(X6,X7) )
| ( ~ leq(X7,X4)
& memberP(X5,X7) ) ) ) ) ) )
| ! [X8] :
( ssItem(X8)
=> ! [X9] :
( ssList(X9)
=> ! [X10] :
( ssList(X10)
=> ( app(app(X9,cons(X8,nil)),X10) != X0
| ! [X11] :
( ssItem(X11)
=> ( ( ~ memberP(X9,X11)
| leq(X11,X8) )
& ( ~ memberP(X10,X11)
| leq(X8,X11) ) ) ) ) ) ) ) ) ) ) ) ),
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
| ? [X4] :
( ssItem(X4)
& ? [X5] :
( ssList(X5)
& ? [X6] :
( ssList(X6)
& app(app(X5,cons(X4,nil)),X6) = X2
& ? [X7] :
( ssItem(X7)
& ( ( ~ leq(X4,X7)
& memberP(X6,X7) )
| ( ~ leq(X7,X4)
& memberP(X5,X7) ) ) ) ) ) )
| ! [X8] :
( ssItem(X8)
=> ! [X9] :
( ssList(X9)
=> ! [X10] :
( ssList(X10)
=> ( app(app(X9,cons(X8,nil)),X10) != X0
| ! [X11] :
( ssItem(X11)
=> ( ( ~ memberP(X9,X11)
| leq(X11,X8) )
& ( ~ memberP(X10,X11)
| leq(X8,X11) ) ) ) ) ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f96]) ).
fof(f221,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( X1 = X3
& X0 = X2
& ! [X4] :
( ~ ssItem(X4)
| ! [X5] :
( ~ ssList(X5)
| ! [X6] :
( ~ ssList(X6)
| app(app(X5,cons(X4,nil)),X6) != X2
| ! [X7] :
( ~ ssItem(X7)
| ( ( leq(X4,X7)
| ~ memberP(X6,X7) )
& ( leq(X7,X4)
| ~ memberP(X5,X7) ) ) ) ) ) )
& ? [X8] :
( ? [X9] :
( ? [X10] :
( app(app(X9,cons(X8,nil)),X10) = X0
& ? [X11] :
( ( ( memberP(X9,X11)
& ~ leq(X11,X8) )
| ( memberP(X10,X11)
& ~ leq(X8,X11) ) )
& ssItem(X11) )
& ssList(X10) )
& ssList(X9) )
& ssItem(X8) )
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) ),
inference(ennf_transformation,[],[f97]) ).
fof(f222,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( X1 = X3
& X0 = X2
& ! [X4] :
( ~ ssItem(X4)
| ! [X5] :
( ~ ssList(X5)
| ! [X6] :
( ~ ssList(X6)
| app(app(X5,cons(X4,nil)),X6) != X2
| ! [X7] :
( ~ ssItem(X7)
| ( ( leq(X4,X7)
| ~ memberP(X6,X7) )
& ( leq(X7,X4)
| ~ memberP(X5,X7) ) ) ) ) ) )
& ? [X8] :
( ? [X9] :
( ? [X10] :
( app(app(X9,cons(X8,nil)),X10) = X0
& ? [X11] :
( ( ( memberP(X9,X11)
& ~ leq(X11,X8) )
| ( memberP(X10,X11)
& ~ leq(X8,X11) ) )
& ssItem(X11) )
& ssList(X10) )
& ssList(X9) )
& ssItem(X8) )
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) ),
inference(flattening,[],[f221]) ).
fof(f296,plain,
( sK54 = sK56
& sK53 = sK55
& ! [X4] :
( ~ ssItem(X4)
| ! [X5] :
( ~ ssList(X5)
| ! [X6] :
( ~ ssList(X6)
| app(app(X5,cons(X4,nil)),X6) != sK55
| ! [X7] :
( ~ ssItem(X7)
| ( ( leq(X4,X7)
| ~ memberP(X6,X7) )
& ( leq(X7,X4)
| ~ memberP(X5,X7) ) ) ) ) ) )
& sK53 = app(app(sK58,cons(sK57,nil)),sK59)
& ( ( memberP(sK58,sK60)
& ~ leq(sK60,sK57) )
| ( memberP(sK59,sK60)
& ~ leq(sK57,sK60) ) )
& ssItem(sK60)
& ssList(sK59)
& ssList(sK58)
& ssItem(sK57)
& ssList(sK56)
& ssList(sK55)
& ssList(sK54)
& ssList(sK53) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK53,sK54,sK55,sK56,sK57,sK58,sK59,sK60]),skolemize(X0,sK53),skolemize(X1,sK54),skolemize(X2,sK55),skolemize(X3,sK56),skolemize(X8,sK57),skolemize(X9,sK58),skolemize(X10,sK59),skolemize(X11,sK60)],[f222]) ).
fof(f500,plain,
ssItem(sK57),
inference(cnf_transformation,[],[f296]) ).
fof(f501,plain,
ssList(sK58),
inference(cnf_transformation,[],[f296]) ).
fof(f502,plain,
ssList(sK59),
inference(cnf_transformation,[],[f296]) ).
fof(f503,plain,
ssItem(sK60),
inference(cnf_transformation,[],[f296]) ).
fof(f504,plain,
( ~ leq(sK60,sK57)
| ~ leq(sK57,sK60) ),
inference(cnf_transformation,[],[f296]) ).
fof(f505,plain,
( ~ leq(sK60,sK57)
| memberP(sK59,sK60) ),
inference(cnf_transformation,[],[f296]) ).
fof(f506,plain,
( memberP(sK58,sK60)
| ~ leq(sK57,sK60) ),
inference(cnf_transformation,[],[f296]) ).
fof(f507,plain,
( memberP(sK58,sK60)
| memberP(sK59,sK60) ),
inference(cnf_transformation,[],[f296]) ).
fof(f508,plain,
sK53 = app(app(sK58,cons(sK57,nil)),sK59),
inference(cnf_transformation,[],[f296]) ).
fof(f509,plain,
! [X6,X7,X4,X5] :
( app(app(X5,cons(X4,nil)),X6) != sK55
| ~ ssList(X5)
| ~ ssList(X6)
| ~ ssItem(X4)
| ~ ssItem(X7)
| leq(X7,X4)
| ~ memberP(X5,X7) ),
inference(cnf_transformation,[],[f296]) ).
fof(f510,plain,
! [X6,X7,X4,X5] :
( app(app(X5,cons(X4,nil)),X6) != sK55
| ~ ssList(X5)
| ~ ssList(X6)
| ~ ssItem(X4)
| ~ ssItem(X7)
| leq(X4,X7)
| ~ memberP(X6,X7) ),
inference(cnf_transformation,[],[f296]) ).
fof(f511,plain,
sK53 = sK55,
inference(cnf_transformation,[],[f296]) ).
fof(f513,plain,
sK55 = app(app(sK58,cons(sK57,nil)),sK59),
inference(definition_unfolding,[],[f508,f511]) ).
fof(f551,definition,
( spl61_1
<=> leq(sK57,sK60) ),
introduced(definition,[new_symbols(definition,[spl61_1])],[avatar_definition]) ).
fof(f553,plain,
( ~ leq(sK57,sK60)
| spl61_1 ),
inference(avatar_component_clause,[],[f551]) ).
fof(f555,definition,
( spl61_2
<=> leq(sK60,sK57) ),
introduced(definition,[new_symbols(definition,[spl61_2])],[avatar_definition]) ).
fof(f557,plain,
( ~ leq(sK60,sK57)
| spl61_2 ),
inference(avatar_component_clause,[],[f555]) ).
fof(f558,plain,
( ~ spl61_1
| ~ spl61_2 ),
inference(avatar_split_clause,[],[f504,f555,f551]) ).
fof(f560,definition,
( spl61_3
<=> memberP(sK59,sK60) ),
introduced(definition,[new_symbols(definition,[spl61_3])],[avatar_definition]) ).
fof(f562,plain,
( memberP(sK59,sK60)
| ~ spl61_3 ),
inference(avatar_component_clause,[],[f560]) ).
fof(f563,plain,
( spl61_3
| ~ spl61_2 ),
inference(avatar_split_clause,[],[f505,f555,f560]) ).
fof(f565,definition,
( spl61_4
<=> memberP(sK58,sK60) ),
introduced(definition,[new_symbols(definition,[spl61_4])],[avatar_definition]) ).
fof(f567,plain,
( memberP(sK58,sK60)
| ~ spl61_4 ),
inference(avatar_component_clause,[],[f565]) ).
fof(f568,plain,
( ~ spl61_1
| spl61_4 ),
inference(avatar_split_clause,[],[f506,f565,f551]) ).
fof(f569,plain,
( spl61_3
| spl61_4 ),
inference(avatar_split_clause,[],[f507,f565,f560]) ).
fof(f605,plain,
! [X0] :
( sK55 != sK55
| ~ ssList(sK58)
| ~ ssList(sK59)
| ~ ssItem(sK57)
| ~ ssItem(X0)
| leq(X0,sK57)
| ~ memberP(sK58,X0) ),
inference(superposition,[],[f509,f513]) ).
fof(f606,plain,
! [X0] :
( ~ ssList(sK58)
| ~ ssList(sK59)
| ~ ssItem(sK57)
| ~ ssItem(X0)
| leq(X0,sK57)
| ~ memberP(sK58,X0) ),
inference(trivial_inequality_removal,[],[f605]) ).
fof(f607,plain,
! [X0] :
( ~ ssList(sK59)
| ~ ssItem(sK57)
| ~ ssItem(X0)
| leq(X0,sK57)
| ~ memberP(sK58,X0) ),
inference(forward_subsumption_resolution,[],[f606,f501]) ).
fof(f608,plain,
! [X0] :
( ~ ssItem(sK57)
| ~ ssItem(X0)
| leq(X0,sK57)
| ~ memberP(sK58,X0) ),
inference(forward_subsumption_resolution,[],[f607,f502]) ).
fof(f609,plain,
! [X0] :
( ~ memberP(sK58,X0)
| leq(X0,sK57)
| ~ ssItem(X0) ),
inference(forward_subsumption_resolution,[],[f608,f500]) ).
fof(f610,plain,
! [X0] :
( sK55 != sK55
| ~ ssList(sK58)
| ~ ssList(sK59)
| ~ ssItem(sK57)
| ~ ssItem(X0)
| leq(sK57,X0)
| ~ memberP(sK59,X0) ),
inference(superposition,[],[f510,f513]) ).
fof(f611,plain,
! [X0] :
( ~ ssList(sK58)
| ~ ssList(sK59)
| ~ ssItem(sK57)
| ~ ssItem(X0)
| leq(sK57,X0)
| ~ memberP(sK59,X0) ),
inference(trivial_inequality_removal,[],[f610]) ).
fof(f612,plain,
! [X0] :
( ~ ssList(sK59)
| ~ ssItem(sK57)
| ~ ssItem(X0)
| leq(sK57,X0)
| ~ memberP(sK59,X0) ),
inference(forward_subsumption_resolution,[],[f611,f501]) ).
fof(f613,plain,
! [X0] :
( ~ ssItem(sK57)
| ~ ssItem(X0)
| leq(sK57,X0)
| ~ memberP(sK59,X0) ),
inference(forward_subsumption_resolution,[],[f612,f502]) ).
fof(f614,plain,
! [X0] :
( ~ memberP(sK59,X0)
| leq(sK57,X0)
| ~ ssItem(X0) ),
inference(forward_subsumption_resolution,[],[f613,f500]) ).
fof(f615,plain,
( leq(sK57,sK60)
| ~ ssItem(sK60)
| ~ spl61_3 ),
inference(resolution,[],[f614,f562]) ).
fof(f616,plain,
( ~ ssItem(sK60)
| spl61_1
| ~ spl61_3 ),
inference(forward_subsumption_resolution,[],[f615,f553]) ).
fof(f617,plain,
( $false
| spl61_1
| ~ spl61_3 ),
inference(forward_subsumption_resolution,[],[f616,f503]) ).
fof(f618,plain,
( spl61_1
| ~ spl61_3 ),
inference(avatar_contradiction_clause,[],[f617]) ).
fof(f619,plain,
( leq(sK60,sK57)
| ~ ssItem(sK60)
| ~ spl61_4 ),
inference(resolution,[],[f567,f609]) ).
fof(f620,plain,
( ~ ssItem(sK60)
| spl61_2
| ~ spl61_4 ),
inference(forward_subsumption_resolution,[],[f619,f557]) ).
fof(f621,plain,
( $false
| spl61_2
| ~ spl61_4 ),
inference(forward_subsumption_resolution,[],[f620,f503]) ).
fof(f622,plain,
( spl61_2
| ~ spl61_4 ),
inference(avatar_contradiction_clause,[],[f621]) ).
cnf(s1,plain,
( ~ spl61_1
| ~ spl61_2 ),
inference(sat_conversion,[],[f558]) ).
cnf(s2,plain,
( ~ spl61_2
| spl61_3 ),
inference(sat_conversion,[],[f563]) ).
cnf(s3,plain,
( ~ spl61_1
| spl61_4 ),
inference(sat_conversion,[],[f568]) ).
cnf(s4,plain,
( spl61_3
| spl61_4 ),
inference(sat_conversion,[],[f569]) ).
cnf(s14,plain,
( spl61_1
| ~ spl61_3 ),
inference(sat_conversion,[],[f618]) ).
cnf(s15,plain,
( spl61_2
| ~ spl61_4 ),
inference(sat_conversion,[],[f622]) ).
cnf(s20,plain,
spl61_3,
inference(rat,[],[s15,s2,s4]) ).
cnf(s21,plain,
spl61_1,
inference(rat,[],[s14,s20]) ).
cnf(s22,plain,
spl61_4,
inference(rat,[],[s3,s21]) ).
cnf(s23,plain,
~ spl61_2,
inference(rat,[],[s1,s21]) ).
cnf(s24,plain,
$false,
inference(rat,[],[s15,s22,s23]) ).
fof(f623,plain,
$false,
inference(avatar_sat_refutation,[],[s24]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC279+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.19 % Computer : n003.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 08:52:27 UTC 2026
% 0.09/0.20 % CPUTime :
% 0.09/0.20 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.23 Running first-order model finding
% 0.09/0.23 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
% 0.21/0.27 % (1439807)Will run a generic schedule for satisfiability detection.
% 0.21/0.27 % (1439815)dis+10_1_sil=32000:sp=arity:random_seed=3887334375:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.21/0.27 % (1439813)% WARNING: option uhcvi not known.
% 0.21/0.27 % (1439815) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1439807-1439815"...
% 0.21/0.27 % (1439815)...printing done.
% 0.21/0.27 % (1439815)Refutation found. Thanks to Tanya!
% 0.21/0.27 % SZS status Theorem for theBenchmark
% 0.21/0.27 % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.27 % (1439815)------------------------------
% 0.21/0.27 % (1439815)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.27 % (1439815)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.27 % (1439815)CaDiCaL version: 2.1.3
% 0.21/0.27 % (1439815)Termination reason: Refutation
% 0.21/0.27 % (1439815)Time elapsed: 0.004 s
% 0.21/0.27 % (1439815)Peak memory usage: 12 MB
% 0.21/0.27 % (1439815)Instructions burned: 11 (million)
% 0.21/0.27 % (1439807)Success in time 0.029 s
% 0.21/0.27 % Vampire exiting
%------------------------------------------------------------------------------