%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWC123-1 : 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 : n009.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 01:02:33 PM UTC 2026
% Result : Unsatisfiable 9.31s 2.39s
% Output : Refutation 10.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 35
% Syntax : Number of formulae : 137 ( 25 unt; 10 def)
% Number of atoms : 396 ( 44 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 482 ( 223 ~; 249 |; 0 &)
% ( 10 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 19 ( 17 usr; 11 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 5 con; 0-2 aty)
% Number of variables : 48 ( 0 sgn 48 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f8,axiom,
ssList(nil),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause8) ).
fof(f11,axiom,
~ singletonP(nil),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause11) ).
fof(f51,axiom,
! [X0,X1] : ssList(skaf45(X0,X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause51) ).
fof(f56,axiom,
! [X0] :
( segmentP(X0,nil)
| ~ ssList(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause56) ).
fof(f64,axiom,
! [X0] :
( equalelemsP(cons(X0,nil))
| ~ ssItem(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause64) ).
fof(f74,axiom,
! [X0] :
( ~ ssList(X0)
| app(nil,X0) = X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause74) ).
fof(f77,axiom,
! [X0] :
( ssList(tl(X0))
| ~ ssList(X0)
| nil = X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause77) ).
fof(f78,axiom,
! [X0] :
( ssItem(hd(X0))
| ~ ssList(X0)
| nil = X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause78) ).
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(f101,axiom,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssList(X1)
| neq(X1,X0)
| X1 = X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause100) ).
fof(f102,plain,
! [X0,X1] :
( neq(X1,X0)
| ~ ssList(X1)
| ~ ssList(X0)
| X0 = X1 ),
inference(reorient_equations,[],[f101]) ).
fof(f107,axiom,
! [X0] :
( ~ ssList(X0)
| cons(hd(X0),tl(X0)) = X0
| nil = X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause104) ).
fof(f119,axiom,
! [X0,X1] :
( cons(X0,nil) != X1
| ~ ssItem(X0)
| ~ ssList(X1)
| singletonP(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause116) ).
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] :
( ~ ssItem(X0)
| ~ ssList(X1)
| cons(X0,X1) = app(cons(X0,nil),X1) ),
inference(reorient_equations,[],[f125]) ).
fof(f143,axiom,
! [X0,X1] :
( ~ frontsegP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0)
| app(X1,skaf45(X0,X1)) = X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause132) ).
fof(f155,axiom,
! [X2,X0,X1] :
( app(X0,X1) != X2
| ~ ssList(X1)
| ~ ssList(X0)
| ~ ssList(X2)
| frontsegP(X2,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause144) ).
fof(f187,axiom,
! [X2,X3,X0,X1] :
( app(app(X0,X1),X2) != X3
| ~ ssList(X2)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ ssList(X3)
| segmentP(X3,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause173) ).
fof(f202,negated_conjecture,
ssList(sk3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_3) ).
fof(f203,negated_conjecture,
ssList(sk4),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_4) ).
fof(f204,negated_conjecture,
sk2 = sk4,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_5) ).
fof(f205,negated_conjecture,
sk1 = sk3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_6) ).
fof(f206,negated_conjecture,
neq(sk2,nil),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_7) ).
fof(f207,negated_conjecture,
frontsegP(sk4,sk3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_8) ).
fof(f209,negated_conjecture,
! [X0] :
( ~ neq(sk3,X0)
| ~ ssList(X0)
| ~ frontsegP(sk4,X0)
| ~ segmentP(X0,sk3)
| ~ equalelemsP(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_10) ).
fof(f210,negated_conjecture,
( ~ neq(sk1,nil)
| ~ segmentP(sk2,sk1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_11) ).
fof(f213,plain,
neq(sk4,nil),
inference(definition_unfolding,[],[f206,f204]) ).
fof(f214,plain,
( ~ neq(sk3,nil)
| ~ segmentP(sk4,sk3) ),
inference(definition_unfolding,[],[f210,f205,f204,f205]) ).
fof(f222,plain,
! [X0] :
( ~ ssList(cons(X0,nil))
| ~ ssItem(X0)
| singletonP(cons(X0,nil)) ),
inference(equality_resolution,[],[f119]) ).
fof(f226,plain,
! [X0,X1] :
( frontsegP(app(X0,X1),X0)
| ~ ssList(X0)
| ~ ssList(app(X0,X1))
| ~ ssList(X1) ),
inference(equality_resolution,[],[f155]) ).
fof(f229,plain,
! [X2,X0,X1] :
( segmentP(app(app(X0,X1),X2),X1)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ ssList(app(app(X0,X1),X2))
| ~ ssList(X2) ),
inference(equality_resolution,[],[f187]) ).
fof(f246,definition,
( spl0_1
<=> segmentP(sk4,sk3) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f248,plain,
( ~ segmentP(sk4,sk3)
| spl0_1 ),
inference(avatar_component_clause,[],[f246]) ).
fof(f250,definition,
( spl0_2
<=> neq(sk3,nil) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f252,plain,
( ~ neq(sk3,nil)
| spl0_2 ),
inference(avatar_component_clause,[],[f250]) ).
fof(f253,plain,
( ~ spl0_1
| ~ spl0_2 ),
inference(avatar_split_clause,[],[f214,f250,f246]) ).
fof(f259,definition,
( spl0_4
<=> ssList(nil) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f260,plain,
( ssList(nil)
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f259]) ).
fof(f295,plain,
spl0_4,
inference(avatar_split_clause,[],[f8,f259]) ).
fof(f300,plain,
( ~ ssList(sk3)
| ~ ssList(sk4)
| sk4 = app(sk3,skaf45(sk4,sk3)) ),
inference(resolution,[],[f143,f207]) ).
fof(f301,plain,
( ~ ssList(sk4)
| sk4 = app(sk3,skaf45(sk4,sk3)) ),
inference(forward_subsumption_resolution,[],[f300,f202]) ).
fof(f302,plain,
sk4 = app(sk3,skaf45(sk4,sk3)),
inference(forward_subsumption_resolution,[],[f301,f203]) ).
fof(f306,plain,
sk3 = app(nil,sk3),
inference(resolution,[],[f74,f202]) ).
fof(f309,plain,
! [X0] :
( segmentP(app(sk3,X0),sk3)
| ~ ssList(nil)
| ~ ssList(sk3)
| ~ ssList(app(sk3,X0))
| ~ ssList(X0) ),
inference(superposition,[],[f229,f306]) ).
fof(f310,plain,
! [X0] :
( segmentP(app(sk3,X0),sk3)
| ~ ssList(nil)
| ~ ssList(sk3)
| ~ ssList(X0) ),
inference(forward_subsumption_resolution,[],[f309,f85]) ).
fof(f311,plain,
( ! [X0] :
( segmentP(app(sk3,X0),sk3)
| ~ ssList(sk3)
| ~ ssList(X0) )
| ~ spl0_4 ),
inference(forward_subsumption_resolution,[],[f310,f260]) ).
fof(f312,plain,
( ! [X0] :
( segmentP(app(sk3,X0),sk3)
| ~ ssList(X0) )
| ~ spl0_4 ),
inference(forward_subsumption_resolution,[],[f311,f202]) ).
fof(f313,plain,
( segmentP(sk4,sk3)
| ~ ssList(skaf45(sk4,sk3))
| ~ spl0_4 ),
inference(superposition,[],[f312,f302]) ).
fof(f314,plain,
( ~ ssList(skaf45(sk4,sk3))
| spl0_1
| ~ spl0_4 ),
inference(forward_subsumption_resolution,[],[f313,f248]) ).
fof(f315,plain,
( $false
| spl0_1
| ~ spl0_4 ),
inference(forward_subsumption_resolution,[],[f314,f51]) ).
fof(f316,plain,
( spl0_1
| ~ spl0_4 ),
inference(avatar_contradiction_clause,[],[f315]) ).
fof(f317,plain,
( ~ ssList(sk3)
| ~ ssList(nil)
| nil = sk3
| spl0_2 ),
inference(resolution,[],[f252,f102]) ).
fof(f318,plain,
( ~ ssList(nil)
| nil = sk3
| spl0_2 ),
inference(forward_subsumption_resolution,[],[f317,f202]) ).
fof(f319,plain,
( nil = sk3
| spl0_2
| ~ spl0_4 ),
inference(forward_subsumption_resolution,[],[f318,f260]) ).
fof(f323,plain,
( ! [X0] :
( ~ neq(nil,X0)
| ~ ssList(X0)
| ~ frontsegP(sk4,X0)
| ~ segmentP(X0,nil)
| ~ equalelemsP(X0) )
| spl0_2
| ~ spl0_4 ),
inference(superposition,[],[f209,f319]) ).
fof(f324,plain,
( ~ neq(nil,nil)
| spl0_2
| ~ spl0_4 ),
inference(superposition,[],[f252,f319]) ).
fof(f328,plain,
( ! [X0] :
( ~ neq(nil,X0)
| ~ ssList(X0)
| ~ frontsegP(sk4,X0)
| ~ equalelemsP(X0) )
| spl0_2
| ~ spl0_4 ),
inference(forward_subsumption_resolution,[],[f323,f56]) ).
fof(f339,plain,
( ! [X0] :
( ~ ssList(X0)
| ~ frontsegP(sk4,X0)
| ~ equalelemsP(X0)
| ~ ssList(nil)
| ~ ssList(X0)
| nil = X0 )
| spl0_2
| ~ spl0_4 ),
inference(resolution,[],[f328,f102]) ).
fof(f340,plain,
( ! [X0] :
( ~ ssList(X0)
| ~ frontsegP(sk4,X0)
| ~ equalelemsP(X0)
| ~ ssList(nil)
| nil = X0 )
| spl0_2
| ~ spl0_4 ),
inference(duplicate_literal_removal,[],[f339]) ).
fof(f341,plain,
( ! [X0] :
( ~ frontsegP(sk4,X0)
| ~ ssList(X0)
| ~ equalelemsP(X0)
| nil = X0 )
| spl0_2
| ~ spl0_4 ),
inference(forward_subsumption_resolution,[],[f340,f260]) ).
fof(f418,plain,
( sk4 = cons(hd(sk4),tl(sk4))
| nil = sk4 ),
inference(resolution,[],[f107,f203]) ).
fof(f420,definition,
( spl0_12
<=> nil = sk4 ),
introduced(definition,[new_symbols(definition,[spl0_12])],[avatar_definition]) ).
fof(f421,plain,
( nil != sk4
| spl0_12 ),
inference(avatar_component_clause,[],[f420]) ).
fof(f422,plain,
( nil = sk4
| ~ spl0_12 ),
inference(avatar_component_clause,[],[f420]) ).
fof(f424,definition,
( spl0_13
<=> sk4 = cons(hd(sk4),tl(sk4)) ),
introduced(definition,[new_symbols(definition,[spl0_13])],[avatar_definition]) ).
fof(f426,plain,
( sk4 = cons(hd(sk4),tl(sk4))
| ~ spl0_13 ),
inference(avatar_component_clause,[],[f424]) ).
fof(f427,plain,
( spl0_12
| spl0_13 ),
inference(avatar_split_clause,[],[f418,f424,f420]) ).
fof(f432,plain,
( neq(nil,nil)
| ~ spl0_12 ),
inference(superposition,[],[f213,f422]) ).
fof(f446,plain,
( $false
| spl0_2
| ~ spl0_4
| ~ spl0_12 ),
inference(forward_subsumption_resolution,[],[f432,f324]) ).
fof(f447,plain,
( spl0_2
| ~ spl0_4
| ~ spl0_12 ),
inference(avatar_contradiction_clause,[],[f446]) ).
fof(f455,definition,
( spl0_14
<=> ssList(tl(sk4)) ),
introduced(definition,[new_symbols(definition,[spl0_14])],[avatar_definition]) ).
fof(f456,plain,
( ssList(tl(sk4))
| ~ spl0_14 ),
inference(avatar_component_clause,[],[f455]) ).
fof(f457,plain,
( ~ ssList(tl(sk4))
| spl0_14 ),
inference(avatar_component_clause,[],[f455]) ).
fof(f467,plain,
( ~ ssList(sk4)
| nil = sk4
| spl0_14 ),
inference(resolution,[],[f77,f457]) ).
fof(f472,plain,
( nil = sk4
| spl0_14 ),
inference(forward_subsumption_resolution,[],[f467,f203]) ).
fof(f473,plain,
( $false
| spl0_12
| spl0_14 ),
inference(forward_subsumption_resolution,[],[f472,f421]) ).
fof(f474,plain,
( spl0_12
| spl0_14 ),
inference(avatar_contradiction_clause,[],[f473]) ).
fof(f650,definition,
( spl0_18
<=> ssItem(hd(sk4)) ),
introduced(definition,[new_symbols(definition,[spl0_18])],[avatar_definition]) ).
fof(f651,plain,
( ssItem(hd(sk4))
| ~ spl0_18 ),
inference(avatar_component_clause,[],[f650]) ).
fof(f652,plain,
( ~ ssItem(hd(sk4))
| spl0_18 ),
inference(avatar_component_clause,[],[f650]) ).
fof(f661,plain,
( ~ ssList(sk4)
| nil = sk4
| spl0_18 ),
inference(resolution,[],[f652,f78]) ).
fof(f662,plain,
( nil = sk4
| spl0_18 ),
inference(forward_subsumption_resolution,[],[f661,f203]) ).
fof(f663,plain,
( $false
| spl0_12
| spl0_18 ),
inference(forward_subsumption_resolution,[],[f662,f421]) ).
fof(f664,plain,
( spl0_12
| spl0_18 ),
inference(avatar_contradiction_clause,[],[f663]) ).
fof(f665,plain,
( ! [X0] :
( ~ ssList(X0)
| cons(hd(sk4),X0) = app(cons(hd(sk4),nil),X0) )
| ~ spl0_18 ),
inference(resolution,[],[f651,f126]) ).
fof(f673,plain,
( cons(hd(sk4),tl(sk4)) = app(cons(hd(sk4),nil),tl(sk4))
| ~ spl0_14
| ~ spl0_18 ),
inference(resolution,[],[f665,f456]) ).
fof(f677,plain,
( sk4 = app(cons(hd(sk4),nil),tl(sk4))
| ~ spl0_13
| ~ spl0_14
| ~ spl0_18 ),
inference(forward_demodulation,[],[f673,f426]) ).
fof(f679,plain,
( frontsegP(sk4,cons(hd(sk4),nil))
| ~ ssList(cons(hd(sk4),nil))
| ~ ssList(sk4)
| ~ ssList(tl(sk4))
| ~ spl0_13
| ~ spl0_14
| ~ spl0_18 ),
inference(superposition,[],[f226,f677]) ).
fof(f685,plain,
( frontsegP(sk4,cons(hd(sk4),nil))
| ~ ssList(cons(hd(sk4),nil))
| ~ ssList(tl(sk4))
| ~ spl0_13
| ~ spl0_14
| ~ spl0_18 ),
inference(forward_subsumption_resolution,[],[f679,f203]) ).
fof(f688,definition,
( spl0_21
<=> ssList(cons(hd(sk4),nil)) ),
introduced(definition,[new_symbols(definition,[spl0_21])],[avatar_definition]) ).
fof(f689,plain,
( ssList(cons(hd(sk4),nil))
| ~ spl0_21 ),
inference(avatar_component_clause,[],[f688]) ).
fof(f690,plain,
( ~ ssList(cons(hd(sk4),nil))
| spl0_21 ),
inference(avatar_component_clause,[],[f688]) ).
fof(f699,plain,
( frontsegP(sk4,cons(hd(sk4),nil))
| ~ ssList(cons(hd(sk4),nil))
| ~ spl0_13
| ~ spl0_14
| ~ spl0_18 ),
inference(forward_subsumption_resolution,[],[f685,f456]) ).
fof(f705,definition,
( spl0_25
<=> frontsegP(sk4,cons(hd(sk4),nil)) ),
introduced(definition,[new_symbols(definition,[spl0_25])],[avatar_definition]) ).
fof(f707,plain,
( frontsegP(sk4,cons(hd(sk4),nil))
| ~ spl0_25 ),
inference(avatar_component_clause,[],[f705]) ).
fof(f708,plain,
( ~ spl0_21
| spl0_25
| ~ spl0_13
| ~ spl0_14
| ~ spl0_18 ),
inference(avatar_split_clause,[],[f699,f650,f455,f424,f705,f688]) ).
fof(f709,plain,
( ~ ssList(nil)
| ~ ssItem(hd(sk4))
| spl0_21 ),
inference(resolution,[],[f690,f86]) ).
fof(f710,plain,
( ~ ssItem(hd(sk4))
| ~ spl0_4
| spl0_21 ),
inference(forward_subsumption_resolution,[],[f709,f260]) ).
fof(f711,plain,
( $false
| ~ spl0_4
| ~ spl0_18
| spl0_21 ),
inference(forward_subsumption_resolution,[],[f710,f651]) ).
fof(f712,plain,
( ~ spl0_4
| ~ spl0_18
| spl0_21 ),
inference(avatar_contradiction_clause,[],[f711]) ).
fof(f720,definition,
( spl0_26
<=> nil = cons(hd(sk4),nil) ),
introduced(definition,[new_symbols(definition,[spl0_26])],[avatar_definition]) ).
fof(f721,plain,
( nil != cons(hd(sk4),nil)
| spl0_26 ),
inference(avatar_component_clause,[],[f720]) ).
fof(f722,plain,
( nil = cons(hd(sk4),nil)
| ~ spl0_26 ),
inference(avatar_component_clause,[],[f720]) ).
fof(f728,plain,
( ~ ssList(cons(hd(sk4),nil))
| ~ equalelemsP(cons(hd(sk4),nil))
| nil = cons(hd(sk4),nil)
| spl0_2
| ~ spl0_4
| ~ spl0_25 ),
inference(resolution,[],[f707,f341]) ).
fof(f744,plain,
( ~ ssList(nil)
| ~ ssItem(hd(sk4))
| singletonP(nil)
| ~ spl0_26 ),
inference(superposition,[],[f222,f722]) ).
fof(f757,plain,
( ~ ssItem(hd(sk4))
| singletonP(nil)
| ~ spl0_4
| ~ spl0_26 ),
inference(forward_subsumption_resolution,[],[f744,f260]) ).
fof(f765,plain,
( singletonP(nil)
| ~ spl0_4
| ~ spl0_18
| ~ spl0_26 ),
inference(forward_subsumption_resolution,[],[f757,f651]) ).
fof(f769,plain,
( $false
| ~ spl0_4
| ~ spl0_18
| ~ spl0_26 ),
inference(forward_subsumption_resolution,[],[f765,f11]) ).
fof(f770,plain,
( ~ spl0_4
| ~ spl0_18
| ~ spl0_26 ),
inference(avatar_contradiction_clause,[],[f769]) ).
fof(f771,plain,
( ~ equalelemsP(cons(hd(sk4),nil))
| nil = cons(hd(sk4),nil)
| spl0_2
| ~ spl0_4
| ~ spl0_21
| ~ spl0_25 ),
inference(forward_subsumption_resolution,[],[f728,f689]) ).
fof(f773,plain,
( ~ equalelemsP(cons(hd(sk4),nil))
| spl0_2
| ~ spl0_4
| ~ spl0_21
| ~ spl0_25
| spl0_26 ),
inference(forward_subsumption_resolution,[],[f771,f721]) ).
fof(f775,plain,
( ~ ssItem(hd(sk4))
| spl0_2
| ~ spl0_4
| ~ spl0_21
| ~ spl0_25
| spl0_26 ),
inference(resolution,[],[f773,f64]) ).
fof(f776,plain,
( $false
| spl0_2
| ~ spl0_4
| ~ spl0_18
| ~ spl0_21
| ~ spl0_25
| spl0_26 ),
inference(forward_subsumption_resolution,[],[f775,f651]) ).
fof(f777,plain,
( spl0_2
| ~ spl0_4
| ~ spl0_18
| ~ spl0_21
| ~ spl0_25
| spl0_26 ),
inference(avatar_contradiction_clause,[],[f776]) ).
cnf(s1,plain,
( ~ spl0_1
| ~ spl0_2 ),
inference(sat_conversion,[],[f253]) ).
cnf(s11,plain,
spl0_4,
inference(sat_conversion,[],[f295]) ).
cnf(s12,plain,
( spl0_1
| ~ spl0_4 ),
inference(sat_conversion,[],[f316]) ).
cnf(s13,plain,
( spl0_12
| spl0_13 ),
inference(sat_conversion,[],[f427]) ).
cnf(s14,plain,
( spl0_2
| ~ spl0_4
| ~ spl0_12 ),
inference(sat_conversion,[],[f447]) ).
cnf(s16,plain,
( spl0_12
| spl0_14 ),
inference(sat_conversion,[],[f474]) ).
cnf(s22,plain,
( spl0_12
| spl0_18 ),
inference(sat_conversion,[],[f664]) ).
cnf(s26,plain,
( ~ spl0_13
| ~ spl0_14
| ~ spl0_18
| ~ spl0_21
| spl0_25 ),
inference(sat_conversion,[],[f708]) ).
cnf(s27,plain,
( ~ spl0_4
| ~ spl0_18
| spl0_21 ),
inference(sat_conversion,[],[f712]) ).
cnf(s32,plain,
( ~ spl0_4
| ~ spl0_18
| ~ spl0_26 ),
inference(sat_conversion,[],[f770]) ).
cnf(s33,plain,
( spl0_2
| ~ spl0_4
| ~ spl0_18
| ~ spl0_21
| ~ spl0_25
| spl0_26 ),
inference(sat_conversion,[],[f777]) ).
cnf(s34,plain,
spl0_1,
inference(rat,[],[s12,s11]) ).
cnf(s39,plain,
~ spl0_2,
inference(rat,[],[s1,s34]) ).
cnf(s40,plain,
~ spl0_12,
inference(rat,[],[s14,s11,s39]) ).
cnf(s41,plain,
spl0_18,
inference(rat,[],[s22,s40]) ).
cnf(s42,plain,
spl0_14,
inference(rat,[],[s16,s40]) ).
cnf(s43,plain,
spl0_13,
inference(rat,[],[s13,s40]) ).
cnf(s44,plain,
~ spl0_26,
inference(rat,[],[s32,s11,s41]) ).
cnf(s45,plain,
spl0_21,
inference(rat,[],[s27,s11,s41]) ).
cnf(s46,plain,
spl0_25,
inference(rat,[],[s26,s42,s45,s41,s43]) ).
cnf(s54,plain,
$false,
inference(rat,[],[s33,s44,s41,s39,s11,s46,s45]) ).
fof(f778,plain,
$false,
inference(avatar_sat_refutation,[],[s54]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC123-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.38 % Computer : n009.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Mon Sep 28 08:02:45 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.42 Running first-order theorem proving
% 0.11/0.42 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
% 9.31/2.39 % (2875616)Input is clausal, will run a generic CNF schedule.
% 9.31/2.39 % (2875647)dis-21_1_sil=8000:lcm=predicate:random_seed=1013223983: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)
% 9.31/2.39 % (2875641)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=3899965154:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 9.31/2.39 % (2875643)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=518927603:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 9.31/2.39 % (2875642)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=3443903006:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 9.31/2.39 % (2875644)lrs+10_1_sil=8000:sp=occurrence:random_seed=2225458534:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 9.31/2.39 % (2875646)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3195180944:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 9.31/2.39 % (2875645)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=1005963073:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 9.31/2.39 % (2875647)Instruction limit reached!
% 9.31/2.39 % (2875647)------------------------------
% 9.31/2.39 % (2875647)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.31/2.39 % (2875647)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.31/2.39 % (2875647)CaDiCaL version: 2.1.3
% 9.31/2.39 % (2875647)Termination reason: Instruction limit
% 9.31/2.39 % (2875647)Termination phase: Saturation
% 9.31/2.39 % (2875647)Time elapsed: 0.055 s
% 9.31/2.39 % (2875647)Peak memory usage: 88 MB
% 9.31/2.39 % (2875647)Instructions burned: 117 (million)
% 9.31/2.39 % (2875644)Instruction limit reached!
% 9.31/2.39 % (2875644)------------------------------
% 9.31/2.39 % (2875644)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.31/2.39 % (2875644)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.31/2.39 % (2875644)CaDiCaL version: 2.1.3
% 9.31/2.39 % (2875644)Termination reason: Instruction limit
% 9.31/2.39 % (2875644)Termination phase: Saturation
% 9.31/2.39 % (2875644)Time elapsed: 0.090 s
% 9.31/2.39 % (2875644)Peak memory usage: 90 MB
% 9.31/2.39 % (2875644)Instructions burned: 107 (million)
% 9.31/2.39 % (2875645)Instruction limit reached!
% 9.31/2.39 % (2875645)------------------------------
% 9.31/2.39 % (2875645)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.31/2.39 % (2875645)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.31/2.39 % (2875645)CaDiCaL version: 2.1.3
% 9.31/2.39 % (2875645)Termination reason: Instruction limit
% 9.31/2.39 % (2875645)Termination phase: Saturation
% 9.31/2.39 % (2875645)Time elapsed: 0.101 s
% 9.31/2.39 % (2875645)Peak memory usage: 88 MB
% 9.31/2.39 % (2875645)Instructions burned: 114 (million)
% 9.31/2.39 % (2875661)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=2536219647:i=143:sd=2:aac=none:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/143Mi)
% 9.31/2.39 % (2875646)Instruction limit reached!
% 9.31/2.39 % (2875646)------------------------------
% 9.31/2.39 % (2875646)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.31/2.39 % (2875646)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.31/2.39 % (2875646)CaDiCaL version: 2.1.3
% 9.31/2.39 % (2875646)Termination reason: Instruction limit
% 9.31/2.39 % (2875646)Termination phase: Saturation
% 9.31/2.39 % (2875646)Time elapsed: 0.196 s
% 9.31/2.39 % (2875646)Peak memory usage: 90 MB
% 9.31/2.39 % (2875646)Instructions burned: 180 (million)
% 9.31/2.39 % (2875661)Instruction limit reached!
% 9.31/2.39 % (2875661)------------------------------
% 9.31/2.39 % (2875661)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.31/2.39 % (2875661)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.31/2.39 % (2875661)CaDiCaL version: 2.1.3
% 9.31/2.39 % (2875661)Termination reason: Instruction limit
% 9.31/2.39 % (2875661)Termination phase: Saturation
% 9.31/2.39 % (2875661)Time elapsed: 0.065 s
% 9.31/2.39 % (2875661)Peak memory usage: 89 MB
% 9.31/2.39 % (2875661)Instructions burned: 144 (million)
% 9.31/2.39 % (2875664)ott-1010_1_to=lpo:sil=16000:sos=on:spb=units:urr=on:bce=on:br=off:random_seed=876821863:st=3:avsq=on:s2a=on:i=189:s2at=1.2:avsqr=1,16:sd=2:bd=all:nm=64:ss=axioms:sgt=30_2996 on theBenchmark for (2996ds/189Mi)
% 9.31/2.39 % (2875665)lrs-1002_1_to=lpo:sil=8000:fde=none:sos=on:random_seed=3186609546:st=4:i=219:sd=3:ss=axioms_2996 on theBenchmark for (2996ds/219Mi)
% 9.31/2.39 % (2875669)lrs+1011_16_to=lpo:sil=8000:drc=off:sp=reverse_frequency:spb=goal_then_units:random_seed=3574951839:avsq=on:i=194:fgj=on:bd=preordered_2995 on theBenchmark for (2995ds/194Mi)
% 9.31/2.39 % (2875668)lrs+10_64_to=lpo:sil=8000:random_seed=1361102905:i=126:bd=preordered_2995 on theBenchmark for (2995ds/126Mi)
% 9.31/2.39 % (2875665)Instruction limit reached!
% 9.31/2.39 % (2875665)------------------------------
% 9.31/2.39 % (2875665)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.31/2.39 % (2875665)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.31/2.39 % (2875665)CaDiCaL version: 2.1.3
% 9.31/2.39 % (2875665)Termination reason: Instruction limit
% 9.31/2.39 % (2875665)Termination phase: Saturation
% 9.31/2.39 % (2875665)Time elapsed: 0.150 s
% 9.31/2.39 % (2875665)Peak memory usage: 88 MB
% 9.31/2.39 % (2875665)Instructions burned: 220 (million)
% 9.31/2.39 % (2875669)Instruction limit reached!
% 9.31/2.39 % (2875669)------------------------------
% 9.31/2.39 % (2875669)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.31/2.39 % (2875669)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.31/2.39 % (2875669)CaDiCaL version: 2.1.3
% 9.31/2.39 % (2875669)Termination reason: Instruction limit
% 9.31/2.39 % (2875669)Termination phase: Saturation
% 9.31/2.39 % (2875669)Time elapsed: 0.095 s
% 9.31/2.39 % (2875669)Peak memory usage: 90 MB
% 9.31/2.39 % (2875669)Instructions burned: 201 (million)
% 9.31/2.39 % (2875664)Instruction limit reached!
% 9.31/2.39 % (2875664)------------------------------
% 9.31/2.39 % (2875664)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.31/2.39 % (2875664)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.31/2.39 % (2875664)CaDiCaL version: 2.1.3
% 9.31/2.39 % (2875664)Termination reason: Instruction limit
% 9.31/2.39 % (2875664)Termination phase: Saturation
% 9.31/2.39 % (2875664)Time elapsed: 0.179 s
% 9.31/2.39 % (2875664)Peak memory usage: 91 MB
% 9.31/2.39 % (2875664)Instructions burned: 190 (million)
% 9.31/2.39 % (2875668)Instruction limit reached!
% 9.31/2.39 % (2875668)------------------------------
% 9.31/2.39 % (2875668)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.31/2.39 % (2875668)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.31/2.39 % (2875668)CaDiCaL version: 2.1.3
% 9.31/2.39 % (2875668)Termination reason: Instruction limit
% 9.31/2.39 % (2875668)Termination phase: Saturation
% 9.31/2.39 % (2875668)Time elapsed: 0.098 s
% 9.31/2.39 % (2875668)Peak memory usage: 90 MB
% 9.31/2.39 % (2875668)Instructions burned: 126 (million)
% 9.31/2.39 % (2875677)lrs+10_1_sil=8000:tgt=full:acc=on:random_seed=195428405:i=157:gtg=all_2993 on theBenchmark for (2993ds/157Mi)
% 9.31/2.39 % (2875678)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=128000:npcc=on:random_seed=2384941812:i=3394:sd=4:ss=included:sgt=64_2993 on theBenchmark for (2993ds/3394Mi)
% 9.31/2.39 % (2875679)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=1683592347:cts=off:s2a=on:i=106:fsr=off:gsp=on:ss=axioms:sgt=16:rawr=on_2993 on theBenchmark for (2993ds/106Mi)
% 9.31/2.39 % (2875680)lrs+2_4096_sil=8000:plsq=on:plsqr=12672147,131072:sos=on:spb=goal:lcm=predicate:random_seed=1244918173:i=107_2992 on theBenchmark for (2992ds/107Mi)
% 9.31/2.39 % (2875679)Instruction limit reached!
% 9.31/2.39 % (2875679)------------------------------
% 9.31/2.39 % (2875679)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.31/2.39 % (2875679)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.31/2.39 % (2875679)CaDiCaL version: 2.1.3
% 9.31/2.39 % (2875679)Termination reason: Instruction limit
% 9.31/2.39 % (2875679)Termination phase: Saturation
% 9.31/2.39 % (2875679)Time elapsed: 0.060 s
% 9.31/2.39 % (2875679)Peak memory usage: 89 MB
% 9.31/2.39 % (2875679)Instructions burned: 107 (million)
% 9.31/2.39 % (2875677)Instruction limit reached!
% 9.31/2.39 % (2875677)------------------------------
% 9.31/2.39 % (2875677)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.31/2.39 % (2875677)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.31/2.39 % (2875677)CaDiCaL version: 2.1.3
% 9.31/2.39 % (2875677)Termination reason: Instruction limit
% 9.31/2.39 % (2875677)Termination phase: Saturation
% 9.31/2.39 % (2875677)Time elapsed: 0.077 s
% 9.31/2.39 % (2875677)Peak memory usage: 91 MB
% 9.31/2.39 % (2875677)Instructions burned: 160 (million)
% 9.31/2.39 % (2875680)Instruction limit reached!
% 9.31/2.39 % (2875680)------------------------------
% 9.31/2.39 % (2875680)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.31/2.39 % (2875680)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.31/2.39 % (2875680)CaDiCaL version: 2.1.3
% 9.31/2.39 % (2875680)Termination reason: Instruction limit
% 9.31/2.39 % (2875680)Termination phase: Saturation
% 9.31/2.39 % (2875680)Time elapsed: 0.067 s
% 9.31/2.39 % (2875680)Peak memory usage: 90 MB
% 9.31/2.39 % (2875680)Instructions burned: 108 (million)
% 9.31/2.39 % (2875687)lrs+1010_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:tgt=ground:npcc=on:sims=off:random_seed=201157988:cond=fast:i=5208:av=off_2991 on theBenchmark for (2991ds/5208Mi)
% 9.31/2.39 % (2875686)lrs+1011_20_sil=64000:tgt=ground:plsq=on:fde=unused:plsqc=1:plsqr=14,1:plsql=on:nwc=0.6:random_seed=4032830599:st=6:i=242:gtgl=5:kws=arity_squared:av=off:gtg=exists_sym:ss=included_2991 on theBenchmark for (2991ds/242Mi)
% 9.31/2.39 % (2875688)lrs+1011_16_sil=32000:erd=off:bce=on:random_seed=4100935744:i=134:sd=2:doe=on:ss=axioms:sgt=14_2990 on theBenchmark for (2990ds/134Mi)
% 9.31/2.39 % (2875641)First to succeed.
% 9.31/2.39 % (2875641)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2875616"
% 9.31/2.39 % (2875688)Instruction limit reached!
% 9.31/2.39 % (2875688)------------------------------
% 9.31/2.39 % (2875688)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.31/2.39 % (2875688)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.31/2.39 % (2875688)CaDiCaL version: 2.1.3
% 9.31/2.39 % (2875688)Termination reason: Instruction limit
% 9.31/2.39 % (2875688)Termination phase: Saturation
% 9.31/2.39 % (2875688)Time elapsed: 0.092 s
% 9.31/2.39 % (2875688)Peak memory usage: 90 MB
% 9.31/2.39 % (2875688)Instructions burned: 134 (million)
% 9.31/2.39 % (2875686)Instruction limit reached!
% 9.31/2.39 % (2875686)------------------------------
% 9.31/2.39 % (2875686)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.31/2.39 % (2875686)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.31/2.39 % (2875686)CaDiCaL version: 2.1.3
% 9.31/2.39 % (2875686)Termination reason: Instruction limit
% 9.31/2.39 % (2875686)Termination phase: Saturation
% 9.31/2.39 % (2875686)Time elapsed: 0.153 s
% 9.31/2.39 % (2875686)Peak memory usage: 89 MB
% 9.31/2.39 % (2875686)Instructions burned: 243 (million)
% 9.31/2.39 % (2875762)ott+10_5:4_to=lpo:sil=8000:prc=on:fde=unused:sp=unary_frequency:spb=goal:urr=on:random_seed=3890023437:i=499:bd=all_2988 on theBenchmark for (2988ds/499Mi)
% 9.31/2.39 % (2875766)lrs+10_64_to=lpo:sil=8000:prc=on:sp=reverse_frequency:nwc=5:alpa=false:flr=on:random_seed=3788757812:i=191:fgj=on:bd=all_2988 on theBenchmark for (2988ds/191Mi)
% 9.31/2.39 % (2875687)Also succeeded, but the first one will report.
% 9.31/2.39 % (2875641)Refutation found. Thanks to Tanya!
% 9.31/2.39 % SZS status Unsatisfiable for theBenchmark
% 9.31/2.39 % SZS output start Proof for theBenchmark
% See solution above
% 10.23/2.49 % (2875641)------------------------------
% 10.23/2.49 % (2875641)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.23/2.49 % (2875641)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.23/2.49 % (2875641)CaDiCaL version: 2.1.3
% 10.23/2.49 % (2875641)Termination reason: Refutation
% 10.23/2.49 % (2875641)Time elapsed: 0.908 s
% 10.23/2.49 % (2875641)Peak memory usage: 131 MB
% 10.23/2.49 % (2875641)Instructions burned: 1050 (million)
% 10.23/2.49 % (2875641)------------------------------
% 10.23/2.49 % (2875641)------------------------------
% 10.23/2.49 % (2875616)Success in time 1.354 s
% 10.23/2.49 % Vampire exiting
%------------------------------------------------------------------------------