%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SWC413+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 : n016.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 02:41:08 PM UTC 2026
% Result : Theorem 4.57s 1.02s
% Output : CNFRefutation 4.57s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 2
% Syntax : Number of formulae : 46 ( 5 unt; 1 def)
% Number of atoms : 322 ( 86 equ)
% Maximal formula atoms : 30 ( 7 avg)
% Number of connectives : 417 ( 141 ~; 143 |; 106 &)
% ( 1 <=>; 26 =>; 0 <=; 0 <~>)
% Maximal formula depth : 23 ( 8 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-4 aty)
% Number of functors : 19 ( 19 usr; 8 con; 0-4 aty)
% Number of variables : 228 ( 172 !; 56 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f96,conjecture,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ! [X] :
( ssList(X)
=> ( ( ( ! [X2] :
( ssItem(X2)
=> ! [X3] :
( ssItem(X3)
=> ! [X4] :
( ssList(X4)
=> app(app(cons(X2,nil),cons(X3,nil)),X4) != V ) ) )
| ? [X8] :
( ? [X9] :
( ? [X10] :
( app(app(cons(X8,nil),cons(X9,nil)),X10) = X
& ssList(X10) )
& ssItem(X9) )
& ssItem(X8) ) )
& ( ! [X5] :
( ssItem(X5)
=> ! [X6] :
( ssItem(X6)
=> ! [X7] :
( ssList(X7)
=> ( app(app(cons(X6,nil),cons(X5,nil)),X7) != W
| app(app(cons(X5,nil),cons(X6,nil)),X7) != X ) ) ) )
| ! [X2] :
( ssItem(X2)
=> ! [X3] :
( ssItem(X3)
=> ! [X4] :
( ssList(X4)
=> app(app(cons(X2,nil),cons(X3,nil)),X4) != V ) ) )
| ? [Y] :
( ? [Z] :
( ? [X1] :
( app(app(cons(Z,nil),cons(Y,nil)),X1) = U
& app(app(cons(Y,nil),cons(Z,nil)),X1) = V
& ssList(X1) )
& ssItem(Z) )
& ssItem(Y) ) ) )
| 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)
=> ( ( ( ! [X2] :
( ssItem(X2)
=> ! [X3] :
( ssItem(X3)
=> ! [X4] :
( ssList(X4)
=> app(app(cons(X2,nil),cons(X3,nil)),X4) != V ) ) )
| ? [X8] :
( ? [X9] :
( ? [X10] :
( app(app(cons(X8,nil),cons(X9,nil)),X10) = X
& ssList(X10) )
& ssItem(X9) )
& ssItem(X8) ) )
& ( ! [X5] :
( ssItem(X5)
=> ! [X6] :
( ssItem(X6)
=> ! [X7] :
( ssList(X7)
=> ( app(app(cons(X6,nil),cons(X5,nil)),X7) != W
| app(app(cons(X5,nil),cons(X6,nil)),X7) != X ) ) ) )
| ! [X2] :
( ssItem(X2)
=> ! [X3] :
( ssItem(X3)
=> ! [X4] :
( ssList(X4)
=> app(app(cons(X2,nil),cons(X3,nil)),X4) != V ) ) )
| ? [Y] :
( ? [Z] :
( ? [X1] :
( app(app(cons(Z,nil),cons(Y,nil)),X1) = U
& app(app(cons(Y,nil),cons(Z,nil)),X1) = V
& ssList(X1) )
& ssItem(Z) )
& ssItem(Y) ) ) )
| U != W
| V != X ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f96]) ).
fof(f415,plain,
? [U] :
( ? [V] :
( ? [W] :
( ? [X] :
( ( ( ? [X2] :
( ? [X3] :
( ? [X4] :
( app(app(cons(X2,nil),cons(X3,nil)),X4) = V
& ssList(X4) )
& ssItem(X3) )
& ssItem(X2) )
& ! [X8] :
( ! [X9] :
( ! [X10] :
( app(app(cons(X8,nil),cons(X9,nil)),X10) != X
| ~ ssList(X10) )
| ~ ssItem(X9) )
| ~ ssItem(X8) ) )
| ( ? [X5] :
( ? [X6] :
( ? [X7] :
( app(app(cons(X6,nil),cons(X5,nil)),X7) = W
& app(app(cons(X5,nil),cons(X6,nil)),X7) = X
& ssList(X7) )
& ssItem(X6) )
& ssItem(X5) )
& ? [X2] :
( ? [X3] :
( ? [X4] :
( app(app(cons(X2,nil),cons(X3,nil)),X4) = V
& ssList(X4) )
& ssItem(X3) )
& ssItem(X2) )
& ! [Y] :
( ! [Z] :
( ! [X1] :
( app(app(cons(Z,nil),cons(Y,nil)),X1) != U
| app(app(cons(Y,nil),cons(Z,nil)),X1) != V
| ~ ssList(X1) )
| ~ ssItem(Z) )
| ~ ssItem(Y) ) ) )
& U = W
& V = X
& ssList(X) )
& ssList(W) )
& ssList(V) )
& ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f97]) ).
fof(f416,definition,
! [U,V,W,X] :
( sP0_prd(X,W,V,U)
<=> ( ? [X5] :
( ? [X6] :
( ? [X7] :
( app(app(cons(X6,nil),cons(X5,nil)),X7) = W
& app(app(cons(X5,nil),cons(X6,nil)),X7) = X
& ssList(X7) )
& ssItem(X6) )
& ssItem(X5) )
& ? [X2] :
( ? [X3] :
( ? [X4] :
( app(app(cons(X2,nil),cons(X3,nil)),X4) = V
& ssList(X4) )
& ssItem(X3) )
& ssItem(X2) )
& ! [Y] :
( ! [Z] :
( ! [X1] :
( app(app(cons(Z,nil),cons(Y,nil)),X1) != U
| app(app(cons(Y,nil),cons(Z,nil)),X1) != V
| ~ ssList(X1) )
| ~ ssItem(Z) )
| ~ ssItem(Y) ) ) ),
introduced(definition,[new_symbols(definition,[sP0_prd])],[]) ).
fof(f417,plain,
? [U] :
( ? [V] :
( ? [W] :
( ? [X] :
( ( ( ? [X2] :
( ? [X3] :
( ? [X4] :
( app(app(cons(X2,nil),cons(X3,nil)),X4) = V
& ssList(X4) )
& ssItem(X3) )
& ssItem(X2) )
& ! [X8] :
( ! [X9] :
( ! [X10] :
( app(app(cons(X8,nil),cons(X9,nil)),X10) != X
| ~ ssList(X10) )
| ~ ssItem(X9) )
| ~ ssItem(X8) ) )
| sP0_prd(X,W,V,U) )
& U = W
& V = X
& ssList(X) )
& ssList(W) )
& ssList(V) )
& ssList(U) ),
inference(formula_renaming,[status(thm)],[f415,f416]) ).
fof(f418,plain,
( ( ( app(app(cons(sK51_skl,nil),cons(sK52_skl,nil)),sK53_skl) = sK48_skl
& ssList(sK53_skl)
& ssItem(sK52_skl)
& ssItem(sK51_skl)
& ! [X8] :
( ! [X9] :
( ! [X10] :
( app(app(cons(X8,nil),cons(X9,nil)),X10) != sK50_skl
| ~ ssList(X10) )
| ~ ssItem(X9) )
| ~ ssItem(X8) ) )
| sP0_prd(sK50_skl,sK49_skl,sK48_skl,sK47_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]),skolemize(U,sK47_skl),skolemize(V,sK48_skl),skolemize(W,sK49_skl),skolemize(X,sK50_skl),skolemize(X2,sK51_skl),skolemize(X3,sK52_skl),skolemize(X4,sK53_skl)],[f417]) ).
fof(f423,plain,
sK48_skl = sK50_skl,
inference(cnf_transformation,[status(thm)],[f418]) ).
fof(f424,plain,
sK47_skl = sK49_skl,
inference(cnf_transformation,[status(thm)],[f418]) ).
fof(f425,plain,
! [X0,X1,X2] :
( app(app(cons(X0,nil),cons(X1,nil)),X2) != sK50_skl
| ~ ssList(X2)
| ~ ssItem(X1)
| ~ ssItem(X0)
| sP0_prd(sK50_skl,sK49_skl,sK48_skl,sK47_skl) ),
inference(cnf_transformation,[status(thm)],[f418]) ).
fof(f426,plain,
( ssItem(sK51_skl)
| sP0_prd(sK50_skl,sK49_skl,sK48_skl,sK47_skl) ),
inference(cnf_transformation,[status(thm)],[f418]) ).
fof(f427,plain,
( ssItem(sK52_skl)
| sP0_prd(sK50_skl,sK49_skl,sK48_skl,sK47_skl) ),
inference(cnf_transformation,[status(thm)],[f418]) ).
fof(f428,plain,
( ssList(sK53_skl)
| sP0_prd(sK50_skl,sK49_skl,sK48_skl,sK47_skl) ),
inference(cnf_transformation,[status(thm)],[f418]) ).
fof(f429,plain,
( app(app(cons(sK51_skl,nil),cons(sK52_skl,nil)),sK53_skl) = sK48_skl
| sP0_prd(sK50_skl,sK49_skl,sK48_skl,sK47_skl) ),
inference(cnf_transformation,[status(thm)],[f418]) ).
fof(f430,plain,
! [U,V,W,X] :
( ( ! [X5] :
( ! [X6] :
( ! [X7] :
( app(app(cons(X6,nil),cons(X5,nil)),X7) != W
| app(app(cons(X5,nil),cons(X6,nil)),X7) != X
| ~ ssList(X7) )
| ~ ssItem(X6) )
| ~ ssItem(X5) )
| ! [X2] :
( ! [X3] :
( ! [X4] :
( app(app(cons(X2,nil),cons(X3,nil)),X4) != V
| ~ ssList(X4) )
| ~ ssItem(X3) )
| ~ ssItem(X2) )
| ? [Y] :
( ? [Z] :
( ? [X1] :
( app(app(cons(Z,nil),cons(Y,nil)),X1) = U
& app(app(cons(Y,nil),cons(Z,nil)),X1) = V
& ssList(X1) )
& ssItem(Z) )
& ssItem(Y) )
| sP0_prd(X,W,V,U) )
& ( ( ? [X5] :
( ? [X6] :
( ? [X7] :
( app(app(cons(X6,nil),cons(X5,nil)),X7) = W
& app(app(cons(X5,nil),cons(X6,nil)),X7) = X
& ssList(X7) )
& ssItem(X6) )
& ssItem(X5) )
& ? [X2] :
( ? [X3] :
( ? [X4] :
( app(app(cons(X2,nil),cons(X3,nil)),X4) = V
& ssList(X4) )
& ssItem(X3) )
& ssItem(X2) )
& ! [Y] :
( ! [Z] :
( ! [X1] :
( app(app(cons(Z,nil),cons(Y,nil)),X1) != U
| app(app(cons(Y,nil),cons(Z,nil)),X1) != V
| ~ ssList(X1) )
| ~ ssItem(Z) )
| ~ ssItem(Y) ) )
| ~ sP0_prd(X,W,V,U) ) ),
inference(NNF_transformation,[status(thm)],[f416]) ).
fof(f431,plain,
( ! [U,V,W,X] :
( ! [X5] :
( ! [X6] :
( ! [X7] :
( app(app(cons(X6,nil),cons(X5,nil)),X7) != W
| app(app(cons(X5,nil),cons(X6,nil)),X7) != X
| ~ ssList(X7) )
| ~ ssItem(X6) )
| ~ ssItem(X5) )
| ! [X2] :
( ! [X3] :
( ! [X4] :
( app(app(cons(X2,nil),cons(X3,nil)),X4) != V
| ~ ssList(X4) )
| ~ ssItem(X3) )
| ~ ssItem(X2) )
| ? [Y] :
( ? [Z] :
( ? [X1] :
( app(app(cons(Z,nil),cons(Y,nil)),X1) = U
& app(app(cons(Y,nil),cons(Z,nil)),X1) = V
& ssList(X1) )
& ssItem(Z) )
& ssItem(Y) )
| sP0_prd(X,W,V,U) )
& ! [U,V,W,X] :
( ( ? [X5] :
( ? [X6] :
( ? [X7] :
( app(app(cons(X6,nil),cons(X5,nil)),X7) = W
& app(app(cons(X5,nil),cons(X6,nil)),X7) = X
& ssList(X7) )
& ssItem(X6) )
& ssItem(X5) )
& ? [X2] :
( ? [X3] :
( ? [X4] :
( app(app(cons(X2,nil),cons(X3,nil)),X4) = V
& ssList(X4) )
& ssItem(X3) )
& ssItem(X2) )
& ! [Y] :
( ! [Z] :
( ! [X1] :
( app(app(cons(Z,nil),cons(Y,nil)),X1) != U
| app(app(cons(Y,nil),cons(Z,nil)),X1) != V
| ~ ssList(X1) )
| ~ ssItem(Z) )
| ~ ssItem(Y) ) )
| ~ sP0_prd(X,W,V,U) ) ),
inference(miniscoping,[status(thm)],[f430]) ).
fof(f432,plain,
( ! [U,V,W,X] :
( ! [X5] :
( ! [X6] :
( ! [X7] :
( app(app(cons(X6,nil),cons(X5,nil)),X7) != W
| app(app(cons(X5,nil),cons(X6,nil)),X7) != X
| ~ ssList(X7) )
| ~ ssItem(X6) )
| ~ ssItem(X5) )
| ! [X2] :
( ! [X3] :
( ! [X4] :
( app(app(cons(X2,nil),cons(X3,nil)),X4) != V
| ~ ssList(X4) )
| ~ ssItem(X3) )
| ~ ssItem(X2) )
| ( app(app(cons(sK61_skl(X,W,V,U),nil),cons(sK60_skl(X,W,V,U),nil)),sK62_skl(X,W,V,U)) = U
& app(app(cons(sK60_skl(X,W,V,U),nil),cons(sK61_skl(X,W,V,U),nil)),sK62_skl(X,W,V,U)) = V
& ssList(sK62_skl(X,W,V,U))
& ssItem(sK61_skl(X,W,V,U))
& ssItem(sK60_skl(X,W,V,U)) )
| sP0_prd(X,W,V,U) )
& ! [U,V,W,X] :
( ( app(app(cons(sK58_skl(X,W,V,U),nil),cons(sK57_skl(X,W,V,U),nil)),sK59_skl(X,W,V,U)) = W
& app(app(cons(sK57_skl(X,W,V,U),nil),cons(sK58_skl(X,W,V,U),nil)),sK59_skl(X,W,V,U)) = X
& ssList(sK59_skl(X,W,V,U))
& ssItem(sK58_skl(X,W,V,U))
& ssItem(sK57_skl(X,W,V,U))
& app(app(cons(sK54_skl(X,W,V,U),nil),cons(sK55_skl(X,W,V,U),nil)),sK56_skl(X,W,V,U)) = V
& ssList(sK56_skl(X,W,V,U))
& ssItem(sK55_skl(X,W,V,U))
& ssItem(sK54_skl(X,W,V,U))
& ! [Y] :
( ! [Z] :
( ! [X1] :
( app(app(cons(Z,nil),cons(Y,nil)),X1) != U
| app(app(cons(Y,nil),cons(Z,nil)),X1) != V
| ~ ssList(X1) )
| ~ ssItem(Z) )
| ~ ssItem(Y) ) )
| ~ sP0_prd(X,W,V,U) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK54_skl,sK55_skl,sK56_skl,sK57_skl,sK58_skl,sK59_skl,sK60_skl,sK61_skl,sK62_skl]),skolemize(X2,sK54_skl(X,W,V,U)),skolemize(X3,sK55_skl(X,W,V,U)),skolemize(X4,sK56_skl(X,W,V,U)),skolemize(X5,sK57_skl(X,W,V,U)),skolemize(X6,sK58_skl(X,W,V,U)),skolemize(X7,sK59_skl(X,W,V,U)),skolemize(Y,sK60_skl(X,W,V,U)),skolemize(Z,sK61_skl(X,W,V,U)),skolemize(X1,sK62_skl(X,W,V,U))],[f431]) ).
fof(f433,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( app(app(cons(X5,nil),cons(X4,nil)),X6) != X3
| app(app(cons(X4,nil),cons(X5,nil)),X6) != X2
| ~ ssList(X6)
| ~ ssItem(X5)
| ~ ssItem(X4)
| ~ sP0_prd(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(thm)],[f432]) ).
fof(f438,plain,
! [X0,X1,X2,X3] :
( ssItem(sK57_skl(X0,X1,X2,X3))
| ~ sP0_prd(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(thm)],[f432]) ).
fof(f439,plain,
! [X0,X1,X2,X3] :
( ssItem(sK58_skl(X0,X1,X2,X3))
| ~ sP0_prd(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(thm)],[f432]) ).
fof(f440,plain,
! [X0,X1,X2,X3] :
( ssList(sK59_skl(X0,X1,X2,X3))
| ~ sP0_prd(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(thm)],[f432]) ).
fof(f441,plain,
! [X0,X1,X2,X3] :
( app(app(cons(sK57_skl(X0,X1,X2,X3),nil),cons(sK58_skl(X0,X1,X2,X3),nil)),sK59_skl(X0,X1,X2,X3)) = X0
| ~ sP0_prd(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(thm)],[f432]) ).
fof(f442,plain,
! [X0,X1,X2,X3] :
( app(app(cons(sK58_skl(X0,X1,X2,X3),nil),cons(sK57_skl(X0,X1,X2,X3),nil)),sK59_skl(X0,X1,X2,X3)) = X1
| ~ sP0_prd(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(thm)],[f432]) ).
fof(f462,plain,
! [X0,X1,X2] :
( app(app(cons(X0,nil),cons(X1,nil)),X2) != sK50_skl
| ~ ssList(X2)
| ~ ssItem(X1)
| ~ ssItem(X0)
| sP0_prd(sK48_skl,sK49_skl,sK48_skl,sK47_skl) ),
inference(forward_demodulation,[status(thm)],[f423,f425]) ).
fof(f463,plain,
! [X0,X1,X2] :
( app(app(cons(X0,nil),cons(X1,nil)),X2) != sK50_skl
| ~ ssList(X2)
| ~ ssItem(X1)
| ~ ssItem(X0)
| sP0_prd(sK48_skl,sK47_skl,sK48_skl,sK47_skl) ),
inference(forward_demodulation,[status(thm)],[f424,f462]) ).
fof(f464,plain,
! [X0,X1,X2] :
( app(app(cons(X0,nil),cons(X1,nil)),X2) != sK48_skl
| ~ ssList(X2)
| ~ ssItem(X1)
| ~ ssItem(X0)
| sP0_prd(sK48_skl,sK47_skl,sK48_skl,sK47_skl) ),
inference(forward_demodulation,[status(thm)],[f423,f463]) ).
fof(f468,plain,
( ssItem(sK51_skl)
| sP0_prd(sK48_skl,sK49_skl,sK48_skl,sK47_skl) ),
inference(forward_demodulation,[status(thm)],[f423,f426]) ).
fof(f469,plain,
( ssItem(sK51_skl)
| sP0_prd(sK48_skl,sK47_skl,sK48_skl,sK47_skl) ),
inference(forward_demodulation,[status(thm)],[f424,f468]) ).
fof(f470,plain,
( ssItem(sK52_skl)
| sP0_prd(sK48_skl,sK49_skl,sK48_skl,sK47_skl) ),
inference(forward_demodulation,[status(thm)],[f423,f427]) ).
fof(f471,plain,
( ssItem(sK52_skl)
| sP0_prd(sK48_skl,sK47_skl,sK48_skl,sK47_skl) ),
inference(forward_demodulation,[status(thm)],[f424,f470]) ).
fof(f482,plain,
( ssList(sK53_skl)
| sP0_prd(sK48_skl,sK49_skl,sK48_skl,sK47_skl) ),
inference(forward_demodulation,[status(thm)],[f423,f428]) ).
fof(f483,plain,
( ssList(sK53_skl)
| sP0_prd(sK48_skl,sK47_skl,sK48_skl,sK47_skl) ),
inference(forward_demodulation,[status(thm)],[f424,f482]) ).
fof(f484,plain,
( app(app(cons(sK51_skl,nil),cons(sK52_skl,nil)),sK53_skl) = sK48_skl
| sP0_prd(sK48_skl,sK49_skl,sK48_skl,sK47_skl) ),
inference(forward_demodulation,[status(thm)],[f423,f429]) ).
fof(f485,plain,
( app(app(cons(sK51_skl,nil),cons(sK52_skl,nil)),sK53_skl) = sK48_skl
| sP0_prd(sK48_skl,sK47_skl,sK48_skl,sK47_skl) ),
inference(forward_demodulation,[status(thm)],[f424,f484]) ).
fof(f486,plain,
( ~ ssList(sK53_skl)
| ~ ssItem(sK52_skl)
| ~ ssItem(sK51_skl)
| sP0_prd(sK48_skl,sK47_skl,sK48_skl,sK47_skl)
| sP0_prd(sK48_skl,sK47_skl,sK48_skl,sK47_skl) ),
inference(resolution,[status(thm)],[f485,f464]) ).
fof(f489,plain,
( ~ ssList(sK53_skl)
| ~ ssItem(sK52_skl)
| ~ ssItem(sK51_skl)
| sP0_prd(sK48_skl,sK47_skl,sK48_skl,sK47_skl) ),
inference(duplicate_literals_removal,[status(thm)],[f486]) ).
fof(f490,plain,
( ~ ssList(sK53_skl)
| ~ ssItem(sK52_skl)
| sP0_prd(sK48_skl,sK47_skl,sK48_skl,sK47_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f489,f469]) ).
fof(f522,plain,
sP0_prd(sK48_skl,sK47_skl,sK48_skl,sK47_skl),
inference(backward_subsumption_resolution,[status(thm)],[f483,f523]) ).
fof(f523,plain,
( ~ ssList(sK53_skl)
| sP0_prd(sK48_skl,sK47_skl,sK48_skl,sK47_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f490,f471]) ).
fof(f534,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( ~ sP0_prd(X4,X3,X5,X6)
| app(app(cons(sK57_skl(X4,X3,X5,X6),nil),cons(sK58_skl(X4,X3,X5,X6),nil)),sK59_skl(X4,X3,X5,X6)) != X2
| ~ ssList(sK59_skl(X4,X3,X5,X6))
| ~ ssItem(sK58_skl(X4,X3,X5,X6))
| ~ ssItem(sK57_skl(X4,X3,X5,X6))
| ~ sP0_prd(X0,X1,X2,X3) ),
inference(resolution,[status(thm)],[f433,f442]) ).
fof(f548,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( ~ sP0_prd(X4,X3,X5,X6)
| app(app(cons(sK57_skl(X4,X3,X5,X6),nil),cons(sK58_skl(X4,X3,X5,X6),nil)),sK59_skl(X4,X3,X5,X6)) != X2
| ~ ssList(sK59_skl(X4,X3,X5,X6))
| ~ ssItem(sK58_skl(X4,X3,X5,X6))
| ~ sP0_prd(X0,X1,X2,X3) ),
inference(forward_subsumption_resolution,[status(thm)],[f534,f438]) ).
fof(f1304,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( ~ sP0_prd(X4,X3,X5,X6)
| app(app(cons(sK57_skl(X4,X3,X5,X6),nil),cons(sK58_skl(X4,X3,X5,X6),nil)),sK59_skl(X4,X3,X5,X6)) != X2
| ~ ssList(sK59_skl(X4,X3,X5,X6))
| ~ sP0_prd(X0,X1,X2,X3) ),
inference(forward_subsumption_resolution,[status(thm)],[f548,f439]) ).
fof(f1305,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ sP0_prd(X2,X3,X4,X5)
| ~ sP0_prd(X2,X3,X4,X5)
| ~ ssList(sK59_skl(X2,X3,X4,X5))
| ~ sP0_prd(X0,X1,X2,X3) ),
inference(resolution,[status(thm)],[f1304,f441]) ).
fof(f1324,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ sP0_prd(X2,X3,X4,X5)
| ~ ssList(sK59_skl(X2,X3,X4,X5))
| ~ sP0_prd(X0,X1,X2,X3) ),
inference(duplicate_literals_removal,[status(thm)],[f1305]) ).
fof(f1325,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ sP0_prd(X2,X3,X4,X5)
| ~ sP0_prd(X0,X1,X2,X3) ),
inference(forward_subsumption_resolution,[status(thm)],[f1324,f440]) ).
fof(f1346,plain,
! [X0,X1] : ~ sP0_prd(X0,X1,sK48_skl,sK47_skl),
inference(resolution,[status(thm)],[f1325,f522]) ).
fof(f1348,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[f522,f1346]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC413+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n016.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 : Mon Sep 21 08:27:24 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.38 % Drodi V4.1.1
% 4.57/1.02 % Refutation found
% 4.57/1.02 % SZS status Theorem for theBenchmark: Theorem is valid
% 4.57/1.02 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 4.57/1.06 % Elapsed time: 0.676745 seconds
% 4.57/1.06 % CPU time: 4.995346 seconds
% 4.57/1.06 % Total memory used: 182.993 MB
% 4.57/1.06 % Net memory used: 177.776 MB
%------------------------------------------------------------------------------