%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SWC413+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 : n016.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 03:09:41 PM UTC 2026
% Result : Theorem 41.94s 9.96s
% Output : CNFRefutation 41.94s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 6
% Syntax : Number of formulae : 81 ( 9 unt; 2 def)
% Number of atoms : 475 ( 129 equ)
% Maximal formula atoms : 28 ( 5 avg)
% Number of connectives : 528 ( 179 ~; 176 |; 132 &)
% ( 0 <=>; 41 =>; 0 <=; 0 <~>)
% Maximal formula depth : 23 ( 7 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-4 aty)
% Number of functors : 16 ( 16 usr; 10 con; 0-2 aty)
% Number of variables : 269 ( 0 sgn 191 !; 78 ?; 47 :)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
? [X0] :
( ? [X1] :
( X0 != X1
& ssItem(X1) )
& ssItem(X0) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax2) ).
fof(f25,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssItem(X1)
=> tl(cons(X1,X0)) = X0 ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax25) ).
fof(f96,conjecture,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( ( ( ! [X7] :
( ssItem(X7)
=> ! [X8] :
( ssItem(X8)
=> ! [X9] :
( ssList(X9)
=> app(app(cons(X7,nil),cons(X8,nil)),X9) != X1 ) ) )
| ? [X13] :
( ? [X14] :
( ? [X15] :
( app(app(cons(X13,nil),cons(X14,nil)),X15) = X3
& ssList(X15) )
& ssItem(X14) )
& ssItem(X13) ) )
& ( ! [X10] :
( ssItem(X10)
=> ! [X11] :
( ssItem(X11)
=> ! [X12] :
( ssList(X12)
=> ( app(app(cons(X11,nil),cons(X10,nil)),X12) != X2
| app(app(cons(X10,nil),cons(X11,nil)),X12) != X3 ) ) ) )
| ! [X7] :
( ssItem(X7)
=> ! [X8] :
( ssItem(X8)
=> ! [X9] :
( ssList(X9)
=> app(app(cons(X7,nil),cons(X8,nil)),X9) != X1 ) ) )
| ? [X4] :
( ? [X5] :
( ? [X6] :
( app(app(cons(X5,nil),cons(X4,nil)),X6) = X0
& app(app(cons(X4,nil),cons(X5,nil)),X6) = X1
& ssList(X6) )
& ssItem(X5) )
& ssItem(X4) ) ) )
| 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)
=> ( ( ( ! [X7] :
( ssItem(X7)
=> ! [X8] :
( ssItem(X8)
=> ! [X9] :
( ssList(X9)
=> app(app(cons(X7,nil),cons(X8,nil)),X9) != X1 ) ) )
| ? [X13] :
( ? [X14] :
( ? [X15] :
( app(app(cons(X13,nil),cons(X14,nil)),X15) = X3
& ssList(X15) )
& ssItem(X14) )
& ssItem(X13) ) )
& ( ! [X10] :
( ssItem(X10)
=> ! [X11] :
( ssItem(X11)
=> ! [X12] :
( ssList(X12)
=> ( app(app(cons(X11,nil),cons(X10,nil)),X12) != X2
| app(app(cons(X10,nil),cons(X11,nil)),X12) != X3 ) ) ) )
| ! [X7] :
( ssItem(X7)
=> ! [X8] :
( ssItem(X8)
=> ! [X9] :
( ssList(X9)
=> app(app(cons(X7,nil),cons(X8,nil)),X9) != X1 ) ) )
| ? [X4] :
( ? [X5] :
( ? [X6] :
( app(app(cons(X5,nil),cons(X4,nil)),X6) = X0
& app(app(cons(X4,nil),cons(X5,nil)),X6) = X1
& ssList(X6) )
& ssItem(X5) )
& ssItem(X4) ) ) )
| X0 != X2
| X1 != X3 ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f96]) ).
fof(f98,plain,
~ ! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( ( ( ! [X16] :
( ssItem(X16)
=> ! [X17] :
( ssItem(X17)
=> ! [X18] :
( ssList(X18)
=> app(app(cons(X16,nil),cons(X17,nil)),X18) != X1 ) ) )
| ? [X13] :
( ? [X14] :
( ? [X15] :
( app(app(cons(X13,nil),cons(X14,nil)),X15) = X3
& ssList(X15) )
& ssItem(X14) )
& ssItem(X13) ) )
& ( ! [X10] :
( ssItem(X10)
=> ! [X11] :
( ssItem(X11)
=> ! [X12] :
( ssList(X12)
=> ( app(app(cons(X11,nil),cons(X10,nil)),X12) != X2
| app(app(cons(X10,nil),cons(X11,nil)),X12) != X3 ) ) ) )
| ! [X7] :
( ssItem(X7)
=> ! [X8] :
( ssItem(X8)
=> ! [X9] :
( ssList(X9)
=> app(app(cons(X7,nil),cons(X8,nil)),X9) != X1 ) ) )
| ? [X4] :
( ? [X5] :
( ? [X6] :
( app(app(cons(X5,nil),cons(X4,nil)),X6) = X0
& app(app(cons(X4,nil),cons(X5,nil)),X6) = X1
& ssList(X6) )
& ssItem(X5) )
& ssItem(X4) ) ) )
| X0 != X2
| X1 != X3 ) ) ) ) ),
inference(rectify,[],[f97]) ).
fof(f132,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssItem(X1)
| tl(cons(X1,X0)) = X0 ) ),
inference(ennf_transformation,[],[f25]) ).
fof(f222,plain,
? [X0] :
( ssList(X0)
& ? [X1] :
( ssList(X1)
& ? [X2] :
( ssList(X2)
& ? [X3] :
( ssList(X3)
& ( ( ? [X16] :
( ssItem(X16)
& ? [X17] :
( ssItem(X17)
& ? [X18] :
( ssList(X18)
& app(app(cons(X16,nil),cons(X17,nil)),X18) = X1 ) ) )
& ! [X13] :
( ! [X14] :
( ! [X15] :
( app(app(cons(X13,nil),cons(X14,nil)),X15) != X3
| ~ ssList(X15) )
| ~ ssItem(X14) )
| ~ ssItem(X13) ) )
| ( ? [X10] :
( ssItem(X10)
& ? [X11] :
( ssItem(X11)
& ? [X12] :
( ssList(X12)
& app(app(cons(X11,nil),cons(X10,nil)),X12) = X2
& app(app(cons(X10,nil),cons(X11,nil)),X12) = X3 ) ) )
& ? [X7] :
( ssItem(X7)
& ? [X8] :
( ssItem(X8)
& ? [X9] :
( ssList(X9)
& app(app(cons(X7,nil),cons(X8,nil)),X9) = X1 ) ) )
& ! [X4] :
( ! [X5] :
( ! [X6] :
( app(app(cons(X5,nil),cons(X4,nil)),X6) != X0
| app(app(cons(X4,nil),cons(X5,nil)),X6) != X1
| ~ ssList(X6) )
| ~ ssItem(X5) )
| ~ ssItem(X4) ) ) )
& X0 = X2
& X1 = X3 ) ) ) ),
inference(ennf_transformation,[],[f98]) ).
fof(f223,plain,
? [X0] :
( ssList(X0)
& ? [X1] :
( ssList(X1)
& ? [X2] :
( ssList(X2)
& ? [X3] :
( ssList(X3)
& ( ( ? [X16] :
( ssItem(X16)
& ? [X17] :
( ssItem(X17)
& ? [X18] :
( ssList(X18)
& app(app(cons(X16,nil),cons(X17,nil)),X18) = X1 ) ) )
& ! [X13] :
( ! [X14] :
( ! [X15] :
( app(app(cons(X13,nil),cons(X14,nil)),X15) != X3
| ~ ssList(X15) )
| ~ ssItem(X14) )
| ~ ssItem(X13) ) )
| ( ? [X10] :
( ssItem(X10)
& ? [X11] :
( ssItem(X11)
& ? [X12] :
( ssList(X12)
& app(app(cons(X11,nil),cons(X10,nil)),X12) = X2
& app(app(cons(X10,nil),cons(X11,nil)),X12) = X3 ) ) )
& ? [X7] :
( ssItem(X7)
& ? [X8] :
( ssItem(X8)
& ? [X9] :
( ssList(X9)
& app(app(cons(X7,nil),cons(X8,nil)),X9) = X1 ) ) )
& ! [X4] :
( ! [X5] :
( ! [X6] :
( app(app(cons(X5,nil),cons(X4,nil)),X6) != X0
| app(app(cons(X4,nil),cons(X5,nil)),X6) != X1
| ~ ssList(X6) )
| ~ ssItem(X5) )
| ~ ssItem(X4) ) ) )
& X0 = X2
& X1 = X3 ) ) ) ),
inference(flattening,[],[f222]) ).
fof(f237,plain,
( sK8 != sK9
& ssItem(sK9)
& ssItem(sK8) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8,sK9]),skolemize(X0,sK8),skolemize(X1,sK9)],[f2]) ).
fof(f300,plain,
! [X1,X0,X2,X3] :
( ~ sP7(X1,X0,X2,X3)
| ( sP6(X3,X2)
& ? [X7] :
( ssItem(X7)
& ? [X8] :
( ssItem(X8)
& ? [X9] :
( ssList(X9)
& app(app(cons(X7,nil),cons(X8,nil)),X9) = X1 ) ) )
& ! [X4] :
( ! [X5] :
( ! [X6] :
( app(app(cons(X5,nil),cons(X4,nil)),X6) != X0
| app(app(cons(X4,nil),cons(X5,nil)),X6) != X1
| ~ ssList(X6) )
| ~ ssItem(X5) )
| ~ ssItem(X4) ) ) ),
inference(nnf_transformation,[],[f234]) ).
fof(f301,plain,
! [X0,X1,X2,X3] :
( ~ sP7(X0,X1,X2,X3)
| ( sP6(X3,X2)
& ? [X7] :
( ssItem(X7)
& ? [X8] :
( ssItem(X8)
& ? [X9] :
( ssList(X9)
& app(app(cons(X7,nil),cons(X8,nil)),X9) = X0 ) ) )
& ! [X4] :
( ! [X5] :
( ! [X6] :
( app(app(cons(X5,nil),cons(X4,nil)),X6) != X1
| app(app(cons(X4,nil),cons(X5,nil)),X6) != X0
| ~ ssList(X6) )
| ~ ssItem(X5) )
| ~ ssItem(X4) ) ) ),
inference(rectify,[],[f300]) ).
fof(f302,plain,
! [X0,X1,X2,X3] :
( ~ sP7(X0,X1,X2,X3)
| ( sP6(X3,X2)
& ssItem(sK55(X0))
& ssItem(sK56(X0))
& ssList(sK57(X0))
& app(app(cons(sK55(X0),nil),cons(sK56(X0),nil)),sK57(X0)) = X0
& ! [X4] :
( ! [X5] :
( ! [X6] :
( app(app(cons(X5,nil),cons(X4,nil)),X6) != X1
| app(app(cons(X4,nil),cons(X5,nil)),X6) != X0
| ~ ssList(X6) )
| ~ ssItem(X5) )
| ~ ssItem(X4) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK55,sK56,sK57]),skolemize(X7,sK55(X0)),skolemize(X8,sK56(X0)),skolemize(X9,sK57(X0))],[f301]) ).
fof(f306,plain,
? [X0] :
( ssList(X0)
& ? [X1] :
( ssList(X1)
& ? [X2] :
( ssList(X2)
& ? [X3] :
( ssList(X3)
& ( ( ? [X7] :
( ssItem(X7)
& ? [X8] :
( ssItem(X8)
& ? [X9] :
( ssList(X9)
& app(app(cons(X7,nil),cons(X8,nil)),X9) = X1 ) ) )
& ! [X4] :
( ! [X5] :
( ! [X6] :
( app(app(cons(X4,nil),cons(X5,nil)),X6) != X3
| ~ ssList(X6) )
| ~ ssItem(X5) )
| ~ ssItem(X4) ) )
| sP7(X1,X0,X2,X3) )
& X0 = X2
& X1 = X3 ) ) ) ),
inference(rectify,[],[f235]) ).
fof(f307,plain,
( ssList(sK61)
& ssList(sK62)
& ssList(sK63)
& ssList(sK64)
& ( ( ssItem(sK65)
& ssItem(sK66)
& ssList(sK67)
& sK62 = app(app(cons(sK65,nil),cons(sK66,nil)),sK67)
& ! [X4] :
( ! [X5] :
( ! [X6] :
( app(app(cons(X4,nil),cons(X5,nil)),X6) != sK64
| ~ ssList(X6) )
| ~ ssItem(X5) )
| ~ ssItem(X4) ) )
| sP7(sK62,sK61,sK63,sK64) )
& sK61 = sK63
& sK62 = sK64 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK61,sK62,sK63,sK64,sK65,sK66,sK67]),skolemize(X0,sK61),skolemize(X1,sK62),skolemize(X2,sK63),skolemize(X3,sK64),skolemize(X7,sK65),skolemize(X8,sK66),skolemize(X9,sK67)],[f306]) ).
fof(f311,plain,
ssItem(sK9),
inference(cnf_transformation,[],[f237]) ).
fof(f411,plain,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssItem(X1)
| tl(cons(X1,X0)) = X0 ),
inference(cnf_transformation,[],[f132]) ).
fof(f507,plain,
! [X2,X3,X0,X1] :
( ~ sP7(X0,X1,X2,X3)
| sP6(X3,X2) ),
inference(cnf_transformation,[],[f302]) ).
fof(f511,plain,
! [X2,X3,X0,X1] :
( ~ sP7(X0,X1,X2,X3)
| app(app(cons(sK55(X0),nil),cons(sK56(X0),nil)),sK57(X0)) = X0 ),
inference(cnf_transformation,[],[f302]) ).
fof(f512,plain,
! [X2,X3,X0,X1,X6,X4,X5] :
( ~ sP7(X0,X1,X2,X3)
| app(app(cons(X5,nil),cons(X4,nil)),X6) != X1
| app(app(cons(X4,nil),cons(X5,nil)),X6) != X0
| ~ ssList(X6)
| ~ ssItem(X5)
| ~ ssItem(X4) ),
inference(cnf_transformation,[],[f302]) ).
fof(f518,plain,
ssList(sK61),
inference(cnf_transformation,[],[f307]) ).
fof(f522,plain,
( ssItem(sK65)
| sP7(sK62,sK61,sK63,sK64) ),
inference(cnf_transformation,[],[f307]) ).
fof(f523,plain,
( ssItem(sK66)
| sP7(sK62,sK61,sK63,sK64) ),
inference(cnf_transformation,[],[f307]) ).
fof(f524,plain,
( ssList(sK67)
| sP7(sK62,sK61,sK63,sK64) ),
inference(cnf_transformation,[],[f307]) ).
fof(f525,plain,
( sK62 = app(app(cons(sK65,nil),cons(sK66,nil)),sK67)
| sP7(sK62,sK61,sK63,sK64) ),
inference(cnf_transformation,[],[f307]) ).
fof(f526,plain,
! [X6,X4,X5] :
( app(app(cons(X4,nil),cons(X5,nil)),X6) != sK64
| ~ ssList(X6)
| ~ ssItem(X5)
| ~ ssItem(X4)
| sP7(sK62,sK61,sK63,sK64) ),
inference(cnf_transformation,[],[f307]) ).
fof(f527,plain,
sK61 = sK63,
inference(cnf_transformation,[],[f307]) ).
fof(f528,plain,
sK62 = sK64,
inference(cnf_transformation,[],[f307]) ).
fof(f529,plain,
! [X6,X4,X5] :
( app(app(cons(X4,nil),cons(X5,nil)),X6) != sK64
| ~ ssList(X6)
| ~ ssItem(X5)
| ~ ssItem(X4)
| sP7(sK64,sK63,sK63,sK64) ),
inference(definition_unfolding,[],[f526,f528,f527]) ).
fof(f530,plain,
( sK64 = app(app(cons(sK65,nil),cons(sK66,nil)),sK67)
| sP7(sK64,sK63,sK63,sK64) ),
inference(definition_unfolding,[],[f525,f528,f527,f528]) ).
fof(f531,plain,
( ssList(sK67)
| sP7(sK64,sK63,sK63,sK64) ),
inference(definition_unfolding,[],[f524,f528,f527]) ).
fof(f532,plain,
( ssItem(sK66)
| sP7(sK64,sK63,sK63,sK64) ),
inference(definition_unfolding,[],[f523,f528,f527]) ).
fof(f533,plain,
( ssItem(sK65)
| sP7(sK64,sK63,sK63,sK64) ),
inference(definition_unfolding,[],[f522,f528,f527]) ).
fof(f535,plain,
ssList(sK63),
inference(definition_unfolding,[],[f518,f527]) ).
fof(f563,plain,
! [X2,X3,X1,X6,X4,X5] :
( ~ sP7(app(app(cons(X4,nil),cons(X5,nil)),X6),X1,X2,X3)
| app(app(cons(X5,nil),cons(X4,nil)),X6) != X1
| ~ ssList(X6)
| ~ ssItem(X5)
| ~ ssItem(X4) ),
inference(equality_resolution,[],[f512]) ).
fof(f564,plain,
! [X2,X3,X6,X4,X5] :
( ~ sP7(app(app(cons(X4,nil),cons(X5,nil)),X6),app(app(cons(X5,nil),cons(X4,nil)),X6),X2,X3)
| ~ ssList(X6)
| ~ ssItem(X5)
| ~ ssItem(X4) ),
inference(equality_resolution,[],[f563]) ).
tcf(c_52,plain,
ssItem(sK9),
inference(cnf_transformation,[],[f311]) ).
tcf(c_152,plain,
! [X0: $i,X1: $i] :
( ( tl(cons(X0,X1)) = X1 )
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f411]) ).
tcf(c_246,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ~ ssList(X2)
| ~ ssItem(X1)
| ~ ssItem(X0)
| ~ sP7(app(app(cons(X0,nil),cons(X1,nil)),X2),app(app(cons(X1,nil),cons(X0,nil)),X2),X3,X4) ),
inference(cnf_transformation,[],[f564]) ).
tcf(c_247,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( app(app(cons(sK55(X0),nil),cons(sK56(X0),nil)),sK57(X0)) = X0 )
| ~ sP7(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f511]) ).
tcf(c_251,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( sP6(X3,X2)
| ~ sP7(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f507]) ).
tcf(c_257,negated_conjecture,
! [X0: $i,X1: $i,X2: $i] :
( sP7(sK64,sK63,sK63,sK64)
| ~ ssList(X2)
| ~ ssItem(X1)
| ~ ssItem(X0)
| ( app(app(cons(X0,nil),cons(X1,nil)),X2) != sK64 ) ),
inference(cnf_transformation,[],[f529]) ).
tcf(c_258,negated_conjecture,
( sP7(sK64,sK63,sK63,sK64)
| ( app(app(cons(sK65,nil),cons(sK66,nil)),sK67) = sK64 ) ),
inference(cnf_transformation,[],[f530]) ).
tcf(c_259,negated_conjecture,
( ssList(sK67)
| sP7(sK64,sK63,sK63,sK64) ),
inference(cnf_transformation,[],[f531]) ).
tcf(c_260,negated_conjecture,
( ssItem(sK66)
| sP7(sK64,sK63,sK63,sK64) ),
inference(cnf_transformation,[],[f532]) ).
tcf(c_261,negated_conjecture,
( ssItem(sK65)
| sP7(sK64,sK63,sK63,sK64) ),
inference(cnf_transformation,[],[f533]) ).
tcf(c_265,negated_conjecture,
ssList(sK63),
inference(cnf_transformation,[],[f535]) ).
tcf(c_482,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
( sP7(X0,X2,X4,X6)
| ~ sP7(X1,X3,X5,X7)
| ( X6 != X7 )
| ( X4 != X5 )
| ( X2 != X3 )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_561,plain,
( sP7(sK64,sK63,sK63,sK64)
| ~ ssList(sK67)
| ~ ssItem(sK66)
| ~ ssItem(sK65) ),
inference(resolution,[status(thm)],[c_257,c_258]) ).
tcf(c_572,plain,
! [X0: $i] :
( ( tl(cons(sK9,X0)) = X0 )
| ~ ssItem(sK9)
| ~ ssList(X0) ),
inference(instantiation,[status(thm)],[c_152]) ).
tcf(c_579,plain,
sP7(sK64,sK63,sK63,sK64),
inference(global_subsumption_just,[status(thm)],[c_561,c_261,c_260,c_259,c_561]) ).
tcf(c_598,plain,
( sP6(sK64,sK63)
| ~ sP7(sK64,sK63,sK63,sK64) ),
inference(instantiation,[status(thm)],[c_251]) ).
tcf(c_604,plain,
( ( app(app(cons(sK55(sK64),nil),cons(sK56(sK64),nil)),sK57(sK64)) = sK64 )
| ~ sP7(sK64,sK63,sK63,sK64) ),
inference(instantiation,[status(thm)],[c_247]) ).
tcf(c_673,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( sP7(X0,X1,X2,X3)
| ~ sP7(sK64,sK63,sK63,sK64)
| ( X3 != sK64 )
| ( X2 != sK63 )
| ( X1 != sK63 )
| ( X0 != sK64 ) ),
inference(instantiation,[status(thm)],[c_482]) ).
tcf(c_3265,plain,
! [X0: $i,X1: $i,X2: $i] :
( sP7(X0,X1,tl(cons(sK9,sK63)),X2)
| ~ sP7(sK64,sK63,sK63,sK64)
| ( X2 != sK64 )
| ( X1 != sK63 )
| ( X0 != sK64 )
| ( tl(cons(sK9,sK63)) != sK63 ) ),
inference(instantiation,[status(thm)],[c_673]) ).
tcf(c_3266,plain,
( ( tl(cons(sK9,sK63)) = sK63 )
| ~ ssList(sK63)
| ~ ssItem(sK9) ),
inference(instantiation,[status(thm)],[c_572]) ).
tcf(c_8064,plain,
! [X0: $i,X1: $i] :
( sP7(X0,X1,tl(cons(sK9,sK63)),app(app(cons(sK55(sK64),nil),cons(sK56(sK64),nil)),sK57(sK64)))
| ~ sP7(sK64,sK63,sK63,sK64)
| ( X1 != sK63 )
| ( X0 != sK64 )
| ( tl(cons(sK9,sK63)) != sK63 )
| ( app(app(cons(sK55(sK64),nil),cons(sK56(sK64),nil)),sK57(sK64)) != sK64 ) ),
inference(instantiation,[status(thm)],[c_3265]) ).
tcf(c_13288,plain,
! [X0: $i] :
( sP7(X0,app(app(cons(sK59(sK64,sK63),nil),cons(sK58(sK64,sK63),nil)),sK60(sK64,sK63)),tl(cons(sK9,sK63)),app(app(cons(sK55(sK64),nil),cons(sK56(sK64),nil)),sK57(sK64)))
| ~ sP7(sK64,sK63,sK63,sK64)
| ( X0 != sK64 )
| ( tl(cons(sK9,sK63)) != sK63 )
| ( app(app(cons(sK55(sK64),nil),cons(sK56(sK64),nil)),sK57(sK64)) != sK64 )
| ( app(app(cons(sK59(sK64,sK63),nil),cons(sK58(sK64,sK63),nil)),sK60(sK64,sK63)) != sK63 ) ),
inference(instantiation,[status(thm)],[c_8064]) ).
tcf(c_21395,plain,
( sP7(app(app(cons(sK58(sK64,sK63),nil),cons(sK59(sK64,sK63),nil)),sK60(sK64,sK63)),app(app(cons(sK59(sK64,sK63),nil),cons(sK58(sK64,sK63),nil)),sK60(sK64,sK63)),tl(cons(sK9,sK63)),app(app(cons(sK55(sK64),nil),cons(sK56(sK64),nil)),sK57(sK64)))
| ~ sP7(sK64,sK63,sK63,sK64)
| ( tl(cons(sK9,sK63)) != sK63 )
| ( app(app(cons(sK55(sK64),nil),cons(sK56(sK64),nil)),sK57(sK64)) != sK64 )
| ( app(app(cons(sK59(sK64,sK63),nil),cons(sK58(sK64,sK63),nil)),sK60(sK64,sK63)) != sK63 )
| ( app(app(cons(sK58(sK64,sK63),nil),cons(sK59(sK64,sK63),nil)),sK60(sK64,sK63)) != sK64 ) ),
inference(instantiation,[status(thm)],[c_13288]) ).
tcf(c_21396,plain,
( ~ ssList(sK60(sK64,sK63))
| ~ ssItem(sK59(sK64,sK63))
| ~ ssItem(sK58(sK64,sK63))
| ~ sP7(app(app(cons(sK58(sK64,sK63),nil),cons(sK59(sK64,sK63),nil)),sK60(sK64,sK63)),app(app(cons(sK59(sK64,sK63),nil),cons(sK58(sK64,sK63),nil)),sK60(sK64,sK63)),tl(cons(sK9,sK63)),app(app(cons(sK55(sK64),nil),cons(sK56(sK64),nil)),sK57(sK64))) ),
inference(instantiation,[status(thm)],[c_246]) ).
fof(f233,definition,
! [X3,X2] :
( ~ sP6(X3,X2)
| ? [X10] :
( ssItem(X10)
& ? [X11] :
( ssItem(X11)
& ? [X12] :
( ssList(X12)
& app(app(cons(X11,nil),cons(X10,nil)),X12) = X2
& app(app(cons(X10,nil),cons(X11,nil)),X12) = X3 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP6])],[predicate_definition_introduction]) ).
fof(f234,definition,
! [X1,X0,X2,X3] :
( ~ sP7(X1,X0,X2,X3)
| ( sP6(X3,X2)
& ? [X7] :
( ssItem(X7)
& ? [X8] :
( ssItem(X8)
& ? [X9] :
( ssList(X9)
& app(app(cons(X7,nil),cons(X8,nil)),X9) = X1 ) ) )
& ! [X4] :
( ! [X5] :
( ! [X6] :
( app(app(cons(X5,nil),cons(X4,nil)),X6) != X0
| app(app(cons(X4,nil),cons(X5,nil)),X6) != X1
| ~ ssList(X6) )
| ~ ssItem(X5) )
| ~ ssItem(X4) ) ) ),
introduced(definition,[new_symbols(definition,[sP7])],[predicate_definition_introduction]) ).
fof(f235,plain,
? [X0] :
( ssList(X0)
& ? [X1] :
( ssList(X1)
& ? [X2] :
( ssList(X2)
& ? [X3] :
( ssList(X3)
& ( ( ? [X16] :
( ssItem(X16)
& ? [X17] :
( ssItem(X17)
& ? [X18] :
( ssList(X18)
& app(app(cons(X16,nil),cons(X17,nil)),X18) = X1 ) ) )
& ! [X13] :
( ! [X14] :
( ! [X15] :
( app(app(cons(X13,nil),cons(X14,nil)),X15) != X3
| ~ ssList(X15) )
| ~ ssItem(X14) )
| ~ ssItem(X13) ) )
| sP7(X1,X0,X2,X3) )
& X0 = X2
& X1 = X3 ) ) ) ),
inference(definition_folding,[],[f223,f234,f233]) ).
fof(f303,plain,
! [X3,X2] :
( ~ sP6(X3,X2)
| ? [X10] :
( ssItem(X10)
& ? [X11] :
( ssItem(X11)
& ? [X12] :
( ssList(X12)
& app(app(cons(X11,nil),cons(X10,nil)),X12) = X2
& app(app(cons(X10,nil),cons(X11,nil)),X12) = X3 ) ) ) ),
inference(nnf_transformation,[],[f233]) ).
fof(f304,plain,
! [X0,X1] :
( ~ sP6(X0,X1)
| ? [X2] :
( ssItem(X2)
& ? [X3] :
( ssItem(X3)
& ? [X4] :
( ssList(X4)
& app(app(cons(X3,nil),cons(X2,nil)),X4) = X1
& app(app(cons(X2,nil),cons(X3,nil)),X4) = X0 ) ) ) ),
inference(rectify,[],[f303]) ).
fof(f305,plain,
! [X0,X1] :
( ~ sP6(X0,X1)
| ( ssItem(sK58(X0,X1))
& ssItem(sK59(X0,X1))
& ssList(sK60(X0,X1))
& app(app(cons(sK59(X0,X1),nil),cons(sK58(X0,X1),nil)),sK60(X0,X1)) = X1
& app(app(cons(sK58(X0,X1),nil),cons(sK59(X0,X1),nil)),sK60(X0,X1)) = X0 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK58,sK59,sK60]),skolemize(X2,sK58(X0,X1)),skolemize(X3,sK59(X0,X1)),skolemize(X4,sK60(X0,X1))],[f304]) ).
fof(f513,plain,
! [X0,X1] :
( ~ sP6(X0,X1)
| ssItem(sK58(X0,X1)) ),
inference(cnf_transformation,[],[f305]) ).
fof(f514,plain,
! [X0,X1] :
( ~ sP6(X0,X1)
| ssItem(sK59(X0,X1)) ),
inference(cnf_transformation,[],[f305]) ).
fof(f515,plain,
! [X0,X1] :
( ~ sP6(X0,X1)
| ssList(sK60(X0,X1)) ),
inference(cnf_transformation,[],[f305]) ).
fof(f516,plain,
! [X0,X1] :
( ~ sP6(X0,X1)
| app(app(cons(sK59(X0,X1),nil),cons(sK58(X0,X1),nil)),sK60(X0,X1)) = X1 ),
inference(cnf_transformation,[],[f305]) ).
fof(f517,plain,
! [X0,X1] :
( ~ sP6(X0,X1)
| app(app(cons(sK58(X0,X1),nil),cons(sK59(X0,X1),nil)),sK60(X0,X1)) = X0 ),
inference(cnf_transformation,[],[f305]) ).
tcf(c_252,plain,
! [X0: $i,X1: $i] :
( ( app(app(cons(sK58(X0,X1),nil),cons(sK59(X0,X1),nil)),sK60(X0,X1)) = X0 )
| ~ sP6(X0,X1) ),
inference(cnf_transformation,[],[f517]) ).
tcf(c_253,plain,
! [X0: $i,X1: $i] :
( ( app(app(cons(sK59(X0,X1),nil),cons(sK58(X0,X1),nil)),sK60(X0,X1)) = X1 )
| ~ sP6(X0,X1) ),
inference(cnf_transformation,[],[f516]) ).
tcf(c_254,plain,
! [X0: $i,X1: $i] :
( ssList(sK60(X0,X1))
| ~ sP6(X0,X1) ),
inference(cnf_transformation,[],[f515]) ).
tcf(c_255,plain,
! [X0: $i,X1: $i] :
( ssItem(sK59(X0,X1))
| ~ sP6(X0,X1) ),
inference(cnf_transformation,[],[f514]) ).
tcf(c_256,plain,
! [X0: $i,X1: $i] :
( ssItem(sK58(X0,X1))
| ~ sP6(X0,X1) ),
inference(cnf_transformation,[],[f513]) ).
tcf(c_895,plain,
( ( app(app(cons(sK59(sK64,sK63),nil),cons(sK58(sK64,sK63),nil)),sK60(sK64,sK63)) = sK63 )
| ~ sP6(sK64,sK63) ),
inference(instantiation,[status(thm)],[c_253]) ).
tcf(c_896,plain,
( ( app(app(cons(sK58(sK64,sK63),nil),cons(sK59(sK64,sK63),nil)),sK60(sK64,sK63)) = sK64 )
| ~ sP6(sK64,sK63) ),
inference(instantiation,[status(thm)],[c_252]) ).
tcf(c_897,plain,
( ssItem(sK58(sK64,sK63))
| ~ sP6(sK64,sK63) ),
inference(instantiation,[status(thm)],[c_256]) ).
tcf(c_898,plain,
( ssItem(sK59(sK64,sK63))
| ~ sP6(sK64,sK63) ),
inference(instantiation,[status(thm)],[c_255]) ).
tcf(c_899,plain,
( ssList(sK60(sK64,sK63))
| ~ sP6(sK64,sK63) ),
inference(instantiation,[status(thm)],[c_254]) ).
tcf(c_21397,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_21396,c_21395,c_3266,c_895,c_896,c_897,c_898,c_899,c_604,c_598,c_579,c_52,c_265]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC413+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.12/0.38 % Computer : n016.cluster.edu
% 0.12/0.38 % Model : x86_64 x86_64
% 0.12/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.38 % Memory : 8046.5625MB
% 0.12/0.38 % OS : Linux 6.8.0-71-generic
% 0.12/0.38 % CPULimit : 300
% 0.12/0.38 % WCLimit : 300
% 0.12/0.38 % DateTime : Thu Sep 24 18:11:58 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.38 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.12/0.42 Running first-order theorem proving
% 0.12/0.42 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
% 0.12/0.43
% 0.12/0.43 % ======== iProver multi-core TPTP/SMT =========
% 0.12/0.43
% 0.12/0.43 % Detected problem language: tptp
% 0.12/0.45 % Proving...
% 41.94/9.96 % SZS status Started for theBenchmark.p
% 41.94/9.96 % SZS status Theorem for theBenchmark.p
% 41.94/9.96
% 41.94/9.96 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 41.94/9.96
% 41.94/9.96 % ------ iProver source info
% 41.94/9.96
% 41.94/9.96 % git: date: 2026-07-19 20:42:38 +0200
% 41.94/9.96 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 41.94/9.96 % git: non_committed_changes: false
% 41.94/9.96
% 41.94/9.96 % ------ Parsing...
% 41.94/9.96 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 41.94/9.96
% 41.94/9.96 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 1 0s sf_e %
% 41.94/9.96
% 41.94/9.96 % ------ Preprocessing...%
% 41.94/9.96
% 41.94/9.96 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 41.94/9.96 % ------ Proving...
% 41.94/9.96 % ------ Problem Properties
% 41.94/9.96
% 41.94/9.96 %
% 41.94/9.96 % clauses 211
% 41.94/9.96 % conjectures 7
% 41.94/9.96 % EPR 68
% 41.94/9.96 % Horn 137
% 41.94/9.96 % unary 18
% 41.94/9.96 % binary 62
% 41.94/9.96 % lits 690
% 41.94/9.96 % lits eq 85
% 41.94/9.96 % fd_pure 0
% 41.94/9.96 % fd_pseudo 0
% 41.94/9.96 % fd_cond 21
% 41.94/9.96 % fd_pseudo_cond 16
% 41.94/9.96 % AC symbols 0
% 41.94/9.96
% 41.94/9.96 % ------ Input Options Time Limit: Unbounded
% 41.94/9.96
% 41.94/9.96
% 41.94/9.96 % ------
% 41.94/9.96 % Current options:
% 41.94/9.96 % ------
% 41.94/9.96
% 41.94/9.96
% 41.94/9.96 %
% 41.94/9.96
% 41.94/9.96 % ------ Proving...
% 41.94/9.96 %
% 41.94/9.96
% 41.94/9.96 % SZS status Theorem for theBenchmark.p
% 41.94/9.96
% 41.94/9.96 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 41.94/9.96
% 41.94/9.96
%------------------------------------------------------------------------------