%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SWC412-1 : 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 : n002.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 1.61s 1.07s
% Output : CNFRefutation 1.61s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 39
% Syntax : Number of formulae : 147 ( 19 unt; 0 def)
% Number of atoms : 439 ( 148 equ)
% Maximal formula atoms : 9 ( 2 avg)
% Number of connectives : 515 ( 223 ~; 292 |; 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 : 14 ( 14 usr; 12 con; 0-2 aty)
% Number of variables : 125 ( 0 sgn 125 !; 0 ?; 45 :)
% Comments :
%------------------------------------------------------------------------------
fof(f8,axiom,
ssList(nil),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause8) ).
fof(f73,axiom,
! [X0] :
( app(X0,nil) = X0
| ~ ssList(X0) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause73) ).
fof(f125,axiom,
! [X0,X1] :
( app(cons(X0,nil),X1) = cons(X0,X1)
| ~ ssList(X1)
| ~ ssItem(X0) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause120) ).
fof(f126,plain,
! [X0,X1] :
( cons(X0,X1) = app(cons(X0,nil),X1)
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(reorient_equations,[],[f125]) ).
fof(f202,negated_conjecture,
ssList(sk3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_3) ).
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),X5),cons(X4,nil)) != sk4
| app(app(cons(X4,nil),X5),cons(X3,nil)) = sk3
| ~ ssList(X5)
| ~ ssItem(X4)
| ~ ssItem(X3)
| app(app(cons(X0,nil),cons(X1,nil)),X2) != sk4
| ~ 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),X5),cons(X4,nil))
| sk3 = app(app(cons(X4,nil),X5),cons(X3,nil))
| ~ ssList(X5)
| ~ ssItem(X4)
| ~ ssItem(X3)
| sk4 != app(app(cons(X0,nil),cons(X1,nil)),X2)
| ~ ssList(X2)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(reorient_equations,[],[f206]) ).
fof(f216,negated_conjecture,
! [X2,X0,X1] :
( ssItem(sk11)
| app(app(cons(X0,nil),cons(X1,nil)),X2) != sk4
| ~ ssList(X2)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_12) ).
fof(f217,plain,
! [X2,X0,X1] :
( ssItem(sk11)
| sk4 != app(app(cons(X0,nil),cons(X1,nil)),X2)
| ~ ssList(X2)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(reorient_equations,[],[f216]) ).
fof(f218,negated_conjecture,
! [X2,X0,X1] :
( ssItem(sk12)
| app(app(cons(X0,nil),cons(X1,nil)),X2) != sk4
| ~ ssList(X2)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_13) ).
fof(f219,plain,
! [X2,X0,X1] :
( ssItem(sk12)
| sk4 != app(app(cons(X0,nil),cons(X1,nil)),X2)
| ~ ssList(X2)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(reorient_equations,[],[f218]) ).
fof(f220,negated_conjecture,
! [X2,X0,X1] :
( ssList(sk13)
| app(app(cons(X0,nil),cons(X1,nil)),X2) != sk4
| ~ ssList(X2)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_14) ).
fof(f221,plain,
! [X2,X0,X1] :
( ssList(sk13)
| sk4 != app(app(cons(X0,nil),cons(X1,nil)),X2)
| ~ ssList(X2)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(reorient_equations,[],[f220]) ).
fof(f222,negated_conjecture,
! [X2,X0,X1] :
( app(app(cons(sk11,nil),sk13),cons(sk12,nil)) = sk2
| app(app(cons(X0,nil),cons(X1,nil)),X2) != sk4
| ~ ssList(X2)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_15) ).
fof(f223,plain,
! [X2,X0,X1] :
( sk2 = app(app(cons(sk11,nil),sk13),cons(sk12,nil))
| sk4 != app(app(cons(X0,nil),cons(X1,nil)),X2)
| ~ ssList(X2)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(reorient_equations,[],[f222]) ).
fof(f224,negated_conjecture,
! [X2,X0,X1] :
( app(app(cons(sk12,nil),sk13),cons(sk11,nil)) != sk1
| app(app(cons(X0,nil),cons(X1,nil)),X2) != sk4
| ~ ssList(X2)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_16) ).
fof(f225,plain,
! [X2,X0,X1] :
( sk1 != app(app(cons(sk12,nil),sk13),cons(sk11,nil))
| sk4 != app(app(cons(X0,nil),cons(X1,nil)),X2)
| ~ ssList(X2)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(reorient_equations,[],[f224]) ).
fof(f226,negated_conjecture,
! [X2,X0,X1] :
( app(app(cons(X0,nil),X2),cons(X1,nil)) != sk4
| app(app(cons(X1,nil),X2),cons(X0,nil)) = sk3
| ~ ssList(X2)
| ~ ssItem(X1)
| ~ ssItem(X0)
| ssItem(sk5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_17) ).
fof(f227,plain,
! [X2,X0,X1] :
( sk4 != app(app(cons(X0,nil),X2),cons(X1,nil))
| sk3 = app(app(cons(X1,nil),X2),cons(X0,nil))
| ~ ssList(X2)
| ~ ssItem(X1)
| ~ ssItem(X0)
| ssItem(sk5) ),
inference(reorient_equations,[],[f226]) ).
fof(f228,negated_conjecture,
! [X2,X0,X1] :
( app(app(cons(X0,nil),X2),cons(X1,nil)) != sk4
| app(app(cons(X1,nil),X2),cons(X0,nil)) = sk3
| ~ ssList(X2)
| ~ ssItem(X1)
| ~ ssItem(X0)
| ssItem(sk6) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_18) ).
fof(f229,plain,
! [X2,X0,X1] :
( sk4 != app(app(cons(X0,nil),X2),cons(X1,nil))
| sk3 = app(app(cons(X1,nil),X2),cons(X0,nil))
| ~ ssList(X2)
| ~ ssItem(X1)
| ~ ssItem(X0)
| ssItem(sk6) ),
inference(reorient_equations,[],[f228]) ).
fof(f230,negated_conjecture,
! [X2,X0,X1] :
( app(app(cons(X0,nil),X2),cons(X1,nil)) != sk4
| app(app(cons(X1,nil),X2),cons(X0,nil)) = sk3
| ~ ssList(X2)
| ~ ssItem(X1)
| ~ ssItem(X0)
| ssList(sk7) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_19) ).
fof(f231,plain,
! [X2,X0,X1] :
( sk4 != app(app(cons(X0,nil),X2),cons(X1,nil))
| sk3 = app(app(cons(X1,nil),X2),cons(X0,nil))
| ~ ssList(X2)
| ~ ssItem(X1)
| ~ ssItem(X0)
| ssList(sk7) ),
inference(reorient_equations,[],[f230]) ).
fof(f232,negated_conjecture,
! [X2,X0,X1] :
( app(app(cons(X0,nil),X2),cons(X1,nil)) != sk4
| app(app(cons(X1,nil),X2),cons(X0,nil)) = sk3
| ~ ssList(X2)
| ~ ssItem(X1)
| ~ ssItem(X0)
| app(app(cons(sk5,nil),cons(sk6,nil)),sk7) = sk2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_20) ).
fof(f233,plain,
! [X2,X0,X1] :
( sk4 != app(app(cons(X0,nil),X2),cons(X1,nil))
| sk3 = app(app(cons(X1,nil),X2),cons(X0,nil))
| ~ ssList(X2)
| ~ ssItem(X1)
| ~ ssItem(X0)
| sk2 = app(app(cons(sk5,nil),cons(sk6,nil)),sk7) ),
inference(reorient_equations,[],[f232]) ).
fof(f234,negated_conjecture,
( ssItem(sk8)
| ssItem(sk5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_21) ).
fof(f239,negated_conjecture,
( ssItem(sk11)
| ssItem(sk5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_25) ).
fof(f240,negated_conjecture,
( ssItem(sk12)
| ssItem(sk5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_26) ).
fof(f241,negated_conjecture,
( ssList(sk13)
| ssItem(sk5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_27) ).
fof(f242,negated_conjecture,
( app(app(cons(sk11,nil),sk13),cons(sk12,nil)) = sk2
| ssItem(sk5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_28) ).
fof(f243,plain,
( sk2 = app(app(cons(sk11,nil),sk13),cons(sk12,nil))
| ssItem(sk5) ),
inference(reorient_equations,[],[f242]) ).
fof(f244,negated_conjecture,
( app(app(cons(sk12,nil),sk13),cons(sk11,nil)) != sk1
| ssItem(sk5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_29) ).
fof(f245,plain,
( sk1 != app(app(cons(sk12,nil),sk13),cons(sk11,nil))
| ssItem(sk5) ),
inference(reorient_equations,[],[f244]) ).
fof(f246,negated_conjecture,
( ssItem(sk8)
| ssItem(sk6) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_30) ).
fof(f251,negated_conjecture,
( ssItem(sk8)
| ssList(sk7) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_34) ).
fof(f264,negated_conjecture,
( ssItem(sk11)
| ssItem(sk6) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_42) ).
fof(f265,negated_conjecture,
( ssItem(sk12)
| ssItem(sk6) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_43) ).
fof(f266,negated_conjecture,
( ssList(sk13)
| ssItem(sk6) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_44) ).
fof(f267,negated_conjecture,
( app(app(cons(sk11,nil),sk13),cons(sk12,nil)) = sk2
| ssItem(sk6) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_45) ).
fof(f268,plain,
( sk2 = app(app(cons(sk11,nil),sk13),cons(sk12,nil))
| ssItem(sk6) ),
inference(reorient_equations,[],[f267]) ).
fof(f269,negated_conjecture,
( app(app(cons(sk12,nil),sk13),cons(sk11,nil)) != sk1
| ssItem(sk6) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_46) ).
fof(f270,plain,
( sk1 != app(app(cons(sk12,nil),sk13),cons(sk11,nil))
| ssItem(sk6) ),
inference(reorient_equations,[],[f269]) ).
fof(f271,negated_conjecture,
( ssItem(sk11)
| ssList(sk7) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_47) ).
fof(f272,negated_conjecture,
( ssItem(sk11)
| app(app(cons(sk5,nil),cons(sk6,nil)),sk7) = sk2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_48) ).
fof(f273,plain,
( ssItem(sk11)
| sk2 = app(app(cons(sk5,nil),cons(sk6,nil)),sk7) ),
inference(reorient_equations,[],[f272]) ).
fof(f274,negated_conjecture,
( ssItem(sk12)
| ssList(sk7) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_49) ).
fof(f275,negated_conjecture,
( ssList(sk13)
| ssList(sk7) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_50) ).
fof(f276,negated_conjecture,
( app(app(cons(sk11,nil),sk13),cons(sk12,nil)) = sk2
| ssList(sk7) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_51) ).
fof(f277,plain,
( sk2 = app(app(cons(sk11,nil),sk13),cons(sk12,nil))
| ssList(sk7) ),
inference(reorient_equations,[],[f276]) ).
fof(f278,negated_conjecture,
( app(app(cons(sk12,nil),sk13),cons(sk11,nil)) != sk1
| ssList(sk7) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_52) ).
fof(f279,plain,
( sk1 != app(app(cons(sk12,nil),sk13),cons(sk11,nil))
| ssList(sk7) ),
inference(reorient_equations,[],[f278]) ).
fof(f280,negated_conjecture,
( ssItem(sk12)
| app(app(cons(sk5,nil),cons(sk6,nil)),sk7) = sk2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_53) ).
fof(f281,plain,
( ssItem(sk12)
| sk2 = app(app(cons(sk5,nil),cons(sk6,nil)),sk7) ),
inference(reorient_equations,[],[f280]) ).
fof(f282,negated_conjecture,
( ssList(sk13)
| app(app(cons(sk5,nil),cons(sk6,nil)),sk7) = sk2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_54) ).
fof(f283,plain,
( ssList(sk13)
| sk2 = app(app(cons(sk5,nil),cons(sk6,nil)),sk7) ),
inference(reorient_equations,[],[f282]) ).
fof(f284,negated_conjecture,
( app(app(cons(sk11,nil),sk13),cons(sk12,nil)) = sk2
| app(app(cons(sk5,nil),cons(sk6,nil)),sk7) = sk2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_55) ).
fof(f285,plain,
( sk2 = app(app(cons(sk11,nil),sk13),cons(sk12,nil))
| sk2 = app(app(cons(sk5,nil),cons(sk6,nil)),sk7) ),
inference(reorient_equations,[],[f284]) ).
fof(f286,negated_conjecture,
( app(app(cons(sk12,nil),sk13),cons(sk11,nil)) != sk1
| app(app(cons(sk5,nil),cons(sk6,nil)),sk7) = sk2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_56) ).
fof(f287,plain,
( sk1 != app(app(cons(sk12,nil),sk13),cons(sk11,nil))
| sk2 = app(app(cons(sk5,nil),cons(sk6,nil)),sk7) ),
inference(reorient_equations,[],[f286]) ).
fof(f291,plain,
! [X2,X0,X1] :
( sk4 = app(app(cons(sk11,nil),sk13),cons(sk12,nil))
| sk4 != app(app(cons(X0,nil),cons(X1,nil)),X2)
| ~ ssList(X2)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(definition_unfolding,[],[f223,f204]) ).
fof(f292,plain,
! [X2,X0,X1] :
( sk3 != app(app(cons(sk12,nil),sk13),cons(sk11,nil))
| sk4 != app(app(cons(X0,nil),cons(X1,nil)),X2)
| ~ ssList(X2)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(definition_unfolding,[],[f225,f205]) ).
fof(f293,plain,
! [X2,X0,X1] :
( sk4 != app(app(cons(X0,nil),X2),cons(X1,nil))
| sk3 = app(app(cons(X1,nil),X2),cons(X0,nil))
| ~ ssList(X2)
| ~ ssItem(X1)
| ~ ssItem(X0)
| sk4 = app(app(cons(sk5,nil),cons(sk6,nil)),sk7) ),
inference(definition_unfolding,[],[f233,f204]) ).
fof(f295,plain,
( sk4 = app(app(cons(sk11,nil),sk13),cons(sk12,nil))
| ssItem(sk5) ),
inference(definition_unfolding,[],[f243,f204]) ).
fof(f296,plain,
( sk3 != app(app(cons(sk12,nil),sk13),cons(sk11,nil))
| ssItem(sk5) ),
inference(definition_unfolding,[],[f245,f205]) ).
fof(f303,plain,
( sk4 = app(app(cons(sk11,nil),sk13),cons(sk12,nil))
| ssItem(sk6) ),
inference(definition_unfolding,[],[f268,f204]) ).
fof(f304,plain,
( sk3 != app(app(cons(sk12,nil),sk13),cons(sk11,nil))
| ssItem(sk6) ),
inference(definition_unfolding,[],[f270,f205]) ).
fof(f305,plain,
( ssItem(sk11)
| sk4 = app(app(cons(sk5,nil),cons(sk6,nil)),sk7) ),
inference(definition_unfolding,[],[f273,f204]) ).
fof(f306,plain,
( sk4 = app(app(cons(sk11,nil),sk13),cons(sk12,nil))
| ssList(sk7) ),
inference(definition_unfolding,[],[f277,f204]) ).
fof(f307,plain,
( sk3 != app(app(cons(sk12,nil),sk13),cons(sk11,nil))
| ssList(sk7) ),
inference(definition_unfolding,[],[f279,f205]) ).
fof(f308,plain,
( ssItem(sk12)
| sk4 = app(app(cons(sk5,nil),cons(sk6,nil)),sk7) ),
inference(definition_unfolding,[],[f281,f204]) ).
fof(f309,plain,
( ssList(sk13)
| sk4 = app(app(cons(sk5,nil),cons(sk6,nil)),sk7) ),
inference(definition_unfolding,[],[f283,f204]) ).
fof(f310,plain,
( sk4 = app(app(cons(sk11,nil),sk13),cons(sk12,nil))
| sk4 = app(app(cons(sk5,nil),cons(sk6,nil)),sk7) ),
inference(definition_unfolding,[],[f285,f204,f204]) ).
fof(f311,plain,
( sk3 != app(app(cons(sk12,nil),sk13),cons(sk11,nil))
| sk4 = app(app(cons(sk5,nil),cons(sk6,nil)),sk7) ),
inference(definition_unfolding,[],[f287,f204,f205]) ).
tcf(c_292,negated_conjecture,
ssList(sk3),
inference(cnf_transformation,[],[f202]) ).
tcf(c_294,negated_conjecture,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( app(app(cons(X5,nil),X4),cons(X3,nil)) = sk3 )
| ~ ssItem(X5)
| ~ ssItem(X3)
| ~ ssItem(X1)
| ~ ssItem(X0)
| ~ ssList(X4)
| ~ ssList(X2)
| ( app(app(cons(X3,nil),X4),cons(X5,nil)) != sk4 )
| ( app(app(cons(X0,nil),cons(X1,nil)),X2) != sk4 ) ),
inference(cnf_transformation,[],[f207]) ).
tcf(c_299,negated_conjecture,
! [X0: $i,X1: $i,X2: $i] :
( ssItem(sk11)
| ~ ssItem(X1)
| ~ ssItem(X0)
| ~ ssList(X2)
| ( app(app(cons(X0,nil),cons(X1,nil)),X2) != sk4 ) ),
inference(cnf_transformation,[],[f217]) ).
tcf(c_300,negated_conjecture,
! [X0: $i,X1: $i,X2: $i] :
( ssItem(sk12)
| ~ ssItem(X1)
| ~ ssItem(X0)
| ~ ssList(X2)
| ( app(app(cons(X0,nil),cons(X1,nil)),X2) != sk4 ) ),
inference(cnf_transformation,[],[f219]) ).
tcf(c_301,negated_conjecture,
! [X0: $i,X1: $i,X2: $i] :
( ssList(sk13)
| ~ ssItem(X1)
| ~ ssItem(X0)
| ~ ssList(X2)
| ( app(app(cons(X0,nil),cons(X1,nil)),X2) != sk4 ) ),
inference(cnf_transformation,[],[f221]) ).
tcf(c_302,negated_conjecture,
! [X0: $i,X1: $i,X2: $i] :
( ( app(app(cons(sk11,nil),sk13),cons(sk12,nil)) = sk4 )
| ~ ssItem(X1)
| ~ ssItem(X0)
| ~ ssList(X2)
| ( app(app(cons(X0,nil),cons(X1,nil)),X2) != sk4 ) ),
inference(cnf_transformation,[],[f291]) ).
tcf(c_303,negated_conjecture,
! [X0: $i,X1: $i,X2: $i] :
( ~ ssItem(X1)
| ~ ssItem(X0)
| ~ ssList(X2)
| ( app(app(cons(sk12,nil),sk13),cons(sk11,nil)) != sk3 )
| ( app(app(cons(X0,nil),cons(X1,nil)),X2) != sk4 ) ),
inference(cnf_transformation,[],[f292]) ).
tcf(c_304,negated_conjecture,
! [X0: $i,X1: $i,X2: $i] :
( ssItem(sk5)
| ( app(app(cons(X2,nil),X1),cons(X0,nil)) = sk3 )
| ~ ssItem(X2)
| ~ ssItem(X0)
| ~ ssList(X1)
| ( app(app(cons(X0,nil),X1),cons(X2,nil)) != sk4 ) ),
inference(cnf_transformation,[],[f227]) ).
tcf(c_305,negated_conjecture,
! [X0: $i,X1: $i,X2: $i] :
( ssItem(sk6)
| ( app(app(cons(X2,nil),X1),cons(X0,nil)) = sk3 )
| ~ ssItem(X2)
| ~ ssItem(X0)
| ~ ssList(X1)
| ( app(app(cons(X0,nil),X1),cons(X2,nil)) != sk4 ) ),
inference(cnf_transformation,[],[f229]) ).
tcf(c_306,negated_conjecture,
! [X0: $i,X1: $i,X2: $i] :
( ssList(sk7)
| ( app(app(cons(X2,nil),X1),cons(X0,nil)) = sk3 )
| ~ ssItem(X2)
| ~ ssItem(X0)
| ~ ssList(X1)
| ( app(app(cons(X0,nil),X1),cons(X2,nil)) != sk4 ) ),
inference(cnf_transformation,[],[f231]) ).
tcf(c_307,negated_conjecture,
! [X0: $i,X1: $i,X2: $i] :
( ( app(app(cons(sk5,nil),cons(sk6,nil)),sk7) = sk4 )
| ( app(app(cons(X2,nil),X1),cons(X0,nil)) = sk3 )
| ~ ssItem(X2)
| ~ ssItem(X0)
| ~ ssList(X1)
| ( app(app(cons(X0,nil),X1),cons(X2,nil)) != sk4 ) ),
inference(cnf_transformation,[],[f293]) ).
tcf(c_308,negated_conjecture,
( ssItem(sk5)
| ssItem(sk8) ),
inference(cnf_transformation,[],[f234]) ).
tcf(c_312,negated_conjecture,
( ssItem(sk5)
| ssItem(sk11) ),
inference(cnf_transformation,[],[f239]) ).
tcf(c_313,negated_conjecture,
( ssItem(sk5)
| ssItem(sk12) ),
inference(cnf_transformation,[],[f240]) ).
tcf(c_314,negated_conjecture,
( ssItem(sk5)
| ssList(sk13) ),
inference(cnf_transformation,[],[f241]) ).
tcf(c_315,negated_conjecture,
( ssItem(sk5)
| ( app(app(cons(sk11,nil),sk13),cons(sk12,nil)) = sk4 ) ),
inference(cnf_transformation,[],[f295]) ).
tcf(c_316,negated_conjecture,
( ssItem(sk5)
| ( app(app(cons(sk12,nil),sk13),cons(sk11,nil)) != sk3 ) ),
inference(cnf_transformation,[],[f296]) ).
tcf(c_317,negated_conjecture,
( ssItem(sk6)
| ssItem(sk8) ),
inference(cnf_transformation,[],[f246]) ).
tcf(c_321,negated_conjecture,
( ssItem(sk8)
| ssList(sk7) ),
inference(cnf_transformation,[],[f251]) ).
tcf(c_329,negated_conjecture,
( ssItem(sk6)
| ssItem(sk11) ),
inference(cnf_transformation,[],[f264]) ).
tcf(c_330,negated_conjecture,
( ssItem(sk6)
| ssItem(sk12) ),
inference(cnf_transformation,[],[f265]) ).
tcf(c_331,negated_conjecture,
( ssItem(sk6)
| ssList(sk13) ),
inference(cnf_transformation,[],[f266]) ).
tcf(c_332,negated_conjecture,
( ssItem(sk6)
| ( app(app(cons(sk11,nil),sk13),cons(sk12,nil)) = sk4 ) ),
inference(cnf_transformation,[],[f303]) ).
tcf(c_333,negated_conjecture,
( ssItem(sk6)
| ( app(app(cons(sk12,nil),sk13),cons(sk11,nil)) != sk3 ) ),
inference(cnf_transformation,[],[f304]) ).
tcf(c_334,negated_conjecture,
( ssItem(sk11)
| ssList(sk7) ),
inference(cnf_transformation,[],[f271]) ).
tcf(c_335,negated_conjecture,
( ssItem(sk11)
| ( app(app(cons(sk5,nil),cons(sk6,nil)),sk7) = sk4 ) ),
inference(cnf_transformation,[],[f305]) ).
tcf(c_336,negated_conjecture,
( ssItem(sk12)
| ssList(sk7) ),
inference(cnf_transformation,[],[f274]) ).
tcf(c_337,negated_conjecture,
( ssList(sk7)
| ssList(sk13) ),
inference(cnf_transformation,[],[f275]) ).
tcf(c_338,negated_conjecture,
( ssList(sk7)
| ( app(app(cons(sk11,nil),sk13),cons(sk12,nil)) = sk4 ) ),
inference(cnf_transformation,[],[f306]) ).
tcf(c_339,negated_conjecture,
( ssList(sk7)
| ( app(app(cons(sk12,nil),sk13),cons(sk11,nil)) != sk3 ) ),
inference(cnf_transformation,[],[f307]) ).
tcf(c_340,negated_conjecture,
( ssItem(sk12)
| ( app(app(cons(sk5,nil),cons(sk6,nil)),sk7) = sk4 ) ),
inference(cnf_transformation,[],[f308]) ).
tcf(c_341,negated_conjecture,
( ssList(sk13)
| ( app(app(cons(sk5,nil),cons(sk6,nil)),sk7) = sk4 ) ),
inference(cnf_transformation,[],[f309]) ).
tcf(c_342,negated_conjecture,
( ( app(app(cons(sk11,nil),sk13),cons(sk12,nil)) = sk4 )
| ( app(app(cons(sk5,nil),cons(sk6,nil)),sk7) = sk4 ) ),
inference(cnf_transformation,[],[f310]) ).
tcf(c_343,negated_conjecture,
( ( app(app(cons(sk5,nil),cons(sk6,nil)),sk7) = sk4 )
| ( app(app(cons(sk12,nil),sk13),cons(sk11,nil)) != sk3 ) ),
inference(cnf_transformation,[],[f311]) ).
tcf(c_349,plain,
! [X0: $i,X1: $i] :
( ( app(cons(X1,nil),X0) = cons(X1,X0) )
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f126]) ).
tcf(c_353,plain,
! [X0: $i] :
( ( app(X0,nil) = X0 )
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f73]) ).
tcf(c_354,plain,
ssList(nil),
inference(cnf_transformation,[],[f8]) ).
tcf(c_2069,negated_conjecture,
! [X0: $i,X1: $i,X2: $i] :
( ~ iPr_def_10
| ( app(app(cons(X1,nil),X2),cons(X0,nil)) = sk3 )
| ( app(app(cons(X0,nil),X2),cons(X1,nil)) != 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) != 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_3204,plain,
( ( app(sk7,nil) = sk7 )
| ( app(app(cons(sk11,nil),sk13),cons(sk12,nil)) = sk4 ) ),
inference(superposition,[status(thm)],[c_338,c_353]) ).
tcf(c_3235,plain,
( ( app(sk13,nil) = sk13 )
| ( app(app(cons(sk5,nil),cons(sk6,nil)),sk7) = sk4 ) ),
inference(superposition,[status(thm)],[c_341,c_353]) ).
tcf(c_3390,plain,
! [X0: $i] :
( ssList(sk7)
| ( app(cons(sk8,nil),X0) = cons(sk8,X0) )
| ~ ssList(X0) ),
inference(superposition,[status(thm)],[c_321,c_349]) ).
tcf(c_3391,plain,
! [X0: $i] :
( ssItem(sk6)
| ( app(cons(sk8,nil),X0) = cons(sk8,X0) )
| ~ ssList(X0) ),
inference(superposition,[status(thm)],[c_317,c_349]) ).
tcf(c_3392,plain,
! [X0: $i] :
( ssItem(sk5)
| ( app(cons(sk8,nil),X0) = cons(sk8,X0) )
| ~ ssList(X0) ),
inference(superposition,[status(thm)],[c_308,c_349]) ).
tcf(c_3887,plain,
( ( app(app(cons(sk11,nil),sk13),cons(sk12,nil)) = sk4 )
| ~ ssItem(sk6)
| ~ ssItem(sk5)
| ~ ssList(sk7) ),
inference(superposition,[status(thm)],[c_342,c_302]) ).
tcf(c_4822,plain,
( ssList(sk7)
| ( app(cons(sk8,nil),nil) = cons(sk8,nil) ) ),
inference(superposition,[status(thm)],[c_354,c_3390]) ).
tcf(c_5007,plain,
( ssItem(sk6)
| ( app(cons(sk8,nil),nil) = cons(sk8,nil) ) ),
inference(superposition,[status(thm)],[c_354,c_3391]) ).
tcf(c_5116,plain,
( ssItem(sk5)
| ( app(cons(sk8,nil),sk3) = cons(sk8,sk3) ) ),
inference(superposition,[status(thm)],[c_292,c_3392]) ).
tcf(c_5275,negated_conjecture,
app(app(cons(sk11,nil),sk13),cons(sk12,nil)) = sk4,
inference(global_subsumption_just,[status(thm)],[c_315,c_338,c_332,c_315,c_3887]) ).
tcf(c_5318,plain,
app(app(cons(sk11,nil),sk13),cons(sk12,nil)) = sk4,
inference(global_subsumption_just,[status(thm)],[c_3204,c_5275]) ).
tcf(c_5322,plain,
( ( app(app(cons(sk12,nil),sk13),cons(sk11,nil)) = sk3 )
| ~ iPr_def_10
| ~ ssItem(sk12)
| ~ ssItem(sk11)
| ~ ssList(sk13) ),
inference(superposition,[status(thm)],[c_5318,c_2069]) ).
tcf(c_5323,plain,
( ( app(app(cons(sk12,nil),sk13),cons(sk11,nil)) = sk3 )
| ( app(app(cons(sk5,nil),cons(sk6,nil)),sk7) = sk4 )
| ~ ssItem(sk12)
| ~ ssItem(sk11)
| ~ ssList(sk13) ),
inference(superposition,[status(thm)],[c_5318,c_307]) ).
tcf(c_5324,plain,
( ssList(sk7)
| ( app(app(cons(sk12,nil),sk13),cons(sk11,nil)) = sk3 )
| ~ ssItem(sk12)
| ~ ssItem(sk11)
| ~ ssList(sk13) ),
inference(superposition,[status(thm)],[c_5318,c_306]) ).
tcf(c_5325,plain,
( ssItem(sk6)
| ( app(app(cons(sk12,nil),sk13),cons(sk11,nil)) = sk3 )
| ~ ssItem(sk12)
| ~ ssItem(sk11)
| ~ ssList(sk13) ),
inference(superposition,[status(thm)],[c_5318,c_305]) ).
tcf(c_5326,plain,
( ssItem(sk5)
| ( app(app(cons(sk12,nil),sk13),cons(sk11,nil)) = sk3 )
| ~ ssItem(sk12)
| ~ ssItem(sk11)
| ~ ssList(sk13) ),
inference(superposition,[status(thm)],[c_5318,c_304]) ).
tcf(c_5379,plain,
ssList(sk7),
inference(global_subsumption_just,[status(thm)],[c_4822,c_337,c_336,c_334,c_339,c_5324]) ).
tcf(c_5436,plain,
ssItem(sk6),
inference(global_subsumption_just,[status(thm)],[c_5007,c_331,c_330,c_329,c_333,c_5325]) ).
tcf(c_5442,plain,
ssItem(sk5),
inference(global_subsumption_just,[status(thm)],[c_5116,c_314,c_313,c_312,c_316,c_5326]) ).
tcf(c_5722,plain,
app(app(cons(sk5,nil),cons(sk6,nil)),sk7) = sk4,
inference(global_subsumption_just,[status(thm)],[c_3235,c_341,c_340,c_335,c_343,c_5323]) ).
tcf(c_5727,plain,
( ~ ssItem(sk6)
| ~ ssItem(sk5)
| ~ ssList(sk7)
| ( app(app(cons(sk12,nil),sk13),cons(sk11,nil)) != sk3 ) ),
inference(superposition,[status(thm)],[c_5722,c_303]) ).
tcf(c_5729,plain,
( ~ iPr_def_11
| ~ ssItem(sk6)
| ~ ssItem(sk5)
| ~ ssList(sk7) ),
inference(superposition,[status(thm)],[c_5722,c_2070]) ).
tcf(c_5730,plain,
( ssList(sk13)
| ~ ssItem(sk6)
| ~ ssItem(sk5)
| ~ ssList(sk7) ),
inference(superposition,[status(thm)],[c_5722,c_301]) ).
tcf(c_5731,plain,
( ssItem(sk12)
| ~ ssItem(sk6)
| ~ ssItem(sk5)
| ~ ssList(sk7) ),
inference(superposition,[status(thm)],[c_5722,c_300]) ).
tcf(c_5732,plain,
( ssItem(sk11)
| ~ ssItem(sk6)
| ~ ssItem(sk5)
| ~ ssList(sk7) ),
inference(superposition,[status(thm)],[c_5722,c_299]) ).
tcf(c_5746,plain,
ssItem(sk11),
inference(forward_subsumption_resolution,[status(thm)],[c_5732,c_5436,c_5442,c_5379]) ).
tcf(c_5747,plain,
ssItem(sk12),
inference(forward_subsumption_resolution,[status(thm)],[c_5731,c_5436,c_5442,c_5379]) ).
tcf(c_5748,plain,
ssList(sk13),
inference(forward_subsumption_resolution,[status(thm)],[c_5730,c_5436,c_5442,c_5379]) ).
tcf(c_5749,plain,
~ iPr_def_11,
inference(forward_subsumption_resolution,[status(thm)],[c_5729,c_5436,c_5442,c_5379]) ).
tcf(c_5755,plain,
app(app(cons(sk12,nil),sk13),cons(sk11,nil)) != sk3,
inference(forward_subsumption_resolution,[status(thm)],[c_5727,c_5436,c_5442,c_5379]) ).
tcf(c_5770,plain,
iPr_def_10,
inference(backward_subsumption_resolution,[status(thm)],[c_2071,c_5749]) ).
tcf(c_5777,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_5755,c_5746,c_5747,c_5748,c_5770,c_5322]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC412-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.09/0.36 % Computer : n002.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Thu Sep 24 18:10:04 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.40 Running first-order theorem proving
% 0.10/0.40 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
% 0.10/0.41
% 0.10/0.41 % ======== iProver multi-core TPTP/SMT =========
% 0.10/0.41
% 0.10/0.41 % Detected problem language: tptp
% 0.10/0.42 % Proving...
% 1.61/1.07 % SZS status Started for theBenchmark.p
% 1.61/1.07 % SZS status Unsatisfiable for theBenchmark.p
% 1.61/1.07
% 1.61/1.07 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 1.61/1.07
% 1.61/1.07 % ------ iProver source info
% 1.61/1.07
% 1.61/1.07 % git: date: 2026-07-19 20:42:38 +0200
% 1.61/1.07 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 1.61/1.07 % git: non_committed_changes: false
% 1.61/1.07
% 1.61/1.07 % ------ Parsing...% successful
% 1.61/1.07
% 1.61/1.07
% 1.61/1.07 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 1.61/1.07
% 1.61/1.07 % ------ 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 %
% 1.61/1.07
% 1.61/1.07 % ------ Preprocessing... gs_s sp: 2 0s gs_e snvd_s sp: 0 0s snvd_e %
% 1.61/1.07
% 1.61/1.07 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 1.61/1.07 % ------ Proving...
% 1.61/1.07 % ------ Problem Properties
% 1.61/1.07
% 1.61/1.07 %
% 1.61/1.07 % clauses 71
% 1.61/1.07 % conjectures 54
% 1.61/1.07 % EPR 22
% 1.61/1.07 % Horn 34
% 1.61/1.07 % unary 4
% 1.61/1.07 % binary 39
% 1.61/1.07 % lits 215
% 1.61/1.07 % lits eq 65
% 1.61/1.07 % fd_pure 0
% 1.61/1.07 % fd_pseudo 0
% 1.61/1.07 % fd_cond 2
% 1.61/1.07 % fd_pseudo_cond 4
% 1.61/1.07 % AC symbols 0
% 1.61/1.07
% 1.61/1.07 % ------ Schedule dynamic 5 is on
% 1.61/1.07
% 1.61/1.07 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 1.61/1.07
% 1.61/1.07
% 1.61/1.07 % ------
% 1.61/1.07 % Current options:
% 1.61/1.07 % ------
% 1.61/1.07
% 1.61/1.07
% 1.61/1.07 %
% 1.61/1.07
% 1.61/1.07 % ------ Proving...
% 1.61/1.07 %
% 1.61/1.07
% 1.61/1.07 % SZS status Unsatisfiable for theBenchmark.p
% 1.61/1.07
% 1.61/1.07 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 1.61/1.07
% 1.61/1.07
%------------------------------------------------------------------------------