%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SWC274+1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n006.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri Sep 25 03:09:06 PM UTC 2026
% Result : Theorem 10.68s 2.25s
% Output : CNFRefutation 10.68s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 4
% Syntax : Number of formulae : 62 ( 11 unt; 0 def)
% Number of atoms : 426 ( 66 equ)
% Maximal formula atoms : 27 ( 6 avg)
% Number of connectives : 586 ( 222 ~; 232 |; 100 &)
% ( 8 <=>; 24 =>; 0 <=; 0 <~>)
% Maximal formula depth : 30 ( 9 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 : 8 ( 6 usr; 1 prp; 0-2 aty)
% Number of functors : 19 ( 19 usr; 7 con; 0-2 aty)
% Number of variables : 185 ( 0 sgn 143 !; 42 ?; 15 :)
% Comments :
%------------------------------------------------------------------------------
fof(f11,axiom,
! [X0] :
( ssList(X0)
=> ( totalorderedP(X0)
<=> ! [X1] :
( ssItem(X1)
=> ! [X2] :
( ssItem(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ! [X5] :
( ssList(X5)
=> ( app(app(X3,cons(X1,X4)),cons(X2,X5)) = X0
=> leq(X1,X2) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax11) ).
fof(f12,axiom,
! [X0] :
( ssList(X0)
=> ( strictorderedP(X0)
<=> ! [X1] :
( ssItem(X1)
=> ! [X2] :
( ssItem(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ! [X5] :
( ssList(X5)
=> ( app(app(X3,cons(X1,X4)),cons(X2,X5)) = X0
=> lt(X1,X2) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax12) ).
fof(f93,axiom,
! [X0] :
( ssItem(X0)
=> ! [X1] :
( ssItem(X1)
=> ( lt(X0,X1)
<=> ( leq(X0,X1)
& X0 != X1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax93) ).
fof(f96,conjecture,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ( nil = X2
& nil != X3 )
| totalorderedP(X0)
| ! [X4] :
( ssList(X4)
=> ! [X5] :
( ? [X10] :
( ? [X11] :
( ? [X12] :
( ? [X13] :
( lt(X12,X10)
& app(X13,cons(X12,nil)) = X2
& ssList(X13) )
& ssItem(X12) )
& app(cons(X10,nil),X11) = X5
& ssList(X11) )
& ssItem(X10) )
| ? [X6] :
( ? [X7] :
( ? [X8] :
( ? [X9] :
( lt(X6,X8)
& app(cons(X8,nil),X9) = X2
& ssList(X9) )
& ssItem(X8) )
& app(X7,cons(X6,nil)) = X4
& ssList(X7) )
& ssItem(X6) )
| ~ strictorderedP(X2)
| app(app(X4,X2),X5) != X3
| ~ ssList(X5) ) )
| X0 != X2
| X1 != X3
| ~ ssList(X3) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1) ).
fof(f97,negated_conjecture,
~ ! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ( nil = X2
& nil != X3 )
| totalorderedP(X0)
| ! [X4] :
( ssList(X4)
=> ! [X5] :
( ? [X10] :
( ? [X11] :
( ? [X12] :
( ? [X13] :
( lt(X12,X10)
& app(X13,cons(X12,nil)) = X2
& ssList(X13) )
& ssItem(X12) )
& app(cons(X10,nil),X11) = X5
& ssList(X11) )
& ssItem(X10) )
| ? [X6] :
( ? [X7] :
( ? [X8] :
( ? [X9] :
( lt(X6,X8)
& app(cons(X8,nil),X9) = X2
& ssList(X9) )
& ssItem(X8) )
& app(X7,cons(X6,nil)) = X4
& ssList(X7) )
& ssItem(X6) )
| ~ strictorderedP(X2)
| app(app(X4,X2),X5) != X3
| ~ ssList(X5) ) )
| X0 != X2
| X1 != X3
| ~ ssList(X3) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f96]) ).
fof(f98,plain,
? [X0] :
( ssList(X0)
& ? [X1] :
( ssList(X1)
& ? [X2] :
( ssList(X2)
& ? [X3] :
( ( nil != X2
| nil = X3 )
& ~ totalorderedP(X0)
& ? [X4] :
( ssList(X4)
& ? [X5] :
( ! [X10] :
( ! [X11] :
( ! [X12] :
( ! [X13] :
( ~ lt(X12,X10)
| app(X13,cons(X12,nil)) != X2
| ~ ssList(X13) )
| ~ ssItem(X12) )
| app(cons(X10,nil),X11) != X5
| ~ ssList(X11) )
| ~ ssItem(X10) )
& ! [X6] :
( ! [X7] :
( ! [X8] :
( ! [X9] :
( ~ lt(X6,X8)
| app(cons(X8,nil),X9) != X2
| ~ ssList(X9) )
| ~ ssItem(X8) )
| app(X7,cons(X6,nil)) != X4
| ~ ssList(X7) )
| ~ ssItem(X6) )
& strictorderedP(X2)
& app(app(X4,X2),X5) = X3
& ssList(X5) ) )
& X0 = X2
& X1 = X3
& ssList(X3) ) ) ) ),
inference(ennf_transformation,[],[f97]) ).
fof(f117,plain,
! [X0] :
( ~ ssItem(X0)
| ! [X1] :
( ~ ssItem(X1)
| ( lt(X0,X1)
<=> ( leq(X0,X1)
& X0 != X1 ) ) ) ),
inference(ennf_transformation,[],[f93]) ).
fof(f129,plain,
! [X0] :
( ~ ssList(X0)
| ( totalorderedP(X0)
<=> ! [X1] :
( ~ ssItem(X1)
| ! [X2] :
( ~ ssItem(X2)
| ! [X3] :
( ~ ssList(X3)
| ! [X4] :
( ~ ssList(X4)
| ! [X5] :
( ~ ssList(X5)
| app(app(X3,cons(X1,X4)),cons(X2,X5)) != X0
| leq(X1,X2) ) ) ) ) ) ) ),
inference(ennf_transformation,[],[f11]) ).
fof(f130,plain,
! [X0] :
( ~ ssList(X0)
| ( totalorderedP(X0)
<=> ! [X1] :
( ~ ssItem(X1)
| ! [X2] :
( ~ ssItem(X2)
| ! [X3] :
( ~ ssList(X3)
| ! [X4] :
( ~ ssList(X4)
| ! [X5] :
( ~ ssList(X5)
| app(app(X3,cons(X1,X4)),cons(X2,X5)) != X0
| leq(X1,X2) ) ) ) ) ) ) ),
inference(flattening,[],[f129]) ).
fof(f133,plain,
! [X0] :
( ~ ssList(X0)
| ( strictorderedP(X0)
<=> ! [X1] :
( ~ ssItem(X1)
| ! [X2] :
( ~ ssItem(X2)
| ! [X3] :
( ~ ssList(X3)
| ! [X4] :
( ~ ssList(X4)
| ! [X5] :
( ~ ssList(X5)
| app(app(X3,cons(X1,X4)),cons(X2,X5)) != X0
| lt(X1,X2) ) ) ) ) ) ) ),
inference(ennf_transformation,[],[f12]) ).
fof(f134,plain,
! [X0] :
( ~ ssList(X0)
| ( strictorderedP(X0)
<=> ! [X1] :
( ~ ssItem(X1)
| ! [X2] :
( ~ ssItem(X2)
| ! [X3] :
( ~ ssList(X3)
| ! [X4] :
( ~ ssList(X4)
| ! [X5] :
( ~ ssList(X5)
| app(app(X3,cons(X1,X4)),cons(X2,X5)) != X0
| lt(X1,X2) ) ) ) ) ) ) ),
inference(flattening,[],[f133]) ).
fof(f158,plain,
( ssList(sK0)
& ssList(sK1)
& ssList(sK2)
& ( nil != sK2
| nil = sK3 )
& ~ totalorderedP(sK0)
& ssList(sK4)
& ! [X10] :
( ! [X11] :
( ! [X12] :
( ! [X13] :
( ~ lt(X12,X10)
| app(X13,cons(X12,nil)) != sK2
| ~ ssList(X13) )
| ~ ssItem(X12) )
| app(cons(X10,nil),X11) != sK5
| ~ ssList(X11) )
| ~ ssItem(X10) )
& ! [X6] :
( ! [X7] :
( ! [X8] :
( ! [X9] :
( ~ lt(X6,X8)
| app(cons(X8,nil),X9) != sK2
| ~ ssList(X9) )
| ~ ssItem(X8) )
| app(X7,cons(X6,nil)) != sK4
| ~ ssList(X7) )
| ~ ssItem(X6) )
& strictorderedP(sK2)
& sK3 = app(app(sK4,sK2),sK5)
& ssList(sK5)
& sK0 = sK2
& sK1 = sK3
& ssList(sK3) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4,sK5]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3),skolemize(X4,sK4),skolemize(X5,sK5)],[f98]) ).
fof(f163,plain,
! [X0] :
( ~ ssItem(X0)
| ! [X1] :
( ~ ssItem(X1)
| ( ( ~ lt(X0,X1)
| ( leq(X0,X1)
& X0 != X1 ) )
& ( ~ leq(X0,X1)
| X0 = X1
| lt(X0,X1) ) ) ) ),
inference(nnf_transformation,[],[f117]) ).
fof(f164,plain,
! [X0] :
( ~ ssItem(X0)
| ! [X1] :
( ~ ssItem(X1)
| ( ( ~ lt(X0,X1)
| ( leq(X0,X1)
& X0 != X1 ) )
& ( ~ leq(X0,X1)
| X0 = X1
| lt(X0,X1) ) ) ) ),
inference(flattening,[],[f163]) ).
fof(f167,plain,
! [X0] :
( ~ ssList(X0)
| ( ( ~ totalorderedP(X0)
| ! [X1] :
( ~ ssItem(X1)
| ! [X2] :
( ~ ssItem(X2)
| ! [X3] :
( ~ ssList(X3)
| ! [X4] :
( ~ ssList(X4)
| ! [X5] :
( ~ ssList(X5)
| app(app(X3,cons(X1,X4)),cons(X2,X5)) != X0
| leq(X1,X2) ) ) ) ) ) )
& ( ? [X1] :
( ssItem(X1)
& ? [X2] :
( ssItem(X2)
& ? [X3] :
( ssList(X3)
& ? [X4] :
( ssList(X4)
& ? [X5] :
( ssList(X5)
& app(app(X3,cons(X1,X4)),cons(X2,X5)) = X0
& ~ leq(X1,X2) ) ) ) ) )
| totalorderedP(X0) ) ) ),
inference(nnf_transformation,[],[f130]) ).
fof(f168,plain,
! [X0] :
( ~ ssList(X0)
| ( ( ~ totalorderedP(X0)
| ! [X6] :
( ~ ssItem(X6)
| ! [X7] :
( ~ ssItem(X7)
| ! [X8] :
( ~ ssList(X8)
| ! [X9] :
( ~ ssList(X9)
| ! [X10] :
( ~ ssList(X10)
| app(app(X8,cons(X6,X9)),cons(X7,X10)) != X0
| leq(X6,X7) ) ) ) ) ) )
& ( ? [X1] :
( ssItem(X1)
& ? [X2] :
( ssItem(X2)
& ? [X3] :
( ssList(X3)
& ? [X4] :
( ssList(X4)
& ? [X5] :
( ssList(X5)
& app(app(X3,cons(X1,X4)),cons(X2,X5)) = X0
& ~ leq(X1,X2) ) ) ) ) )
| totalorderedP(X0) ) ) ),
inference(rectify,[],[f167]) ).
fof(f169,plain,
! [X0] :
( ~ ssList(X0)
| ( ( ~ totalorderedP(X0)
| ! [X6] :
( ~ ssItem(X6)
| ! [X7] :
( ~ ssItem(X7)
| ! [X8] :
( ~ ssList(X8)
| ! [X9] :
( ~ ssList(X9)
| ! [X10] :
( ~ ssList(X10)
| app(app(X8,cons(X6,X9)),cons(X7,X10)) != X0
| leq(X6,X7) ) ) ) ) ) )
& ( ( ssItem(sK10(X0))
& ssItem(sK11(X0))
& ssList(sK12(X0))
& ssList(sK13(X0))
& ssList(sK14(X0))
& app(app(sK12(X0),cons(sK10(X0),sK13(X0))),cons(sK11(X0),sK14(X0))) = X0
& ~ leq(sK10(X0),sK11(X0)) )
| totalorderedP(X0) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10,sK11,sK12,sK13,sK14]),skolemize(X1,sK10(X0)),skolemize(X2,sK11(X0)),skolemize(X3,sK12(X0)),skolemize(X4,sK13(X0)),skolemize(X5,sK14(X0))],[f168]) ).
fof(f172,plain,
! [X0] :
( ~ ssList(X0)
| ( ( ~ strictorderedP(X0)
| ! [X1] :
( ~ ssItem(X1)
| ! [X2] :
( ~ ssItem(X2)
| ! [X3] :
( ~ ssList(X3)
| ! [X4] :
( ~ ssList(X4)
| ! [X5] :
( ~ ssList(X5)
| app(app(X3,cons(X1,X4)),cons(X2,X5)) != X0
| lt(X1,X2) ) ) ) ) ) )
& ( ? [X1] :
( ssItem(X1)
& ? [X2] :
( ssItem(X2)
& ? [X3] :
( ssList(X3)
& ? [X4] :
( ssList(X4)
& ? [X5] :
( ssList(X5)
& app(app(X3,cons(X1,X4)),cons(X2,X5)) = X0
& ~ lt(X1,X2) ) ) ) ) )
| strictorderedP(X0) ) ) ),
inference(nnf_transformation,[],[f134]) ).
fof(f173,plain,
! [X0] :
( ~ ssList(X0)
| ( ( ~ strictorderedP(X0)
| ! [X6] :
( ~ ssItem(X6)
| ! [X7] :
( ~ ssItem(X7)
| ! [X8] :
( ~ ssList(X8)
| ! [X9] :
( ~ ssList(X9)
| ! [X10] :
( ~ ssList(X10)
| app(app(X8,cons(X6,X9)),cons(X7,X10)) != X0
| lt(X6,X7) ) ) ) ) ) )
& ( ? [X1] :
( ssItem(X1)
& ? [X2] :
( ssItem(X2)
& ? [X3] :
( ssList(X3)
& ? [X4] :
( ssList(X4)
& ? [X5] :
( ssList(X5)
& app(app(X3,cons(X1,X4)),cons(X2,X5)) = X0
& ~ lt(X1,X2) ) ) ) ) )
| strictorderedP(X0) ) ) ),
inference(rectify,[],[f172]) ).
fof(f174,plain,
! [X0] :
( ~ ssList(X0)
| ( ( ~ strictorderedP(X0)
| ! [X6] :
( ~ ssItem(X6)
| ! [X7] :
( ~ ssItem(X7)
| ! [X8] :
( ~ ssList(X8)
| ! [X9] :
( ~ ssList(X9)
| ! [X10] :
( ~ ssList(X10)
| app(app(X8,cons(X6,X9)),cons(X7,X10)) != X0
| lt(X6,X7) ) ) ) ) ) )
& ( ( ssItem(sK15(X0))
& ssItem(sK16(X0))
& ssList(sK17(X0))
& ssList(sK18(X0))
& ssList(sK19(X0))
& app(app(sK17(X0),cons(sK15(X0),sK18(X0))),cons(sK16(X0),sK19(X0))) = X0
& ~ lt(sK15(X0),sK16(X0)) )
| strictorderedP(X0) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK15,sK16,sK17,sK18,sK19]),skolemize(X1,sK15(X0)),skolemize(X2,sK16(X0)),skolemize(X3,sK17(X0)),skolemize(X4,sK18(X0)),skolemize(X5,sK19(X0))],[f173]) ).
fof(f177,plain,
ssList(sK0),
inference(cnf_transformation,[],[f158]) ).
fof(f181,plain,
~ totalorderedP(sK0),
inference(cnf_transformation,[],[f158]) ).
fof(f185,plain,
strictorderedP(sK2),
inference(cnf_transformation,[],[f158]) ).
fof(f188,plain,
sK0 = sK2,
inference(cnf_transformation,[],[f158]) ).
fof(f214,plain,
! [X0,X1] :
( ~ ssItem(X0)
| ~ ssItem(X1)
| ~ lt(X0,X1)
| leq(X0,X1) ),
inference(cnf_transformation,[],[f164]) ).
fof(f230,plain,
! [X0] :
( ~ ssList(X0)
| ssItem(sK10(X0))
| totalorderedP(X0) ),
inference(cnf_transformation,[],[f169]) ).
fof(f231,plain,
! [X0] :
( ~ ssList(X0)
| ssItem(sK11(X0))
| totalorderedP(X0) ),
inference(cnf_transformation,[],[f169]) ).
fof(f232,plain,
! [X0] :
( ~ ssList(X0)
| ssList(sK12(X0))
| totalorderedP(X0) ),
inference(cnf_transformation,[],[f169]) ).
fof(f233,plain,
! [X0] :
( ~ ssList(X0)
| ssList(sK13(X0))
| totalorderedP(X0) ),
inference(cnf_transformation,[],[f169]) ).
fof(f234,plain,
! [X0] :
( ~ ssList(X0)
| ssList(sK14(X0))
| totalorderedP(X0) ),
inference(cnf_transformation,[],[f169]) ).
fof(f235,plain,
! [X0] :
( ~ ssList(X0)
| app(app(sK12(X0),cons(sK10(X0),sK13(X0))),cons(sK11(X0),sK14(X0))) = X0
| totalorderedP(X0) ),
inference(cnf_transformation,[],[f169]) ).
fof(f236,plain,
! [X0] :
( ~ ssList(X0)
| ~ leq(sK10(X0),sK11(X0))
| totalorderedP(X0) ),
inference(cnf_transformation,[],[f169]) ).
fof(f244,plain,
! [X10,X0,X8,X6,X9,X7] :
( ~ ssList(X0)
| ~ strictorderedP(X0)
| ~ ssItem(X6)
| ~ ssItem(X7)
| ~ ssList(X8)
| ~ ssList(X9)
| ~ ssList(X10)
| app(app(X8,cons(X6,X9)),cons(X7,X10)) != X0
| lt(X6,X7) ),
inference(cnf_transformation,[],[f174]) ).
fof(f267,plain,
~ totalorderedP(sK2),
inference(definition_unfolding,[],[f181,f188]) ).
fof(f269,plain,
ssList(sK2),
inference(definition_unfolding,[],[f177,f188]) ).
fof(f278,plain,
! [X10,X8,X6,X9,X7] :
( ~ ssList(app(app(X8,cons(X6,X9)),cons(X7,X10)))
| ~ strictorderedP(app(app(X8,cons(X6,X9)),cons(X7,X10)))
| ~ ssItem(X6)
| ~ ssItem(X7)
| ~ ssList(X8)
| ~ ssList(X9)
| ~ ssList(X10)
| lt(X6,X7) ),
inference(equality_resolution,[],[f244]) ).
tcf(c_52,negated_conjecture,
strictorderedP(sK2),
inference(cnf_transformation,[],[f185]) ).
tcf(c_56,negated_conjecture,
~ totalorderedP(sK2),
inference(cnf_transformation,[],[f267]) ).
tcf(c_60,negated_conjecture,
ssList(sK2),
inference(cnf_transformation,[],[f269]) ).
tcf(c_86,plain,
! [X0: $i,X1: $i] :
( leq(X0,X1)
| ~ ssItem(X1)
| ~ ssItem(X0)
| ~ lt(X0,X1) ),
inference(cnf_transformation,[],[f214]) ).
tcf(c_98,plain,
! [X0: $i] :
( totalorderedP(X0)
| ~ ssList(X0)
| ~ leq(sK10(X0),sK11(X0)) ),
inference(cnf_transformation,[],[f236]) ).
tcf(c_99,plain,
! [X0: $i] :
( totalorderedP(X0)
| ( app(app(sK12(X0),cons(sK10(X0),sK13(X0))),cons(sK11(X0),sK14(X0))) = X0 )
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f235]) ).
tcf(c_100,plain,
! [X0: $i] :
( totalorderedP(X0)
| ssList(sK14(X0))
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f234]) ).
tcf(c_101,plain,
! [X0: $i] :
( totalorderedP(X0)
| ssList(sK13(X0))
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f233]) ).
tcf(c_102,plain,
! [X0: $i] :
( totalorderedP(X0)
| ssList(sK12(X0))
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f232]) ).
tcf(c_103,plain,
! [X0: $i] :
( totalorderedP(X0)
| ssItem(sK11(X0))
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f231]) ).
tcf(c_104,plain,
! [X0: $i] :
( totalorderedP(X0)
| ssItem(sK10(X0))
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f230]) ).
tcf(c_119,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( lt(X1,X3)
| ~ ssItem(X3)
| ~ ssItem(X1)
| ~ ssList(X4)
| ~ ssList(X2)
| ~ ssList(X0)
| ~ strictorderedP(app(app(X0,cons(X1,X2)),cons(X3,X4)))
| ~ ssList(app(app(X0,cons(X1,X2)),cons(X3,X4))) ),
inference(cnf_transformation,[],[f278]) ).
tcf(c_4237,plain,
( totalorderedP(sK2)
| ssList(sK14(sK2))
| ~ ssList(sK2) ),
inference(instantiation,[status(thm)],[c_100]) ).
tcf(c_4244,plain,
( totalorderedP(sK2)
| ssList(sK13(sK2))
| ~ ssList(sK2) ),
inference(instantiation,[status(thm)],[c_101]) ).
tcf(c_4317,plain,
( totalorderedP(sK2)
| ssList(sK12(sK2))
| ~ ssList(sK2) ),
inference(instantiation,[status(thm)],[c_102]) ).
tcf(c_4338,plain,
( totalorderedP(sK2)
| ssItem(sK11(sK2))
| ~ ssList(sK2) ),
inference(instantiation,[status(thm)],[c_103]) ).
tcf(c_4339,plain,
( totalorderedP(sK2)
| ssItem(sK10(sK2))
| ~ ssList(sK2) ),
inference(instantiation,[status(thm)],[c_104]) ).
tcf(c_4415,plain,
( totalorderedP(sK2)
| ~ ssList(sK2)
| ~ leq(sK10(sK2),sK11(sK2)) ),
inference(instantiation,[status(thm)],[c_98]) ).
tcf(c_5417,plain,
! [X0: $i] :
( leq(sK10(sK2),X0)
| ~ ssItem(X0)
| ~ ssItem(sK10(sK2))
| ~ lt(sK10(sK2),X0) ),
inference(instantiation,[status(thm)],[c_86]) ).
tcf(c_9644,plain,
( totalorderedP(sK2)
| ( app(app(sK12(sK2),cons(sK10(sK2),sK13(sK2))),cons(sK11(sK2),sK14(sK2))) = sK2 ) ),
inference(superposition,[status(thm)],[c_60,c_99]) ).
tcf(c_9669,plain,
app(app(sK12(sK2),cons(sK10(sK2),sK13(sK2))),cons(sK11(sK2),sK14(sK2))) = sK2,
inference(forward_subsumption_resolution,[status(thm)],[c_9644,c_56]) ).
tcf(c_14175,plain,
( lt(sK10(sK2),sK11(sK2))
| ~ ssList(sK2)
| ~ ssItem(sK11(sK2))
| ~ ssItem(sK10(sK2))
| ~ ssList(sK14(sK2))
| ~ ssList(sK13(sK2))
| ~ ssList(sK12(sK2))
| ~ strictorderedP(app(app(sK12(sK2),cons(sK10(sK2),sK13(sK2))),cons(sK11(sK2),sK14(sK2)))) ),
inference(superposition,[status(thm)],[c_9669,c_119]) ).
tcf(c_14188,plain,
( lt(sK10(sK2),sK11(sK2))
| ~ strictorderedP(sK2)
| ~ ssList(sK2)
| ~ ssItem(sK11(sK2))
| ~ ssItem(sK10(sK2))
| ~ ssList(sK14(sK2))
| ~ ssList(sK13(sK2))
| ~ ssList(sK12(sK2)) ),
inference(light_normalisation,[status(thm)],[c_14175,c_9669]) ).
tcf(c_14189,plain,
( lt(sK10(sK2),sK11(sK2))
| ~ ssItem(sK11(sK2))
| ~ ssItem(sK10(sK2))
| ~ ssList(sK14(sK2))
| ~ ssList(sK13(sK2))
| ~ ssList(sK12(sK2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_14188,c_52,c_60]) ).
tcf(c_18110,plain,
( leq(sK10(sK2),sK11(sK2))
| ~ ssItem(sK11(sK2))
| ~ ssItem(sK10(sK2))
| ~ lt(sK10(sK2),sK11(sK2)) ),
inference(instantiation,[status(thm)],[c_5417]) ).
tcf(c_18111,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_18110,c_14189,c_4415,c_4339,c_4338,c_4317,c_4244,c_4237,c_56,c_60]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC274+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.09/0.35 % Computer : n006.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Thu Sep 24 17:20:56 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.12/0.39 Running first-order theorem proving
% 0.12/0.40 Running: /export/starexec/sandbox/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.12/0.41
% 0.12/0.41 % ======== iProver multi-core TPTP/SMT =========
% 0.12/0.41
% 0.12/0.41 % Detected problem language: tptp
% 0.12/0.42 % Proving...
% 10.68/2.25 % SZS status Started for theBenchmark.p
% 10.68/2.25 % SZS status Theorem for theBenchmark.p
% 10.68/2.25
% 10.68/2.25 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 10.68/2.25
% 10.68/2.25 % ------ iProver source info
% 10.68/2.25
% 10.68/2.25 % git: date: 2026-07-19 20:42:38 +0200
% 10.68/2.25 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 10.68/2.25 % git: non_committed_changes: false
% 10.68/2.25
% 10.68/2.25 % ------ Parsing...
% 10.68/2.25 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 10.68/2.25
% 10.68/2.25 % ------ 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 %
% 10.68/2.25
% 10.68/2.25 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 10.68/2.25
% 10.68/2.25 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 10.68/2.25 % ------ Proving...
% 10.68/2.25 % ------ Problem Properties
% 10.68/2.25
% 10.68/2.25 %
% 10.68/2.25 % clauses 80
% 10.68/2.25 % conjectures 10
% 10.68/2.25 % EPR 22
% 10.68/2.25 % Horn 48
% 10.68/2.25 % unary 14
% 10.68/2.25 % binary 7
% 10.68/2.25 % lits 272
% 10.68/2.25 % lits eq 63
% 10.68/2.25 % fd_pure 0
% 10.68/2.25 % fd_pseudo 0
% 10.68/2.25 % fd_cond 18
% 10.68/2.25 % fd_pseudo_cond 7
% 10.68/2.25 % AC symbols 0
% 10.68/2.25
% 10.68/2.25 % ------ Schedule dynamic 5 is on
% 10.68/2.25
% 10.68/2.25 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 10.68/2.25
% 10.68/2.25
% 10.68/2.25 % ------
% 10.68/2.25 % Current options:
% 10.68/2.25 % ------
% 10.68/2.25
% 10.68/2.25
% 10.68/2.25 %
% 10.68/2.25
% 10.68/2.25 % ------ Proving...
% 10.68/2.25 %
% 10.68/2.25
% 10.68/2.25 % SZS status Theorem for theBenchmark.p
% 10.68/2.25
% 10.68/2.25 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 10.68/2.25
% 10.68/2.25
%------------------------------------------------------------------------------