%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SWC344+1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n008.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 : Thu Sep 24 02:40:52 PM UTC 2026
% Result : Theorem 0.14s 0.60s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 3
% Syntax : Number of formulae : 78 ( 12 unt; 2 def)
% Number of atoms : 566 ( 153 equ)
% Maximal formula atoms : 46 ( 7 avg)
% Number of connectives : 798 ( 310 ~; 298 |; 160 &)
% ( 2 <=>; 28 =>; 0 <=; 0 <~>)
% Maximal formula depth : 33 ( 9 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-3 aty)
% Number of functors : 17 ( 17 usr; 7 con; 0-3 aty)
% Number of variables : 320 ( 252 !; 68 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f96,conjecture,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ! [X] :
( ssList(X)
=> ( ( ( nil = V
| nil != U )
& ? [X9] :
( ? [X10] :
( strictorderedP(U)
& ! [X15] :
( ssItem(X15)
=> ! [X16] :
( ssList(X16)
=> ( ! [X17] :
( ssItem(X17)
=> ! [X18] :
( ssList(X18)
=> ( ~ lt(X17,X15)
| app(X18,cons(X17,nil)) != U ) ) )
| app(cons(X15,nil),X16) != X10 ) ) )
& ! [X11] :
( ssItem(X11)
=> ! [X12] :
( ssList(X12)
=> ( ! [X13] :
( ssItem(X13)
=> ! [X14] :
( ssList(X14)
=> ( ~ lt(X11,X13)
| app(cons(X13,nil),X14) != U ) ) )
| app(X12,cons(X11,nil)) != X9 ) ) )
& app(app(X9,U),X10) = V
& ssList(X10) )
& ssList(X9) ) )
| ( nil = W
& nil != X )
| ! [Y] :
( ssList(Y)
=> ! [Z] :
( ssList(Z)
=> ( ? [X5] :
( ? [X6] :
( ? [X7] :
( ? [X8] :
( lt(X7,X5)
& app(X8,cons(X7,nil)) = W
& ssList(X8) )
& ssItem(X7) )
& app(cons(X5,nil),X6) = Z
& ssList(X6) )
& ssItem(X5) )
| ? [X1] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( lt(X1,X3)
& app(cons(X3,nil),X4) = W
& ssList(X4) )
& ssItem(X3) )
& app(X2,cons(X1,nil)) = Y
& ssList(X2) )
& ssItem(X1) )
| ~ strictorderedP(W)
| app(app(Y,W),Z) != X ) ) )
| U != W
| V != X ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f97,negated_conjecture,
~ ! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ! [X] :
( ssList(X)
=> ( ( ( nil = V
| nil != U )
& ? [X9] :
( ? [X10] :
( strictorderedP(U)
& ! [X15] :
( ssItem(X15)
=> ! [X16] :
( ssList(X16)
=> ( ! [X17] :
( ssItem(X17)
=> ! [X18] :
( ssList(X18)
=> ( ~ lt(X17,X15)
| app(X18,cons(X17,nil)) != U ) ) )
| app(cons(X15,nil),X16) != X10 ) ) )
& ! [X11] :
( ssItem(X11)
=> ! [X12] :
( ssList(X12)
=> ( ! [X13] :
( ssItem(X13)
=> ! [X14] :
( ssList(X14)
=> ( ~ lt(X11,X13)
| app(cons(X13,nil),X14) != U ) ) )
| app(X12,cons(X11,nil)) != X9 ) ) )
& app(app(X9,U),X10) = V
& ssList(X10) )
& ssList(X9) ) )
| ( nil = W
& nil != X )
| ! [Y] :
( ssList(Y)
=> ! [Z] :
( ssList(Z)
=> ( ? [X5] :
( ? [X6] :
( ? [X7] :
( ? [X8] :
( lt(X7,X5)
& app(X8,cons(X7,nil)) = W
& ssList(X8) )
& ssItem(X7) )
& app(cons(X5,nil),X6) = Z
& ssList(X6) )
& ssItem(X5) )
| ? [X1] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( lt(X1,X3)
& app(cons(X3,nil),X4) = W
& ssList(X4) )
& ssItem(X3) )
& app(X2,cons(X1,nil)) = Y
& ssList(X2) )
& ssItem(X1) )
| ~ strictorderedP(W)
| app(app(Y,W),Z) != X ) ) )
| U != W
| V != X ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f96]) ).
fof(f415,plain,
? [U] :
( ? [V] :
( ? [W] :
( ? [X] :
( ( ( nil != V
& nil = U )
| ! [X9] :
( ! [X10] :
( ~ strictorderedP(U)
| ? [X15] :
( ? [X16] :
( ? [X17] :
( ? [X18] :
( lt(X17,X15)
& app(X18,cons(X17,nil)) = U
& ssList(X18) )
& ssItem(X17) )
& app(cons(X15,nil),X16) = X10
& ssList(X16) )
& ssItem(X15) )
| ? [X11] :
( ? [X12] :
( ? [X13] :
( ? [X14] :
( lt(X11,X13)
& app(cons(X13,nil),X14) = U
& ssList(X14) )
& ssItem(X13) )
& app(X12,cons(X11,nil)) = X9
& ssList(X12) )
& ssItem(X11) )
| app(app(X9,U),X10) != V
| ~ ssList(X10) )
| ~ ssList(X9) ) )
& ( nil != W
| nil = X )
& ? [Y] :
( ? [Z] :
( ! [X5] :
( ! [X6] :
( ! [X7] :
( ! [X8] :
( ~ lt(X7,X5)
| app(X8,cons(X7,nil)) != W
| ~ ssList(X8) )
| ~ ssItem(X7) )
| app(cons(X5,nil),X6) != Z
| ~ ssList(X6) )
| ~ ssItem(X5) )
& ! [X1] :
( ! [X2] :
( ! [X3] :
( ! [X4] :
( ~ lt(X1,X3)
| app(cons(X3,nil),X4) != W
| ~ ssList(X4) )
| ~ ssItem(X3) )
| app(X2,cons(X1,nil)) != Y
| ~ ssList(X2) )
| ~ ssItem(X1) )
& strictorderedP(W)
& app(app(Y,W),Z) = X
& ssList(Z) )
& ssList(Y) )
& U = W
& V = X
& ssList(X) )
& ssList(W) )
& ssList(V) )
& ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f97]) ).
fof(f416,definition,
! [U,X9,X11] :
( sP0_prd(X11,X9,U)
<=> ( ? [X12] :
( ? [X13] :
( ? [X14] :
( lt(X11,X13)
& app(cons(X13,nil),X14) = U
& ssList(X14) )
& ssItem(X13) )
& app(X12,cons(X11,nil)) = X9
& ssList(X12) )
& ssItem(X11) ) ),
introduced(definition,[new_symbols(definition,[sP0_prd])],[]) ).
fof(f417,definition,
! [U,X10,X15] :
( sP1_prd(X15,X10,U)
<=> ( ? [X16] :
( ? [X17] :
( ? [X18] :
( lt(X17,X15)
& app(X18,cons(X17,nil)) = U
& ssList(X18) )
& ssItem(X17) )
& app(cons(X15,nil),X16) = X10
& ssList(X16) )
& ssItem(X15) ) ),
introduced(definition,[new_symbols(definition,[sP1_prd])],[]) ).
fof(f418,plain,
? [U] :
( ? [V] :
( ? [W] :
( ? [X] :
( ( ( nil != V
& nil = U )
| ! [X9] :
( ! [X10] :
( ~ strictorderedP(U)
| ? [X15] : sP1_prd(X15,X10,U)
| ? [X11] : sP0_prd(X11,X9,U)
| app(app(X9,U),X10) != V
| ~ ssList(X10) )
| ~ ssList(X9) ) )
& ( nil != W
| nil = X )
& ? [Y] :
( ? [Z] :
( ! [X5] :
( ! [X6] :
( ! [X7] :
( ! [X8] :
( ~ lt(X7,X5)
| app(X8,cons(X7,nil)) != W
| ~ ssList(X8) )
| ~ ssItem(X7) )
| app(cons(X5,nil),X6) != Z
| ~ ssList(X6) )
| ~ ssItem(X5) )
& ! [X1] :
( ! [X2] :
( ! [X3] :
( ! [X4] :
( ~ lt(X1,X3)
| app(cons(X3,nil),X4) != W
| ~ ssList(X4) )
| ~ ssItem(X3) )
| app(X2,cons(X1,nil)) != Y
| ~ ssList(X2) )
| ~ ssItem(X1) )
& strictorderedP(W)
& app(app(Y,W),Z) = X
& ssList(Z) )
& ssList(Y) )
& U = W
& V = X
& ssList(X) )
& ssList(W) )
& ssList(V) )
& ssList(U) ),
inference(formula_renaming,[status(thm)],[f415,f417,f416]) ).
fof(f419,plain,
? [U] :
( ? [V] :
( ? [W] :
( ? [X] :
( ( ( nil != V
& nil = U )
| ! [X9] :
( ~ strictorderedP(U)
| ! [X10] :
( ? [X15] : sP1_prd(X15,X10,U)
| ? [X11] : sP0_prd(X11,X9,U)
| app(app(X9,U),X10) != V
| ~ ssList(X10) )
| ~ ssList(X9) ) )
& ( nil != W
| nil = X )
& ? [Y] :
( ? [Z] :
( ! [X5] :
( ! [X7] :
( ~ lt(X7,X5)
| ! [X8] :
( app(X8,cons(X7,nil)) != W
| ~ ssList(X8) )
| ~ ssItem(X7) )
| ! [X6] :
( app(cons(X5,nil),X6) != Z
| ~ ssList(X6) )
| ~ ssItem(X5) )
& ! [X1] :
( ! [X3] :
( ~ lt(X1,X3)
| ! [X4] :
( app(cons(X3,nil),X4) != W
| ~ ssList(X4) )
| ~ ssItem(X3) )
| ! [X2] :
( app(X2,cons(X1,nil)) != Y
| ~ ssList(X2) )
| ~ ssItem(X1) )
& strictorderedP(W)
& app(app(Y,W),Z) = X
& ssList(Z) )
& ssList(Y) )
& U = W
& V = X
& ssList(X) )
& ssList(W) )
& ssList(V) )
& ssList(U) ),
inference(miniscoping,[status(thm)],[f418]) ).
fof(f420,plain,
( ( ( nil != sK48_skl
& nil = sK47_skl )
| ! [X9] :
( ~ strictorderedP(sK47_skl)
| ! [X10] :
( sP1_prd(sK54_skl(X10,X9),X10,sK47_skl)
| sP0_prd(sK53_skl(X10,X9),X9,sK47_skl)
| app(app(X9,sK47_skl),X10) != sK48_skl
| ~ ssList(X10) )
| ~ ssList(X9) ) )
& ( nil != sK49_skl
| nil = sK50_skl )
& ! [X5] :
( ! [X7] :
( ~ lt(X7,X5)
| ! [X8] :
( app(X8,cons(X7,nil)) != sK49_skl
| ~ ssList(X8) )
| ~ ssItem(X7) )
| ! [X6] :
( app(cons(X5,nil),X6) != sK52_skl
| ~ ssList(X6) )
| ~ ssItem(X5) )
& ! [X1] :
( ! [X3] :
( ~ lt(X1,X3)
| ! [X4] :
( app(cons(X3,nil),X4) != sK49_skl
| ~ ssList(X4) )
| ~ ssItem(X3) )
| ! [X2] :
( app(X2,cons(X1,nil)) != sK51_skl
| ~ ssList(X2) )
| ~ ssItem(X1) )
& strictorderedP(sK49_skl)
& app(app(sK51_skl,sK49_skl),sK52_skl) = sK50_skl
& ssList(sK52_skl)
& ssList(sK51_skl)
& sK47_skl = sK49_skl
& sK48_skl = sK50_skl
& ssList(sK50_skl)
& ssList(sK49_skl)
& ssList(sK48_skl)
& ssList(sK47_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK47_skl,sK48_skl,sK49_skl,sK50_skl,sK51_skl,sK52_skl,sK53_skl,sK54_skl]),skolemize(U,sK47_skl),skolemize(V,sK48_skl),skolemize(W,sK49_skl),skolemize(X,sK50_skl),skolemize(Y,sK51_skl),skolemize(Z,sK52_skl),skolemize(X11,sK53_skl(X10,X9)),skolemize(X15,sK54_skl(X10,X9))],[f419]) ).
fof(f425,plain,
sK48_skl = sK50_skl,
inference(cnf_transformation,[status(thm)],[f420]) ).
fof(f426,plain,
sK47_skl = sK49_skl,
inference(cnf_transformation,[status(thm)],[f420]) ).
fof(f427,plain,
ssList(sK51_skl),
inference(cnf_transformation,[status(thm)],[f420]) ).
fof(f428,plain,
ssList(sK52_skl),
inference(cnf_transformation,[status(thm)],[f420]) ).
fof(f429,plain,
app(app(sK51_skl,sK49_skl),sK52_skl) = sK50_skl,
inference(cnf_transformation,[status(thm)],[f420]) ).
fof(f430,plain,
strictorderedP(sK49_skl),
inference(cnf_transformation,[status(thm)],[f420]) ).
fof(f431,plain,
! [X0,X1,X2,X3] :
( ~ lt(X0,X2)
| app(cons(X2,nil),X3) != sK49_skl
| ~ ssList(X3)
| ~ ssItem(X2)
| app(X1,cons(X0,nil)) != sK51_skl
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[status(thm)],[f420]) ).
fof(f432,plain,
! [X0,X1,X2,X3] :
( ~ lt(X2,X0)
| app(X3,cons(X2,nil)) != sK49_skl
| ~ ssList(X3)
| ~ ssItem(X2)
| app(cons(X0,nil),X1) != sK52_skl
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[status(thm)],[f420]) ).
fof(f433,plain,
( nil != sK49_skl
| nil = sK50_skl ),
inference(cnf_transformation,[status(thm)],[f420]) ).
fof(f434,plain,
! [X0,X1] :
( nil = sK47_skl
| ~ strictorderedP(sK47_skl)
| sP1_prd(sK54_skl(X1,X0),X1,sK47_skl)
| sP0_prd(sK53_skl(X1,X0),X0,sK47_skl)
| app(app(X0,sK47_skl),X1) != sK48_skl
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f420]) ).
fof(f435,plain,
! [X0,X1] :
( nil != sK48_skl
| ~ strictorderedP(sK47_skl)
| sP1_prd(sK54_skl(X1,X0),X1,sK47_skl)
| sP0_prd(sK53_skl(X1,X0),X0,sK47_skl)
| app(app(X0,sK47_skl),X1) != sK48_skl
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f420]) ).
fof(f436,plain,
! [U,X9,X11] :
( ( ! [X12] :
( ! [X13] :
( ! [X14] :
( ~ lt(X11,X13)
| app(cons(X13,nil),X14) != U
| ~ ssList(X14) )
| ~ ssItem(X13) )
| app(X12,cons(X11,nil)) != X9
| ~ ssList(X12) )
| ~ ssItem(X11)
| sP0_prd(X11,X9,U) )
& ( ( ? [X12] :
( ? [X13] :
( ? [X14] :
( lt(X11,X13)
& app(cons(X13,nil),X14) = U
& ssList(X14) )
& ssItem(X13) )
& app(X12,cons(X11,nil)) = X9
& ssList(X12) )
& ssItem(X11) )
| ~ sP0_prd(X11,X9,U) ) ),
inference(NNF_transformation,[status(thm)],[f416]) ).
fof(f437,plain,
( ! [U,X9,X11] :
( ! [X12] :
( ! [X13] :
( ! [X14] :
( ~ lt(X11,X13)
| app(cons(X13,nil),X14) != U
| ~ ssList(X14) )
| ~ ssItem(X13) )
| app(X12,cons(X11,nil)) != X9
| ~ ssList(X12) )
| ~ ssItem(X11)
| sP0_prd(X11,X9,U) )
& ! [U,X9,X11] :
( ( ? [X12] :
( ? [X13] :
( ? [X14] :
( lt(X11,X13)
& app(cons(X13,nil),X14) = U
& ssList(X14) )
& ssItem(X13) )
& app(X12,cons(X11,nil)) = X9
& ssList(X12) )
& ssItem(X11) )
| ~ sP0_prd(X11,X9,U) ) ),
inference(miniscoping,[status(thm)],[f436]) ).
fof(f438,plain,
( ! [U,X9,X11] :
( ! [X12] :
( ! [X13] :
( ! [X14] :
( ~ lt(X11,X13)
| app(cons(X13,nil),X14) != U
| ~ ssList(X14) )
| ~ ssItem(X13) )
| app(X12,cons(X11,nil)) != X9
| ~ ssList(X12) )
| ~ ssItem(X11)
| sP0_prd(X11,X9,U) )
& ! [U,X9,X11] :
( ( lt(X11,sK56_skl(X11,X9,U))
& app(cons(sK56_skl(X11,X9,U),nil),sK57_skl(X11,X9,U)) = U
& ssList(sK57_skl(X11,X9,U))
& ssItem(sK56_skl(X11,X9,U))
& app(sK55_skl(X11,X9,U),cons(X11,nil)) = X9
& ssList(sK55_skl(X11,X9,U))
& ssItem(X11) )
| ~ sP0_prd(X11,X9,U) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK55_skl,sK56_skl,sK57_skl]),skolemize(X12,sK55_skl(X11,X9,U)),skolemize(X13,sK56_skl(X11,X9,U)),skolemize(X14,sK57_skl(X11,X9,U))],[f437]) ).
fof(f439,plain,
! [X0,X1,X2] :
( ssItem(X0)
| ~ sP0_prd(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f438]) ).
fof(f440,plain,
! [X0,X1,X2] :
( ssList(sK55_skl(X0,X1,X2))
| ~ sP0_prd(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f438]) ).
fof(f441,plain,
! [X0,X1,X2] :
( app(sK55_skl(X0,X1,X2),cons(X0,nil)) = X1
| ~ sP0_prd(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f438]) ).
fof(f442,plain,
! [X0,X1,X2] :
( ssItem(sK56_skl(X0,X1,X2))
| ~ sP0_prd(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f438]) ).
fof(f443,plain,
! [X0,X1,X2] :
( ssList(sK57_skl(X0,X1,X2))
| ~ sP0_prd(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f438]) ).
fof(f444,plain,
! [X0,X1,X2] :
( app(cons(sK56_skl(X0,X1,X2),nil),sK57_skl(X0,X1,X2)) = X2
| ~ sP0_prd(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f438]) ).
fof(f445,plain,
! [X0,X1,X2] :
( lt(X0,sK56_skl(X0,X1,X2))
| ~ sP0_prd(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f438]) ).
fof(f447,plain,
! [U,X10,X15] :
( ( ! [X16] :
( ! [X17] :
( ! [X18] :
( ~ lt(X17,X15)
| app(X18,cons(X17,nil)) != U
| ~ ssList(X18) )
| ~ ssItem(X17) )
| app(cons(X15,nil),X16) != X10
| ~ ssList(X16) )
| ~ ssItem(X15)
| sP1_prd(X15,X10,U) )
& ( ( ? [X16] :
( ? [X17] :
( ? [X18] :
( lt(X17,X15)
& app(X18,cons(X17,nil)) = U
& ssList(X18) )
& ssItem(X17) )
& app(cons(X15,nil),X16) = X10
& ssList(X16) )
& ssItem(X15) )
| ~ sP1_prd(X15,X10,U) ) ),
inference(NNF_transformation,[status(thm)],[f417]) ).
fof(f448,plain,
( ! [U,X10,X15] :
( ! [X16] :
( ! [X17] :
( ! [X18] :
( ~ lt(X17,X15)
| app(X18,cons(X17,nil)) != U
| ~ ssList(X18) )
| ~ ssItem(X17) )
| app(cons(X15,nil),X16) != X10
| ~ ssList(X16) )
| ~ ssItem(X15)
| sP1_prd(X15,X10,U) )
& ! [U,X10,X15] :
( ( ? [X16] :
( ? [X17] :
( ? [X18] :
( lt(X17,X15)
& app(X18,cons(X17,nil)) = U
& ssList(X18) )
& ssItem(X17) )
& app(cons(X15,nil),X16) = X10
& ssList(X16) )
& ssItem(X15) )
| ~ sP1_prd(X15,X10,U) ) ),
inference(miniscoping,[status(thm)],[f447]) ).
fof(f449,plain,
( ! [U,X10,X15] :
( ! [X16] :
( ! [X17] :
( ! [X18] :
( ~ lt(X17,X15)
| app(X18,cons(X17,nil)) != U
| ~ ssList(X18) )
| ~ ssItem(X17) )
| app(cons(X15,nil),X16) != X10
| ~ ssList(X16) )
| ~ ssItem(X15)
| sP1_prd(X15,X10,U) )
& ! [U,X10,X15] :
( ( lt(sK59_skl(X15,X10,U),X15)
& app(sK60_skl(X15,X10,U),cons(sK59_skl(X15,X10,U),nil)) = U
& ssList(sK60_skl(X15,X10,U))
& ssItem(sK59_skl(X15,X10,U))
& app(cons(X15,nil),sK58_skl(X15,X10,U)) = X10
& ssList(sK58_skl(X15,X10,U))
& ssItem(X15) )
| ~ sP1_prd(X15,X10,U) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK58_skl,sK59_skl,sK60_skl]),skolemize(X16,sK58_skl(X15,X10,U)),skolemize(X17,sK59_skl(X15,X10,U)),skolemize(X18,sK60_skl(X15,X10,U))],[f448]) ).
fof(f450,plain,
! [X0,X1,X2] :
( ssItem(X0)
| ~ sP1_prd(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f449]) ).
fof(f451,plain,
! [X0,X1,X2] :
( ssList(sK58_skl(X0,X1,X2))
| ~ sP1_prd(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f449]) ).
fof(f452,plain,
! [X0,X1,X2] :
( app(cons(X0,nil),sK58_skl(X0,X1,X2)) = X1
| ~ sP1_prd(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f449]) ).
fof(f453,plain,
! [X0,X1,X2] :
( ssItem(sK59_skl(X0,X1,X2))
| ~ sP1_prd(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f449]) ).
fof(f454,plain,
! [X0,X1,X2] :
( ssList(sK60_skl(X0,X1,X2))
| ~ sP1_prd(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f449]) ).
fof(f455,plain,
! [X0,X1,X2] :
( app(sK60_skl(X0,X1,X2),cons(sK59_skl(X0,X1,X2),nil)) = X2
| ~ sP1_prd(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f449]) ).
fof(f456,plain,
! [X0,X1,X2] :
( lt(sK59_skl(X0,X1,X2),X0)
| ~ sP1_prd(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f449]) ).
fof(f492,plain,
app(app(sK51_skl,sK47_skl),sK52_skl) = sK50_skl,
inference(forward_demodulation,[status(thm)],[f426,f429]) ).
fof(f493,plain,
app(app(sK51_skl,sK47_skl),sK52_skl) = sK48_skl,
inference(forward_demodulation,[status(thm)],[f425,f492]) ).
fof(f494,plain,
strictorderedP(sK47_skl),
inference(forward_demodulation,[status(thm)],[f426,f430]) ).
fof(f495,plain,
! [X0,X1,X2,X3] :
( ~ lt(X0,X2)
| app(cons(X2,nil),X3) != sK47_skl
| ~ ssList(X3)
| ~ ssItem(X2)
| app(X1,cons(X0,nil)) != sK51_skl
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(forward_demodulation,[status(thm)],[f426,f431]) ).
fof(f496,plain,
! [X0,X1,X2,X3] :
( ~ lt(X2,X0)
| app(X3,cons(X2,nil)) != sK47_skl
| ~ ssList(X3)
| ~ ssItem(X2)
| app(cons(X0,nil),X1) != sK52_skl
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(forward_demodulation,[status(thm)],[f426,f432]) ).
fof(f497,plain,
( nil != sK49_skl
| nil = sK48_skl ),
inference(forward_demodulation,[status(thm)],[f425,f433]) ).
fof(f498,plain,
( nil != sK47_skl
| nil = sK48_skl ),
inference(forward_demodulation,[status(thm)],[f426,f497]) ).
fof(f499,plain,
! [X0,X1] :
( nil = sK47_skl
| sP1_prd(sK54_skl(X1,X0),X1,sK47_skl)
| sP0_prd(sK53_skl(X1,X0),X0,sK47_skl)
| app(app(X0,sK47_skl),X1) != sK48_skl
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f434,f494]) ).
fof(f500,plain,
! [X0,X1] :
( nil != sK48_skl
| sP1_prd(sK54_skl(X1,X0),X1,sK47_skl)
| sP0_prd(sK53_skl(X1,X0),X0,sK47_skl)
| app(app(X0,sK47_skl),X1) != sK48_skl
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f435,f494]) ).
fof(f523,plain,
( nil != sK48_skl
| sP1_prd(sK54_skl(sK52_skl,sK51_skl),sK52_skl,sK47_skl)
| sP0_prd(sK53_skl(sK52_skl,sK51_skl),sK51_skl,sK47_skl)
| ~ ssList(sK52_skl)
| ~ ssList(sK51_skl) ),
inference(resolution,[status(thm)],[f493,f500]) ).
fof(f524,plain,
( nil = sK47_skl
| sP1_prd(sK54_skl(sK52_skl,sK51_skl),sK52_skl,sK47_skl)
| sP0_prd(sK53_skl(sK52_skl,sK51_skl),sK51_skl,sK47_skl)
| ~ ssList(sK52_skl)
| ~ ssList(sK51_skl) ),
inference(resolution,[status(thm)],[f493,f499]) ).
fof(f530,plain,
( nil != sK48_skl
| sP1_prd(sK54_skl(sK52_skl,sK51_skl),sK52_skl,sK47_skl)
| sP0_prd(sK53_skl(sK52_skl,sK51_skl),sK51_skl,sK47_skl)
| ~ ssList(sK52_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f523,f427]) ).
fof(f531,plain,
( nil = sK47_skl
| sP1_prd(sK54_skl(sK52_skl,sK51_skl),sK52_skl,sK47_skl)
| sP0_prd(sK53_skl(sK52_skl,sK51_skl),sK51_skl,sK47_skl)
| ~ ssList(sK52_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f524,f427]) ).
fof(f537,plain,
( nil != sK47_skl
| sP1_prd(sK54_skl(sK52_skl,sK51_skl),sK52_skl,sK47_skl)
| sP0_prd(sK53_skl(sK52_skl,sK51_skl),sK51_skl,sK47_skl)
| ~ ssList(sK52_skl) ),
inference(resolution,[status(thm)],[f530,f498]) ).
fof(f538,plain,
( sP1_prd(sK54_skl(sK52_skl,sK51_skl),sK52_skl,sK47_skl)
| sP0_prd(sK53_skl(sK52_skl,sK51_skl),sK51_skl,sK47_skl)
| ~ ssList(sK52_skl) ),
inference(backward_subsumption_resolution,[status(thm)],[f531,f539]) ).
fof(f539,plain,
( nil != sK47_skl
| sP1_prd(sK54_skl(sK52_skl,sK51_skl),sK52_skl,sK47_skl)
| sP0_prd(sK53_skl(sK52_skl,sK51_skl),sK51_skl,sK47_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f537,f428]) ).
fof(f540,plain,
( sP1_prd(sK54_skl(sK52_skl,sK51_skl),sK52_skl,sK47_skl)
| sP0_prd(sK53_skl(sK52_skl,sK51_skl),sK51_skl,sK47_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f538,f428]) ).
fof(f547,plain,
! [X0,X1,X2,X3] :
( ~ sP0_prd(X0,sK51_skl,X1)
| ~ lt(X0,X2)
| app(cons(X2,nil),X3) != sK47_skl
| ~ ssList(X3)
| ~ ssItem(X2)
| ~ ssList(sK55_skl(X0,sK51_skl,X1))
| ~ ssItem(X0) ),
inference(resolution,[status(thm)],[f495,f441]) ).
fof(f549,plain,
! [X0,X1,X2,X3] :
( ~ sP0_prd(X0,sK51_skl,X1)
| ~ lt(X0,X2)
| app(cons(X2,nil),X3) != sK47_skl
| ~ ssList(X3)
| ~ ssItem(X2)
| ~ ssList(sK55_skl(X0,sK51_skl,X1)) ),
inference(forward_subsumption_resolution,[status(thm)],[f547,f439]) ).
fof(f551,plain,
! [X0,X1,X2,X3] :
( ~ sP1_prd(X0,sK52_skl,X1)
| ~ lt(X2,X0)
| app(X3,cons(X2,nil)) != sK47_skl
| ~ ssList(X3)
| ~ ssItem(X2)
| ~ ssList(sK58_skl(X0,sK52_skl,X1))
| ~ ssItem(X0) ),
inference(resolution,[status(thm)],[f496,f452]) ).
fof(f553,plain,
! [X0,X1,X2,X3] :
( ~ sP1_prd(X0,sK52_skl,X1)
| ~ lt(X2,X0)
| app(X3,cons(X2,nil)) != sK47_skl
| ~ ssList(X3)
| ~ ssItem(X2)
| ~ ssList(sK58_skl(X0,sK52_skl,X1)) ),
inference(forward_subsumption_resolution,[status(thm)],[f551,f450]) ).
fof(f593,plain,
! [X0,X1,X2,X3] :
( ~ sP0_prd(X2,X3,sK47_skl)
| ~ sP0_prd(X0,sK51_skl,X1)
| ~ lt(X0,sK56_skl(X2,X3,sK47_skl))
| ~ ssList(sK57_skl(X2,X3,sK47_skl))
| ~ ssItem(sK56_skl(X2,X3,sK47_skl))
| ~ ssList(sK55_skl(X0,sK51_skl,X1)) ),
inference(resolution,[status(thm)],[f549,f444]) ).
fof(f595,plain,
! [X0,X1,X2,X3] :
( ~ sP0_prd(X0,X1,sK47_skl)
| ~ sP0_prd(X2,sK51_skl,X3)
| ~ lt(X2,sK56_skl(X0,X1,sK47_skl))
| ~ ssList(sK57_skl(X0,X1,sK47_skl))
| ~ ssItem(sK56_skl(X0,X1,sK47_skl)) ),
inference(forward_subsumption_resolution,[status(thm)],[f593,f440]) ).
fof(f600,plain,
! [X0,X1,X2,X3] :
( ~ sP1_prd(X2,X3,sK47_skl)
| ~ sP1_prd(X0,sK52_skl,X1)
| ~ lt(sK59_skl(X2,X3,sK47_skl),X0)
| ~ ssList(sK60_skl(X2,X3,sK47_skl))
| ~ ssItem(sK59_skl(X2,X3,sK47_skl))
| ~ ssList(sK58_skl(X0,sK52_skl,X1)) ),
inference(resolution,[status(thm)],[f553,f455]) ).
fof(f602,plain,
! [X0,X1,X2,X3] :
( ~ sP1_prd(X0,X1,sK47_skl)
| ~ sP1_prd(X2,sK52_skl,X3)
| ~ lt(sK59_skl(X0,X1,sK47_skl),X2)
| ~ ssList(sK60_skl(X0,X1,sK47_skl))
| ~ ssItem(sK59_skl(X0,X1,sK47_skl)) ),
inference(forward_subsumption_resolution,[status(thm)],[f600,f451]) ).
fof(f619,plain,
! [X0,X1,X2] :
( ~ sP0_prd(X0,X1,sK47_skl)
| ~ sP0_prd(X0,X1,sK47_skl)
| ~ sP0_prd(X0,sK51_skl,X2)
| ~ ssList(sK57_skl(X0,X1,sK47_skl))
| ~ ssItem(sK56_skl(X0,X1,sK47_skl)) ),
inference(resolution,[status(thm)],[f595,f445]) ).
fof(f621,plain,
! [X0,X1,X2] :
( ~ sP0_prd(X0,X1,sK47_skl)
| ~ sP0_prd(X0,sK51_skl,X2)
| ~ ssList(sK57_skl(X0,X1,sK47_skl))
| ~ ssItem(sK56_skl(X0,X1,sK47_skl)) ),
inference(duplicate_literals_removal,[status(thm)],[f619]) ).
fof(f622,plain,
! [X0,X1,X2] :
( ~ sP0_prd(X0,X1,sK47_skl)
| ~ sP0_prd(X0,sK51_skl,X2)
| ~ ssList(sK57_skl(X0,X1,sK47_skl)) ),
inference(forward_subsumption_resolution,[status(thm)],[f621,f442]) ).
fof(f623,plain,
! [X0,X1,X2] :
( ~ sP1_prd(X0,X1,sK47_skl)
| ~ sP1_prd(X0,X1,sK47_skl)
| ~ sP1_prd(X0,sK52_skl,X2)
| ~ ssList(sK60_skl(X0,X1,sK47_skl))
| ~ ssItem(sK59_skl(X0,X1,sK47_skl)) ),
inference(resolution,[status(thm)],[f602,f456]) ).
fof(f625,plain,
! [X0,X1,X2] :
( ~ sP1_prd(X0,X1,sK47_skl)
| ~ sP1_prd(X0,sK52_skl,X2)
| ~ ssList(sK60_skl(X0,X1,sK47_skl))
| ~ ssItem(sK59_skl(X0,X1,sK47_skl)) ),
inference(duplicate_literals_removal,[status(thm)],[f623]) ).
fof(f626,plain,
! [X0,X1,X2] :
( ~ sP1_prd(X0,X1,sK47_skl)
| ~ sP1_prd(X0,sK52_skl,X2)
| ~ ssList(sK60_skl(X0,X1,sK47_skl)) ),
inference(forward_subsumption_resolution,[status(thm)],[f625,f453]) ).
fof(f645,plain,
! [X0,X1,X2] :
( ~ sP0_prd(X0,X2,sK47_skl)
| ~ sP0_prd(X0,X2,sK47_skl)
| ~ sP0_prd(X0,sK51_skl,X1) ),
inference(resolution,[status(thm)],[f622,f443]) ).
fof(f646,plain,
! [X0,X1,X2] :
( ~ sP0_prd(X0,X2,sK47_skl)
| ~ sP0_prd(X0,sK51_skl,X1) ),
inference(duplicate_literals_removal,[status(thm)],[f645]) ).
fof(f652,plain,
! [X0,X1,X2] :
( ~ sP1_prd(X0,X2,sK47_skl)
| ~ sP1_prd(X0,X2,sK47_skl)
| ~ sP1_prd(X0,sK52_skl,X1) ),
inference(resolution,[status(thm)],[f626,f454]) ).
fof(f653,plain,
! [X0,X1,X2] :
( ~ sP1_prd(X0,X2,sK47_skl)
| ~ sP1_prd(X0,sK52_skl,X1) ),
inference(duplicate_literals_removal,[status(thm)],[f652]) ).
fof(f654,plain,
! [X0] :
( sP0_prd(sK53_skl(sK52_skl,sK51_skl),sK51_skl,sK47_skl)
| ~ sP1_prd(sK54_skl(sK52_skl,sK51_skl),X0,sK47_skl) ),
inference(resolution,[status(thm)],[f653,f540]) ).
fof(f655,plain,
sP0_prd(sK53_skl(sK52_skl,sK51_skl),sK51_skl,sK47_skl),
inference(backward_subsumption_resolution,[status(thm)],[f540,f654]) ).
fof(f656,plain,
! [X0] : ~ sP0_prd(sK53_skl(sK52_skl,sK51_skl),X0,sK47_skl),
inference(resolution,[status(thm)],[f655,f646]) ).
fof(f659,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[f655,f656]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC344+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n008.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Mon Sep 21 08:18:09 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.39 % Drodi V4.1.1
% 0.14/0.60 % Refutation found
% 0.14/0.60 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.14/0.60 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.14/0.64 % Elapsed time: 0.265816 seconds
% 0.14/0.64 % CPU time: 1.708560 seconds
% 0.14/0.64 % Total memory used: 127.666 MB
% 0.14/0.64 % Net memory used: 126.338 MB
%------------------------------------------------------------------------------