%------------------------------------------------------------------------------
% 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/sandbox2/benchmark/theBenchmark.p THM
% Computer : n012.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 : Unsatisfiable 0.06s 5.99s
% Output : CNFRefutation 0.06s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 29
% Syntax : Number of formulae : 111 ( 16 unt; 0 def)
% Number of atoms : 346 ( 117 equ)
% Maximal formula atoms : 9 ( 3 avg)
% Number of connectives : 430 ( 195 ~; 235 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 4 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 6 ( 4 usr; 3 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 11 con; 0-2 aty)
% Number of variables : 107 ( 0 sgn 107 !; 0 ?; 40 :)
% Comments :
%------------------------------------------------------------------------------
fof(f73,axiom,
! [X0] :
( app(X0,nil) = X0
| ~ ssList(X0) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause73) ).
fof(f204,negated_conjecture,
sk2 = sk4,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_5) ).
fof(f205,negated_conjecture,
sk1 = sk3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_6) ).
fof(f206,negated_conjecture,
! [X2,X3,X0,X1,X4,X5] :
( app(app(cons(X3,nil),cons(X4,nil)),X5) != sk4
| ~ ssList(X5)
| ~ ssItem(X4)
| ~ ssItem(X3)
| app(app(cons(X1,nil),cons(X0,nil)),X2) != sk1
| app(app(cons(X0,nil),cons(X1,nil)),X2) != sk2
| ~ ssList(X2)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_7) ).
fof(f207,plain,
! [X2,X3,X0,X1,X4,X5] :
( sk4 != app(app(cons(X3,nil),cons(X4,nil)),X5)
| ~ ssList(X5)
| ~ ssItem(X4)
| ~ ssItem(X3)
| sk1 != app(app(cons(X1,nil),cons(X0,nil)),X2)
| sk2 != app(app(cons(X0,nil),cons(X1,nil)),X2)
| ~ ssList(X2)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(reorient_equations,[],[f206]) ).
fof(f208,negated_conjecture,
! [X2,X0,X1] :
( ssItem(sk11)
| app(app(cons(X1,nil),cons(X0,nil)),X2) != sk1
| app(app(cons(X0,nil),cons(X1,nil)),X2) != sk2
| ~ ssList(X2)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_8) ).
fof(f209,plain,
! [X2,X0,X1] :
( ssItem(sk11)
| sk1 != app(app(cons(X1,nil),cons(X0,nil)),X2)
| sk2 != app(app(cons(X0,nil),cons(X1,nil)),X2)
| ~ ssList(X2)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(reorient_equations,[],[f208]) ).
fof(f214,negated_conjecture,
! [X2,X0,X1] :
( app(app(cons(sk11,nil),cons(sk12,nil)),sk13) = sk2
| app(app(cons(X1,nil),cons(X0,nil)),X2) != sk1
| app(app(cons(X0,nil),cons(X1,nil)),X2) != sk2
| ~ ssList(X2)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_11) ).
fof(f215,plain,
! [X2,X0,X1] :
( sk2 = app(app(cons(sk11,nil),cons(sk12,nil)),sk13)
| sk1 != app(app(cons(X1,nil),cons(X0,nil)),X2)
| sk2 != app(app(cons(X0,nil),cons(X1,nil)),X2)
| ~ ssList(X2)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(reorient_equations,[],[f214]) ).
fof(f224,negated_conjecture,
! [X2,X0,X1] :
( app(app(cons(X0,nil),cons(X1,nil)),X2) != sk4
| ~ ssList(X2)
| ~ ssItem(X1)
| ~ ssItem(X0)
| ssItem(sk8) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_16) ).
fof(f225,plain,
! [X2,X0,X1] :
( sk4 != app(app(cons(X0,nil),cons(X1,nil)),X2)
| ~ ssList(X2)
| ~ ssItem(X1)
| ~ ssItem(X0)
| ssItem(sk8) ),
inference(reorient_equations,[],[f224]) ).
fof(f226,negated_conjecture,
! [X2,X0,X1] :
( app(app(cons(X0,nil),cons(X1,nil)),X2) != sk4
| ~ ssList(X2)
| ~ ssItem(X1)
| ~ ssItem(X0)
| ssItem(sk9) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_17) ).
fof(f227,plain,
! [X2,X0,X1] :
( sk4 != app(app(cons(X0,nil),cons(X1,nil)),X2)
| ~ ssList(X2)
| ~ ssItem(X1)
| ~ ssItem(X0)
| ssItem(sk9) ),
inference(reorient_equations,[],[f226]) ).
fof(f228,negated_conjecture,
! [X2,X0,X1] :
( app(app(cons(X0,nil),cons(X1,nil)),X2) != sk4
| ~ ssList(X2)
| ~ ssItem(X1)
| ~ ssItem(X0)
| ssList(sk10) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_18) ).
fof(f229,plain,
! [X2,X0,X1] :
( sk4 != app(app(cons(X0,nil),cons(X1,nil)),X2)
| ~ ssList(X2)
| ~ ssItem(X1)
| ~ ssItem(X0)
| ssList(sk10) ),
inference(reorient_equations,[],[f228]) ).
fof(f230,negated_conjecture,
! [X2,X0,X1] :
( app(app(cons(X0,nil),cons(X1,nil)),X2) != sk4
| ~ ssList(X2)
| ~ ssItem(X1)
| ~ ssItem(X0)
| app(app(cons(sk8,nil),cons(sk9,nil)),sk10) = sk4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_19) ).
fof(f231,plain,
! [X2,X0,X1] :
( sk4 != app(app(cons(X0,nil),cons(X1,nil)),X2)
| ~ ssList(X2)
| ~ ssItem(X1)
| ~ ssItem(X0)
| sk4 = app(app(cons(sk8,nil),cons(sk9,nil)),sk10) ),
inference(reorient_equations,[],[f230]) ).
fof(f232,negated_conjecture,
! [X2,X0,X1] :
( app(app(cons(X0,nil),cons(X1,nil)),X2) != sk4
| ~ ssList(X2)
| ~ ssItem(X1)
| ~ ssItem(X0)
| app(app(cons(sk9,nil),cons(sk8,nil)),sk10) = sk3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_20) ).
fof(f233,plain,
! [X2,X0,X1] :
( sk4 != app(app(cons(X0,nil),cons(X1,nil)),X2)
| ~ ssList(X2)
| ~ ssItem(X1)
| ~ ssItem(X0)
| sk3 = app(app(cons(sk9,nil),cons(sk8,nil)),sk10) ),
inference(reorient_equations,[],[f232]) ).
fof(f257,negated_conjecture,
( ssItem(sk11)
| ssItem(sk8) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_37) ).
fof(f258,negated_conjecture,
( ssItem(sk11)
| ssItem(sk9) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_38) ).
fof(f259,negated_conjecture,
( ssItem(sk11)
| ssList(sk10) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_39) ).
fof(f260,negated_conjecture,
( ssItem(sk11)
| app(app(cons(sk8,nil),cons(sk9,nil)),sk10) = sk4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_40) ).
fof(f261,plain,
( ssItem(sk11)
| sk4 = app(app(cons(sk8,nil),cons(sk9,nil)),sk10) ),
inference(reorient_equations,[],[f260]) ).
fof(f262,negated_conjecture,
( ssItem(sk11)
| app(app(cons(sk9,nil),cons(sk8,nil)),sk10) = sk3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_41) ).
fof(f263,plain,
( ssItem(sk11)
| sk3 = app(app(cons(sk9,nil),cons(sk8,nil)),sk10) ),
inference(reorient_equations,[],[f262]) ).
fof(f264,negated_conjecture,
( ssItem(sk12)
| ssItem(sk8) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_42) ).
fof(f265,negated_conjecture,
( ssList(sk13)
| ssItem(sk8) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_43) ).
fof(f266,negated_conjecture,
( app(app(cons(sk11,nil),cons(sk12,nil)),sk13) = sk2
| ssItem(sk8) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_44) ).
fof(f267,plain,
( sk2 = app(app(cons(sk11,nil),cons(sk12,nil)),sk13)
| ssItem(sk8) ),
inference(reorient_equations,[],[f266]) ).
fof(f268,negated_conjecture,
( ssItem(sk12)
| ssItem(sk9) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_45) ).
fof(f269,negated_conjecture,
( ssItem(sk12)
| ssList(sk10) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_46) ).
fof(f270,negated_conjecture,
( ssItem(sk12)
| app(app(cons(sk8,nil),cons(sk9,nil)),sk10) = sk4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_47) ).
fof(f271,plain,
( ssItem(sk12)
| sk4 = app(app(cons(sk8,nil),cons(sk9,nil)),sk10) ),
inference(reorient_equations,[],[f270]) ).
fof(f274,negated_conjecture,
( ssList(sk13)
| ssItem(sk9) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_49) ).
fof(f275,negated_conjecture,
( app(app(cons(sk11,nil),cons(sk12,nil)),sk13) = sk2
| ssItem(sk9) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_50) ).
fof(f276,plain,
( sk2 = app(app(cons(sk11,nil),cons(sk12,nil)),sk13)
| ssItem(sk9) ),
inference(reorient_equations,[],[f275]) ).
fof(f277,negated_conjecture,
( ssList(sk13)
| ssList(sk10) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_51) ).
fof(f278,negated_conjecture,
( ssList(sk13)
| app(app(cons(sk8,nil),cons(sk9,nil)),sk10) = sk4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_52) ).
fof(f279,plain,
( ssList(sk13)
| sk4 = app(app(cons(sk8,nil),cons(sk9,nil)),sk10) ),
inference(reorient_equations,[],[f278]) ).
fof(f282,negated_conjecture,
( app(app(cons(sk11,nil),cons(sk12,nil)),sk13) = sk2
| ssList(sk10) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_54) ).
fof(f283,plain,
( sk2 = app(app(cons(sk11,nil),cons(sk12,nil)),sk13)
| ssList(sk10) ),
inference(reorient_equations,[],[f282]) ).
fof(f284,negated_conjecture,
( app(app(cons(sk11,nil),cons(sk12,nil)),sk13) = sk2
| app(app(cons(sk8,nil),cons(sk9,nil)),sk10) = sk4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_55) ).
fof(f285,plain,
( sk2 = app(app(cons(sk11,nil),cons(sk12,nil)),sk13)
| sk4 = app(app(cons(sk8,nil),cons(sk9,nil)),sk10) ),
inference(reorient_equations,[],[f284]) ).
fof(f286,negated_conjecture,
( app(app(cons(sk11,nil),cons(sk12,nil)),sk13) = sk2
| app(app(cons(sk9,nil),cons(sk8,nil)),sk10) = sk3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_56) ).
fof(f287,plain,
( sk2 = app(app(cons(sk11,nil),cons(sk12,nil)),sk13)
| sk3 = app(app(cons(sk9,nil),cons(sk8,nil)),sk10) ),
inference(reorient_equations,[],[f286]) ).
fof(f290,plain,
! [X2,X3,X0,X1,X4,X5] :
( sk4 != app(app(cons(X3,nil),cons(X4,nil)),X5)
| ~ ssList(X5)
| ~ ssItem(X4)
| ~ ssItem(X3)
| sk3 != app(app(cons(X1,nil),cons(X0,nil)),X2)
| sk4 != app(app(cons(X0,nil),cons(X1,nil)),X2)
| ~ ssList(X2)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(definition_unfolding,[],[f207,f204,f205]) ).
fof(f291,plain,
! [X2,X0,X1] :
( ssItem(sk11)
| sk3 != app(app(cons(X1,nil),cons(X0,nil)),X2)
| sk4 != app(app(cons(X0,nil),cons(X1,nil)),X2)
| ~ ssList(X2)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(definition_unfolding,[],[f209,f204,f205]) ).
fof(f294,plain,
! [X2,X0,X1] :
( sk4 = app(app(cons(sk11,nil),cons(sk12,nil)),sk13)
| sk3 != app(app(cons(X1,nil),cons(X0,nil)),X2)
| sk4 != app(app(cons(X0,nil),cons(X1,nil)),X2)
| ~ ssList(X2)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(definition_unfolding,[],[f215,f204,f205,f204]) ).
fof(f303,plain,
( sk4 = app(app(cons(sk11,nil),cons(sk12,nil)),sk13)
| ssItem(sk8) ),
inference(definition_unfolding,[],[f267,f204]) ).
fof(f304,plain,
( sk4 = app(app(cons(sk11,nil),cons(sk12,nil)),sk13)
| ssItem(sk9) ),
inference(definition_unfolding,[],[f276,f204]) ).
fof(f305,plain,
( sk4 = app(app(cons(sk11,nil),cons(sk12,nil)),sk13)
| ssList(sk10) ),
inference(definition_unfolding,[],[f283,f204]) ).
fof(f306,plain,
( sk4 = app(app(cons(sk11,nil),cons(sk12,nil)),sk13)
| sk4 = app(app(cons(sk8,nil),cons(sk9,nil)),sk10) ),
inference(definition_unfolding,[],[f285,f204]) ).
fof(f307,plain,
( sk4 = app(app(cons(sk11,nil),cons(sk12,nil)),sk13)
| sk3 = app(app(cons(sk9,nil),cons(sk8,nil)),sk10) ),
inference(definition_unfolding,[],[f287,f204]) ).
tcf(c_294,negated_conjecture,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ~ ssItem(X4)
| ~ ssItem(X3)
| ~ ssItem(X1)
| ~ ssItem(X0)
| ~ ssList(X5)
| ~ ssList(X2)
| ( app(app(cons(X3,nil),cons(X4,nil)),X5) != sk4 )
| ( app(app(cons(X1,nil),cons(X0,nil)),X2) != sk4 )
| ( app(app(cons(X0,nil),cons(X1,nil)),X2) != sk3 ) ),
inference(cnf_transformation,[],[f290]) ).
tcf(c_295,negated_conjecture,
! [X0: $i,X1: $i,X2: $i] :
( ssItem(sk11)
| ~ ssItem(X1)
| ~ ssItem(X0)
| ~ ssList(X2)
| ( app(app(cons(X1,nil),cons(X0,nil)),X2) != sk4 )
| ( app(app(cons(X0,nil),cons(X1,nil)),X2) != sk3 ) ),
inference(cnf_transformation,[],[f291]) ).
tcf(c_298,negated_conjecture,
! [X0: $i,X1: $i,X2: $i] :
( ( app(app(cons(sk11,nil),cons(sk12,nil)),sk13) = sk4 )
| ~ ssItem(X1)
| ~ ssItem(X0)
| ~ ssList(X2)
| ( app(app(cons(X1,nil),cons(X0,nil)),X2) != sk4 )
| ( app(app(cons(X0,nil),cons(X1,nil)),X2) != sk3 ) ),
inference(cnf_transformation,[],[f294]) ).
tcf(c_303,negated_conjecture,
! [X0: $i,X1: $i,X2: $i] :
( ssItem(sk8)
| ~ ssItem(X1)
| ~ ssItem(X0)
| ~ ssList(X2)
| ( app(app(cons(X0,nil),cons(X1,nil)),X2) != sk4 ) ),
inference(cnf_transformation,[],[f225]) ).
tcf(c_304,negated_conjecture,
! [X0: $i,X1: $i,X2: $i] :
( ssItem(sk9)
| ~ ssItem(X1)
| ~ ssItem(X0)
| ~ ssList(X2)
| ( app(app(cons(X0,nil),cons(X1,nil)),X2) != sk4 ) ),
inference(cnf_transformation,[],[f227]) ).
tcf(c_305,negated_conjecture,
! [X0: $i,X1: $i,X2: $i] :
( ssList(sk10)
| ~ ssItem(X1)
| ~ ssItem(X0)
| ~ ssList(X2)
| ( app(app(cons(X0,nil),cons(X1,nil)),X2) != sk4 ) ),
inference(cnf_transformation,[],[f229]) ).
tcf(c_306,negated_conjecture,
! [X0: $i,X1: $i,X2: $i] :
( ( app(app(cons(sk8,nil),cons(sk9,nil)),sk10) = sk4 )
| ~ ssItem(X1)
| ~ ssItem(X0)
| ~ ssList(X2)
| ( app(app(cons(X0,nil),cons(X1,nil)),X2) != sk4 ) ),
inference(cnf_transformation,[],[f231]) ).
tcf(c_307,negated_conjecture,
! [X0: $i,X1: $i,X2: $i] :
( ( app(app(cons(sk9,nil),cons(sk8,nil)),sk10) = sk3 )
| ~ ssItem(X1)
| ~ ssItem(X0)
| ~ ssList(X2)
| ( app(app(cons(X0,nil),cons(X1,nil)),X2) != sk4 ) ),
inference(cnf_transformation,[],[f233]) ).
tcf(c_324,negated_conjecture,
( ssItem(sk8)
| ssItem(sk11) ),
inference(cnf_transformation,[],[f257]) ).
tcf(c_325,negated_conjecture,
( ssItem(sk9)
| ssItem(sk11) ),
inference(cnf_transformation,[],[f258]) ).
tcf(c_326,negated_conjecture,
( ssItem(sk11)
| ssList(sk10) ),
inference(cnf_transformation,[],[f259]) ).
tcf(c_327,negated_conjecture,
( ssItem(sk11)
| ( app(app(cons(sk8,nil),cons(sk9,nil)),sk10) = sk4 ) ),
inference(cnf_transformation,[],[f261]) ).
tcf(c_328,negated_conjecture,
( ssItem(sk11)
| ( app(app(cons(sk9,nil),cons(sk8,nil)),sk10) = sk3 ) ),
inference(cnf_transformation,[],[f263]) ).
tcf(c_329,negated_conjecture,
( ssItem(sk8)
| ssItem(sk12) ),
inference(cnf_transformation,[],[f264]) ).
tcf(c_330,negated_conjecture,
( ssItem(sk8)
| ssList(sk13) ),
inference(cnf_transformation,[],[f265]) ).
tcf(c_331,negated_conjecture,
( ssItem(sk8)
| ( app(app(cons(sk11,nil),cons(sk12,nil)),sk13) = sk4 ) ),
inference(cnf_transformation,[],[f303]) ).
tcf(c_332,negated_conjecture,
( ssItem(sk9)
| ssItem(sk12) ),
inference(cnf_transformation,[],[f268]) ).
tcf(c_333,negated_conjecture,
( ssItem(sk12)
| ssList(sk10) ),
inference(cnf_transformation,[],[f269]) ).
tcf(c_334,negated_conjecture,
( ssItem(sk12)
| ( app(app(cons(sk8,nil),cons(sk9,nil)),sk10) = sk4 ) ),
inference(cnf_transformation,[],[f271]) ).
tcf(c_336,negated_conjecture,
( ssItem(sk9)
| ssList(sk13) ),
inference(cnf_transformation,[],[f274]) ).
tcf(c_337,negated_conjecture,
( ssItem(sk9)
| ( app(app(cons(sk11,nil),cons(sk12,nil)),sk13) = sk4 ) ),
inference(cnf_transformation,[],[f304]) ).
tcf(c_338,negated_conjecture,
( ssList(sk10)
| ssList(sk13) ),
inference(cnf_transformation,[],[f277]) ).
tcf(c_339,negated_conjecture,
( ssList(sk13)
| ( app(app(cons(sk8,nil),cons(sk9,nil)),sk10) = sk4 ) ),
inference(cnf_transformation,[],[f279]) ).
tcf(c_341,negated_conjecture,
( ssList(sk10)
| ( app(app(cons(sk11,nil),cons(sk12,nil)),sk13) = sk4 ) ),
inference(cnf_transformation,[],[f305]) ).
tcf(c_342,negated_conjecture,
( ( app(app(cons(sk8,nil),cons(sk9,nil)),sk10) = sk4 )
| ( app(app(cons(sk11,nil),cons(sk12,nil)),sk13) = sk4 ) ),
inference(cnf_transformation,[],[f306]) ).
tcf(c_343,negated_conjecture,
( ( app(app(cons(sk9,nil),cons(sk8,nil)),sk10) = sk3 )
| ( app(app(cons(sk11,nil),cons(sk12,nil)),sk13) = sk4 ) ),
inference(cnf_transformation,[],[f307]) ).
tcf(c_353,plain,
! [X0: $i] :
( ( app(X0,nil) = X0 )
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f73]) ).
tcf(c_2069,negated_conjecture,
! [X0: $i,X1: $i,X2: $i] :
( ~ iPr_def_10
| ( app(app(cons(X0,nil),cons(X1,nil)),X2) != sk4 )
| ~ ssList(X2)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_10])],[c_294]) ).
tcf(c_2070,negated_conjecture,
! [X0: $i,X1: $i,X2: $i] :
( ~ iPr_def_11
| ( app(app(cons(X0,nil),cons(X1,nil)),X2) != sk3 )
| ( app(app(cons(X1,nil),cons(X0,nil)),X2) != sk4 )
| ~ ssList(X2)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_11])],[c_294]) ).
tcf(c_2071,negated_conjecture,
( iPr_def_11
| iPr_def_10 ),
inference(splitting,[splitting(split),new_symbols(definition,[])],[c_294]) ).
tcf(c_3272,plain,
( ( app(sk13,nil) = sk13 )
| ( app(app(cons(sk8,nil),cons(sk9,nil)),sk10) = sk4 ) ),
inference(superposition,[status(thm)],[c_339,c_353]) ).
tcf(c_3842,plain,
( ( app(app(cons(sk11,nil),cons(sk12,nil)),sk13) = sk4 )
| ~ iPr_def_10
| ~ ssItem(sk9)
| ~ ssItem(sk8)
| ~ ssList(sk10) ),
inference(superposition,[status(thm)],[c_342,c_2069]) ).
tcf(c_4730,plain,
( ( app(app(cons(sk11,nil),cons(sk12,nil)),sk13) = sk4 )
| ~ iPr_def_11
| ~ ssItem(sk9)
| ~ ssItem(sk8)
| ~ ssList(sk10)
| ( app(app(cons(sk8,nil),cons(sk9,nil)),sk10) != sk4 ) ),
inference(superposition,[status(thm)],[c_343,c_2070]) ).
tcf(c_4780,negated_conjecture,
app(app(cons(sk11,nil),cons(sk12,nil)),sk13) = sk4,
inference(global_subsumption_just,[status(thm)],[c_298,c_341,c_337,c_331,c_342,c_2071,c_3842,c_4730]) ).
tcf(c_4787,plain,
( ( app(app(cons(sk8,nil),cons(sk9,nil)),sk10) = sk4 )
| ~ ssItem(sk12)
| ~ ssItem(sk11)
| ~ ssList(sk13) ),
inference(superposition,[status(thm)],[c_4780,c_306]) ).
tcf(c_4790,plain,
( ssList(sk10)
| ~ ssItem(sk12)
| ~ ssItem(sk11)
| ~ ssList(sk13) ),
inference(superposition,[status(thm)],[c_4780,c_305]) ).
tcf(c_4791,plain,
( ssItem(sk9)
| ~ ssItem(sk12)
| ~ ssItem(sk11)
| ~ ssList(sk13) ),
inference(superposition,[status(thm)],[c_4780,c_304]) ).
tcf(c_4792,plain,
( ssItem(sk8)
| ~ ssItem(sk12)
| ~ ssItem(sk11)
| ~ ssList(sk13) ),
inference(superposition,[status(thm)],[c_4780,c_303]) ).
tcf(c_4916,plain,
ssList(sk10),
inference(global_subsumption_just,[status(thm)],[c_4790,c_338,c_333,c_326,c_4790]) ).
tcf(c_4962,plain,
ssItem(sk9),
inference(global_subsumption_just,[status(thm)],[c_4791,c_336,c_332,c_325,c_4791]) ).
tcf(c_4968,plain,
ssItem(sk8),
inference(global_subsumption_just,[status(thm)],[c_4792,c_330,c_329,c_324,c_4792]) ).
tcf(c_5147,plain,
app(app(cons(sk8,nil),cons(sk9,nil)),sk10) = sk4,
inference(global_subsumption_just,[status(thm)],[c_3272,c_339,c_334,c_327,c_4787]) ).
tcf(c_5154,plain,
( ( app(app(cons(sk9,nil),cons(sk8,nil)),sk10) = sk3 )
| ~ ssItem(sk9)
| ~ ssItem(sk8)
| ~ ssList(sk10) ),
inference(superposition,[status(thm)],[c_5147,c_307]) ).
tcf(c_5156,plain,
( ~ iPr_def_10
| ~ ssItem(sk9)
| ~ ssItem(sk8)
| ~ ssList(sk10) ),
inference(superposition,[status(thm)],[c_5147,c_2069]) ).
tcf(c_5164,plain,
~ iPr_def_10,
inference(forward_subsumption_resolution,[status(thm)],[c_5156,c_4962,c_4968,c_4916]) ).
tcf(c_5170,plain,
app(app(cons(sk9,nil),cons(sk8,nil)),sk10) = sk3,
inference(forward_subsumption_resolution,[status(thm)],[c_5154,c_4962,c_4968,c_4916]) ).
tcf(c_5201,plain,
iPr_def_11,
inference(backward_subsumption_resolution,[status(thm)],[c_2071,c_5164]) ).
tcf(c_5763,negated_conjecture,
ssItem(sk8),
inference(global_subsumption_just,[status(thm)],[c_324,c_330,c_329,c_324,c_4792]) ).
tcf(c_5765,negated_conjecture,
ssItem(sk9),
inference(global_subsumption_just,[status(thm)],[c_325,c_336,c_332,c_325,c_4791]) ).
tcf(c_5767,negated_conjecture,
ssList(sk10),
inference(global_subsumption_just,[status(thm)],[c_326,c_338,c_333,c_326,c_4790]) ).
tcf(c_6236,negated_conjecture,
app(app(cons(sk8,nil),cons(sk9,nil)),sk10) = sk4,
inference(global_subsumption_just,[status(thm)],[c_327,c_339,c_334,c_327,c_4787]) ).
tcf(c_6239,negated_conjecture,
app(app(cons(sk9,nil),cons(sk8,nil)),sk10) = sk3,
inference(global_subsumption_just,[status(thm)],[c_328,c_5170]) ).
tcf(c_7298,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( app(app(cons(X0,nil),cons(X1,nil)),X2) != sk3 )
| ( app(app(cons(X1,nil),cons(X0,nil)),X2) != sk4 )
| ~ ssList(X2)
| ~ ssItem(X0)
| ~ ssItem(X1) ),
inference(global_subsumption_just,[status(thm)],[c_295,c_2070,c_5201]) ).
tcf(c_7299,negated_conjecture,
! [X0: $i,X1: $i,X2: $i] :
( ~ ssItem(X1)
| ~ ssItem(X0)
| ~ ssList(X2)
| ( app(app(cons(X1,nil),cons(X0,nil)),X2) != sk4 )
| ( app(app(cons(X0,nil),cons(X1,nil)),X2) != sk3 ) ),
inference(renaming,[status(thm)],[c_7298]) ).
tcf(c_7312,plain,
( ~ ssItem(sk9)
| ~ ssItem(sk8)
| ~ ssList(sk10)
| ( app(app(cons(sk8,nil),cons(sk9,nil)),sk10) != sk4 ) ),
inference(superposition,[status(thm)],[c_6239,c_7299]) ).
tcf(c_7313,plain,
( ~ ssItem(sk9)
| ~ ssItem(sk8)
| ~ ssList(sk10) ),
inference(ground_joinability,[status(thm)],[c_7312,c_6236]) ).
tcf(c_7314,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_7313,c_5765,c_5763,c_5767]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SWC413-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.02 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.03/5.32 % Computer : n012.cluster.edu
% 0.03/5.32 % Model : x86_64 x86_64
% 0.03/5.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.03/5.32 % Memory : 8046.5625MB
% 0.03/5.32 % OS : Linux 6.8.0-71-generic
% 0.03/5.32 % CPULimit : 300
% 0.03/5.32 % WCLimit : 300
% 0.03/5.32 % DateTime : Thu Sep 24 18:06:56 UTC 2026
% 0.03/5.32 % CPUTime :
% 0.03/5.32 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.03/5.34 Running first-order theorem proving
% 0.03/5.34 Running: /export/starexec/sandbox2/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.03/5.35
% 0.03/5.35 % ======== iProver multi-core TPTP/SMT =========
% 0.03/5.35
% 0.03/5.35 % Detected problem language: tptp
% 0.03/5.35 % Proving...
% 0.06/5.99 % SZS status Started for theBenchmark.p
% 0.06/5.99 % SZS status Unsatisfiable for theBenchmark.p
% 0.06/5.99
% 0.06/5.99 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 0.06/5.99
% 0.06/5.99 % ------ iProver source info
% 0.06/5.99
% 0.06/5.99 % git: date: 2026-07-19 20:42:38 +0200
% 0.06/5.99 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 0.06/5.99 % git: non_committed_changes: false
% 0.06/5.99
% 0.06/5.99 % ------ Parsing...% successful
% 0.06/5.99
% 0.06/5.99
% 0.06/5.99 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 0.06/5.99
% 0.06/5.99 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e %
% 0.06/5.99
% 0.06/5.99 % ------ Preprocessing... gs_s sp: 2 0s gs_e snvd_s sp: 0 0s snvd_e %
% 0.06/5.99
% 0.06/5.99 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 0.06/5.99 % ------ Proving...
% 0.06/5.99 % ------ Problem Properties
% 0.06/5.99
% 0.06/5.99 %
% 0.06/5.99 % clauses 71
% 0.06/5.99 % conjectures 54
% 0.06/5.99 % EPR 22
% 0.06/5.99 % Horn 34
% 0.06/5.99 % unary 4
% 0.06/5.99 % binary 39
% 0.06/5.99 % lits 215
% 0.06/5.99 % lits eq 65
% 0.06/5.99 % fd_pure 0
% 0.06/5.99 % fd_pseudo 0
% 0.06/5.99 % fd_cond 2
% 0.06/5.99 % fd_pseudo_cond 4
% 0.06/5.99 % AC symbols 0
% 0.06/5.99
% 0.06/5.99 % ------ Schedule dynamic 5 is on
% 0.06/5.99
% 0.06/5.99 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 0.06/5.99
% 0.06/5.99
% 0.06/5.99 % ------
% 0.06/5.99 % Current options:
% 0.06/5.99 % ------
% 0.06/5.99
% 0.06/5.99
% 0.06/5.99 %
% 0.06/5.99
% 0.06/5.99 % ------ Proving...
% 0.06/5.99 %
% 0.06/5.99
% 0.06/5.99 % SZS status Unsatisfiable for theBenchmark.p
% 0.06/5.99
% 0.06/5.99 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 0.06/5.99
% 0.06/5.99
%------------------------------------------------------------------------------