%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SWC027+1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n005.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 02:39:39 PM UTC 2026
% Result : Theorem 0.02s 0.41s
% Output : CNFRefutation 0.02s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 6
% Syntax : Number of formulae : 55 ( 11 unt; 2 def)
% Number of atoms : 231 ( 101 equ)
% Maximal formula atoms : 19 ( 4 avg)
% Number of connectives : 262 ( 86 ~; 91 |; 70 &)
% ( 2 <=>; 13 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 6 con; 0-3 aty)
% Number of variables : 78 ( 64 !; 14 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f17,axiom,
ssList(nil),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f18,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssItem(V)
=> cons(V,U) != U ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f38,axiom,
! [U] :
( ssItem(U)
=> ~ memberP(nil,U) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f96,conjecture,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ! [X] :
( ssList(X)
=> ( ( ( nil = V
| nil != U )
& ( nil = U
| nil != V ) )
| ( ( nil != W
| nil != X )
& ! [Y] :
( ssItem(Y)
=> ( ? [Z] :
( leq(Y,Z)
& memberP(X,Z)
& Y != Z
& ssItem(Z) )
| ~ memberP(X,Y)
| cons(Y,nil) != W ) ) )
| U != W
| V != X ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f97,negated_conjecture,
~ ! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ! [X] :
( ssList(X)
=> ( ( ( nil = V
| nil != U )
& ( nil = U
| nil != V ) )
| ( ( nil != W
| nil != X )
& ! [Y] :
( ssItem(Y)
=> ( ? [Z] :
( leq(Y,Z)
& memberP(X,Z)
& Y != Z
& ssItem(Z) )
| ~ memberP(X,Y)
| cons(Y,nil) != W ) ) )
| U != W
| V != X ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f96]) ).
fof(f223,plain,
ssList(nil),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f224,plain,
! [U] :
( ! [V] :
( cons(V,U) != U
| ~ ssItem(V) )
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f18]) ).
fof(f225,plain,
! [X0,X1] :
( cons(X1,X0) != X0
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f224]) ).
fof(f278,plain,
! [U] :
( ~ memberP(nil,U)
| ~ ssItem(U) ),
inference(pre_NNF_transformation,[status(thm)],[f38]) ).
fof(f279,plain,
! [X0] :
( ~ memberP(nil,X0)
| ~ ssItem(X0) ),
inference(cnf_transformation,[status(thm)],[f278]) ).
fof(f415,plain,
? [U] :
( ? [V] :
( ? [W] :
( ? [X] :
( ( ( nil != V
& nil = U )
| ( nil != U
& nil = V ) )
& ( ( nil = W
& nil = X )
| ? [Y] :
( ! [Z] :
( ~ leq(Y,Z)
| ~ memberP(X,Z)
| Y = Z
| ~ ssItem(Z) )
& memberP(X,Y)
& cons(Y,nil) = W
& ssItem(Y) ) )
& U = W
& V = X
& ssList(X) )
& ssList(W) )
& ssList(V) )
& ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f97]) ).
fof(f416,definition,
! [W,X,Y] :
( sP0_prd(Y,X,W)
<=> ( ! [Z] :
( ~ leq(Y,Z)
| ~ memberP(X,Z)
| Y = Z
| ~ ssItem(Z) )
& memberP(X,Y)
& cons(Y,nil) = W
& ssItem(Y) ) ),
introduced(definition,[new_symbols(definition,[sP0_prd])],[]) ).
fof(f417,definition,
! [U,V] :
( sP1_prd(V,U)
<=> ( nil != U
& nil = V ) ),
introduced(definition,[new_symbols(definition,[sP1_prd])],[]) ).
fof(f418,plain,
? [U] :
( ? [V] :
( ? [W] :
( ? [X] :
( ( ( nil != V
& nil = U )
| sP1_prd(V,U) )
& ( ( nil = W
& nil = X )
| ? [Y] : sP0_prd(Y,X,W) )
& U = W
& V = X
& ssList(X) )
& ssList(W) )
& ssList(V) )
& ssList(U) ),
inference(formula_renaming,[status(thm)],[f415,f417,f416]) ).
fof(f419,plain,
( ( ( nil != sK48_skl
& nil = sK47_skl )
| sP1_prd(sK48_skl,sK47_skl) )
& ( ( nil = sK49_skl
& nil = sK50_skl )
| sP0_prd(sK51_skl,sK50_skl,sK49_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]),skolemize(U,sK47_skl),skolemize(V,sK48_skl),skolemize(W,sK49_skl),skolemize(X,sK50_skl),skolemize(Y,sK51_skl)],[f418]) ).
fof(f424,plain,
sK48_skl = sK50_skl,
inference(cnf_transformation,[status(thm)],[f419]) ).
fof(f425,plain,
sK47_skl = sK49_skl,
inference(cnf_transformation,[status(thm)],[f419]) ).
fof(f426,plain,
( nil = sK50_skl
| sP0_prd(sK51_skl,sK50_skl,sK49_skl) ),
inference(cnf_transformation,[status(thm)],[f419]) ).
fof(f427,plain,
( nil = sK49_skl
| sP0_prd(sK51_skl,sK50_skl,sK49_skl) ),
inference(cnf_transformation,[status(thm)],[f419]) ).
fof(f428,plain,
( nil = sK47_skl
| sP1_prd(sK48_skl,sK47_skl) ),
inference(cnf_transformation,[status(thm)],[f419]) ).
fof(f429,plain,
( nil != sK48_skl
| sP1_prd(sK48_skl,sK47_skl) ),
inference(cnf_transformation,[status(thm)],[f419]) ).
fof(f430,plain,
! [W,X,Y] :
( ( ? [Z] :
( leq(Y,Z)
& memberP(X,Z)
& Y != Z
& ssItem(Z) )
| ~ memberP(X,Y)
| cons(Y,nil) != W
| ~ ssItem(Y)
| sP0_prd(Y,X,W) )
& ( ( ! [Z] :
( ~ leq(Y,Z)
| ~ memberP(X,Z)
| Y = Z
| ~ ssItem(Z) )
& memberP(X,Y)
& cons(Y,nil) = W
& ssItem(Y) )
| ~ sP0_prd(Y,X,W) ) ),
inference(NNF_transformation,[status(thm)],[f416]) ).
fof(f431,plain,
( ! [W,X,Y] :
( ? [Z] :
( leq(Y,Z)
& memberP(X,Z)
& Y != Z
& ssItem(Z) )
| ~ memberP(X,Y)
| cons(Y,nil) != W
| ~ ssItem(Y)
| sP0_prd(Y,X,W) )
& ! [W,X,Y] :
( ( ! [Z] :
( ~ leq(Y,Z)
| ~ memberP(X,Z)
| Y = Z
| ~ ssItem(Z) )
& memberP(X,Y)
& cons(Y,nil) = W
& ssItem(Y) )
| ~ sP0_prd(Y,X,W) ) ),
inference(miniscoping,[status(thm)],[f430]) ).
fof(f432,plain,
( ! [W,X,Y] :
( ( leq(Y,sK52_skl(Y,X,W))
& memberP(X,sK52_skl(Y,X,W))
& Y != sK52_skl(Y,X,W)
& ssItem(sK52_skl(Y,X,W)) )
| ~ memberP(X,Y)
| cons(Y,nil) != W
| ~ ssItem(Y)
| sP0_prd(Y,X,W) )
& ! [W,X,Y] :
( ( ! [Z] :
( ~ leq(Y,Z)
| ~ memberP(X,Z)
| Y = Z
| ~ ssItem(Z) )
& memberP(X,Y)
& cons(Y,nil) = W
& ssItem(Y) )
| ~ sP0_prd(Y,X,W) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK52_skl]),skolemize(Z,sK52_skl(Y,X,W))],[f431]) ).
fof(f433,plain,
! [X0,X1,X2] :
( ssItem(X0)
| ~ sP0_prd(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f432]) ).
fof(f434,plain,
! [X0,X1,X2] :
( cons(X0,nil) = X2
| ~ sP0_prd(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f432]) ).
fof(f435,plain,
! [X0,X1,X2] :
( memberP(X1,X0)
| ~ sP0_prd(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f432]) ).
fof(f441,plain,
! [U,V] :
( ( nil = U
| nil != V
| sP1_prd(V,U) )
& ( ( nil != U
& nil = V )
| ~ sP1_prd(V,U) ) ),
inference(NNF_transformation,[status(thm)],[f417]) ).
fof(f442,plain,
( ! [U,V] :
( nil = U
| nil != V
| sP1_prd(V,U) )
& ! [U,V] :
( ( nil != U
& nil = V )
| ~ sP1_prd(V,U) ) ),
inference(miniscoping,[status(thm)],[f441]) ).
fof(f443,plain,
! [X0,X1] :
( nil = X0
| ~ sP1_prd(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f442]) ).
fof(f444,plain,
! [X0,X1] :
( nil != X1
| ~ sP1_prd(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f442]) ).
fof(f480,plain,
! [X0] : ~ sP1_prd(X0,nil),
inference(destructive_equality_resolution,[status(thm)],[f444]) ).
fof(f487,plain,
( nil = sK50_skl
| sP0_prd(sK51_skl,sK48_skl,sK49_skl) ),
inference(forward_demodulation,[status(thm)],[f424,f426]) ).
fof(f488,plain,
( nil = sK50_skl
| sP0_prd(sK51_skl,sK48_skl,sK47_skl) ),
inference(forward_demodulation,[status(thm)],[f425,f487]) ).
fof(f489,plain,
( nil = sK48_skl
| sP0_prd(sK51_skl,sK48_skl,sK47_skl) ),
inference(forward_demodulation,[status(thm)],[f424,f488]) ).
fof(f491,plain,
( ssItem(sK51_skl)
| nil = sK48_skl ),
inference(resolution,[status(thm)],[f489,f433]) ).
fof(f492,plain,
( nil = sK48_skl
| nil = sK47_skl ),
inference(resolution,[status(thm)],[f428,f443]) ).
fof(f502,plain,
( nil = sK48_skl
| cons(sK51_skl,nil) = sK47_skl ),
inference(resolution,[status(thm)],[f434,f489]) ).
fof(f503,plain,
( nil = sK49_skl
| sP0_prd(sK51_skl,sK48_skl,sK49_skl) ),
inference(forward_demodulation,[status(thm)],[f424,f427]) ).
fof(f504,plain,
( nil = sK49_skl
| sP0_prd(sK51_skl,sK48_skl,sK47_skl) ),
inference(forward_demodulation,[status(thm)],[f425,f503]) ).
fof(f505,plain,
( nil = sK47_skl
| sP0_prd(sK51_skl,sK48_skl,sK47_skl) ),
inference(forward_demodulation,[status(thm)],[f425,f504]) ).
fof(f507,plain,
( memberP(sK48_skl,sK51_skl)
| nil = sK47_skl ),
inference(resolution,[status(thm)],[f505,f435]) ).
fof(f508,plain,
( ssItem(sK51_skl)
| nil = sK47_skl ),
inference(resolution,[status(thm)],[f505,f433]) ).
fof(f513,plain,
( nil = sK47_skl
| memberP(nil,sK51_skl)
| nil = sK47_skl ),
inference(paramodulation,[status(thm)],[f492,f507]) ).
fof(f514,plain,
( memberP(nil,sK51_skl)
| nil = sK47_skl ),
inference(duplicate_literals_removal,[status(thm)],[f513]) ).
fof(f515,plain,
( ~ ssItem(sK51_skl)
| nil = sK47_skl ),
inference(resolution,[status(thm)],[f514,f279]) ).
fof(f516,plain,
nil = sK47_skl,
inference(forward_subsumption_resolution,[status(thm)],[f515,f508]) ).
fof(f521,plain,
( nil != sK48_skl
| sP1_prd(sK48_skl,nil) ),
inference(backward_demodulation,[status(thm)],[f516,f429]) ).
fof(f527,plain,
nil != sK48_skl,
inference(forward_subsumption_resolution,[status(thm)],[f521,f480]) ).
fof(f529,plain,
ssItem(sK51_skl),
inference(backward_subsumption_resolution,[status(thm)],[f491,f527]) ).
fof(f543,plain,
( nil = sK48_skl
| cons(sK51_skl,nil) = nil ),
inference(forward_demodulation,[status(thm)],[f516,f502]) ).
fof(f544,plain,
cons(sK51_skl,nil) = nil,
inference(forward_subsumption_resolution,[status(thm)],[f543,f527]) ).
fof(f545,plain,
( ~ ssItem(sK51_skl)
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f544,f225]) ).
fof(f556,plain,
~ ssItem(sK51_skl),
inference(forward_subsumption_resolution,[status(thm)],[f545,f223]) ).
fof(f566,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f556,f529]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC027+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n005.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.02/0.35 % CPULimit : 300
% 0.02/0.35 % WCLimit : 300
% 0.02/0.35 % DateTime : Mon Sep 21 07:49:48 UTC 2026
% 0.02/0.36 % CPUTime :
% 0.02/0.37 % Drodi V4.1.1
% 0.02/0.41 % Refutation found
% 0.02/0.41 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.02/0.41 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.02/0.44 % Elapsed time: 0.072687 seconds
% 0.02/0.44 % CPU time: 0.190759 seconds
% 0.02/0.44 % Total memory used: 111.185 MB
% 0.02/0.44 % Net memory used: 111.020 MB
%------------------------------------------------------------------------------