%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWC091+1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n018.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 01:02:24 PM UTC 2026
% Result : Theorem 4.60s 1.52s
% Output : Refutation 5.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 31
% Syntax : Number of formulae : 221 ( 36 unt; 14 def)
% Number of atoms : 764 ( 102 equ)
% Maximal formula atoms : 18 ( 3 avg)
% Number of connectives : 933 ( 390 ~; 416 |; 74 &)
% ( 22 <=>; 31 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 23 ( 21 usr; 15 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 5 con; 0-2 aty)
% Number of variables : 161 ( 0 sgn 133 !; 28 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f4,axiom,
! [X0] :
( ssList(X0)
=> ( singletonP(X0)
<=> ? [X1] :
( ssItem(X1)
& cons(X1,nil) = X0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax4) ).
fof(f5,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ( frontsegP(X0,X1)
<=> ? [X2] :
( ssList(X2)
& app(X1,X2) = X0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax5) ).
fof(f7,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ( segmentP(X0,X1)
<=> ? [X2] :
( ssList(X2)
& ? [X3] :
( ssList(X3)
& app(app(X2,X1),X3) = X0 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax7) ).
fof(f15,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ( neq(X0,X1)
<=> X0 != X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax15) ).
fof(f16,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssItem(X1)
=> ssList(cons(X1,X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax16) ).
fof(f17,axiom,
ssList(nil),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax17) ).
fof(f22,axiom,
! [X0] :
( ssList(X0)
=> ( nil != X0
=> ssItem(hd(X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax22) ).
fof(f24,axiom,
! [X0] :
( ssList(X0)
=> ( nil != X0
=> ssList(tl(X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax24) ).
fof(f26,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ssList(app(X0,X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax26) ).
fof(f28,axiom,
! [X0] :
( ssList(X0)
=> app(nil,X0) = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax28) ).
fof(f39,axiom,
~ singletonP(nil),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax39) ).
fof(f55,axiom,
! [X0] :
( ssList(X0)
=> segmentP(X0,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax55) ).
fof(f57,axiom,
! [X0] :
( ssList(X0)
=> segmentP(X0,nil) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax57) ).
fof(f65,axiom,
! [X0] :
( ssItem(X0)
=> totalorderedP(cons(X0,nil)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax65) ).
fof(f78,axiom,
! [X0] :
( ssList(X0)
=> ( nil != X0
=> cons(hd(X0),tl(X0)) = X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax78) ).
fof(f81,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssItem(X1)
=> cons(X1,X0) = app(cons(X1,nil),X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax81) ).
fof(f96,conjecture,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( X1 != X3
| X0 != X2
| ~ neq(X1,nil)
| ~ frontsegP(X3,X2)
| ~ totalorderedP(X2)
| ? [X4] :
( ssList(X4)
& neq(X4,nil)
& segmentP(X1,X4)
& segmentP(X0,X4) )
| ? [X5] :
( ssList(X5)
& neq(X2,X5)
& frontsegP(X3,X5)
& segmentP(X5,X2)
& totalorderedP(X5) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1) ).
fof(f97,negated_conjecture,
~ ! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( X1 != X3
| X0 != X2
| ~ neq(X1,nil)
| ~ frontsegP(X3,X2)
| ~ totalorderedP(X2)
| ? [X4] :
( ssList(X4)
& neq(X4,nil)
& segmentP(X1,X4)
& segmentP(X0,X4) )
| ? [X5] :
( ssList(X5)
& neq(X2,X5)
& frontsegP(X3,X5)
& segmentP(X5,X2)
& totalorderedP(X5) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f96]) ).
fof(f100,plain,
! [X0] :
( ( singletonP(X0)
<=> ? [X1] :
( ssItem(X1)
& cons(X1,nil) = X0 ) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f4]) ).
fof(f101,plain,
! [X0] :
( ! [X1] :
( ( frontsegP(X0,X1)
<=> ? [X2] :
( ssList(X2)
& app(X1,X2) = X0 ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f5]) ).
fof(f103,plain,
! [X0] :
( ! [X1] :
( ( segmentP(X0,X1)
<=> ? [X2] :
( ssList(X2)
& ? [X3] :
( ssList(X3)
& app(app(X2,X1),X3) = X0 ) ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f7]) ).
fof(f118,plain,
! [X0] :
( ! [X1] :
( ( neq(X0,X1)
<=> X0 != X1 )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f15]) ).
fof(f119,plain,
! [X0] :
( ! [X1] :
( ssList(cons(X1,X0))
| ~ ssItem(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f16]) ).
fof(f126,plain,
! [X0] :
( ssItem(hd(X0))
| nil = X0
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f22]) ).
fof(f127,plain,
! [X0] :
( ssItem(hd(X0))
| nil = X0
| ~ ssList(X0) ),
inference(flattening,[],[f126]) ).
fof(f129,plain,
! [X0] :
( ssList(tl(X0))
| nil = X0
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f24]) ).
fof(f130,plain,
! [X0] :
( ssList(tl(X0))
| nil = X0
| ~ ssList(X0) ),
inference(flattening,[],[f129]) ).
fof(f132,plain,
! [X0] :
( ! [X1] :
( ssList(app(X0,X1))
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f26]) ).
fof(f134,plain,
! [X0] :
( app(nil,X0) = X0
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f28]) ).
fof(f172,plain,
! [X0] :
( segmentP(X0,X0)
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f55]) ).
fof(f175,plain,
! [X0] :
( segmentP(X0,nil)
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f57]) ).
fof(f180,plain,
! [X0] :
( totalorderedP(cons(X0,nil))
| ~ ssItem(X0) ),
inference(ennf_transformation,[],[f65]) ).
fof(f192,plain,
! [X0] :
( cons(hd(X0),tl(X0)) = X0
| nil = X0
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f78]) ).
fof(f193,plain,
! [X0] :
( cons(hd(X0),tl(X0)) = X0
| nil = X0
| ~ ssList(X0) ),
inference(flattening,[],[f192]) ).
fof(f198,plain,
! [X0] :
( ! [X1] :
( cons(X1,X0) = app(cons(X1,nil),X0)
| ~ ssItem(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f81]) ).
fof(f221,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( X1 = X3
& X0 = X2
& neq(X1,nil)
& frontsegP(X3,X2)
& totalorderedP(X2)
& ! [X4] :
( ~ ssList(X4)
| ~ neq(X4,nil)
| ~ segmentP(X1,X4)
| ~ segmentP(X0,X4) )
& ! [X5] :
( ~ ssList(X5)
| ~ neq(X2,X5)
| ~ frontsegP(X3,X5)
| ~ segmentP(X5,X2)
| ~ totalorderedP(X5) )
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) ),
inference(ennf_transformation,[],[f97]) ).
fof(f222,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( X1 = X3
& X0 = X2
& neq(X1,nil)
& frontsegP(X3,X2)
& totalorderedP(X2)
& ! [X4] :
( ~ ssList(X4)
| ~ neq(X4,nil)
| ~ segmentP(X1,X4)
| ~ segmentP(X0,X4) )
& ! [X5] :
( ~ ssList(X5)
| ~ neq(X2,X5)
| ~ frontsegP(X3,X5)
| ~ segmentP(X5,X2)
| ~ totalorderedP(X5) )
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) ),
inference(flattening,[],[f221]) ).
fof(f237,plain,
! [X0] :
( ( ( singletonP(X0)
| ! [X1] :
( ~ ssItem(X1)
| cons(X1,nil) != X0 ) )
& ( ? [X1] :
( ssItem(X1)
& cons(X1,nil) = X0 )
| ~ singletonP(X0) ) )
| ~ ssList(X0) ),
inference(nnf_transformation,[],[f100]) ).
fof(f238,plain,
! [X0] :
( ( ( singletonP(X0)
| ! [X1] :
( ~ ssItem(X1)
| cons(X1,nil) != X0 ) )
& ( ? [X2] :
( ssItem(X2)
& cons(X2,nil) = X0 )
| ~ singletonP(X0) ) )
| ~ ssList(X0) ),
inference(rectify,[],[f237]) ).
fof(f239,plain,
! [X0] :
( ( ( singletonP(X0)
| ! [X1] :
( ~ ssItem(X1)
| cons(X1,nil) != X0 ) )
& ( ( ssItem(sK10(X0))
& cons(sK10(X0),nil) = X0 )
| ~ singletonP(X0) ) )
| ~ ssList(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10]),skolemize(X2,sK10(X0))],[f238]) ).
fof(f240,plain,
! [X0] :
( ! [X1] :
( ( ( frontsegP(X0,X1)
| ! [X2] :
( ~ ssList(X2)
| app(X1,X2) != X0 ) )
& ( ? [X2] :
( ssList(X2)
& app(X1,X2) = X0 )
| ~ frontsegP(X0,X1) ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(nnf_transformation,[],[f101]) ).
fof(f241,plain,
! [X0] :
( ! [X1] :
( ( ( frontsegP(X0,X1)
| ! [X2] :
( ~ ssList(X2)
| app(X1,X2) != X0 ) )
& ( ? [X3] :
( ssList(X3)
& app(X1,X3) = X0 )
| ~ frontsegP(X0,X1) ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(rectify,[],[f240]) ).
fof(f242,plain,
! [X0] :
( ! [X1] :
( ( ( frontsegP(X0,X1)
| ! [X2] :
( ~ ssList(X2)
| app(X1,X2) != X0 ) )
& ( ( ssList(sK11(X0,X1))
& app(X1,sK11(X0,X1)) = X0 )
| ~ frontsegP(X0,X1) ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11]),skolemize(X3,sK11(X0,X1))],[f241]) ).
fof(f246,plain,
! [X0] :
( ! [X1] :
( ( ( segmentP(X0,X1)
| ! [X2] :
( ~ ssList(X2)
| ! [X3] :
( ~ ssList(X3)
| app(app(X2,X1),X3) != X0 ) ) )
& ( ? [X2] :
( ssList(X2)
& ? [X3] :
( ssList(X3)
& app(app(X2,X1),X3) = X0 ) )
| ~ segmentP(X0,X1) ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(nnf_transformation,[],[f103]) ).
fof(f247,plain,
! [X0] :
( ! [X1] :
( ( ( segmentP(X0,X1)
| ! [X2] :
( ~ ssList(X2)
| ! [X3] :
( ~ ssList(X3)
| app(app(X2,X1),X3) != X0 ) ) )
& ( ? [X4] :
( ssList(X4)
& ? [X5] :
( ssList(X5)
& app(app(X4,X1),X5) = X0 ) )
| ~ segmentP(X0,X1) ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(rectify,[],[f246]) ).
fof(f248,plain,
! [X0] :
( ! [X1] :
( ( ( segmentP(X0,X1)
| ! [X2] :
( ~ ssList(X2)
| ! [X3] :
( ~ ssList(X3)
| app(app(X2,X1),X3) != X0 ) ) )
& ( ( ssList(sK13(X0,X1))
& ssList(sK14(X0,X1))
& app(app(sK13(X0,X1),X1),sK14(X0,X1)) = X0 )
| ~ segmentP(X0,X1) ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK13,sK14]),skolemize(X4,sK13(X0,X1)),skolemize(X5,sK14(X0,X1))],[f247]) ).
fof(f273,plain,
! [X0] :
( ! [X1] :
( ( ( neq(X0,X1)
| X0 = X1 )
& ( X0 != X1
| ~ neq(X0,X1) ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(nnf_transformation,[],[f118]) ).
fof(f296,plain,
( sK54 = sK56
& sK53 = sK55
& neq(sK54,nil)
& frontsegP(sK56,sK55)
& totalorderedP(sK55)
& ! [X4] :
( ~ ssList(X4)
| ~ neq(X4,nil)
| ~ segmentP(sK54,X4)
| ~ segmentP(sK53,X4) )
& ! [X5] :
( ~ ssList(X5)
| ~ neq(sK55,X5)
| ~ frontsegP(sK56,X5)
| ~ segmentP(X5,sK55)
| ~ totalorderedP(X5) )
& ssList(sK56)
& ssList(sK55)
& ssList(sK54)
& ssList(sK53) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK53,sK54,sK55,sK56]),skolemize(X0,sK53),skolemize(X1,sK54),skolemize(X2,sK55),skolemize(X3,sK56)],[f222]) ).
fof(f308,plain,
! [X0,X1] :
( singletonP(X0)
| ~ ssItem(X1)
| cons(X1,nil) != X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f239]) ).
fof(f309,plain,
! [X0,X1] :
( ~ frontsegP(X0,X1)
| app(X1,sK11(X0,X1)) = X0
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f242]) ).
fof(f310,plain,
! [X0,X1] :
( ssList(sK11(X0,X1))
| ~ frontsegP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f242]) ).
fof(f311,plain,
! [X2,X0,X1] :
( frontsegP(X0,X1)
| ~ ssList(X2)
| app(X1,X2) != X0
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f242]) ).
fof(f318,plain,
! [X2,X3,X0,X1] :
( segmentP(X0,X1)
| ~ ssList(X2)
| ~ ssList(X3)
| app(app(X2,X1),X3) != X0
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f248]) ).
fof(f387,plain,
! [X0,X1] :
( neq(X0,X1)
| X0 = X1
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f273]) ).
fof(f388,plain,
! [X0,X1] :
( ssList(cons(X1,X0))
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f119]) ).
fof(f389,plain,
ssList(nil),
inference(cnf_transformation,[],[f17]) ).
fof(f397,plain,
! [X0] :
( ssItem(hd(X0))
| nil = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f127]) ).
fof(f399,plain,
! [X0] :
( ssList(tl(X0))
| nil = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f130]) ).
fof(f401,plain,
! [X0,X1] :
( ssList(app(X0,X1))
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f132]) ).
fof(f403,plain,
! [X0] :
( ~ ssList(X0)
| app(nil,X0) = X0 ),
inference(cnf_transformation,[],[f134]) ).
fof(f420,plain,
~ singletonP(nil),
inference(cnf_transformation,[],[f39]) ).
fof(f440,plain,
! [X0] :
( segmentP(X0,X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f172]) ).
fof(f442,plain,
! [X0] :
( segmentP(X0,nil)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f175]) ).
fof(f451,plain,
! [X0] :
( totalorderedP(cons(X0,nil))
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f180]) ).
fof(f474,plain,
! [X0] :
( ~ ssList(X0)
| nil = X0
| cons(hd(X0),tl(X0)) = X0 ),
inference(cnf_transformation,[],[f193]) ).
fof(f477,plain,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssItem(X1)
| cons(X1,X0) = app(cons(X1,nil),X0) ),
inference(cnf_transformation,[],[f198]) ).
fof(f496,plain,
ssList(sK53),
inference(cnf_transformation,[],[f296]) ).
fof(f497,plain,
ssList(sK54),
inference(cnf_transformation,[],[f296]) ).
fof(f500,plain,
! [X5] :
( ~ segmentP(X5,sK55)
| ~ neq(sK55,X5)
| ~ frontsegP(sK56,X5)
| ~ ssList(X5)
| ~ totalorderedP(X5) ),
inference(cnf_transformation,[],[f296]) ).
fof(f501,plain,
! [X4] :
( ~ ssList(X4)
| ~ neq(X4,nil)
| ~ segmentP(sK54,X4)
| ~ segmentP(sK53,X4) ),
inference(cnf_transformation,[],[f296]) ).
fof(f503,plain,
frontsegP(sK56,sK55),
inference(cnf_transformation,[],[f296]) ).
fof(f504,plain,
neq(sK54,nil),
inference(cnf_transformation,[],[f296]) ).
fof(f505,plain,
sK53 = sK55,
inference(cnf_transformation,[],[f296]) ).
fof(f506,plain,
sK54 = sK56,
inference(cnf_transformation,[],[f296]) ).
fof(f507,plain,
neq(sK56,nil),
inference(definition_unfolding,[],[f504,f506]) ).
fof(f508,plain,
! [X4] :
( ~ segmentP(sK56,X4)
| ~ neq(X4,nil)
| ~ ssList(X4)
| ~ segmentP(sK55,X4) ),
inference(definition_unfolding,[],[f501,f506,f505]) ).
fof(f509,plain,
ssList(sK56),
inference(definition_unfolding,[],[f497,f506]) ).
fof(f510,plain,
ssList(sK55),
inference(definition_unfolding,[],[f496,f505]) ).
fof(f513,plain,
! [X1] :
( ~ ssList(cons(X1,nil))
| ~ ssItem(X1)
| singletonP(cons(X1,nil)) ),
inference(equality_resolution,[],[f308]) ).
fof(f514,plain,
! [X2,X1] :
( frontsegP(app(X1,X2),X1)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(app(X1,X2)) ),
inference(equality_resolution,[],[f311]) ).
fof(f516,plain,
! [X2,X3,X1] :
( segmentP(app(app(X2,X1),X3),X1)
| ~ ssList(X2)
| ~ ssList(X3)
| ~ ssList(X1)
| ~ ssList(app(app(X2,X1),X3)) ),
inference(equality_resolution,[],[f318]) ).
fof(f546,definition,
( spl57_1
<=> ssList(nil) ),
introduced(definition,[new_symbols(definition,[spl57_1])],[avatar_definition]) ).
fof(f547,plain,
( ssList(nil)
| ~ spl57_1 ),
inference(avatar_component_clause,[],[f546]) ).
fof(f555,definition,
( spl57_3
<=> ! [X0] :
( totalorderedP(cons(X0,nil))
| ~ ssItem(X0) ) ),
introduced(definition,[new_symbols(definition,[spl57_3])],[avatar_definition]) ).
fof(f556,plain,
( ! [X0] :
( totalorderedP(cons(X0,nil))
| ~ ssItem(X0) )
| ~ spl57_3 ),
inference(avatar_component_clause,[],[f555]) ).
fof(f558,plain,
spl57_3,
inference(avatar_split_clause,[],[f451,f555]) ).
fof(f574,plain,
spl57_1,
inference(avatar_split_clause,[],[f389,f546]) ).
fof(f576,plain,
! [X2,X1] :
( frontsegP(app(X1,X2),X1)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(forward_subsumption_resolution,[],[f514,f401]) ).
fof(f577,plain,
( sK56 = app(sK55,sK11(sK56,sK55))
| ~ ssList(sK55)
| ~ ssList(sK56) ),
inference(resolution,[],[f309,f503]) ).
fof(f578,plain,
( sK56 = app(sK55,sK11(sK56,sK55))
| ~ ssList(sK56) ),
inference(forward_subsumption_resolution,[],[f577,f510]) ).
fof(f579,plain,
sK56 = app(sK55,sK11(sK56,sK55)),
inference(forward_subsumption_resolution,[],[f578,f509]) ).
fof(f592,definition,
( spl57_7
<=> ssList(sK11(sK56,sK55)) ),
introduced(definition,[new_symbols(definition,[spl57_7])],[avatar_definition]) ).
fof(f593,plain,
( ssList(sK11(sK56,sK55))
| ~ spl57_7 ),
inference(avatar_component_clause,[],[f592]) ).
fof(f594,plain,
( ~ ssList(sK11(sK56,sK55))
| spl57_7 ),
inference(avatar_component_clause,[],[f592]) ).
fof(f599,plain,
( ~ frontsegP(sK56,sK55)
| ~ ssList(sK55)
| ~ ssList(sK56)
| spl57_7 ),
inference(resolution,[],[f310,f594]) ).
fof(f600,plain,
( ~ ssList(sK55)
| ~ ssList(sK56)
| spl57_7 ),
inference(forward_subsumption_resolution,[],[f599,f503]) ).
fof(f601,plain,
( ~ ssList(sK56)
| spl57_7 ),
inference(forward_subsumption_resolution,[],[f600,f510]) ).
fof(f602,plain,
( $false
| spl57_7 ),
inference(forward_subsumption_resolution,[],[f601,f509]) ).
fof(f603,plain,
spl57_7,
inference(avatar_contradiction_clause,[],[f602]) ).
fof(f608,plain,
sK55 = app(nil,sK55),
inference(resolution,[],[f403,f510]) ).
fof(f610,plain,
! [X0] :
( segmentP(app(sK55,X0),sK55)
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssList(sK55)
| ~ ssList(app(sK55,X0)) ),
inference(superposition,[],[f516,f608]) ).
fof(f611,plain,
( ! [X0] :
( segmentP(app(sK55,X0),sK55)
| ~ ssList(X0)
| ~ ssList(sK55)
| ~ ssList(app(sK55,X0)) )
| ~ spl57_1 ),
inference(forward_subsumption_resolution,[],[f610,f547]) ).
fof(f612,plain,
( ! [X0] :
( segmentP(app(sK55,X0),sK55)
| ~ ssList(X0)
| ~ ssList(app(sK55,X0)) )
| ~ spl57_1 ),
inference(forward_subsumption_resolution,[],[f611,f510]) ).
fof(f614,plain,
( segmentP(sK56,sK55)
| ~ ssList(sK11(sK56,sK55))
| ~ ssList(sK56)
| ~ spl57_1 ),
inference(superposition,[],[f612,f579]) ).
fof(f616,plain,
( segmentP(sK56,sK55)
| ~ ssList(sK56)
| ~ spl57_1
| ~ spl57_7 ),
inference(forward_subsumption_resolution,[],[f614,f593]) ).
fof(f617,plain,
( segmentP(sK56,sK55)
| ~ spl57_1
| ~ spl57_7 ),
inference(forward_subsumption_resolution,[],[f616,f509]) ).
fof(f618,plain,
( ~ neq(sK55,nil)
| ~ ssList(sK55)
| ~ segmentP(sK55,sK55)
| ~ spl57_1
| ~ spl57_7 ),
inference(resolution,[],[f617,f508]) ).
fof(f621,plain,
( ~ neq(sK55,nil)
| ~ segmentP(sK55,sK55)
| ~ spl57_1
| ~ spl57_7 ),
inference(forward_subsumption_resolution,[],[f618,f510]) ).
fof(f624,definition,
( spl57_9
<=> segmentP(sK55,sK55) ),
introduced(definition,[new_symbols(definition,[spl57_9])],[avatar_definition]) ).
fof(f626,plain,
( ~ segmentP(sK55,sK55)
| spl57_9 ),
inference(avatar_component_clause,[],[f624]) ).
fof(f628,definition,
( spl57_10
<=> neq(sK55,nil) ),
introduced(definition,[new_symbols(definition,[spl57_10])],[avatar_definition]) ).
fof(f630,plain,
( ~ neq(sK55,nil)
| spl57_10 ),
inference(avatar_component_clause,[],[f628]) ).
fof(f631,plain,
( ~ spl57_9
| ~ spl57_10
| ~ spl57_1
| ~ spl57_7 ),
inference(avatar_split_clause,[],[f621,f592,f546,f628,f624]) ).
fof(f641,plain,
( ~ ssList(sK55)
| spl57_9 ),
inference(resolution,[],[f626,f440]) ).
fof(f642,plain,
( $false
| spl57_9 ),
inference(forward_subsumption_resolution,[],[f641,f510]) ).
fof(f643,plain,
spl57_9,
inference(avatar_contradiction_clause,[],[f642]) ).
fof(f645,plain,
( nil = sK55
| ~ ssList(nil)
| ~ ssList(sK55)
| spl57_10 ),
inference(resolution,[],[f630,f387]) ).
fof(f646,plain,
( nil = sK55
| ~ ssList(sK55)
| ~ spl57_1
| spl57_10 ),
inference(forward_subsumption_resolution,[],[f645,f547]) ).
fof(f647,plain,
( nil = sK55
| ~ spl57_1
| spl57_10 ),
inference(forward_subsumption_resolution,[],[f646,f510]) ).
fof(f648,plain,
( ! [X0] :
( ~ segmentP(X0,nil)
| ~ neq(nil,X0)
| ~ frontsegP(sK56,X0)
| ~ ssList(X0)
| ~ totalorderedP(X0) )
| ~ spl57_1
| spl57_10 ),
inference(superposition,[],[f500,f647]) ).
fof(f652,plain,
( sK56 = app(nil,sK11(sK56,nil))
| ~ spl57_1
| spl57_10 ),
inference(superposition,[],[f579,f647]) ).
fof(f658,plain,
( ~ neq(nil,nil)
| ~ spl57_1
| spl57_10 ),
inference(superposition,[],[f630,f647]) ).
fof(f659,plain,
( ! [X0] :
( ~ frontsegP(sK56,X0)
| ~ neq(nil,X0)
| ~ ssList(X0)
| ~ totalorderedP(X0) )
| ~ spl57_1
| spl57_10 ),
inference(forward_subsumption_resolution,[],[f648,f442]) ).
fof(f682,plain,
( sK11(sK56,sK55) = app(nil,sK11(sK56,sK55))
| ~ spl57_7 ),
inference(resolution,[],[f593,f403]) ).
fof(f684,plain,
( sK11(sK56,nil) = app(nil,sK11(sK56,nil))
| ~ spl57_1
| ~ spl57_7
| spl57_10 ),
inference(forward_demodulation,[],[f682,f647]) ).
fof(f686,plain,
( sK56 = sK11(sK56,nil)
| ~ spl57_1
| ~ spl57_7
| spl57_10 ),
inference(forward_demodulation,[],[f684,f652]) ).
fof(f788,plain,
( nil = sK11(sK56,sK55)
| sK11(sK56,sK55) = cons(hd(sK11(sK56,sK55)),tl(sK11(sK56,sK55)))
| ~ spl57_7 ),
inference(resolution,[],[f474,f593]) ).
fof(f792,definition,
( spl57_13
<=> sK56 = cons(hd(sK56),tl(sK56)) ),
introduced(definition,[new_symbols(definition,[spl57_13])],[avatar_definition]) ).
fof(f794,plain,
( sK56 = cons(hd(sK56),tl(sK56))
| ~ spl57_13 ),
inference(avatar_component_clause,[],[f792]) ).
fof(f796,definition,
( spl57_14
<=> nil = sK56 ),
introduced(definition,[new_symbols(definition,[spl57_14])],[avatar_definition]) ).
fof(f797,plain,
( nil != sK56
| spl57_14 ),
inference(avatar_component_clause,[],[f796]) ).
fof(f798,plain,
( nil = sK56
| ~ spl57_14 ),
inference(avatar_component_clause,[],[f796]) ).
fof(f800,plain,
( nil = sK11(sK56,nil)
| sK11(sK56,sK55) = cons(hd(sK11(sK56,sK55)),tl(sK11(sK56,sK55)))
| ~ spl57_1
| ~ spl57_7
| spl57_10 ),
inference(forward_demodulation,[],[f788,f647]) ).
fof(f802,plain,
( nil = sK56
| sK11(sK56,sK55) = cons(hd(sK11(sK56,sK55)),tl(sK11(sK56,sK55)))
| ~ spl57_1
| ~ spl57_7
| spl57_10 ),
inference(forward_demodulation,[],[f800,f686]) ).
fof(f803,plain,
( sK11(sK56,nil) = cons(hd(sK11(sK56,nil)),tl(sK11(sK56,nil)))
| nil = sK56
| ~ spl57_1
| ~ spl57_7
| spl57_10 ),
inference(forward_demodulation,[],[f802,f647]) ).
fof(f804,plain,
( sK56 = cons(hd(sK56),tl(sK56))
| nil = sK56
| ~ spl57_1
| ~ spl57_7
| spl57_10 ),
inference(forward_demodulation,[],[f803,f686]) ).
fof(f805,plain,
( spl57_14
| spl57_13
| ~ spl57_1
| ~ spl57_7
| spl57_10 ),
inference(avatar_split_clause,[],[f804,f628,f592,f546,f792,f796]) ).
fof(f807,plain,
( neq(nil,nil)
| ~ spl57_14 ),
inference(superposition,[],[f507,f798]) ).
fof(f837,plain,
( $false
| ~ spl57_1
| spl57_10
| ~ spl57_14 ),
inference(forward_subsumption_resolution,[],[f807,f658]) ).
fof(f838,plain,
( ~ spl57_1
| spl57_10
| ~ spl57_14 ),
inference(avatar_contradiction_clause,[],[f837]) ).
fof(f848,definition,
( spl57_15
<=> ssList(tl(sK56)) ),
introduced(definition,[new_symbols(definition,[spl57_15])],[avatar_definition]) ).
fof(f849,plain,
( ssList(tl(sK56))
| ~ spl57_15 ),
inference(avatar_component_clause,[],[f848]) ).
fof(f850,plain,
( ~ ssList(tl(sK56))
| spl57_15 ),
inference(avatar_component_clause,[],[f848]) ).
fof(f852,definition,
( spl57_16
<=> ssItem(hd(sK56)) ),
introduced(definition,[new_symbols(definition,[spl57_16])],[avatar_definition]) ).
fof(f853,plain,
( ssItem(hd(sK56))
| ~ spl57_16 ),
inference(avatar_component_clause,[],[f852]) ).
fof(f854,plain,
( ~ ssItem(hd(sK56))
| spl57_16 ),
inference(avatar_component_clause,[],[f852]) ).
fof(f868,plain,
( nil = sK56
| ~ ssList(sK56)
| spl57_15 ),
inference(resolution,[],[f850,f399]) ).
fof(f869,plain,
( ~ ssList(sK56)
| spl57_14
| spl57_15 ),
inference(forward_subsumption_resolution,[],[f868,f797]) ).
fof(f870,plain,
( $false
| spl57_14
| spl57_15 ),
inference(forward_subsumption_resolution,[],[f869,f509]) ).
fof(f871,plain,
( spl57_14
| spl57_15 ),
inference(avatar_contradiction_clause,[],[f870]) ).
fof(f872,plain,
( nil = sK56
| ~ ssList(sK56)
| spl57_16 ),
inference(resolution,[],[f854,f397]) ).
fof(f873,plain,
( ~ ssList(sK56)
| spl57_14
| spl57_16 ),
inference(forward_subsumption_resolution,[],[f872,f797]) ).
fof(f874,plain,
( $false
| spl57_14
| spl57_16 ),
inference(forward_subsumption_resolution,[],[f873,f509]) ).
fof(f875,plain,
( spl57_14
| spl57_16 ),
inference(avatar_contradiction_clause,[],[f874]) ).
fof(f877,plain,
( ! [X0] :
( ~ ssItem(X0)
| cons(X0,tl(sK56)) = app(cons(X0,nil),tl(sK56)) )
| ~ spl57_15 ),
inference(resolution,[],[f849,f477]) ).
fof(f894,plain,
( cons(hd(sK56),tl(sK56)) = app(cons(hd(sK56),nil),tl(sK56))
| ~ spl57_15
| ~ spl57_16 ),
inference(resolution,[],[f877,f853]) ).
fof(f932,plain,
( sK56 = app(cons(hd(sK56),nil),tl(sK56))
| ~ spl57_13
| ~ spl57_15
| ~ spl57_16 ),
inference(forward_demodulation,[],[f894,f794]) ).
fof(f934,plain,
( frontsegP(sK56,cons(hd(sK56),nil))
| ~ ssList(tl(sK56))
| ~ ssList(cons(hd(sK56),nil))
| ~ spl57_13
| ~ spl57_15
| ~ spl57_16 ),
inference(superposition,[],[f576,f932]) ).
fof(f938,plain,
( frontsegP(sK56,cons(hd(sK56),nil))
| ~ ssList(cons(hd(sK56),nil))
| ~ spl57_13
| ~ spl57_15
| ~ spl57_16 ),
inference(forward_subsumption_resolution,[],[f934,f849]) ).
fof(f941,definition,
( spl57_22
<=> ssList(cons(hd(sK56),nil)) ),
introduced(definition,[new_symbols(definition,[spl57_22])],[avatar_definition]) ).
fof(f942,plain,
( ssList(cons(hd(sK56),nil))
| ~ spl57_22 ),
inference(avatar_component_clause,[],[f941]) ).
fof(f943,plain,
( ~ ssList(cons(hd(sK56),nil))
| spl57_22 ),
inference(avatar_component_clause,[],[f941]) ).
fof(f949,definition,
( spl57_24
<=> frontsegP(sK56,cons(hd(sK56),nil)) ),
introduced(definition,[new_symbols(definition,[spl57_24])],[avatar_definition]) ).
fof(f951,plain,
( frontsegP(sK56,cons(hd(sK56),nil))
| ~ spl57_24 ),
inference(avatar_component_clause,[],[f949]) ).
fof(f952,plain,
( ~ spl57_22
| spl57_24
| ~ spl57_13
| ~ spl57_15
| ~ spl57_16 ),
inference(avatar_split_clause,[],[f938,f852,f848,f792,f949,f941]) ).
fof(f957,plain,
( ~ ssItem(hd(sK56))
| ~ ssList(nil)
| spl57_22 ),
inference(resolution,[],[f943,f388]) ).
fof(f958,plain,
( ~ ssList(nil)
| ~ spl57_16
| spl57_22 ),
inference(forward_subsumption_resolution,[],[f957,f853]) ).
fof(f959,plain,
( $false
| ~ spl57_1
| ~ spl57_16
| spl57_22 ),
inference(forward_subsumption_resolution,[],[f958,f547]) ).
fof(f960,plain,
( ~ spl57_1
| ~ spl57_16
| spl57_22 ),
inference(avatar_contradiction_clause,[],[f959]) ).
fof(f971,definition,
( spl57_27
<=> nil = cons(hd(sK56),nil) ),
introduced(definition,[new_symbols(definition,[spl57_27])],[avatar_definition]) ).
fof(f972,plain,
( nil != cons(hd(sK56),nil)
| spl57_27 ),
inference(avatar_component_clause,[],[f971]) ).
fof(f973,plain,
( nil = cons(hd(sK56),nil)
| ~ spl57_27 ),
inference(avatar_component_clause,[],[f971]) ).
fof(f975,plain,
( ~ neq(nil,cons(hd(sK56),nil))
| ~ ssList(cons(hd(sK56),nil))
| ~ totalorderedP(cons(hd(sK56),nil))
| ~ spl57_1
| spl57_10
| ~ spl57_24 ),
inference(resolution,[],[f951,f659]) ).
fof(f978,plain,
( ~ neq(nil,cons(hd(sK56),nil))
| ~ totalorderedP(cons(hd(sK56),nil))
| ~ spl57_1
| spl57_10
| ~ spl57_22
| ~ spl57_24 ),
inference(forward_subsumption_resolution,[],[f975,f942]) ).
fof(f985,plain,
( ~ ssList(nil)
| ~ ssItem(hd(sK56))
| singletonP(nil)
| ~ spl57_27 ),
inference(superposition,[],[f513,f973]) ).
fof(f998,plain,
( ~ ssItem(hd(sK56))
| singletonP(nil)
| ~ spl57_1
| ~ spl57_27 ),
inference(forward_subsumption_resolution,[],[f985,f547]) ).
fof(f1006,plain,
( singletonP(nil)
| ~ spl57_1
| ~ spl57_16
| ~ spl57_27 ),
inference(forward_subsumption_resolution,[],[f998,f853]) ).
fof(f1009,plain,
( $false
| ~ spl57_1
| ~ spl57_16
| ~ spl57_27 ),
inference(forward_subsumption_resolution,[],[f1006,f420]) ).
fof(f1010,plain,
( ~ spl57_1
| ~ spl57_16
| ~ spl57_27 ),
inference(avatar_contradiction_clause,[],[f1009]) ).
fof(f1012,definition,
( spl57_28
<=> totalorderedP(cons(hd(sK56),nil)) ),
introduced(definition,[new_symbols(definition,[spl57_28])],[avatar_definition]) ).
fof(f1014,plain,
( ~ totalorderedP(cons(hd(sK56),nil))
| spl57_28 ),
inference(avatar_component_clause,[],[f1012]) ).
fof(f1016,definition,
( spl57_29
<=> neq(nil,cons(hd(sK56),nil)) ),
introduced(definition,[new_symbols(definition,[spl57_29])],[avatar_definition]) ).
fof(f1018,plain,
( ~ neq(nil,cons(hd(sK56),nil))
| spl57_29 ),
inference(avatar_component_clause,[],[f1016]) ).
fof(f1019,plain,
( ~ spl57_28
| ~ spl57_29
| ~ spl57_1
| spl57_10
| ~ spl57_22
| ~ spl57_24 ),
inference(avatar_split_clause,[],[f978,f949,f941,f628,f546,f1016,f1012]) ).
fof(f1020,plain,
( ~ ssItem(hd(sK56))
| ~ spl57_3
| spl57_28 ),
inference(resolution,[],[f1014,f556]) ).
fof(f1021,plain,
( $false
| ~ spl57_3
| ~ spl57_16
| spl57_28 ),
inference(forward_subsumption_resolution,[],[f1020,f853]) ).
fof(f1022,plain,
( ~ spl57_3
| ~ spl57_16
| spl57_28 ),
inference(avatar_contradiction_clause,[],[f1021]) ).
fof(f1024,plain,
( nil = cons(hd(sK56),nil)
| ~ ssList(cons(hd(sK56),nil))
| ~ ssList(nil)
| spl57_29 ),
inference(resolution,[],[f1018,f387]) ).
fof(f1025,plain,
( ~ ssList(cons(hd(sK56),nil))
| ~ ssList(nil)
| spl57_27
| spl57_29 ),
inference(forward_subsumption_resolution,[],[f1024,f972]) ).
fof(f1027,plain,
( ~ ssList(nil)
| ~ spl57_22
| spl57_27
| spl57_29 ),
inference(forward_subsumption_resolution,[],[f1025,f942]) ).
fof(f1037,plain,
( $false
| ~ spl57_1
| ~ spl57_22
| spl57_27
| spl57_29 ),
inference(forward_subsumption_resolution,[],[f1027,f547]) ).
fof(f1038,plain,
( ~ spl57_1
| ~ spl57_22
| spl57_27
| spl57_29 ),
inference(avatar_contradiction_clause,[],[f1037]) ).
cnf(s4,plain,
spl57_3,
inference(sat_conversion,[],[f558]) ).
cnf(s8,plain,
spl57_1,
inference(sat_conversion,[],[f574]) ).
cnf(s10,plain,
spl57_7,
inference(sat_conversion,[],[f603]) ).
cnf(s11,plain,
( ~ spl57_1
| ~ spl57_7
| ~ spl57_9
| ~ spl57_10 ),
inference(sat_conversion,[],[f631]) ).
cnf(s13,plain,
spl57_9,
inference(sat_conversion,[],[f643]) ).
cnf(s17,plain,
( ~ spl57_1
| ~ spl57_7
| spl57_10
| spl57_13
| spl57_14 ),
inference(sat_conversion,[],[f805]) ).
cnf(s21,plain,
( ~ spl57_1
| spl57_10
| ~ spl57_14 ),
inference(sat_conversion,[],[f838]) ).
cnf(s26,plain,
( spl57_14
| spl57_15 ),
inference(sat_conversion,[],[f871]) ).
cnf(s27,plain,
( spl57_14
| spl57_16 ),
inference(sat_conversion,[],[f875]) ).
cnf(s31,plain,
( ~ spl57_13
| ~ spl57_15
| ~ spl57_16
| ~ spl57_22
| spl57_24 ),
inference(sat_conversion,[],[f952]) ).
cnf(s33,plain,
( ~ spl57_1
| ~ spl57_16
| spl57_22 ),
inference(sat_conversion,[],[f960]) ).
cnf(s38,plain,
( ~ spl57_1
| ~ spl57_16
| ~ spl57_27 ),
inference(sat_conversion,[],[f1010]) ).
cnf(s39,plain,
( ~ spl57_1
| spl57_10
| ~ spl57_22
| ~ spl57_24
| ~ spl57_28
| ~ spl57_29 ),
inference(sat_conversion,[],[f1019]) ).
cnf(s40,plain,
( ~ spl57_3
| ~ spl57_16
| spl57_28 ),
inference(sat_conversion,[],[f1022]) ).
cnf(s42,plain,
( ~ spl57_1
| ~ spl57_22
| spl57_27
| spl57_29 ),
inference(sat_conversion,[],[f1038]) ).
cnf(s43,plain,
( ~ spl57_1
| ~ spl57_7
| ~ spl57_10 ),
inference(rat,[],[s11,s13]) ).
cnf(s45,plain,
~ spl57_10,
inference(rat,[],[s43,s10,s8]) ).
cnf(s46,plain,
~ spl57_14,
inference(rat,[],[s21,s8,s45]) ).
cnf(s48,plain,
spl57_13,
inference(rat,[],[s17,s46,s8,s10,s45]) ).
cnf(s49,plain,
spl57_16,
inference(rat,[],[s27,s46]) ).
cnf(s50,plain,
spl57_15,
inference(rat,[],[s26,s46]) ).
cnf(s52,plain,
~ spl57_27,
inference(rat,[],[s38,s8,s49]) ).
cnf(s53,plain,
spl57_22,
inference(rat,[],[s33,s8,s49]) ).
cnf(s57,plain,
spl57_29,
inference(rat,[],[s42,s52,s8,s53]) ).
cnf(s60,plain,
spl57_24,
inference(rat,[],[s31,s50,s48,s49,s53]) ).
cnf(s62,plain,
~ spl57_28,
inference(rat,[],[s39,s57,s53,s45,s8,s60]) ).
cnf(s63,plain,
~ spl57_3,
inference(rat,[],[s40,s49,s62]) ).
cnf(s67,plain,
$false,
inference(rat,[],[s4,s63]) ).
fof(f1039,plain,
$false,
inference(avatar_sat_refutation,[],[s67]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC091+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.37 % Computer : n018.cluster.edu
% 0.12/0.37 % Model : x86_64 x86_64
% 0.12/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.37 % Memory : 8046.5625MB
% 0.12/0.37 % OS : Linux 6.8.0-71-generic
% 0.12/0.37 % CPULimit : 300
% 0.12/0.37 % WCLimit : 300
% 0.12/0.37 % DateTime : Mon Sep 28 07:51:09 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.41 Running first-order theorem proving
% 0.12/0.41 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.60/1.52 % (3214760)Detected formulas, will run a generic FOF schedule.
% 4.60/1.52 % (3214765)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=3186910986:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 4.60/1.52 % (3214769)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=4089425865:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 4.60/1.52 % (3214768)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1395198014:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 4.60/1.52 % (3214766)lrs+11_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:lma=off:spb=units:urr=ec_only:bce=on:s2agt=64:updr=off:random_seed=3592467397:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 4.60/1.52 % (3214767)lrs+1010_1_anc=all:sfv=off:to=kbo:ncem=casc2026/models/loop7.pt:sil=128000:npcc=on:prc=on:sos=all:bsr=unit_only:sac=on:random_seed=902039441:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 4.60/1.52 % (3214771)dis-21_1_sil=8000:lcm=predicate:random_seed=3449101815:st=5:avsq=on:i=129:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/129Mi)
% 4.60/1.52 % (3214770)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=796001282:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 4.60/1.52 % (3214768)Instruction limit reached!
% 4.60/1.52 % (3214768)------------------------------
% 4.60/1.52 % (3214768)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.60/1.52 % (3214768)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.60/1.52 % (3214768)CaDiCaL version: 2.1.3
% 4.60/1.52 % (3214768)Termination reason: Instruction limit
% 4.60/1.52 % (3214768)Termination phase: Saturation
% 4.60/1.52 % (3214768)Time elapsed: 0.069 s
% 4.60/1.52 % (3214768)Peak memory usage: 89 MB
% 4.60/1.52 % (3214768)Instructions burned: 110 (million)
% 4.60/1.52 % (3214769)Instruction limit reached!
% 4.60/1.52 % (3214769)------------------------------
% 4.60/1.52 % (3214769)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.60/1.52 % (3214769)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.60/1.52 % (3214769)CaDiCaL version: 2.1.3
% 4.60/1.52 % (3214769)Termination reason: Instruction limit
% 4.60/1.52 % (3214769)Termination phase: Saturation
% 4.60/1.52 % (3214769)Time elapsed: 0.073 s
% 4.60/1.52 % (3214769)Peak memory usage: 88 MB
% 4.60/1.52 % (3214769)Instructions burned: 120 (million)
% 4.60/1.52 % (3214771)Instruction limit reached!
% 4.60/1.52 % (3214771)------------------------------
% 4.60/1.52 % (3214771)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.60/1.52 % (3214771)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.60/1.52 % (3214771)CaDiCaL version: 2.1.3
% 4.60/1.52 % (3214771)Termination reason: Instruction limit
% 4.60/1.52 % (3214771)Termination phase: Saturation
% 4.60/1.52 % (3214771)Time elapsed: 0.075 s
% 4.60/1.52 % (3214771)Peak memory usage: 90 MB
% 4.60/1.52 % (3214771)Instructions burned: 130 (million)
% 4.60/1.52 % (3214770)Instruction limit reached!
% 4.60/1.52 % (3214770)------------------------------
% 4.60/1.52 % (3214770)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.60/1.52 % (3214770)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.60/1.52 % (3214770)CaDiCaL version: 2.1.3
% 4.60/1.52 % (3214770)Termination reason: Instruction limit
% 4.60/1.52 % (3214770)Termination phase: Saturation
% 4.60/1.52 % (3214770)Time elapsed: 0.091 s
% 4.60/1.52 % (3214770)Peak memory usage: 90 MB
% 4.60/1.52 % (3214770)Instructions burned: 139 (million)
% 4.60/1.52 % (3214779)lrs+10_1_sil=8000:sp=occurrence:random_seed=3688681336:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 4.60/1.52 % (3214781)lrs+1011_1_sil=32000:sp=occurrence:random_seed=3028349607:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 4.60/1.52 % (3214780)lrs+10_1_sil=32000:urr=on:br=off:random_seed=2051297362:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 4.60/1.52 % (3214782)dis+10_5:1_slsqr=1,4:sil=8000:fde=unused:erd=off:urr=full:fd=off:s2agt=8:br=off:slsq=on:random_seed=586859836:s2a=on:i=248:s2at=1.23:gtg=position_2997 on theBenchmark for (2997ds/248Mi)
% 4.60/1.52 % (3214780)Instruction limit reached!
% 4.60/1.52 % (3214780)------------------------------
% 4.60/1.52 % (3214780)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.60/1.52 % (3214780)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.60/1.52 % (3214780)CaDiCaL version: 2.1.3
% 4.60/1.52 % (3214780)Termination reason: Instruction limit
% 4.60/1.52 % (3214780)Termination phase: Saturation
% 4.60/1.52 % (3214780)Time elapsed: 0.074 s
% 4.60/1.52 % (3214780)Peak memory usage: 91 MB
% 4.60/1.52 % (3214780)Instructions burned: 159 (million)
% 4.60/1.52 % (3214765)First to succeed.
% 4.60/1.52 % (3214765)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3214760"
% 4.60/1.52 % (3214782)Instruction limit reached!
% 4.60/1.52 % (3214782)------------------------------
% 4.60/1.52 % (3214782)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.60/1.52 % (3214782)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.60/1.52 % (3214782)CaDiCaL version: 2.1.3
% 4.60/1.52 % (3214782)Termination reason: Instruction limit
% 4.60/1.52 % (3214782)Termination phase: Saturation
% 4.60/1.52 % (3214782)Time elapsed: 0.126 s
% 4.60/1.52 % (3214782)Peak memory usage: 93 MB
% 4.60/1.52 % (3214782)Instructions burned: 248 (million)
% 4.60/1.52 % (3214779)Instruction limit reached!
% 4.60/1.52 % (3214779)------------------------------
% 4.60/1.52 % (3214779)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.60/1.52 % (3214779)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.60/1.52 % (3214779)CaDiCaL version: 2.1.3
% 4.60/1.52 % (3214779)Termination reason: Instruction limit
% 4.60/1.52 % (3214779)Termination phase: Saturation
% 4.60/1.52 % (3214779)Time elapsed: 0.164 s
% 4.60/1.52 % (3214779)Peak memory usage: 92 MB
% 4.60/1.52 % (3214779)Instructions burned: 285 (million)
% 4.60/1.52 % (3214781)Instruction limit reached!
% 4.60/1.52 % (3214781)------------------------------
% 4.60/1.52 % (3214781)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.60/1.52 % (3214781)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.60/1.52 % (3214781)CaDiCaL version: 2.1.3
% 4.60/1.52 % (3214781)Termination reason: Instruction limit
% 4.60/1.52 % (3214781)Termination phase: Saturation
% 4.60/1.52 % (3214781)Time elapsed: 0.199 s
% 4.60/1.52 % (3214781)Peak memory usage: 94 MB
% 4.60/1.52 % (3214781)Instructions burned: 326 (million)
% 4.60/1.52 % (3214787)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=3712395000:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2995 on theBenchmark for (2995ds/294Mi)
% 4.60/1.52 % (3214765)Refutation found. Thanks to Tanya!
% 4.60/1.52 % SZS status Theorem for theBenchmark
% 4.60/1.52 % SZS output start Proof for theBenchmark
% See solution above
% 5.24/1.66 % (3214765)------------------------------
% 5.24/1.66 % (3214765)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.24/1.66 % (3214765)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.24/1.66 % (3214765)CaDiCaL version: 2.1.3
% 5.24/1.66 % (3214765)Termination reason: Refutation
% 5.24/1.66 % (3214765)Time elapsed: 0.380 s
% 5.24/1.66 % (3214765)Peak memory usage: 132 MB
% 5.24/1.66 % (3214765)Instructions burned: 1040 (million)
% 5.24/1.66 % (3214765)------------------------------
% 5.24/1.66 % (3214765)------------------------------
% 5.24/1.66 % (3214760)Success in time 0.665 s
% 5.24/1.66 % Vampire exiting
%------------------------------------------------------------------------------