%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SWC003+1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n006.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 : Fri Sep 25 03:07:28 PM UTC 2026
% Result : Theorem 4.15s 6.28s
% Output : CNFRefutation 4.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 14
% Syntax : Number of formulae : 101 ( 32 unt; 8 def)
% Number of atoms : 539 ( 146 equ)
% Maximal formula atoms : 24 ( 5 avg)
% Number of connectives : 598 ( 246 ~; 232 |; 97 &)
% ( 4 <=>; 19 =>; 0 <=; 0 <~>)
% Maximal formula depth : 27 ( 7 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 19 ( 17 usr; 8 prp; 0-4 aty)
% Number of functors : 8 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 236 ( 0 sgn 197 !; 39 ?; 80 :)
% Comments :
%------------------------------------------------------------------------------
fof(f4,axiom,
! [X0] :
( ssList(X0)
=> ( singletonP(X0)
<=> ? [X1] :
( cons(X1,nil) = X0
& ssItem(X1) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax4) ).
fof(f15,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ( neq(X0,X1)
<=> X0 != X1 ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax15) ).
fof(f16,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssItem(X1)
=> ssList(cons(X1,X0)) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax16) ).
fof(f17,axiom,
ssList(nil),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax17) ).
fof(f39,axiom,
~ singletonP(nil),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax39) ).
fof(f96,conjecture,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( ( ( neq(X3,nil)
| ~ neq(X1,nil) )
& ( ! [X7] :
( ssItem(X7)
=> ! [X8] :
( ssList(X8)
=> ! [X9] :
( ssList(X9)
=> ( ? [X10] :
( geq(X10,X7)
& memberP(X3,X10)
& X7 != X10
& ssItem(X10) )
| app(X8,X9) != X2
| app(app(X8,cons(X7,nil)),X9) != X3 ) ) ) )
| ? [X4] :
( ? [X5] :
( ? [X6] :
( neq(X5,nil)
& app(X4,X6) = X0
& app(app(X4,X5),X6) = X1
& ssList(X6) )
& ssList(X5) )
& ssList(X4) )
| ~ neq(X1,nil) ) )
| X0 != X2
| X1 != X3 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1) ).
fof(f97,negated_conjecture,
~ ! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( ( ( neq(X3,nil)
| ~ neq(X1,nil) )
& ( ! [X7] :
( ssItem(X7)
=> ! [X8] :
( ssList(X8)
=> ! [X9] :
( ssList(X9)
=> ( ? [X10] :
( geq(X10,X7)
& memberP(X3,X10)
& X7 != X10
& ssItem(X10) )
| app(X8,X9) != X2
| app(app(X8,cons(X7,nil)),X9) != X3 ) ) ) )
| ? [X4] :
( ? [X5] :
( ? [X6] :
( neq(X5,nil)
& app(X4,X6) = X0
& app(app(X4,X5),X6) = X1
& ssList(X6) )
& ssList(X5) )
& ssList(X4) )
| ~ neq(X1,nil) ) )
| X0 != X2
| X1 != X3 ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f96]) ).
fof(f100,plain,
! [X0] :
( ~ ssList(X0)
| ( singletonP(X0)
<=> ? [X1] :
( cons(X1,nil) = X0
& ssItem(X1) ) ) ),
inference(ennf_transformation,[],[f4]) ).
fof(f118,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssList(X1)
| ( neq(X0,X1)
<=> X0 != X1 ) ) ),
inference(ennf_transformation,[],[f15]) ).
fof(f119,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssItem(X1)
| ssList(cons(X1,X0)) ) ),
inference(ennf_transformation,[],[f16]) ).
fof(f221,plain,
? [X0] :
( ssList(X0)
& ? [X1] :
( ssList(X1)
& ? [X2] :
( ssList(X2)
& ? [X3] :
( ssList(X3)
& ( ( ~ neq(X3,nil)
& neq(X1,nil) )
| ( ? [X7] :
( ssItem(X7)
& ? [X8] :
( ssList(X8)
& ? [X9] :
( ssList(X9)
& ! [X10] :
( ~ geq(X10,X7)
| ~ memberP(X3,X10)
| X7 = X10
| ~ ssItem(X10) )
& app(X8,X9) = X2
& app(app(X8,cons(X7,nil)),X9) = X3 ) ) )
& ! [X4] :
( ! [X5] :
( ! [X6] :
( ~ neq(X5,nil)
| app(X4,X6) != X0
| app(app(X4,X5),X6) != X1
| ~ ssList(X6) )
| ~ ssList(X5) )
| ~ ssList(X4) )
& neq(X1,nil) ) )
& X0 = X2
& X1 = X3 ) ) ) ),
inference(ennf_transformation,[],[f97]) ).
fof(f222,plain,
? [X0] :
( ssList(X0)
& ? [X1] :
( ssList(X1)
& ? [X2] :
( ssList(X2)
& ? [X3] :
( ssList(X3)
& ( ( ~ neq(X3,nil)
& neq(X1,nil) )
| ( ? [X7] :
( ssItem(X7)
& ? [X8] :
( ssList(X8)
& ? [X9] :
( ssList(X9)
& ! [X10] :
( ~ geq(X10,X7)
| ~ memberP(X3,X10)
| X7 = X10
| ~ ssItem(X10) )
& app(X8,X9) = X2
& app(app(X8,cons(X7,nil)),X9) = X3 ) ) )
& ! [X4] :
( ! [X5] :
( ! [X6] :
( ~ neq(X5,nil)
| app(X4,X6) != X0
| app(app(X4,X5),X6) != X1
| ~ ssList(X6) )
| ~ ssList(X5) )
| ~ ssList(X4) )
& neq(X1,nil) ) )
& X0 = X2
& X1 = X3 ) ) ) ),
inference(flattening,[],[f221]) ).
fof(f239,plain,
! [X0] :
( ~ ssList(X0)
| ( ( ~ singletonP(X0)
| ? [X1] :
( cons(X1,nil) = X0
& ssItem(X1) ) )
& ( ! [X1] :
( cons(X1,nil) != X0
| ~ ssItem(X1) )
| singletonP(X0) ) ) ),
inference(nnf_transformation,[],[f100]) ).
fof(f240,plain,
! [X0] :
( ~ ssList(X0)
| ( ( ~ singletonP(X0)
| ? [X2] :
( cons(X2,nil) = X0
& ssItem(X2) ) )
& ( ! [X1] :
( cons(X1,nil) != X0
| ~ ssItem(X1) )
| singletonP(X0) ) ) ),
inference(rectify,[],[f239]) ).
fof(f241,plain,
! [X0] :
( ~ ssList(X0)
| ( ( ~ singletonP(X0)
| ( cons(sK11(X0),nil) = X0
& ssItem(sK11(X0)) ) )
& ( ! [X1] :
( cons(X1,nil) != X0
| ~ ssItem(X1) )
| singletonP(X0) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11]),skolemize(X2,sK11(X0))],[f240]) ).
fof(f275,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssList(X1)
| ( ( ~ neq(X0,X1)
| X0 != X1 )
& ( X0 = X1
| neq(X0,X1) ) ) ) ),
inference(nnf_transformation,[],[f118]) ).
fof(f301,plain,
( ssList(sK57)
& ssList(sK58)
& ssList(sK59)
& ssList(sK60)
& ( ( ~ neq(sK60,nil)
& neq(sK58,nil) )
| sP6(sK58,sK57,sK60,sK59) )
& sK57 = sK59
& sK58 = sK60 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK57,sK58,sK59,sK60]),skolemize(X0,sK57),skolemize(X1,sK58),skolemize(X2,sK59),skolemize(X3,sK60)],[f233]) ).
fof(f313,plain,
! [X0,X1] :
( ~ ssList(X0)
| cons(X1,nil) != X0
| ~ ssItem(X1)
| singletonP(X0) ),
inference(cnf_transformation,[],[f241]) ).
fof(f392,plain,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssList(X1)
| X0 = X1
| neq(X0,X1) ),
inference(cnf_transformation,[],[f275]) ).
fof(f393,plain,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssItem(X1)
| ssList(cons(X1,X0)) ),
inference(cnf_transformation,[],[f119]) ).
fof(f394,plain,
ssList(nil),
inference(cnf_transformation,[],[f17]) ).
fof(f425,plain,
~ singletonP(nil),
inference(cnf_transformation,[],[f39]) ).
fof(f513,plain,
( ~ neq(sK60,nil)
| sP6(sK58,sK57,sK60,sK59) ),
inference(cnf_transformation,[],[f301]) ).
fof(f514,plain,
( neq(sK58,nil)
| sP6(sK58,sK57,sK60,sK59) ),
inference(cnf_transformation,[],[f301]) ).
fof(f515,plain,
sK57 = sK59,
inference(cnf_transformation,[],[f301]) ).
fof(f516,plain,
sK58 = sK60,
inference(cnf_transformation,[],[f301]) ).
fof(f517,plain,
( neq(sK60,nil)
| sP6(sK60,sK59,sK60,sK59) ),
inference(definition_unfolding,[],[f514,f516,f515,f516]) ).
fof(f518,plain,
( ~ neq(sK60,nil)
| sP6(sK60,sK59,sK60,sK59) ),
inference(definition_unfolding,[],[f513,f516,f515]) ).
fof(f523,plain,
! [X1] :
( ~ ssList(cons(X1,nil))
| ~ ssItem(X1)
| singletonP(cons(X1,nil)) ),
inference(equality_resolution,[],[f313]) ).
tcf(c_58,plain,
! [X0: $i] :
( singletonP(cons(X0,nil))
| ~ ssItem(X0)
| ~ ssList(cons(X0,nil)) ),
inference(cnf_transformation,[],[f523]) ).
tcf(c_138,plain,
! [X0: $i,X1: $i] :
( neq(X0,X1)
| ( X0 = X1 )
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f392]) ).
tcf(c_140,plain,
! [X0: $i,X1: $i] :
( ssList(cons(X0,X1))
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f393]) ).
tcf(c_141,plain,
ssList(nil),
inference(cnf_transformation,[],[f394]) ).
tcf(c_172,plain,
~ singletonP(nil),
inference(cnf_transformation,[],[f425]) ).
tcf(c_254,negated_conjecture,
( neq(sK60,nil)
| sP6(sK60,sK59,sK60,sK59) ),
inference(cnf_transformation,[],[f517]) ).
tcf(c_255,negated_conjecture,
( sP6(sK60,sK59,sK60,sK59)
| ~ neq(sK60,nil) ),
inference(cnf_transformation,[],[f518]) ).
tcf(c_378,negated_conjecture,
sP6(sK60,sK59,sK60,sK59),
inference(global_subsumption_just,[status(thm)],[c_254,c_254,c_255]) ).
tcf(c_380,negated_conjecture,
sP6(sK60,sK59,sK60,sK59),
inference(global_subsumption_just,[status(thm)],[c_255,c_378]) ).
tcf(c_9095,definition,
iPr_def_10 = sK55(sK60,sK59),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_9096,definition,
iPr_def_11 = sK54(sK60,sK59),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_9097,definition,
iPr_def_12 = cons(iPr_def_11,nil),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_9098,definition,
iPr_def_13 = app(iPr_def_10,iPr_def_12),
introduced(definition,[new_symbols(definition,[iPr_def_13])],[]) ).
tcf(c_9099,definition,
iPr_def_14 = sK56(sK60,sK59),
introduced(definition,[new_symbols(definition,[iPr_def_14])],[]) ).
tcf(c_9100,definition,
iPr_def_15 = app(iPr_def_13,iPr_def_14),
introduced(definition,[new_symbols(definition,[iPr_def_15])],[]) ).
tcf(c_9101,definition,
iPr_def_16 = app(iPr_def_10,iPr_def_14),
introduced(definition,[new_symbols(definition,[iPr_def_16])],[]) ).
tcf(c_12324,plain,
( singletonP(cons(iPr_def_11,nil))
| ~ ssList(iPr_def_12)
| ~ ssItem(iPr_def_11) ),
inference(superposition,[status(thm)],[c_9097,c_58]) ).
tcf(c_12325,plain,
( singletonP(iPr_def_12)
| ~ ssList(iPr_def_12)
| ~ ssItem(iPr_def_11) ),
inference(light_normalisation,[status(thm)],[c_12324,c_9097]) ).
tcf(c_12717,plain,
( ssList(iPr_def_12)
| ~ ssList(nil)
| ~ ssItem(iPr_def_11) ),
inference(superposition,[status(thm)],[c_9097,c_140]) ).
fof(f232,definition,
! [X1,X0,X3,X2] :
( ~ sP6(X1,X0,X3,X2)
| ( ? [X7] :
( ssItem(X7)
& ? [X8] :
( ssList(X8)
& ? [X9] :
( ssList(X9)
& ! [X10] :
( ~ geq(X10,X7)
| ~ memberP(X3,X10)
| X7 = X10
| ~ ssItem(X10) )
& app(X8,X9) = X2
& app(app(X8,cons(X7,nil)),X9) = X3 ) ) )
& ! [X4] :
( ! [X5] :
( ! [X6] :
( ~ neq(X5,nil)
| app(X4,X6) != X0
| app(app(X4,X5),X6) != X1
| ~ ssList(X6) )
| ~ ssList(X5) )
| ~ ssList(X4) )
& neq(X1,nil) ) ),
introduced(definition,[new_symbols(definition,[sP6])],[predicate_definition_introduction]) ).
fof(f233,plain,
? [X0] :
( ssList(X0)
& ? [X1] :
( ssList(X1)
& ? [X2] :
( ssList(X2)
& ? [X3] :
( ssList(X3)
& ( ( ~ neq(X3,nil)
& neq(X1,nil) )
| sP6(X1,X0,X3,X2) )
& X0 = X2
& X1 = X3 ) ) ) ),
inference(definition_folding,[],[f222,f232]) ).
fof(f298,plain,
! [X1,X0,X3,X2] :
( ~ sP6(X1,X0,X3,X2)
| ( ? [X7] :
( ssItem(X7)
& ? [X8] :
( ssList(X8)
& ? [X9] :
( ssList(X9)
& ! [X10] :
( ~ geq(X10,X7)
| ~ memberP(X3,X10)
| X7 = X10
| ~ ssItem(X10) )
& app(X8,X9) = X2
& app(app(X8,cons(X7,nil)),X9) = X3 ) ) )
& ! [X4] :
( ! [X5] :
( ! [X6] :
( ~ neq(X5,nil)
| app(X4,X6) != X0
| app(app(X4,X5),X6) != X1
| ~ ssList(X6) )
| ~ ssList(X5) )
| ~ ssList(X4) )
& neq(X1,nil) ) ),
inference(nnf_transformation,[],[f232]) ).
fof(f299,plain,
! [X0,X1,X2,X3] :
( ~ sP6(X0,X1,X2,X3)
| ( ? [X7] :
( ssItem(X7)
& ? [X8] :
( ssList(X8)
& ? [X9] :
( ssList(X9)
& ! [X10] :
( ~ geq(X10,X7)
| ~ memberP(X2,X10)
| X7 = X10
| ~ ssItem(X10) )
& app(X8,X9) = X3
& app(app(X8,cons(X7,nil)),X9) = X2 ) ) )
& ! [X4] :
( ! [X5] :
( ! [X6] :
( ~ neq(X5,nil)
| app(X4,X6) != X1
| app(app(X4,X5),X6) != X0
| ~ ssList(X6) )
| ~ ssList(X5) )
| ~ ssList(X4) )
& neq(X0,nil) ) ),
inference(rectify,[],[f298]) ).
fof(f300,plain,
! [X0,X1,X2,X3] :
( ~ sP6(X0,X1,X2,X3)
| ( ssItem(sK54(X2,X3))
& ssList(sK55(X2,X3))
& ssList(sK56(X2,X3))
& ! [X10] :
( ~ geq(X10,sK54(X2,X3))
| ~ memberP(X2,X10)
| sK54(X2,X3) = X10
| ~ ssItem(X10) )
& app(sK55(X2,X3),sK56(X2,X3)) = X3
& app(app(sK55(X2,X3),cons(sK54(X2,X3),nil)),sK56(X2,X3)) = X2
& ! [X4] :
( ! [X5] :
( ! [X6] :
( ~ neq(X5,nil)
| app(X4,X6) != X1
| app(app(X4,X5),X6) != X0
| ~ ssList(X6) )
| ~ ssList(X5) )
| ~ ssList(X4) )
& neq(X0,nil) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK54,sK55,sK56]),skolemize(X7,sK54(X2,X3)),skolemize(X8,sK55(X2,X3)),skolemize(X9,sK56(X2,X3))],[f299]) ).
fof(f501,plain,
! [X2,X3,X0,X1] :
( ~ sP6(X0,X1,X2,X3)
| ssItem(sK54(X2,X3)) ),
inference(cnf_transformation,[],[f300]) ).
fof(f502,plain,
! [X2,X3,X0,X1] :
( ~ sP6(X0,X1,X2,X3)
| ssList(sK55(X2,X3)) ),
inference(cnf_transformation,[],[f300]) ).
fof(f503,plain,
! [X2,X3,X0,X1] :
( ~ sP6(X0,X1,X2,X3)
| ssList(sK56(X2,X3)) ),
inference(cnf_transformation,[],[f300]) ).
fof(f505,plain,
! [X2,X3,X0,X1] :
( ~ sP6(X0,X1,X2,X3)
| app(sK55(X2,X3),sK56(X2,X3)) = X3 ),
inference(cnf_transformation,[],[f300]) ).
fof(f506,plain,
! [X2,X3,X0,X1] :
( ~ sP6(X0,X1,X2,X3)
| app(app(sK55(X2,X3),cons(sK54(X2,X3),nil)),sK56(X2,X3)) = X2 ),
inference(cnf_transformation,[],[f300]) ).
fof(f507,plain,
! [X2,X3,X0,X1,X6,X4,X5] :
( ~ sP6(X0,X1,X2,X3)
| ~ neq(X5,nil)
| app(X4,X6) != X1
| app(app(X4,X5),X6) != X0
| ~ ssList(X6)
| ~ ssList(X5)
| ~ ssList(X4) ),
inference(cnf_transformation,[],[f300]) ).
fof(f548,plain,
! [X2,X3,X1,X6,X4,X5] :
( ~ sP6(app(app(X4,X5),X6),X1,X2,X3)
| ~ neq(X5,nil)
| app(X4,X6) != X1
| ~ ssList(X6)
| ~ ssList(X5)
| ~ ssList(X4) ),
inference(equality_resolution,[],[f507]) ).
fof(f549,plain,
! [X2,X3,X6,X4,X5] :
( ~ sP6(app(app(X4,X5),X6),app(X4,X6),X2,X3)
| ~ neq(X5,nil)
| ~ ssList(X6)
| ~ ssList(X5)
| ~ ssList(X4) ),
inference(equality_resolution,[],[f548]) ).
tcf(c_247,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0)
| ~ neq(X1,nil)
| ~ sP6(app(app(X0,X1),X2),app(X0,X2),X3,X4) ),
inference(cnf_transformation,[],[f549]) ).
tcf(c_248,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( app(app(sK55(X2,X3),cons(sK54(X2,X3),nil)),sK56(X2,X3)) = X2 )
| ~ sP6(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f506]) ).
tcf(c_249,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( app(sK55(X2,X3),sK56(X2,X3)) = X3 )
| ~ sP6(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f505]) ).
tcf(c_251,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ssList(sK56(X2,X3))
| ~ sP6(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f503]) ).
tcf(c_252,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ssList(sK55(X2,X3))
| ~ sP6(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f502]) ).
tcf(c_253,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ssItem(sK54(X2,X3))
| ~ sP6(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f501]) ).
tcf(c_3293,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ssItem(sK54(X2,X3))
| ( X3 != sK59 )
| ( X2 != sK60 )
| ( X1 != sK59 )
| ( X0 != sK60 ) ),
inference(resolution_lifted,[status(thm)],[c_253,c_380]) ).
tcf(c_3294,plain,
ssItem(sK54(sK60,sK59)),
inference(unflattening,[status(thm)],[c_3293]) ).
tcf(c_3298,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ssList(sK55(X2,X3))
| ( X3 != sK59 )
| ( X2 != sK60 )
| ( X1 != sK59 )
| ( X0 != sK60 ) ),
inference(resolution_lifted,[status(thm)],[c_252,c_380]) ).
tcf(c_3299,plain,
ssList(sK55(sK60,sK59)),
inference(unflattening,[status(thm)],[c_3298]) ).
tcf(c_3303,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ssList(sK56(X2,X3))
| ( X3 != sK59 )
| ( X2 != sK60 )
| ( X1 != sK59 )
| ( X0 != sK60 ) ),
inference(resolution_lifted,[status(thm)],[c_251,c_380]) ).
tcf(c_3304,plain,
ssList(sK56(sK60,sK59)),
inference(unflattening,[status(thm)],[c_3303]) ).
tcf(c_3323,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( app(sK55(X2,X3),sK56(X2,X3)) = X3 )
| ( X3 != sK59 )
| ( X2 != sK60 )
| ( X1 != sK59 )
| ( X0 != sK60 ) ),
inference(resolution_lifted,[status(thm)],[c_249,c_380]) ).
tcf(c_3324,plain,
app(sK55(sK60,sK59),sK56(sK60,sK59)) = sK59,
inference(unflattening,[status(thm)],[c_3323]) ).
tcf(c_3328,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( app(app(sK55(X2,X3),cons(sK54(X2,X3),nil)),sK56(X2,X3)) = X2 )
| ( X3 != sK59 )
| ( X2 != sK60 )
| ( X1 != sK59 )
| ( X0 != sK60 ) ),
inference(resolution_lifted,[status(thm)],[c_248,c_380]) ).
tcf(c_3329,plain,
app(app(sK55(sK60,sK59),cons(sK54(sK60,sK59),nil)),sK56(sK60,sK59)) = sK60,
inference(unflattening,[status(thm)],[c_3328]) ).
tcf(c_3338,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0)
| ~ neq(X1,nil)
| ( X4 != sK59 )
| ( X3 != sK60 )
| ( app(X0,X2) != sK59 )
| ( app(app(X0,X1),X2) != sK60 ) ),
inference(resolution_lifted,[status(thm)],[c_247,c_380]) ).
tcf(c_3339,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0)
| ~ neq(X1,nil)
| ( app(X0,X2) != sK59 )
| ( app(app(X0,X1),X2) != sK60 ) ),
inference(unflattening,[status(thm)],[c_3338]) ).
tcf(c_3382,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( X3 = X4 )
| ~ ssList(X4)
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0)
| ( X4 != nil )
| ( X1 != X3 )
| ( app(X0,X2) != sK59 )
| ( app(app(X0,X1),X2) != sK60 ) ),
inference(resolution_lifted,[status(thm)],[c_138,c_3339]) ).
tcf(c_3383,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X1 = nil )
| ~ ssList(nil)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0)
| ( app(X0,X2) != sK59 )
| ( app(app(X0,X1),X2) != sK60 ) ),
inference(unflattening,[status(thm)],[c_3382]) ).
tcf(c_3385,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X1 = nil )
| ( app(app(X0,X1),X2) != sK60 )
| ( app(X0,X2) != sK59 )
| ~ ssList(X0)
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(global_subsumption_just,[status(thm)],[c_3383,c_141,c_3383]) ).
tcf(c_3386,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X1 = nil )
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0)
| ( app(X0,X2) != sK59 )
| ( app(app(X0,X1),X2) != sK60 ) ),
inference(renaming,[status(thm)],[c_3385]) ).
tcf(c_9104,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X1 = nil )
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0)
| ( app(X0,X2) != sK59 )
| ( app(app(X0,X1),X2) != sK60 ) ),
inference(demodulation,[status(thm)],[c_3386]) ).
tcf(c_9105,plain,
iPr_def_15 = sK60,
inference(demodulation,[status(thm)],[c_3329,c_9099,c_9096,c_9097,c_9095,c_9098,c_9100]) ).
tcf(c_9106,plain,
iPr_def_16 = sK59,
inference(demodulation,[status(thm)],[c_3324,c_9101]) ).
tcf(c_9108,plain,
ssList(iPr_def_14),
inference(demodulation,[status(thm)],[c_3304]) ).
tcf(c_9109,plain,
ssList(iPr_def_10),
inference(demodulation,[status(thm)],[c_3299]) ).
tcf(c_9110,plain,
ssItem(iPr_def_11),
inference(demodulation,[status(thm)],[c_3294]) ).
tcf(c_12077,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X1 = nil )
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0)
| ( app(X0,X2) != iPr_def_16 )
| ( app(app(X0,X1),X2) != iPr_def_15 ) ),
inference(light_normalisation,[status(thm)],[c_9104,c_9105,c_9106]) ).
tcf(c_12192,plain,
! [X0: $i] :
( ( nil = iPr_def_12 )
| ~ ssList(iPr_def_12)
| ~ ssList(iPr_def_10)
| ~ ssList(X0)
| ( app(iPr_def_13,X0) != iPr_def_15 )
| ( app(iPr_def_10,X0) != iPr_def_16 ) ),
inference(superposition,[status(thm)],[c_9098,c_12077]) ).
tcf(c_12193,plain,
! [X0: $i] :
( ( nil = iPr_def_12 )
| ~ ssList(iPr_def_12)
| ~ ssList(X0)
| ( app(iPr_def_13,X0) != iPr_def_15 )
| ( app(iPr_def_10,X0) != iPr_def_16 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_12192,c_9109]) ).
tcf(c_12212,plain,
( ( nil = iPr_def_12 )
| ~ ssList(iPr_def_14)
| ~ ssList(iPr_def_12)
| ( app(iPr_def_10,iPr_def_14) != iPr_def_16 ) ),
inference(superposition,[status(thm)],[c_9100,c_12193]) ).
tcf(c_12213,plain,
( ( nil = iPr_def_12 )
| ~ ssList(iPr_def_14)
| ~ ssList(iPr_def_12) ),
inference(ground_joinability,[status(thm)],[c_12212,c_9101]) ).
tcf(c_12214,plain,
( ( nil = iPr_def_12 )
| ~ ssList(iPr_def_12) ),
inference(forward_subsumption_resolution,[status(thm)],[c_12213,c_9108]) ).
tcf(c_12326,plain,
( singletonP(iPr_def_12)
| ~ ssList(iPr_def_12) ),
inference(forward_subsumption_resolution,[status(thm)],[c_12325,c_9110]) ).
tcf(c_12721,plain,
ssList(iPr_def_12),
inference(forward_subsumption_resolution,[status(thm)],[c_12717,c_141,c_9110]) ).
tcf(c_12731,plain,
singletonP(iPr_def_12),
inference(backward_subsumption_resolution,[status(thm)],[c_12326,c_12721]) ).
tcf(c_12733,plain,
nil = iPr_def_12,
inference(backward_subsumption_resolution,[status(thm)],[c_12214,c_12721]) ).
tcf(c_12761,plain,
~ singletonP(iPr_def_12),
inference(demodulation,[status(thm)],[c_172,c_12733]) ).
tcf(c_12779,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_12761,c_12731]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWC003+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/5.37 % Computer : n006.cluster.edu
% 0.10/5.37 % Model : x86_64 x86_64
% 0.10/5.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/5.37 % Memory : 8046.5625MB
% 0.10/5.37 % OS : Linux 6.8.0-71-generic
% 0.10/5.37 % CPULimit : 300
% 0.10/5.37 % WCLimit : 300
% 0.10/5.37 % DateTime : Thu Sep 24 15:51:19 UTC 2026
% 0.10/5.37 % CPUTime :
% 0.10/5.37 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.15/5.40 Running first-order theorem proving
% 0.15/5.40 Running: /export/starexec/sandbox/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.15/5.41
% 0.15/5.41 % ======== iProver multi-core TPTP/SMT =========
% 0.15/5.41
% 0.15/5.41 % Detected problem language: tptp
% 0.15/5.43 % Proving...
% 4.15/6.28 % SZS status Started for theBenchmark.p
% 4.15/6.28 % SZS status Theorem for theBenchmark.p
% 4.15/6.28
% 4.15/6.28 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 4.15/6.28
% 4.15/6.28 % ------ iProver source info
% 4.15/6.28
% 4.15/6.28 % git: date: 2026-07-19 20:42:38 +0200
% 4.15/6.28 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 4.15/6.28 % git: non_committed_changes: false
% 4.15/6.28
% 4.15/6.28 % ------ Parsing...
% 4.15/6.28 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 4.15/6.28
% 4.15/6.28 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe:2:0s pe:4:0s pe:8:0s pe_e sup_sim: 0 sf_s rm: 6 0s sf_e pe_s pe_e %
% 4.15/6.28
% 4.15/6.28 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 4.15/6.28
% 4.15/6.28 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 4.15/6.28 % ------ Proving...
% 4.15/6.28 % ------ Problem Properties
% 4.15/6.28
% 4.15/6.28 %
% 4.15/6.28 % clauses 198
% 4.15/6.28 % conjectures 2
% 4.15/6.28 % EPR 58
% 4.15/6.28 % Horn 130
% 4.15/6.28 % unary 31
% 4.15/6.28 % binary 40
% 4.15/6.28 % lits 647
% 4.15/6.28 % lits eq 94
% 4.15/6.28 % fd_pure 0
% 4.15/6.28 % fd_pseudo 0
% 4.15/6.28 % fd_cond 23
% 4.15/6.28 % fd_pseudo_cond 14
% 4.15/6.28 % AC symbols 0
% 4.15/6.28
% 4.15/6.28 % ------ Schedule dynamic 5 is on
% 4.15/6.28
% 4.15/6.28 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 4.15/6.28
% 4.15/6.28
% 4.15/6.28 % ------
% 4.15/6.28 % Current options:
% 4.15/6.28 % ------
% 4.15/6.28
% 4.15/6.28
% 4.15/6.28 %
% 4.15/6.28
% 4.15/6.28 % ------ Proving...
% 4.15/6.28 %
% 4.15/6.28
% 4.15/6.28 % SZS status Theorem for theBenchmark.p
% 4.15/6.28
% 4.15/6.28 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 4.15/6.28
% 4.15/6.28
%------------------------------------------------------------------------------