%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SWC386+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 : n018.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 02:41:02 PM UTC 2026
% Result : Theorem 0.13s 5.41s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 6
% Syntax : Number of formulae : 58 ( 10 unt; 2 def)
% Number of atoms : 214 ( 81 equ)
% Maximal formula atoms : 17 ( 3 avg)
% Number of connectives : 237 ( 81 ~; 87 |; 52 &)
% ( 4 <=>; 13 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 6 con; 0-2 aty)
% Number of variables : 73 ( 61 !; 12 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f15,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ( neq(U,V)
<=> U != V ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f17,axiom,
ssList(nil),
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)
=> ( ( ( ? [Z] :
( memberP(V,Z)
& cons(Z,nil) = U
& ssItem(Z) )
| ~ neq(V,nil) )
& ( nil = U
| nil != V ) )
| ( ( nil != W
| nil != X )
& ! [Y] :
( ssItem(Y)
=> ( ~ 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)
=> ( ( ( ? [Z] :
( memberP(V,Z)
& cons(Z,nil) = U
& ssItem(Z) )
| ~ neq(V,nil) )
& ( nil = U
| nil != V ) )
| ( ( nil != W
| nil != X )
& ! [Y] :
( ssItem(Y)
=> ( ~ memberP(X,Y)
| cons(Y,nil) != W ) ) )
| U != W
| V != X ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f96]) ).
fof(f217,plain,
! [U] :
( ! [V] :
( ( neq(U,V)
<=> U != V )
| ~ ssList(V) )
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f15]) ).
fof(f218,plain,
! [U] :
( ! [V] :
( ( ( U = V
| neq(U,V) )
& ( U != V
| ~ neq(U,V) ) )
| ~ ssList(V) )
| ~ ssList(U) ),
inference(NNF_transformation,[status(thm)],[f217]) ).
fof(f219,plain,
! [X0,X1] :
( X0 != X1
| ~ neq(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f218]) ).
fof(f223,plain,
ssList(nil),
inference(cnf_transformation,[status(thm)],[f17]) ).
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] :
( ( ( ! [Z] :
( ~ memberP(V,Z)
| cons(Z,nil) != U
| ~ ssItem(Z) )
& neq(V,nil) )
| ( nil != U
& nil = V ) )
& ( ( nil = W
& nil = X )
| ? [Y] :
( 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)
<=> ( 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] :
( ( ( ! [Z] :
( ~ memberP(V,Z)
| cons(Z,nil) != U
| ~ ssItem(Z) )
& neq(V,nil) )
| 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,
( ( ( ! [Z] :
( ~ memberP(sK48_skl,Z)
| cons(Z,nil) != sK47_skl
| ~ ssItem(Z) )
& neq(sK48_skl,nil) )
| 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,
( neq(sK48_skl,nil)
| sP1_prd(sK48_skl,sK47_skl) ),
inference(cnf_transformation,[status(thm)],[f419]) ).
fof(f429,plain,
! [X0] :
( ~ memberP(sK48_skl,X0)
| cons(X0,nil) != sK47_skl
| ~ ssItem(X0)
| sP1_prd(sK48_skl,sK47_skl) ),
inference(cnf_transformation,[status(thm)],[f419]) ).
fof(f430,plain,
! [W,X,Y] :
( ( ~ memberP(X,Y)
| cons(Y,nil) != W
| ~ ssItem(Y)
| sP0_prd(Y,X,W) )
& ( ( 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] :
( ~ memberP(X,Y)
| cons(Y,nil) != W
| ~ ssItem(Y)
| sP0_prd(Y,X,W) )
& ! [W,X,Y] :
( ( memberP(X,Y)
& cons(Y,nil) = W
& ssItem(Y) )
| ~ sP0_prd(Y,X,W) ) ),
inference(miniscoping,[status(thm)],[f430]) ).
fof(f432,plain,
! [X0,X1,X2] :
( ssItem(X0)
| ~ sP0_prd(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f431]) ).
fof(f433,plain,
! [X0,X1,X2] :
( cons(X0,nil) = X2
| ~ sP0_prd(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f431]) ).
fof(f434,plain,
! [X0,X1,X2] :
( memberP(X1,X0)
| ~ sP0_prd(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f431]) ).
fof(f436,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(f437,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)],[f436]) ).
fof(f438,plain,
! [X0,X1] :
( nil = X0
| ~ sP1_prd(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f437]) ).
fof(f439,plain,
! [X0,X1] :
( nil != X1
| ~ sP1_prd(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f437]) ).
fof(f456,plain,
! [X1] :
( ~ neq(X1,X1)
| ~ ssList(X1)
| ~ ssList(X1) ),
inference(destructive_equality_resolution,[status(thm)],[f219]) ).
fof(f457,plain,
! [X0] :
( ~ neq(X0,X0)
| ~ ssList(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f456]) ).
fof(f472,plain,
! [X0] : ~ sP1_prd(X0,nil),
inference(destructive_equality_resolution,[status(thm)],[f439]) ).
fof(f480,plain,
( nil = sK50_skl
| sP0_prd(sK51_skl,sK48_skl,sK49_skl) ),
inference(forward_demodulation,[status(thm)],[f424,f426]) ).
fof(f481,plain,
( nil = sK50_skl
| sP0_prd(sK51_skl,sK48_skl,sK47_skl) ),
inference(forward_demodulation,[status(thm)],[f425,f480]) ).
fof(f482,plain,
( nil = sK48_skl
| sP0_prd(sK51_skl,sK48_skl,sK47_skl) ),
inference(forward_demodulation,[status(thm)],[f424,f481]) ).
fof(f483,plain,
( ssItem(sK51_skl)
| nil = sK48_skl ),
inference(resolution,[status(thm)],[f482,f432]) ).
fof(f484,plain,
( nil = sK48_skl
| memberP(sK48_skl,sK51_skl) ),
inference(resolution,[status(thm)],[f434,f482]) ).
fof(f485,plain,
( nil = sK48_skl
| cons(sK51_skl,nil) = sK47_skl ),
inference(resolution,[status(thm)],[f433,f482]) ).
fof(f490,plain,
( nil = sK49_skl
| sP0_prd(sK51_skl,sK48_skl,sK49_skl) ),
inference(forward_demodulation,[status(thm)],[f424,f427]) ).
fof(f491,plain,
( nil = sK49_skl
| sP0_prd(sK51_skl,sK48_skl,sK47_skl) ),
inference(forward_demodulation,[status(thm)],[f425,f490]) ).
fof(f492,plain,
( nil = sK47_skl
| sP0_prd(sK51_skl,sK48_skl,sK47_skl) ),
inference(forward_demodulation,[status(thm)],[f425,f491]) ).
fof(f494,plain,
( memberP(sK48_skl,sK51_skl)
| nil = sK47_skl ),
inference(resolution,[status(thm)],[f492,f434]) ).
fof(f495,plain,
( ssItem(sK51_skl)
| nil = sK47_skl ),
inference(resolution,[status(thm)],[f492,f432]) ).
fof(f556,plain,
( nil = sK48_skl
| ~ memberP(sK48_skl,sK51_skl)
| ~ ssItem(sK51_skl)
| sP1_prd(sK48_skl,sK47_skl) ),
inference(resolution,[status(thm)],[f429,f485]) ).
fof(f561,plain,
( nil = sK48_skl
| ~ memberP(sK48_skl,sK51_skl)
| ~ ssItem(sK51_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f556,f438]) ).
fof(f571,plain,
nil = sK48_skl,
inference(backward_subsumption_resolution,[status(thm)],[f484,f572]) ).
fof(f572,plain,
( nil = sK48_skl
| ~ memberP(sK48_skl,sK51_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f561,f483]) ).
fof(f581,plain,
( neq(nil,nil)
| sP1_prd(sK48_skl,sK47_skl) ),
inference(backward_demodulation,[status(thm)],[f571,f428]) ).
fof(f582,plain,
( memberP(nil,sK51_skl)
| nil = sK47_skl ),
inference(backward_demodulation,[status(thm)],[f571,f494]) ).
fof(f589,plain,
( neq(nil,nil)
| sP1_prd(nil,sK47_skl) ),
inference(forward_demodulation,[status(thm)],[f571,f581]) ).
fof(f590,plain,
( ~ ssItem(sK51_skl)
| nil = sK47_skl ),
inference(resolution,[status(thm)],[f582,f279]) ).
fof(f591,plain,
nil = sK47_skl,
inference(forward_subsumption_resolution,[status(thm)],[f590,f495]) ).
fof(f601,plain,
( neq(nil,nil)
| sP1_prd(nil,nil) ),
inference(forward_demodulation,[status(thm)],[f591,f589]) ).
fof(f602,plain,
neq(nil,nil),
inference(forward_subsumption_resolution,[status(thm)],[f601,f472]) ).
fof(f603,plain,
~ ssList(nil),
inference(resolution,[status(thm)],[f602,f457]) ).
fof(f605,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f603,f223]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC386+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/5.37 % Computer : n018.cluster.edu
% 0.10/5.37 % Model : x86_64 x86_64
% 0.10/5.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/5.37 % Memory : 8046.5625MB
% 0.10/5.37 % OS : Linux 6.8.0-71-generic
% 0.10/5.37 % CPULimit : 300
% 0.10/5.37 % WCLimit : 300
% 0.10/5.37 % DateTime : Mon Sep 21 08:22:19 UTC 2026
% 0.10/5.37 % CPUTime :
% 0.10/5.39 % Drodi V4.1.1
% 0.13/5.41 % Refutation found
% 0.13/5.41 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.13/5.41 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/5.44 % Elapsed time: 0.057559 seconds
% 0.13/5.44 % CPU time: 0.169451 seconds
% 0.13/5.44 % Total memory used: 83.576 MB
% 0.13/5.44 % Net memory used: 83.442 MB
%------------------------------------------------------------------------------