%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWC165-1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n026.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 01:02:44 PM UTC 2026
% Result : Unsatisfiable 4.32s 1.58s
% Output : Refutation 5.70s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 30
% Syntax : Number of formulae : 124 ( 25 unt; 9 def)
% Number of atoms : 347 ( 49 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 450 ( 227 ~; 214 |; 0 &)
% ( 9 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 4 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 16 ( 14 usr; 10 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 8 con; 0-2 aty)
% Number of variables : 32 ( 0 sgn 32 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f7,axiom,
cyclefreeP(nil),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause7) ).
fof(f8,axiom,
ssList(nil),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause8) ).
fof(f62,axiom,
! [X0] :
( leq(X0,X0)
| ~ ssItem(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause62) ).
fof(f70,axiom,
! [X0] :
( cyclefreeP(cons(X0,nil))
| ~ ssItem(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause70) ).
fof(f85,axiom,
! [X0,X1] :
( ssList(app(X1,X0))
| ~ ssList(X1)
| ~ ssList(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause85) ).
fof(f86,axiom,
! [X0,X1] :
( ssList(cons(X0,X1))
| ~ ssList(X1)
| ~ ssItem(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause86) ).
fof(f104,axiom,
! [X0,X1] :
( ~ ssItem(X0)
| ~ ssItem(X1)
| neq(X1,X0)
| X1 = X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause102) ).
fof(f105,plain,
! [X0,X1] :
( neq(X1,X0)
| ~ ssItem(X1)
| ~ ssItem(X0)
| X0 = X1 ),
inference(reorient_equations,[],[f104]) ).
fof(f121,axiom,
! [X0,X1] :
( app(X0,X1) != nil
| ~ ssList(X1)
| ~ ssList(X0)
| nil = X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause118) ).
fof(f122,plain,
! [X0,X1] :
( nil != app(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0)
| nil = X0 ),
inference(reorient_equations,[],[f121]) ).
fof(f125,axiom,
! [X0,X1] :
( ~ ssItem(X0)
| ~ ssList(X1)
| app(cons(X0,nil),X1) = cons(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause120) ).
fof(f126,plain,
! [X0,X1] :
( cons(X0,X1) = app(cons(X0,nil),X1)
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(reorient_equations,[],[f125]) ).
fof(f161,axiom,
! [X2,X0,X1] :
( app(app(X2,X1),X0) = app(X2,app(X1,X0))
| ~ ssList(X1)
| ~ ssList(X2)
| ~ ssList(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause149) ).
fof(f199,axiom,
! [X2,X3,X0,X1,X4,X5] :
( ~ leq(X0,X1)
| ~ leq(X1,X0)
| app(app(X2,cons(X0,X3)),cons(X1,X4)) != X5
| ~ ssList(X4)
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssItem(X1)
| ~ ssItem(X0)
| ~ cyclefreeP(X5)
| ~ ssList(X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause185) ).
fof(f202,negated_conjecture,
ssList(sk3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_3) ).
fof(f205,negated_conjecture,
sk1 = sk3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_6) ).
fof(f206,negated_conjecture,
ssItem(sk5),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_7) ).
fof(f207,negated_conjecture,
ssItem(sk6),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_8) ).
fof(f208,negated_conjecture,
ssList(sk7),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_9) ).
fof(f209,negated_conjecture,
ssList(sk8),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_10) ).
fof(f210,negated_conjecture,
app(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),sk8) = sk1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_11) ).
fof(f211,plain,
sk1 = app(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),sk8),
inference(reorient_equations,[],[f210]) ).
fof(f212,negated_conjecture,
~ neq(sk5,sk6),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_12) ).
fof(f214,negated_conjecture,
( ssItem(sk9)
| nil = sk3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_14) ).
fof(f225,negated_conjecture,
( cons(sk9,nil) = sk3
| nil = sk3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_23) ).
fof(f226,plain,
( sk3 = cons(sk9,nil)
| nil = sk3 ),
inference(reorient_equations,[],[f225]) ).
fof(f244,plain,
! [X2,X3,X0,X1,X4] :
( ~ ssList(app(app(X2,cons(X0,X3)),cons(X1,X4)))
| ~ leq(X1,X0)
| ~ ssList(X4)
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssItem(X1)
| ~ ssItem(X0)
| ~ cyclefreeP(app(app(X2,cons(X0,X3)),cons(X1,X4)))
| ~ leq(X0,X1) ),
inference(equality_resolution,[],[f199]) ).
fof(f255,definition,
( spl0_1
<=> nil = sk3 ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f257,plain,
( nil = sk3
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f255]) ).
fof(f272,definition,
( spl0_5
<=> sk3 = cons(sk9,nil) ),
introduced(definition,[new_symbols(definition,[spl0_5])],[avatar_definition]) ).
fof(f274,plain,
( sk3 = cons(sk9,nil)
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f272]) ).
fof(f275,plain,
( spl0_1
| spl0_5 ),
inference(avatar_split_clause,[],[f226,f272,f255]) ).
fof(f297,definition,
( spl0_9
<=> ssItem(sk9) ),
introduced(definition,[new_symbols(definition,[spl0_9])],[avatar_definition]) ).
fof(f299,plain,
( ssItem(sk9)
| ~ spl0_9 ),
inference(avatar_component_clause,[],[f297]) ).
fof(f300,plain,
( spl0_1
| spl0_9 ),
inference(avatar_split_clause,[],[f214,f297,f255]) ).
fof(f305,plain,
( ~ ssItem(sk5)
| ~ ssItem(sk6)
| sk5 = sk6 ),
inference(resolution,[],[f212,f105]) ).
fof(f306,plain,
( ~ ssItem(sk6)
| sk5 = sk6 ),
inference(forward_subsumption_resolution,[],[f305,f206]) ).
fof(f308,definition,
( spl0_10
<=> sk5 = sk6 ),
introduced(definition,[new_symbols(definition,[spl0_10])],[avatar_definition]) ).
fof(f310,plain,
( sk5 = sk6
| ~ spl0_10 ),
inference(avatar_component_clause,[],[f308]) ).
fof(f320,plain,
sk5 = sk6,
inference(forward_subsumption_resolution,[],[f306,f207]) ).
fof(f321,plain,
spl0_10,
inference(avatar_split_clause,[],[f320,f308]) ).
fof(f328,plain,
( cyclefreeP(sk3)
| ~ ssItem(sk9)
| ~ spl0_5 ),
inference(superposition,[],[f70,f274]) ).
fof(f392,plain,
( cyclefreeP(sk3)
| ~ spl0_5
| ~ spl0_9 ),
inference(forward_subsumption_resolution,[],[f328,f299]) ).
fof(f530,plain,
( sk1 = app(app(sk7,cons(sk5,nil)),app(cons(sk6,nil),sk8))
| ~ ssList(cons(sk6,nil))
| ~ ssList(app(sk7,cons(sk5,nil)))
| ~ ssList(sk8) ),
inference(superposition,[],[f211,f161]) ).
fof(f533,plain,
( nil != sk1
| ~ ssList(sk8)
| ~ ssList(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)))
| nil = app(app(sk7,cons(sk5,nil)),cons(sk6,nil)) ),
inference(superposition,[],[f122,f211]) ).
fof(f560,plain,
( nil != sk1
| ~ ssList(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)))
| nil = app(app(sk7,cons(sk5,nil)),cons(sk6,nil)) ),
inference(forward_subsumption_resolution,[],[f533,f209]) ).
fof(f563,plain,
( sk1 = app(app(sk7,cons(sk5,nil)),app(cons(sk6,nil),sk8))
| ~ ssList(cons(sk6,nil))
| ~ ssList(app(sk7,cons(sk5,nil))) ),
inference(forward_subsumption_resolution,[],[f530,f209]) ).
fof(f579,plain,
( nil != sk3
| ~ ssList(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)))
| nil = app(app(sk7,cons(sk5,nil)),cons(sk6,nil)) ),
inference(forward_demodulation,[],[f560,f205]) ).
fof(f582,plain,
( sk1 = app(app(sk7,cons(sk5,nil)),app(cons(sk5,nil),sk8))
| ~ ssList(cons(sk6,nil))
| ~ ssList(app(sk7,cons(sk5,nil)))
| ~ spl0_10 ),
inference(forward_demodulation,[],[f563,f310]) ).
fof(f597,plain,
( sk3 = app(app(sk7,cons(sk5,nil)),app(cons(sk5,nil),sk8))
| ~ ssList(cons(sk6,nil))
| ~ ssList(app(sk7,cons(sk5,nil)))
| ~ spl0_10 ),
inference(forward_demodulation,[],[f582,f205]) ).
fof(f610,definition,
( spl0_27
<=> ssList(app(app(sk7,cons(sk5,nil)),cons(sk5,nil))) ),
introduced(definition,[new_symbols(definition,[spl0_27])],[avatar_definition]) ).
fof(f611,plain,
( ssList(app(app(sk7,cons(sk5,nil)),cons(sk5,nil)))
| ~ spl0_27 ),
inference(avatar_component_clause,[],[f610]) ).
fof(f612,plain,
( ~ ssList(app(app(sk7,cons(sk5,nil)),cons(sk5,nil)))
| spl0_27 ),
inference(avatar_component_clause,[],[f610]) ).
fof(f619,plain,
( ~ ssList(cons(sk5,nil))
| sk3 = app(app(sk7,cons(sk5,nil)),app(cons(sk5,nil),sk8))
| ~ ssList(app(sk7,cons(sk5,nil)))
| ~ spl0_10 ),
inference(forward_demodulation,[],[f597,f310]) ).
fof(f652,definition,
( spl0_34
<=> ssList(app(sk7,cons(sk5,nil))) ),
introduced(definition,[new_symbols(definition,[spl0_34])],[avatar_definition]) ).
fof(f653,plain,
( ssList(app(sk7,cons(sk5,nil)))
| ~ spl0_34 ),
inference(avatar_component_clause,[],[f652]) ).
fof(f654,plain,
( ~ ssList(app(sk7,cons(sk5,nil)))
| spl0_34 ),
inference(avatar_component_clause,[],[f652]) ).
fof(f656,definition,
( spl0_35
<=> sk3 = app(app(sk7,cons(sk5,nil)),app(cons(sk5,nil),sk8)) ),
introduced(definition,[new_symbols(definition,[spl0_35])],[avatar_definition]) ).
fof(f658,plain,
( sk3 = app(app(sk7,cons(sk5,nil)),app(cons(sk5,nil),sk8))
| ~ spl0_35 ),
inference(avatar_component_clause,[],[f656]) ).
fof(f660,definition,
( spl0_36
<=> ssList(cons(sk5,nil)) ),
introduced(definition,[new_symbols(definition,[spl0_36])],[avatar_definition]) ).
fof(f661,plain,
( ssList(cons(sk5,nil))
| ~ spl0_36 ),
inference(avatar_component_clause,[],[f660]) ).
fof(f662,plain,
( ~ ssList(cons(sk5,nil))
| spl0_36 ),
inference(avatar_component_clause,[],[f660]) ).
fof(f664,plain,
( ~ spl0_34
| spl0_35
| ~ spl0_36
| ~ spl0_10 ),
inference(avatar_split_clause,[],[f619,f308,f660,f656,f652]) ).
fof(f677,definition,
( spl0_39
<=> nil = app(app(sk7,cons(sk5,nil)),cons(sk5,nil)) ),
introduced(definition,[new_symbols(definition,[spl0_39])],[avatar_definition]) ).
fof(f679,plain,
( nil = app(app(sk7,cons(sk5,nil)),cons(sk5,nil))
| ~ spl0_39 ),
inference(avatar_component_clause,[],[f677]) ).
fof(f707,plain,
( ~ ssList(nil)
| ~ ssItem(sk5)
| spl0_36 ),
inference(resolution,[],[f662,f86]) ).
fof(f708,plain,
( ~ ssItem(sk5)
| spl0_36 ),
inference(forward_subsumption_resolution,[],[f707,f8]) ).
fof(f709,plain,
( $false
| spl0_36 ),
inference(forward_subsumption_resolution,[],[f708,f206]) ).
fof(f710,plain,
spl0_36,
inference(avatar_contradiction_clause,[],[f709]) ).
fof(f788,plain,
( ~ ssList(sk7)
| ~ ssList(cons(sk5,nil))
| spl0_34 ),
inference(resolution,[],[f654,f85]) ).
fof(f789,plain,
( ~ ssList(cons(sk5,nil))
| spl0_34 ),
inference(forward_subsumption_resolution,[],[f788,f208]) ).
fof(f790,plain,
( $false
| spl0_34
| ~ spl0_36 ),
inference(forward_subsumption_resolution,[],[f789,f661]) ).
fof(f791,plain,
( spl0_34
| ~ spl0_36 ),
inference(avatar_contradiction_clause,[],[f790]) ).
fof(f1261,plain,
( ~ ssList(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)))
| nil = app(app(sk7,cons(sk5,nil)),cons(sk6,nil))
| ~ spl0_1 ),
inference(forward_subsumption_resolution,[],[f579,f257]) ).
fof(f1264,plain,
( ~ ssList(app(app(sk7,cons(sk5,nil)),cons(sk5,nil)))
| nil = app(app(sk7,cons(sk5,nil)),cons(sk6,nil))
| ~ spl0_1
| ~ spl0_10 ),
inference(forward_demodulation,[],[f1261,f310]) ).
fof(f1468,plain,
( ~ ssList(app(sk7,cons(sk5,nil)))
| ~ ssList(cons(sk5,nil))
| spl0_27 ),
inference(resolution,[],[f612,f85]) ).
fof(f1472,plain,
( ~ ssList(cons(sk5,nil))
| spl0_27
| ~ spl0_34 ),
inference(forward_subsumption_resolution,[],[f1468,f653]) ).
fof(f1474,plain,
( $false
| spl0_27
| ~ spl0_34
| ~ spl0_36 ),
inference(forward_subsumption_resolution,[],[f1472,f661]) ).
fof(f1475,plain,
( spl0_27
| ~ spl0_34
| ~ spl0_36 ),
inference(avatar_contradiction_clause,[],[f1474]) ).
fof(f1487,plain,
( nil = app(app(sk7,cons(sk5,nil)),cons(sk6,nil))
| ~ spl0_1
| ~ spl0_10
| ~ spl0_27 ),
inference(forward_subsumption_resolution,[],[f1264,f611]) ).
fof(f1491,plain,
( nil = app(app(sk7,cons(sk5,nil)),cons(sk5,nil))
| ~ spl0_1
| ~ spl0_10
| ~ spl0_27 ),
inference(forward_demodulation,[],[f1487,f310]) ).
fof(f1494,plain,
( spl0_39
| ~ spl0_1
| ~ spl0_10
| ~ spl0_27 ),
inference(avatar_split_clause,[],[f1491,f610,f308,f255,f677]) ).
fof(f1506,plain,
( ~ leq(sk5,sk5)
| ~ ssList(nil)
| ~ ssList(nil)
| ~ ssList(sk7)
| ~ ssItem(sk5)
| ~ ssItem(sk5)
| ~ cyclefreeP(app(app(sk7,cons(sk5,nil)),cons(sk5,nil)))
| ~ leq(sk5,sk5)
| ~ spl0_27 ),
inference(resolution,[],[f611,f244]) ).
fof(f1513,plain,
( ~ leq(sk5,sk5)
| ~ ssList(nil)
| ~ ssList(sk7)
| ~ ssItem(sk5)
| ~ cyclefreeP(app(app(sk7,cons(sk5,nil)),cons(sk5,nil)))
| ~ spl0_27 ),
inference(duplicate_literal_removal,[],[f1506]) ).
fof(f1519,plain,
( ~ ssList(nil)
| ~ ssList(sk7)
| ~ ssItem(sk5)
| ~ cyclefreeP(app(app(sk7,cons(sk5,nil)),cons(sk5,nil)))
| ~ spl0_27 ),
inference(forward_subsumption_resolution,[],[f1513,f62]) ).
fof(f1523,plain,
( ~ ssList(sk7)
| ~ ssItem(sk5)
| ~ cyclefreeP(app(app(sk7,cons(sk5,nil)),cons(sk5,nil)))
| ~ spl0_27 ),
inference(forward_subsumption_resolution,[],[f1519,f8]) ).
fof(f1526,plain,
( ~ ssItem(sk5)
| ~ cyclefreeP(app(app(sk7,cons(sk5,nil)),cons(sk5,nil)))
| ~ spl0_27 ),
inference(forward_subsumption_resolution,[],[f1523,f208]) ).
fof(f1529,plain,
( ~ cyclefreeP(app(app(sk7,cons(sk5,nil)),cons(sk5,nil)))
| ~ spl0_27 ),
inference(forward_subsumption_resolution,[],[f1526,f206]) ).
fof(f1532,plain,
( ~ cyclefreeP(nil)
| ~ spl0_27
| ~ spl0_39 ),
inference(forward_demodulation,[],[f1529,f679]) ).
fof(f1533,plain,
( $false
| ~ spl0_27
| ~ spl0_39 ),
inference(forward_subsumption_resolution,[],[f1532,f7]) ).
fof(f1534,plain,
( ~ spl0_27
| ~ spl0_39 ),
inference(avatar_contradiction_clause,[],[f1533]) ).
fof(f2462,plain,
( sk3 = app(app(sk7,cons(sk5,nil)),cons(sk5,sk8))
| ~ ssList(sk8)
| ~ ssItem(sk5)
| ~ spl0_35 ),
inference(superposition,[],[f658,f126]) ).
fof(f2496,plain,
( sk3 = app(app(sk7,cons(sk5,nil)),cons(sk5,sk8))
| ~ ssItem(sk5)
| ~ spl0_35 ),
inference(forward_subsumption_resolution,[],[f2462,f209]) ).
fof(f2545,plain,
( sk3 = app(app(sk7,cons(sk5,nil)),cons(sk5,sk8))
| ~ spl0_35 ),
inference(forward_subsumption_resolution,[],[f2496,f206]) ).
fof(f6556,plain,
( ~ ssList(sk3)
| ~ leq(sk5,sk5)
| ~ ssList(sk8)
| ~ ssList(nil)
| ~ ssList(sk7)
| ~ ssItem(sk5)
| ~ ssItem(sk5)
| ~ cyclefreeP(sk3)
| ~ leq(sk5,sk5)
| ~ spl0_35 ),
inference(superposition,[],[f244,f2545]) ).
fof(f6588,plain,
( ~ ssList(sk3)
| ~ leq(sk5,sk5)
| ~ ssList(sk8)
| ~ ssList(nil)
| ~ ssList(sk7)
| ~ ssItem(sk5)
| ~ cyclefreeP(sk3)
| ~ spl0_35 ),
inference(duplicate_literal_removal,[],[f6556]) ).
fof(f6602,plain,
( ~ leq(sk5,sk5)
| ~ ssList(sk8)
| ~ ssList(nil)
| ~ ssList(sk7)
| ~ ssItem(sk5)
| ~ cyclefreeP(sk3)
| ~ spl0_35 ),
inference(forward_subsumption_resolution,[],[f6588,f202]) ).
fof(f6618,plain,
( ~ ssList(sk8)
| ~ ssList(nil)
| ~ ssList(sk7)
| ~ ssItem(sk5)
| ~ cyclefreeP(sk3)
| ~ spl0_35 ),
inference(forward_subsumption_resolution,[],[f6602,f62]) ).
fof(f6632,plain,
( ~ ssList(nil)
| ~ ssList(sk7)
| ~ ssItem(sk5)
| ~ cyclefreeP(sk3)
| ~ spl0_35 ),
inference(forward_subsumption_resolution,[],[f6618,f209]) ).
fof(f6645,plain,
( ~ ssList(sk7)
| ~ ssItem(sk5)
| ~ cyclefreeP(sk3)
| ~ spl0_35 ),
inference(forward_subsumption_resolution,[],[f6632,f8]) ).
fof(f6651,plain,
( ~ ssItem(sk5)
| ~ cyclefreeP(sk3)
| ~ spl0_35 ),
inference(forward_subsumption_resolution,[],[f6645,f208]) ).
fof(f6656,plain,
( ~ cyclefreeP(sk3)
| ~ spl0_35 ),
inference(forward_subsumption_resolution,[],[f6651,f206]) ).
fof(f6659,plain,
( $false
| ~ spl0_5
| ~ spl0_9
| ~ spl0_35 ),
inference(forward_subsumption_resolution,[],[f6656,f392]) ).
fof(f6660,plain,
( ~ spl0_5
| ~ spl0_9
| ~ spl0_35 ),
inference(avatar_contradiction_clause,[],[f6659]) ).
cnf(s4,plain,
( spl0_1
| spl0_5 ),
inference(sat_conversion,[],[f275]) ).
cnf(s13,plain,
( spl0_1
| spl0_9 ),
inference(sat_conversion,[],[f300]) ).
cnf(s16,plain,
spl0_10,
inference(sat_conversion,[],[f321]) ).
cnf(s43,plain,
( ~ spl0_10
| ~ spl0_34
| spl0_35
| ~ spl0_36 ),
inference(sat_conversion,[],[f664]) ).
cnf(s49,plain,
spl0_36,
inference(sat_conversion,[],[f710]) ).
cnf(s55,plain,
( spl0_34
| ~ spl0_36 ),
inference(sat_conversion,[],[f791]) ).
cnf(s81,plain,
( spl0_27
| ~ spl0_34
| ~ spl0_36 ),
inference(sat_conversion,[],[f1475]) ).
cnf(s82,plain,
( ~ spl0_1
| ~ spl0_10
| ~ spl0_27
| spl0_39 ),
inference(sat_conversion,[],[f1494]) ).
cnf(s84,plain,
( ~ spl0_27
| ~ spl0_39 ),
inference(sat_conversion,[],[f1534]) ).
cnf(s253,plain,
( ~ spl0_5
| ~ spl0_9
| ~ spl0_35 ),
inference(sat_conversion,[],[f6660]) ).
cnf(s275,plain,
spl0_34,
inference(rat,[],[s55,s49]) ).
cnf(s276,plain,
spl0_27,
inference(rat,[],[s81,s49,s275]) ).
cnf(s277,plain,
~ spl0_39,
inference(rat,[],[s84,s276]) ).
cnf(s282,plain,
( ~ spl0_10
| spl0_35 ),
inference(rat,[],[s43,s49,s275]) ).
cnf(s293,plain,
~ spl0_1,
inference(rat,[],[s82,s277,s276,s16]) ).
cnf(s297,plain,
spl0_35,
inference(rat,[],[s282,s16]) ).
cnf(s315,plain,
spl0_9,
inference(rat,[],[s13,s293]) ).
cnf(s316,plain,
~ spl0_5,
inference(rat,[],[s253,s297,s315]) ).
cnf(s325,plain,
$false,
inference(rat,[],[s4,s316,s293]) ).
fof(f6665,plain,
$false,
inference(avatar_sat_refutation,[],[s325]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC165-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.37 % Computer : n026.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Mon Sep 28 08:17:57 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.41 Running first-order theorem proving
% 0.11/0.41 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
% 4.32/1.58 % (3689536)Input is clausal, will run a generic CNF schedule.
% 4.32/1.58 % (3689545)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=2836358337:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 4.32/1.58 % (3689543)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=1275292490:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 4.32/1.58 % (3689544)lrs+10_1_sil=8000:sp=occurrence:random_seed=788120987:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 4.32/1.58 % (3689541)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=1992703067:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 4.32/1.58 % (3689542)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=2350730113:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 4.32/1.58 % (3689547)dis-21_1_sil=8000:lcm=predicate:random_seed=1051366736:st=5:avsq=on:i=117:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/117Mi)
% 4.32/1.58 % (3689546)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=179211686:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 4.32/1.58 % (3689545)Instruction limit reached!
% 4.32/1.58 % (3689545)------------------------------
% 4.32/1.58 % (3689545)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.32/1.58 % (3689545)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.32/1.58 % (3689545)CaDiCaL version: 2.1.3
% 4.32/1.58 % (3689545)Termination reason: Instruction limit
% 4.32/1.58 % (3689545)Termination phase: Saturation
% 4.32/1.58 % (3689545)Time elapsed: 0.039 s
% 4.32/1.58 % (3689545)Peak memory usage: 89 MB
% 4.32/1.58 % (3689545)Instructions burned: 115 (million)
% 4.32/1.58 % (3689544)Instruction limit reached!
% 4.32/1.58 % (3689544)------------------------------
% 4.32/1.58 % (3689544)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.32/1.58 % (3689544)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.32/1.58 % (3689544)CaDiCaL version: 2.1.3
% 4.32/1.58 % (3689544)Termination reason: Instruction limit
% 4.32/1.58 % (3689544)Termination phase: Saturation
% 4.32/1.58 % (3689544)Time elapsed: 0.063 s
% 4.32/1.58 % (3689544)Peak memory usage: 90 MB
% 4.32/1.58 % (3689544)Instructions burned: 107 (million)
% 4.32/1.58 % (3689547)Instruction limit reached!
% 4.32/1.58 % (3689547)------------------------------
% 4.32/1.58 % (3689547)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.32/1.58 % (3689547)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.32/1.58 % (3689547)CaDiCaL version: 2.1.3
% 4.32/1.58 % (3689547)Termination reason: Instruction limit
% 4.32/1.58 % (3689547)Termination phase: Saturation
% 4.32/1.58 % (3689547)Time elapsed: 0.068 s
% 4.32/1.58 % (3689547)Peak memory usage: 90 MB
% 4.32/1.58 % (3689547)Instructions burned: 118 (million)
% 4.32/1.58 % (3689546)Instruction limit reached!
% 4.32/1.58 % (3689546)------------------------------
% 4.32/1.58 % (3689546)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.32/1.58 % (3689546)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.32/1.58 % (3689546)CaDiCaL version: 2.1.3
% 4.32/1.58 % (3689546)Termination reason: Instruction limit
% 4.32/1.58 % (3689546)Termination phase: Saturation
% 4.32/1.58 % (3689546)Time elapsed: 0.077 s
% 4.32/1.58 % (3689546)Peak memory usage: 90 MB
% 4.32/1.58 % (3689546)Instructions burned: 181 (million)
% 4.32/1.58 % (3689555)dis+1010_3_sil=8000:plsq=on:drc=off:fde=none:plsqc=1:bsd=on:plsqr=7,2:sos=on:spb=goal_then_units:random_seed=611413163:i=143:sd=2:aac=none:ss=axioms:sgt=16_2998 on theBenchmark for (2998ds/143Mi)
% 4.32/1.58 % (3689558)lrs+10_64_to=lpo:sil=8000:random_seed=1848987976:i=126:bd=preordered_2997 on theBenchmark for (2997ds/126Mi)
% 4.32/1.58 % (3689557)lrs-1002_1_to=lpo:sil=8000:fde=none:sos=on:random_seed=314802125:st=4:i=219:sd=3:ss=axioms_2997 on theBenchmark for (2997ds/219Mi)
% 4.32/1.58 % (3689556)ott-1010_1_to=lpo:sil=16000:sos=on:spb=units:urr=on:bce=on:br=off:random_seed=2618945533:st=3:avsq=on:s2a=on:i=189:s2at=1.2:avsqr=1,16:sd=2:bd=all:nm=64:ss=axioms:sgt=30_2997 on theBenchmark for (2997ds/189Mi)
% 4.32/1.58 % (3689558)Instruction limit reached!
% 4.32/1.58 % (3689558)------------------------------
% 4.32/1.58 % (3689558)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.32/1.58 % (3689558)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.32/1.58 % (3689558)CaDiCaL version: 2.1.3
% 4.32/1.58 % (3689558)Termination reason: Instruction limit
% 4.32/1.58 % (3689558)Termination phase: Saturation
% 4.32/1.58 % (3689558)Time elapsed: 0.036 s
% 4.32/1.58 % (3689558)Peak memory usage: 90 MB
% 4.32/1.58 % (3689558)Instructions burned: 127 (million)
% 4.32/1.58 % (3689555)Instruction limit reached!
% 4.32/1.58 % (3689555)------------------------------
% 4.32/1.58 % (3689555)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.32/1.58 % (3689555)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.32/1.58 % (3689555)CaDiCaL version: 2.1.3
% 4.32/1.58 % (3689555)Termination reason: Instruction limit
% 4.32/1.58 % (3689555)Termination phase: Saturation
% 4.32/1.58 % (3689555)Time elapsed: 0.097 s
% 4.32/1.58 % (3689555)Peak memory usage: 90 MB
% 4.32/1.58 % (3689555)Instructions burned: 143 (million)
% 4.32/1.58 % (3689563)lrs+1011_16_to=lpo:sil=8000:drc=off:sp=reverse_frequency:spb=goal_then_units:random_seed=2225939821:avsq=on:i=194:fgj=on:bd=preordered_2996 on theBenchmark for (2996ds/194Mi)
% 4.32/1.58 % (3689556)Instruction limit reached!
% 4.32/1.58 % (3689556)------------------------------
% 4.32/1.58 % (3689556)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.32/1.58 % (3689556)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.32/1.58 % (3689556)CaDiCaL version: 2.1.3
% 4.32/1.58 % (3689556)Termination reason: Instruction limit
% 4.32/1.58 % (3689556)Termination phase: Saturation
% 4.32/1.58 % (3689556)Time elapsed: 0.100 s
% 4.32/1.58 % (3689556)Peak memory usage: 92 MB
% 4.32/1.58 % (3689556)Instructions burned: 190 (million)
% 4.32/1.58 % (3689557)First to succeed.
% 4.32/1.58 % (3689557)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3689536"
% 4.32/1.58 % (3689563)Instruction limit reached!
% 4.32/1.58 % (3689563)------------------------------
% 4.32/1.58 % (3689563)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.32/1.58 % (3689563)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.32/1.58 % (3689563)CaDiCaL version: 2.1.3
% 4.32/1.58 % (3689563)Termination reason: Instruction limit
% 4.32/1.58 % (3689563)Termination phase: Saturation
% 4.32/1.58 % (3689563)Time elapsed: 0.062 s
% 4.32/1.58 % (3689563)Peak memory usage: 90 MB
% 4.32/1.58 % (3689563)Instructions burned: 194 (million)
% 4.32/1.58 % (3689564)lrs+10_1_sil=8000:tgt=full:acc=on:random_seed=4048520434:i=157:gtg=all_2996 on theBenchmark for (2996ds/157Mi)
% 4.32/1.58 % (3689566)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=128000:npcc=on:random_seed=3303427574:i=3394:sd=4:ss=included:sgt=64_2995 on theBenchmark for (2995ds/3394Mi)
% 4.32/1.58 % (3689567)lrs+1011_5_to=lpo:sil=8000:tgt=full:plsq=on:prc=on:drc=off:plsqr=31,4:sp=occurrence:urr=on:nwc=0.8:s2agt=16:br=off:random_seed=1427114247:cts=off:s2a=on:i=106:fsr=off:gsp=on:ss=axioms:sgt=16:rawr=on_2994 on theBenchmark for (2994ds/106Mi)
% 4.32/1.58 % (3689564)Instruction limit reached!
% 4.32/1.58 % (3689564)------------------------------
% 4.32/1.58 % (3689564)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.32/1.58 % (3689564)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.32/1.58 % (3689564)CaDiCaL version: 2.1.3
% 4.32/1.58 % (3689564)Termination reason: Instruction limit
% 4.32/1.58 % (3689564)Termination phase: Saturation
% 4.32/1.58 % (3689564)Time elapsed: 0.096 s
% 4.32/1.58 % (3689564)Peak memory usage: 91 MB
% 4.32/1.58 % (3689564)Instructions burned: 158 (million)
% 4.32/1.58 % (3689567)Instruction limit reached!
% 4.32/1.58 % (3689567)------------------------------
% 4.32/1.58 % (3689567)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.32/1.58 % (3689567)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.32/1.58 % (3689567)CaDiCaL version: 2.1.3
% 4.32/1.58 % (3689567)Termination reason: Instruction limit
% 4.32/1.58 % (3689567)Termination phase: Saturation
% 4.32/1.58 % (3689567)Time elapsed: 0.030 s
% 4.32/1.58 % (3689567)Peak memory usage: 90 MB
% 4.32/1.58 % (3689567)Instructions burned: 108 (million)
% 4.32/1.58 % (3689572)lrs+1011_20_sil=64000:tgt=ground:plsq=on:fde=unused:plsqc=1:plsqr=14,1:plsql=on:nwc=0.6:random_seed=3825097942:st=6:i=242:gtgl=5:kws=arity_squared:av=off:gtg=exists_sym:ss=included_2993 on theBenchmark for (2993ds/242Mi)
% 4.32/1.58 % (3689557)Refutation found. Thanks to Tanya!
% 4.32/1.58 % SZS status Unsatisfiable for theBenchmark
% 4.32/1.58 % SZS output start Proof for theBenchmark
% See solution above
% 5.70/1.78 % (3689557)------------------------------
% 5.70/1.78 % (3689557)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.70/1.78 % (3689557)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.70/1.78 % (3689557)CaDiCaL version: 2.1.3
% 5.70/1.78 % (3689557)Termination reason: Refutation
% 5.70/1.78 % (3689557)Time elapsed: 0.135 s
% 5.70/1.78 % (3689557)Peak memory usage: 92 MB
% 5.70/1.78 % (3689557)Instructions burned: 211 (million)
% 5.70/1.78 % (3689557)------------------------------
% 5.70/1.78 % (3689557)------------------------------
% 5.70/1.78 % (3689536)Success in time 0.728 s
% 5.70/1.78 % Vampire exiting
%------------------------------------------------------------------------------