%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SWC343-1 : 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 : n003.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 03:09:23 PM UTC 2026
% Result : Unsatisfiable 1.65s 1.28s
% Output : CNFRefutation 1.65s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 22
% Syntax : Number of formulae : 129 ( 20 unt; 1 def)
% Number of atoms : 479 ( 202 equ)
% Maximal formula atoms : 7 ( 3 avg)
% Number of connectives : 661 ( 320 ~; 341 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 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 : 7 ( 5 usr; 2 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 6 con; 0-2 aty)
% Number of variables : 113 ( 0 sgn 113 !; 0 ?; 63 :)
% Comments :
%------------------------------------------------------------------------------
fof(f204,negated_conjecture,
sk2 = sk4,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_5) ).
fof(f205,negated_conjecture,
sk1 = sk3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_6) ).
fof(f206,negated_conjecture,
ssList(sk5),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_7) ).
fof(f207,negated_conjecture,
app(sk3,sk5) = sk4,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_8) ).
fof(f208,plain,
sk4 = app(sk3,sk5),
inference(reorient_equations,[],[f207]) ).
fof(f209,negated_conjecture,
strictorderedP(sk3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_9) ).
fof(f210,negated_conjecture,
! [X2,X3,X0,X1] :
( ~ lt(X2,X0)
| app(X3,cons(X2,nil)) != sk3
| ~ ssList(X3)
| ~ ssItem(X2)
| app(cons(X0,nil),X1) != sk5
| ~ ssList(X1)
| ~ ssItem(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_10) ).
fof(f211,plain,
! [X2,X3,X0,X1] :
( ~ lt(X2,X0)
| sk3 != app(X3,cons(X2,nil))
| ~ ssList(X3)
| ~ ssItem(X2)
| app(cons(X0,nil),X1) != sk5
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(reorient_equations,[],[f210]) ).
fof(f212,negated_conjecture,
( nil != sk3
| nil = sk4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_11) ).
fof(f213,negated_conjecture,
! [X0] :
( nil = sk1
| ~ strictorderedP(sk1)
| ssItem(sk6(X0))
| app(sk1,X0) != sk2
| ~ ssList(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_12) ).
fof(f214,plain,
! [X0] :
( nil = sk1
| ~ strictorderedP(sk1)
| ssItem(sk6(X0))
| sk2 != app(sk1,X0)
| ~ ssList(X0) ),
inference(reorient_equations,[],[f213]) ).
fof(f215,negated_conjecture,
! [X0] :
( nil != sk2
| ~ strictorderedP(sk1)
| ssItem(sk6(X0))
| app(sk1,X0) != sk2
| ~ ssList(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_13) ).
fof(f216,plain,
! [X0] :
( nil != sk2
| ~ strictorderedP(sk1)
| ssItem(sk6(X0))
| sk2 != app(sk1,X0)
| ~ ssList(X0) ),
inference(reorient_equations,[],[f215]) ).
fof(f217,negated_conjecture,
! [X0] :
( nil = sk1
| ~ strictorderedP(sk1)
| ssList(sk7(X0))
| app(sk1,X0) != sk2
| ~ ssList(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_14) ).
fof(f218,plain,
! [X0] :
( nil = sk1
| ~ strictorderedP(sk1)
| ssList(sk7(X0))
| sk2 != app(sk1,X0)
| ~ ssList(X0) ),
inference(reorient_equations,[],[f217]) ).
fof(f219,negated_conjecture,
! [X0] :
( nil = sk1
| ~ strictorderedP(sk1)
| app(cons(sk6(X0),nil),sk7(X0)) = X0
| app(sk1,X0) != sk2
| ~ ssList(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_15) ).
fof(f220,plain,
! [X0] :
( nil = sk1
| ~ strictorderedP(sk1)
| app(cons(sk6(X0),nil),sk7(X0)) = X0
| sk2 != app(sk1,X0)
| ~ ssList(X0) ),
inference(reorient_equations,[],[f219]) ).
fof(f221,negated_conjecture,
! [X0] :
( nil = sk1
| ~ strictorderedP(sk1)
| ssItem(sk8(X0))
| app(sk1,X0) != sk2
| ~ ssList(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_16) ).
fof(f222,plain,
! [X0] :
( nil = sk1
| ~ strictorderedP(sk1)
| ssItem(sk8(X0))
| sk2 != app(sk1,X0)
| ~ ssList(X0) ),
inference(reorient_equations,[],[f221]) ).
fof(f223,negated_conjecture,
! [X0] :
( nil = sk1
| ~ strictorderedP(sk1)
| ssList(sk9(X0))
| app(sk1,X0) != sk2
| ~ ssList(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_17) ).
fof(f224,plain,
! [X0] :
( nil = sk1
| ~ strictorderedP(sk1)
| ssList(sk9(X0))
| sk2 != app(sk1,X0)
| ~ ssList(X0) ),
inference(reorient_equations,[],[f223]) ).
fof(f225,negated_conjecture,
! [X0] :
( nil = sk1
| ~ strictorderedP(sk1)
| app(sk9(X0),cons(sk8(X0),nil)) = sk1
| app(sk1,X0) != sk2
| ~ ssList(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_18) ).
fof(f226,plain,
! [X0] :
( nil = sk1
| ~ strictorderedP(sk1)
| sk1 = app(sk9(X0),cons(sk8(X0),nil))
| sk2 != app(sk1,X0)
| ~ ssList(X0) ),
inference(reorient_equations,[],[f225]) ).
fof(f227,negated_conjecture,
! [X0] :
( nil = sk1
| ~ strictorderedP(sk1)
| lt(sk8(X0),sk6(X0))
| app(sk1,X0) != sk2
| ~ ssList(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_19) ).
fof(f228,plain,
! [X0] :
( nil = sk1
| ~ strictorderedP(sk1)
| lt(sk8(X0),sk6(X0))
| sk2 != app(sk1,X0)
| ~ ssList(X0) ),
inference(reorient_equations,[],[f227]) ).
fof(f229,negated_conjecture,
! [X0] :
( nil != sk2
| ~ strictorderedP(sk1)
| ssList(sk7(X0))
| app(sk1,X0) != sk2
| ~ ssList(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_20) ).
fof(f230,plain,
! [X0] :
( nil != sk2
| ~ strictorderedP(sk1)
| ssList(sk7(X0))
| sk2 != app(sk1,X0)
| ~ ssList(X0) ),
inference(reorient_equations,[],[f229]) ).
fof(f231,negated_conjecture,
! [X0] :
( nil != sk2
| ~ strictorderedP(sk1)
| app(cons(sk6(X0),nil),sk7(X0)) = X0
| app(sk1,X0) != sk2
| ~ ssList(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_21) ).
fof(f232,plain,
! [X0] :
( nil != sk2
| ~ strictorderedP(sk1)
| app(cons(sk6(X0),nil),sk7(X0)) = X0
| sk2 != app(sk1,X0)
| ~ ssList(X0) ),
inference(reorient_equations,[],[f231]) ).
fof(f233,negated_conjecture,
! [X0] :
( nil != sk2
| ~ strictorderedP(sk1)
| ssItem(sk8(X0))
| app(sk1,X0) != sk2
| ~ ssList(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_22) ).
fof(f234,plain,
! [X0] :
( nil != sk2
| ~ strictorderedP(sk1)
| ssItem(sk8(X0))
| sk2 != app(sk1,X0)
| ~ ssList(X0) ),
inference(reorient_equations,[],[f233]) ).
fof(f235,negated_conjecture,
! [X0] :
( nil != sk2
| ~ strictorderedP(sk1)
| ssList(sk9(X0))
| app(sk1,X0) != sk2
| ~ ssList(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_23) ).
fof(f236,plain,
! [X0] :
( nil != sk2
| ~ strictorderedP(sk1)
| ssList(sk9(X0))
| sk2 != app(sk1,X0)
| ~ ssList(X0) ),
inference(reorient_equations,[],[f235]) ).
fof(f237,negated_conjecture,
! [X0] :
( nil != sk2
| ~ strictorderedP(sk1)
| app(sk9(X0),cons(sk8(X0),nil)) = sk1
| app(sk1,X0) != sk2
| ~ ssList(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_24) ).
fof(f238,plain,
! [X0] :
( nil != sk2
| ~ strictorderedP(sk1)
| sk1 = app(sk9(X0),cons(sk8(X0),nil))
| sk2 != app(sk1,X0)
| ~ ssList(X0) ),
inference(reorient_equations,[],[f237]) ).
fof(f239,negated_conjecture,
! [X0] :
( nil != sk2
| ~ strictorderedP(sk1)
| lt(sk8(X0),sk6(X0))
| app(sk1,X0) != sk2
| ~ ssList(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_25) ).
fof(f240,plain,
! [X0] :
( nil != sk2
| ~ strictorderedP(sk1)
| lt(sk8(X0),sk6(X0))
| sk2 != app(sk1,X0)
| ~ ssList(X0) ),
inference(reorient_equations,[],[f239]) ).
fof(f243,plain,
! [X0] :
( nil = sk3
| ~ strictorderedP(sk3)
| ssItem(sk6(X0))
| sk4 != app(sk3,X0)
| ~ ssList(X0) ),
inference(definition_unfolding,[],[f214,f204,f205,f205,f205]) ).
fof(f244,plain,
! [X0] :
( nil != sk4
| ~ strictorderedP(sk3)
| ssItem(sk6(X0))
| sk4 != app(sk3,X0)
| ~ ssList(X0) ),
inference(definition_unfolding,[],[f216,f204,f205,f205,f204]) ).
fof(f245,plain,
! [X0] :
( nil = sk3
| ~ strictorderedP(sk3)
| ssList(sk7(X0))
| sk4 != app(sk3,X0)
| ~ ssList(X0) ),
inference(definition_unfolding,[],[f218,f204,f205,f205,f205]) ).
fof(f246,plain,
! [X0] :
( nil = sk3
| ~ strictorderedP(sk3)
| app(cons(sk6(X0),nil),sk7(X0)) = X0
| sk4 != app(sk3,X0)
| ~ ssList(X0) ),
inference(definition_unfolding,[],[f220,f204,f205,f205,f205]) ).
fof(f247,plain,
! [X0] :
( nil = sk3
| ~ strictorderedP(sk3)
| ssItem(sk8(X0))
| sk4 != app(sk3,X0)
| ~ ssList(X0) ),
inference(definition_unfolding,[],[f222,f204,f205,f205,f205]) ).
fof(f248,plain,
! [X0] :
( nil = sk3
| ~ strictorderedP(sk3)
| ssList(sk9(X0))
| sk4 != app(sk3,X0)
| ~ ssList(X0) ),
inference(definition_unfolding,[],[f224,f204,f205,f205,f205]) ).
fof(f249,plain,
! [X0] :
( nil = sk3
| ~ strictorderedP(sk3)
| sk3 = app(sk9(X0),cons(sk8(X0),nil))
| sk4 != app(sk3,X0)
| ~ ssList(X0) ),
inference(definition_unfolding,[],[f226,f204,f205,f205,f205,f205]) ).
fof(f250,plain,
! [X0] :
( nil = sk3
| ~ strictorderedP(sk3)
| lt(sk8(X0),sk6(X0))
| sk4 != app(sk3,X0)
| ~ ssList(X0) ),
inference(definition_unfolding,[],[f228,f204,f205,f205,f205]) ).
fof(f251,plain,
! [X0] :
( nil != sk4
| ~ strictorderedP(sk3)
| ssList(sk7(X0))
| sk4 != app(sk3,X0)
| ~ ssList(X0) ),
inference(definition_unfolding,[],[f230,f204,f205,f205,f204]) ).
fof(f252,plain,
! [X0] :
( nil != sk4
| ~ strictorderedP(sk3)
| app(cons(sk6(X0),nil),sk7(X0)) = X0
| sk4 != app(sk3,X0)
| ~ ssList(X0) ),
inference(definition_unfolding,[],[f232,f204,f205,f205,f204]) ).
fof(f253,plain,
! [X0] :
( nil != sk4
| ~ strictorderedP(sk3)
| ssItem(sk8(X0))
| sk4 != app(sk3,X0)
| ~ ssList(X0) ),
inference(definition_unfolding,[],[f234,f204,f205,f205,f204]) ).
fof(f254,plain,
! [X0] :
( nil != sk4
| ~ strictorderedP(sk3)
| ssList(sk9(X0))
| sk4 != app(sk3,X0)
| ~ ssList(X0) ),
inference(definition_unfolding,[],[f236,f204,f205,f205,f204]) ).
fof(f255,plain,
! [X0] :
( nil != sk4
| ~ strictorderedP(sk3)
| sk3 = app(sk9(X0),cons(sk8(X0),nil))
| sk4 != app(sk3,X0)
| ~ ssList(X0) ),
inference(definition_unfolding,[],[f238,f204,f205,f205,f205,f204]) ).
fof(f256,plain,
! [X0] :
( nil != sk4
| ~ strictorderedP(sk3)
| lt(sk8(X0),sk6(X0))
| sk4 != app(sk3,X0)
| ~ ssList(X0) ),
inference(definition_unfolding,[],[f240,f204,f205,f205,f204]) ).
tcf(c_448,negated_conjecture,
ssList(sk5),
inference(cnf_transformation,[],[f206]) ).
tcf(c_449,negated_conjecture,
app(sk3,sk5) = sk4,
inference(cnf_transformation,[],[f208]) ).
tcf(c_450,negated_conjecture,
strictorderedP(sk3),
inference(cnf_transformation,[],[f209]) ).
tcf(c_451,negated_conjecture,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ~ ssItem(X3)
| ~ ssItem(X0)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ lt(X3,X0)
| ( app(X2,cons(X3,nil)) != sk3 )
| ( app(cons(X0,nil),X1) != sk5 ) ),
inference(cnf_transformation,[],[f211]) ).
tcf(c_452,negated_conjecture,
( ( sk4 = nil )
| ( sk3 != nil ) ),
inference(cnf_transformation,[],[f212]) ).
tcf(c_453,negated_conjecture,
! [X0: $i] :
( ssItem(sk6(X0))
| ( sk3 = nil )
| ~ strictorderedP(sk3)
| ~ ssList(X0)
| ( app(sk3,X0) != sk4 ) ),
inference(cnf_transformation,[],[f243]) ).
tcf(c_454,negated_conjecture,
! [X0: $i] :
( ssItem(sk6(X0))
| ~ strictorderedP(sk3)
| ~ ssList(X0)
| ( sk4 != nil )
| ( app(sk3,X0) != sk4 ) ),
inference(cnf_transformation,[],[f244]) ).
tcf(c_455,negated_conjecture,
! [X0: $i] :
( ssList(sk7(X0))
| ( sk3 = nil )
| ~ strictorderedP(sk3)
| ~ ssList(X0)
| ( app(sk3,X0) != sk4 ) ),
inference(cnf_transformation,[],[f245]) ).
tcf(c_456,negated_conjecture,
! [X0: $i] :
( ( sk3 = nil )
| ( app(cons(sk6(X0),nil),sk7(X0)) = X0 )
| ~ strictorderedP(sk3)
| ~ ssList(X0)
| ( app(sk3,X0) != sk4 ) ),
inference(cnf_transformation,[],[f246]) ).
tcf(c_457,negated_conjecture,
! [X0: $i] :
( ssItem(sk8(X0))
| ( sk3 = nil )
| ~ strictorderedP(sk3)
| ~ ssList(X0)
| ( app(sk3,X0) != sk4 ) ),
inference(cnf_transformation,[],[f247]) ).
tcf(c_458,negated_conjecture,
! [X0: $i] :
( ssList(sk9(X0))
| ( sk3 = nil )
| ~ strictorderedP(sk3)
| ~ ssList(X0)
| ( app(sk3,X0) != sk4 ) ),
inference(cnf_transformation,[],[f248]) ).
tcf(c_459,negated_conjecture,
! [X0: $i] :
( ( sk3 = nil )
| ( app(sk9(X0),cons(sk8(X0),nil)) = sk3 )
| ~ strictorderedP(sk3)
| ~ ssList(X0)
| ( app(sk3,X0) != sk4 ) ),
inference(cnf_transformation,[],[f249]) ).
tcf(c_460,negated_conjecture,
! [X0: $i] :
( lt(sk8(X0),sk6(X0))
| ( sk3 = nil )
| ~ strictorderedP(sk3)
| ~ ssList(X0)
| ( app(sk3,X0) != sk4 ) ),
inference(cnf_transformation,[],[f250]) ).
tcf(c_461,negated_conjecture,
! [X0: $i] :
( ssList(sk7(X0))
| ~ strictorderedP(sk3)
| ~ ssList(X0)
| ( sk4 != nil )
| ( app(sk3,X0) != sk4 ) ),
inference(cnf_transformation,[],[f251]) ).
tcf(c_462,negated_conjecture,
! [X0: $i] :
( ( app(cons(sk6(X0),nil),sk7(X0)) = X0 )
| ~ strictorderedP(sk3)
| ~ ssList(X0)
| ( sk4 != nil )
| ( app(sk3,X0) != sk4 ) ),
inference(cnf_transformation,[],[f252]) ).
tcf(c_463,negated_conjecture,
! [X0: $i] :
( ssItem(sk8(X0))
| ~ strictorderedP(sk3)
| ~ ssList(X0)
| ( sk4 != nil )
| ( app(sk3,X0) != sk4 ) ),
inference(cnf_transformation,[],[f253]) ).
tcf(c_464,negated_conjecture,
! [X0: $i] :
( ssList(sk9(X0))
| ~ strictorderedP(sk3)
| ~ ssList(X0)
| ( sk4 != nil )
| ( app(sk3,X0) != sk4 ) ),
inference(cnf_transformation,[],[f254]) ).
tcf(c_465,negated_conjecture,
! [X0: $i] :
( ( app(sk9(X0),cons(sk8(X0),nil)) = sk3 )
| ~ strictorderedP(sk3)
| ~ ssList(X0)
| ( sk4 != nil )
| ( app(sk3,X0) != sk4 ) ),
inference(cnf_transformation,[],[f255]) ).
tcf(c_466,negated_conjecture,
! [X0: $i] :
( lt(sk8(X0),sk6(X0))
| ~ strictorderedP(sk3)
| ~ ssList(X0)
| ( sk4 != nil )
| ( app(sk3,X0) != sk4 ) ),
inference(cnf_transformation,[],[f256]) ).
tcf(c_600,negated_conjecture,
! [X0: $i] :
( ssList(sk9(X0))
| ~ ssList(X0)
| ( app(sk3,X0) != sk4 ) ),
inference(global_subsumption_just,[status(thm)],[c_458,c_450,c_452,c_458,c_464]) ).
tcf(c_603,negated_conjecture,
! [X0: $i] :
( ssItem(sk8(X0))
| ~ ssList(X0)
| ( app(sk3,X0) != sk4 ) ),
inference(global_subsumption_just,[status(thm)],[c_457,c_450,c_452,c_457,c_463]) ).
tcf(c_606,negated_conjecture,
! [X0: $i] :
( ssList(sk7(X0))
| ~ ssList(X0)
| ( app(sk3,X0) != sk4 ) ),
inference(global_subsumption_just,[status(thm)],[c_455,c_450,c_452,c_455,c_461]) ).
tcf(c_609,negated_conjecture,
! [X0: $i] :
( ssItem(sk6(X0))
| ~ ssList(X0)
| ( app(sk3,X0) != sk4 ) ),
inference(global_subsumption_just,[status(thm)],[c_453,c_450,c_452,c_453,c_454]) ).
tcf(c_612,plain,
! [X0: $i] :
( ssList(sk9(X0))
| ( app(sk3,X0) != sk4 )
| ~ ssList(X0) ),
inference(global_subsumption_just,[status(thm)],[c_464,c_600]) ).
tcf(c_613,negated_conjecture,
! [X0: $i] :
( ssList(sk9(X0))
| ~ ssList(X0)
| ( app(sk3,X0) != sk4 ) ),
inference(renaming,[status(thm)],[c_612]) ).
tcf(c_614,plain,
! [X0: $i] :
( ssItem(sk8(X0))
| ( app(sk3,X0) != sk4 )
| ~ ssList(X0) ),
inference(global_subsumption_just,[status(thm)],[c_463,c_603]) ).
tcf(c_615,negated_conjecture,
! [X0: $i] :
( ssItem(sk8(X0))
| ~ ssList(X0)
| ( app(sk3,X0) != sk4 ) ),
inference(renaming,[status(thm)],[c_614]) ).
tcf(c_616,plain,
! [X0: $i] :
( ssList(sk7(X0))
| ( app(sk3,X0) != sk4 )
| ~ ssList(X0) ),
inference(global_subsumption_just,[status(thm)],[c_461,c_606]) ).
tcf(c_617,negated_conjecture,
! [X0: $i] :
( ssList(sk7(X0))
| ~ ssList(X0)
| ( app(sk3,X0) != sk4 ) ),
inference(renaming,[status(thm)],[c_616]) ).
tcf(c_618,plain,
! [X0: $i] :
( ssItem(sk6(X0))
| ( app(sk3,X0) != sk4 )
| ~ ssList(X0) ),
inference(global_subsumption_just,[status(thm)],[c_454,c_609]) ).
tcf(c_619,negated_conjecture,
! [X0: $i] :
( ssItem(sk6(X0))
| ~ ssList(X0)
| ( app(sk3,X0) != sk4 ) ),
inference(renaming,[status(thm)],[c_618]) ).
tcf(c_620,negated_conjecture,
! [X0: $i] :
( lt(sk8(X0),sk6(X0))
| ~ ssList(X0)
| ( app(sk3,X0) != sk4 ) ),
inference(global_subsumption_just,[status(thm)],[c_460,c_450,c_452,c_460,c_466]) ).
tcf(c_623,plain,
! [X0: $i] :
( lt(sk8(X0),sk6(X0))
| ( app(sk3,X0) != sk4 )
| ~ ssList(X0) ),
inference(global_subsumption_just,[status(thm)],[c_466,c_620]) ).
tcf(c_624,negated_conjecture,
! [X0: $i] :
( lt(sk8(X0),sk6(X0))
| ~ ssList(X0)
| ( app(sk3,X0) != sk4 ) ),
inference(renaming,[status(thm)],[c_623]) ).
tcf(c_625,plain,
! [X0: $i] :
( ~ ssList(X0)
| ( app(sk3,X0) != sk4 )
| ( app(sk9(X0),cons(sk8(X0),nil)) = sk3 ) ),
inference(global_subsumption_just,[status(thm)],[c_459,c_450,c_452,c_459,c_465]) ).
tcf(c_626,negated_conjecture,
! [X0: $i] :
( ( app(sk9(X0),cons(sk8(X0),nil)) = sk3 )
| ~ ssList(X0)
| ( app(sk3,X0) != sk4 ) ),
inference(renaming,[status(thm)],[c_625]) ).
tcf(c_628,plain,
! [X0: $i] :
( ~ ssList(X0)
| ( app(sk3,X0) != sk4 )
| ( app(cons(sk6(X0),nil),sk7(X0)) = X0 ) ),
inference(global_subsumption_just,[status(thm)],[c_456,c_450,c_452,c_456,c_462]) ).
tcf(c_629,negated_conjecture,
! [X0: $i] :
( ( app(cons(sk6(X0),nil),sk7(X0)) = X0 )
| ~ ssList(X0)
| ( app(sk3,X0) != sk4 ) ),
inference(renaming,[status(thm)],[c_628]) ).
tcf(c_631,plain,
! [X0: $i] :
( ( app(sk9(X0),cons(sk8(X0),nil)) = sk3 )
| ( app(sk3,X0) != sk4 )
| ~ ssList(X0) ),
inference(global_subsumption_just,[status(thm)],[c_465,c_626]) ).
tcf(c_632,negated_conjecture,
! [X0: $i] :
( ( app(sk9(X0),cons(sk8(X0),nil)) = sk3 )
| ~ ssList(X0)
| ( app(sk3,X0) != sk4 ) ),
inference(renaming,[status(thm)],[c_631]) ).
tcf(c_633,plain,
! [X0: $i] :
( ( app(cons(sk6(X0),nil),sk7(X0)) = X0 )
| ( app(sk3,X0) != sk4 )
| ~ ssList(X0) ),
inference(global_subsumption_just,[status(thm)],[c_462,c_629]) ).
tcf(c_634,negated_conjecture,
! [X0: $i] :
( ( app(cons(sk6(X0),nil),sk7(X0)) = X0 )
| ~ ssList(X0)
| ( app(sk3,X0) != sk4 ) ),
inference(renaming,[status(thm)],[c_633]) ).
tcf(c_6743,definition,
iPr_def_12 = app(sk3,sk5),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_6744,negated_conjecture,
! [X0: $i] :
( ( app(cons(sk6(X0),nil),sk7(X0)) = X0 )
| ~ ssList(X0)
| ( app(sk3,X0) != sk4 ) ),
inference(demodulation,[status(thm)],[c_634]) ).
tcf(c_6745,negated_conjecture,
! [X0: $i] :
( ( app(sk9(X0),cons(sk8(X0),nil)) = sk3 )
| ~ ssList(X0)
| ( app(sk3,X0) != sk4 ) ),
inference(demodulation,[status(thm)],[c_632]) ).
tcf(c_6746,negated_conjecture,
! [X0: $i] :
( lt(sk8(X0),sk6(X0))
| ~ ssList(X0)
| ( app(sk3,X0) != sk4 ) ),
inference(demodulation,[status(thm)],[c_624]) ).
tcf(c_6747,negated_conjecture,
! [X0: $i] :
( ssItem(sk6(X0))
| ~ ssList(X0)
| ( app(sk3,X0) != sk4 ) ),
inference(demodulation,[status(thm)],[c_619]) ).
tcf(c_6748,negated_conjecture,
! [X0: $i] :
( ssList(sk7(X0))
| ~ ssList(X0)
| ( app(sk3,X0) != sk4 ) ),
inference(demodulation,[status(thm)],[c_617]) ).
tcf(c_6749,negated_conjecture,
! [X0: $i] :
( ssItem(sk8(X0))
| ~ ssList(X0)
| ( app(sk3,X0) != sk4 ) ),
inference(demodulation,[status(thm)],[c_615]) ).
tcf(c_6750,negated_conjecture,
! [X0: $i] :
( ssList(sk9(X0))
| ~ ssList(X0)
| ( app(sk3,X0) != sk4 ) ),
inference(demodulation,[status(thm)],[c_613]) ).
tcf(c_6752,negated_conjecture,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ~ ssItem(X3)
| ~ ssItem(X0)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ lt(X3,X0)
| ( app(X2,cons(X3,nil)) != sk3 )
| ( app(cons(X0,nil),X1) != sk5 ) ),
inference(demodulation,[status(thm)],[c_451]) ).
tcf(c_6754,negated_conjecture,
iPr_def_12 = sk4,
inference(demodulation,[status(thm)],[c_449,c_6743]) ).
tcf(c_6755,negated_conjecture,
ssList(sk5),
inference(demodulation,[status(thm)],[c_448]) ).
tcf(c_9370,plain,
! [X0: $i] :
( ssItem(sk6(X0))
| ~ ssList(X0)
| ( app(sk3,X0) != iPr_def_12 ) ),
inference(light_normalisation,[status(thm)],[c_6747,c_6754]) ).
tcf(c_9380,plain,
! [X0: $i] :
( ssList(sk7(X0))
| ~ ssList(X0)
| ( app(sk3,X0) != iPr_def_12 ) ),
inference(light_normalisation,[status(thm)],[c_6748,c_6754]) ).
tcf(c_9390,plain,
! [X0: $i] :
( ssItem(sk8(X0))
| ~ ssList(X0)
| ( app(sk3,X0) != iPr_def_12 ) ),
inference(light_normalisation,[status(thm)],[c_6749,c_6754]) ).
tcf(c_9400,plain,
! [X0: $i] :
( ssList(sk9(X0))
| ~ ssList(X0)
| ( app(sk3,X0) != iPr_def_12 ) ),
inference(light_normalisation,[status(thm)],[c_6750,c_6754]) ).
tcf(c_9410,plain,
! [X0: $i] :
( lt(sk8(X0),sk6(X0))
| ~ ssList(X0)
| ( app(sk3,X0) != iPr_def_12 ) ),
inference(light_normalisation,[status(thm)],[c_6746,c_6754]) ).
tcf(c_9420,plain,
! [X0: $i] :
( ( app(cons(sk6(X0),nil),sk7(X0)) = X0 )
| ~ ssList(X0)
| ( app(sk3,X0) != iPr_def_12 ) ),
inference(light_normalisation,[status(thm)],[c_6744,c_6754]) ).
tcf(c_9430,plain,
! [X0: $i] :
( ( app(sk9(X0),cons(sk8(X0),nil)) = sk3 )
| ~ ssList(X0)
| ( app(sk3,X0) != iPr_def_12 ) ),
inference(light_normalisation,[status(thm)],[c_6745,c_6754]) ).
tcf(c_9454,plain,
( ( app(sk9(sk5),cons(sk8(sk5),nil)) = sk3 )
| ~ ssList(sk5) ),
inference(superposition,[status(thm)],[c_6743,c_9430]) ).
tcf(c_9455,plain,
( ( app(cons(sk6(sk5),nil),sk7(sk5)) = sk5 )
| ~ ssList(sk5) ),
inference(superposition,[status(thm)],[c_6743,c_9420]) ).
tcf(c_9456,plain,
( lt(sk8(sk5),sk6(sk5))
| ~ ssList(sk5) ),
inference(superposition,[status(thm)],[c_6743,c_9410]) ).
tcf(c_9457,plain,
( ssList(sk9(sk5))
| ~ ssList(sk5) ),
inference(superposition,[status(thm)],[c_6743,c_9400]) ).
tcf(c_9458,plain,
( ssItem(sk8(sk5))
| ~ ssList(sk5) ),
inference(superposition,[status(thm)],[c_6743,c_9390]) ).
tcf(c_9459,plain,
( ssList(sk7(sk5))
| ~ ssList(sk5) ),
inference(superposition,[status(thm)],[c_6743,c_9380]) ).
tcf(c_9460,plain,
( ssItem(sk6(sk5))
| ~ ssList(sk5) ),
inference(superposition,[status(thm)],[c_6743,c_9370]) ).
tcf(c_9461,plain,
ssItem(sk6(sk5)),
inference(forward_subsumption_resolution,[status(thm)],[c_9460,c_6755]) ).
tcf(c_9462,plain,
ssList(sk7(sk5)),
inference(forward_subsumption_resolution,[status(thm)],[c_9459,c_6755]) ).
tcf(c_9463,plain,
ssItem(sk8(sk5)),
inference(forward_subsumption_resolution,[status(thm)],[c_9458,c_6755]) ).
tcf(c_9464,plain,
ssList(sk9(sk5)),
inference(forward_subsumption_resolution,[status(thm)],[c_9457,c_6755]) ).
tcf(c_9465,plain,
lt(sk8(sk5),sk6(sk5)),
inference(forward_subsumption_resolution,[status(thm)],[c_9456,c_6755]) ).
tcf(c_9466,plain,
app(cons(sk6(sk5),nil),sk7(sk5)) = sk5,
inference(forward_subsumption_resolution,[status(thm)],[c_9455,c_6755]) ).
tcf(c_9467,plain,
app(sk9(sk5),cons(sk8(sk5),nil)) = sk3,
inference(forward_subsumption_resolution,[status(thm)],[c_9454,c_6755]) ).
tcf(c_9472,plain,
! [X0: $i,X1: $i] :
( ~ ssItem(X1)
| ~ ssList(X0)
| ~ ssItem(sk6(sk5))
| ~ ssList(sk7(sk5))
| ~ lt(X1,sk6(sk5))
| ( app(X0,cons(X1,nil)) != sk3 ) ),
inference(superposition,[status(thm)],[c_9466,c_6752]) ).
tcf(c_9473,plain,
! [X0: $i,X1: $i] :
( ~ ssItem(X1)
| ~ ssList(X0)
| ~ lt(X1,sk6(sk5))
| ( app(X0,cons(X1,nil)) != sk3 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_9472,c_9461,c_9462]) ).
tcf(c_9487,plain,
( ~ ssItem(sk8(sk5))
| ~ ssList(sk9(sk5))
| ~ lt(sk8(sk5),sk6(sk5)) ),
inference(superposition,[status(thm)],[c_9467,c_9473]) ).
tcf(c_9488,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_9487,c_9463,c_9464,c_9465]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC343-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.09/0.37 % Computer : n003.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Thu Sep 24 17:46:09 UTC 2026
% 0.09/0.38 % CPUTime :
% 0.09/0.38 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.09/0.41 Running first-order theorem proving
% 0.09/0.41 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
% 0.09/0.42
% 0.09/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.09/0.42
% 0.09/0.43 % Detected problem language: tptp
% 0.09/0.44 % Proving...
% 1.65/1.28 % SZS status Started for theBenchmark.p
% 1.65/1.28 % SZS status Unsatisfiable for theBenchmark.p
% 1.65/1.28
% 1.65/1.28 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 1.65/1.28
% 1.65/1.28 % ------ iProver source info
% 1.65/1.28
% 1.65/1.28 % git: date: 2026-07-19 20:42:38 +0200
% 1.65/1.28 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 1.65/1.28 % git: non_committed_changes: false
% 1.65/1.28
% 1.65/1.28 % ------ Parsing...% successful
% 1.65/1.28
% 1.65/1.28
% 1.65/1.28 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 1.65/1.28
% 1.65/1.28 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe_e sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e %
% 1.65/1.28
% 1.65/1.28 % ------ Preprocessing... gs_s sp: 2 0s gs_e snvd_s sp: 0 0s snvd_e %
% 1.65/1.28
% 1.65/1.28 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 1.65/1.28 % ------ Proving...
% 1.65/1.28 % ------ Problem Properties
% 1.65/1.28
% 1.65/1.28 %
% 1.65/1.28 % clauses 192
% 1.65/1.28 % conjectures 14
% 1.65/1.28 % EPR 58
% 1.65/1.28 % Horn 164
% 1.65/1.28 % unary 64
% 1.65/1.28 % binary 22
% 1.65/1.28 % lits 577
% 1.65/1.28 % lits eq 84
% 1.65/1.28 % fd_pure 0
% 1.65/1.28 % fd_pseudo 0
% 1.65/1.28 % fd_cond 15
% 1.65/1.28 % fd_pseudo_cond 14
% 1.65/1.28 % AC symbols 0
% 1.65/1.28
% 1.65/1.28 % ------ Schedule dynamic 5 is on
% 1.65/1.28
% 1.65/1.28 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 1.65/1.28
% 1.65/1.28
% 1.65/1.28 % ------
% 1.65/1.28 % Current options:
% 1.65/1.28 % ------
% 1.65/1.28
% 1.65/1.28
% 1.65/1.28 %
% 1.65/1.28
% 1.65/1.28 % ------ Proving...
% 1.65/1.28 %
% 1.65/1.28
% 1.65/1.28 % SZS status Unsatisfiable for theBenchmark.p
% 1.65/1.28
% 1.65/1.28 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 1.65/1.28
% 1.65/1.28
%------------------------------------------------------------------------------