%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SWC327+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 : n001.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 02:40:48 PM UTC 2026
% Result : Theorem 0.16s 0.46s
% Output : CNFRefutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 31
% Number of leaves : 2
% Syntax : Number of formulae : 56 ( 13 unt; 1 def)
% Number of atoms : 301 ( 130 equ)
% Maximal formula atoms : 26 ( 5 avg)
% Number of connectives : 411 ( 166 ~; 139 |; 89 &)
% ( 1 <=>; 16 =>; 0 <=; 0 <~>)
% Maximal formula depth : 27 ( 7 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 11 ( 11 usr; 6 con; 0-3 aty)
% Number of variables : 139 ( 105 !; 34 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f96,conjecture,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ! [X] :
( ssList(X)
=> ( ( ( nil = V
| nil != U )
& ? [X3] :
( equalelemsP(U)
& ! [X4] :
( ssItem(X4)
=> ! [X5] :
( ssList(X5)
=> ( ! [X6] :
( ssList(X6)
=> app(X6,cons(X4,nil)) != U )
| app(cons(X4,nil),X5) != X3 ) ) )
& app(U,X3) = V
& ssList(X3) ) )
| ( nil = W
& nil != X )
| ! [Y] :
( ssList(Y)
=> ( ? [Z] :
( ? [X1] :
( ? [X2] :
( app(X2,cons(Z,nil)) = W
& ssList(X2) )
& app(cons(Z,nil),X1) = Y
& ssList(X1) )
& ssItem(Z) )
| ~ equalelemsP(W)
| app(W,Y) != X ) )
| 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 )
& ? [X3] :
( equalelemsP(U)
& ! [X4] :
( ssItem(X4)
=> ! [X5] :
( ssList(X5)
=> ( ! [X6] :
( ssList(X6)
=> app(X6,cons(X4,nil)) != U )
| app(cons(X4,nil),X5) != X3 ) ) )
& app(U,X3) = V
& ssList(X3) ) )
| ( nil = W
& nil != X )
| ! [Y] :
( ssList(Y)
=> ( ? [Z] :
( ? [X1] :
( ? [X2] :
( app(X2,cons(Z,nil)) = W
& ssList(X2) )
& app(cons(Z,nil),X1) = Y
& ssList(X1) )
& ssItem(Z) )
| ~ equalelemsP(W)
| app(W,Y) != X ) )
| U != W
| V != X ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f96]) ).
fof(f415,plain,
? [U] :
( ? [V] :
( ? [W] :
( ? [X] :
( ( ( nil != V
& nil = U )
| ! [X3] :
( ~ equalelemsP(U)
| ? [X4] :
( ? [X5] :
( ? [X6] :
( app(X6,cons(X4,nil)) = U
& ssList(X6) )
& app(cons(X4,nil),X5) = X3
& ssList(X5) )
& ssItem(X4) )
| app(U,X3) != V
| ~ ssList(X3) ) )
& ( nil != W
| nil = X )
& ? [Y] :
( ! [Z] :
( ! [X1] :
( ! [X2] :
( app(X2,cons(Z,nil)) != W
| ~ ssList(X2) )
| app(cons(Z,nil),X1) != Y
| ~ ssList(X1) )
| ~ ssItem(Z) )
& equalelemsP(W)
& app(W,Y) = X
& 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,X3,X4] :
( sP0_prd(X4,X3,U)
<=> ( ? [X5] :
( ? [X6] :
( app(X6,cons(X4,nil)) = U
& ssList(X6) )
& app(cons(X4,nil),X5) = X3
& ssList(X5) )
& ssItem(X4) ) ),
introduced(definition,[new_symbols(definition,[sP0_prd])],[]) ).
fof(f417,plain,
? [U] :
( ? [V] :
( ? [W] :
( ? [X] :
( ( ( nil != V
& nil = U )
| ! [X3] :
( ~ equalelemsP(U)
| ? [X4] : sP0_prd(X4,X3,U)
| app(U,X3) != V
| ~ ssList(X3) ) )
& ( nil != W
| nil = X )
& ? [Y] :
( ! [Z] :
( ! [X1] :
( ! [X2] :
( app(X2,cons(Z,nil)) != W
| ~ ssList(X2) )
| app(cons(Z,nil),X1) != Y
| ~ ssList(X1) )
| ~ ssItem(Z) )
& equalelemsP(W)
& app(W,Y) = X
& ssList(Y) )
& U = W
& V = X
& ssList(X) )
& ssList(W) )
& ssList(V) )
& ssList(U) ),
inference(formula_renaming,[status(thm)],[f415,f416]) ).
fof(f418,plain,
? [U] :
( ? [V] :
( ? [W] :
( ? [X] :
( ( ( nil != V
& nil = U )
| ~ equalelemsP(U)
| ! [X3] :
( ? [X4] : sP0_prd(X4,X3,U)
| app(U,X3) != V
| ~ ssList(X3) ) )
& ( nil != W
| nil = X )
& ? [Y] :
( ! [Z] :
( ! [X2] :
( app(X2,cons(Z,nil)) != W
| ~ ssList(X2) )
| ! [X1] :
( app(cons(Z,nil),X1) != Y
| ~ ssList(X1) )
| ~ ssItem(Z) )
& equalelemsP(W)
& app(W,Y) = X
& ssList(Y) )
& U = W
& V = X
& ssList(X) )
& ssList(W) )
& ssList(V) )
& ssList(U) ),
inference(miniscoping,[status(thm)],[f417]) ).
fof(f419,plain,
( ( ( nil != sK48_skl
& nil = sK47_skl )
| ~ equalelemsP(sK47_skl)
| ! [X3] :
( sP0_prd(sK52_skl(X3),X3,sK47_skl)
| app(sK47_skl,X3) != sK48_skl
| ~ ssList(X3) ) )
& ( nil != sK49_skl
| nil = sK50_skl )
& ! [Z] :
( ! [X2] :
( app(X2,cons(Z,nil)) != sK49_skl
| ~ ssList(X2) )
| ! [X1] :
( app(cons(Z,nil),X1) != sK51_skl
| ~ ssList(X1) )
| ~ ssItem(Z) )
& equalelemsP(sK49_skl)
& app(sK49_skl,sK51_skl) = sK50_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]),skolemize(U,sK47_skl),skolemize(V,sK48_skl),skolemize(W,sK49_skl),skolemize(X,sK50_skl),skolemize(Y,sK51_skl),skolemize(X4,sK52_skl(X3))],[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,
ssList(sK51_skl),
inference(cnf_transformation,[status(thm)],[f419]) ).
fof(f427,plain,
app(sK49_skl,sK51_skl) = sK50_skl,
inference(cnf_transformation,[status(thm)],[f419]) ).
fof(f428,plain,
equalelemsP(sK49_skl),
inference(cnf_transformation,[status(thm)],[f419]) ).
fof(f429,plain,
! [X0,X1,X2] :
( app(X2,cons(X0,nil)) != sK49_skl
| ~ ssList(X2)
| app(cons(X0,nil),X1) != sK51_skl
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[status(thm)],[f419]) ).
fof(f430,plain,
( nil != sK49_skl
| nil = sK50_skl ),
inference(cnf_transformation,[status(thm)],[f419]) ).
fof(f431,plain,
! [X0] :
( nil = sK47_skl
| ~ equalelemsP(sK47_skl)
| sP0_prd(sK52_skl(X0),X0,sK47_skl)
| app(sK47_skl,X0) != sK48_skl
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f419]) ).
fof(f432,plain,
! [X0] :
( nil != sK48_skl
| ~ equalelemsP(sK47_skl)
| sP0_prd(sK52_skl(X0),X0,sK47_skl)
| app(sK47_skl,X0) != sK48_skl
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f419]) ).
fof(f433,plain,
! [U,X3,X4] :
( ( ! [X5] :
( ! [X6] :
( app(X6,cons(X4,nil)) != U
| ~ ssList(X6) )
| app(cons(X4,nil),X5) != X3
| ~ ssList(X5) )
| ~ ssItem(X4)
| sP0_prd(X4,X3,U) )
& ( ( ? [X5] :
( ? [X6] :
( app(X6,cons(X4,nil)) = U
& ssList(X6) )
& app(cons(X4,nil),X5) = X3
& ssList(X5) )
& ssItem(X4) )
| ~ sP0_prd(X4,X3,U) ) ),
inference(NNF_transformation,[status(thm)],[f416]) ).
fof(f434,plain,
( ! [U,X3,X4] :
( ! [X5] :
( ! [X6] :
( app(X6,cons(X4,nil)) != U
| ~ ssList(X6) )
| app(cons(X4,nil),X5) != X3
| ~ ssList(X5) )
| ~ ssItem(X4)
| sP0_prd(X4,X3,U) )
& ! [U,X3,X4] :
( ( ? [X5] :
( ? [X6] :
( app(X6,cons(X4,nil)) = U
& ssList(X6) )
& app(cons(X4,nil),X5) = X3
& ssList(X5) )
& ssItem(X4) )
| ~ sP0_prd(X4,X3,U) ) ),
inference(miniscoping,[status(thm)],[f433]) ).
fof(f435,plain,
( ! [U,X3,X4] :
( ! [X5] :
( ! [X6] :
( app(X6,cons(X4,nil)) != U
| ~ ssList(X6) )
| app(cons(X4,nil),X5) != X3
| ~ ssList(X5) )
| ~ ssItem(X4)
| sP0_prd(X4,X3,U) )
& ! [U,X3,X4] :
( ( app(sK54_skl(X4,X3,U),cons(X4,nil)) = U
& ssList(sK54_skl(X4,X3,U))
& app(cons(X4,nil),sK53_skl(X4,X3,U)) = X3
& ssList(sK53_skl(X4,X3,U))
& ssItem(X4) )
| ~ sP0_prd(X4,X3,U) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK53_skl,sK54_skl]),skolemize(X5,sK53_skl(X4,X3,U)),skolemize(X6,sK54_skl(X4,X3,U))],[f434]) ).
fof(f436,plain,
! [X0,X1,X2] :
( ssItem(X0)
| ~ sP0_prd(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f435]) ).
fof(f437,plain,
! [X0,X1,X2] :
( ssList(sK53_skl(X0,X1,X2))
| ~ sP0_prd(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f435]) ).
fof(f438,plain,
! [X0,X1,X2] :
( app(cons(X0,nil),sK53_skl(X0,X1,X2)) = X1
| ~ sP0_prd(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f435]) ).
fof(f439,plain,
! [X0,X1,X2] :
( ssList(sK54_skl(X0,X1,X2))
| ~ sP0_prd(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f435]) ).
fof(f440,plain,
! [X0,X1,X2] :
( app(sK54_skl(X0,X1,X2),cons(X0,nil)) = X2
| ~ sP0_prd(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f435]) ).
fof(f475,plain,
equalelemsP(sK47_skl),
inference(forward_demodulation,[status(thm)],[f425,f428]) ).
fof(f477,plain,
app(sK47_skl,sK51_skl) = sK50_skl,
inference(forward_demodulation,[status(thm)],[f425,f427]) ).
fof(f478,plain,
app(sK47_skl,sK51_skl) = sK48_skl,
inference(forward_demodulation,[status(thm)],[f424,f477]) ).
fof(f479,plain,
( nil != sK49_skl
| nil = sK48_skl ),
inference(forward_demodulation,[status(thm)],[f424,f430]) ).
fof(f480,plain,
( nil != sK47_skl
| nil = sK48_skl ),
inference(forward_demodulation,[status(thm)],[f425,f479]) ).
fof(f481,plain,
! [X0,X1,X2] :
( app(X2,cons(X0,nil)) != sK47_skl
| ~ ssList(X2)
| app(cons(X0,nil),X1) != sK51_skl
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(forward_demodulation,[status(thm)],[f425,f429]) ).
fof(f486,plain,
! [X0,X1,X2] :
( app(X2,cons(X0,nil)) != sK47_skl
| ~ ssList(X2)
| ~ ssList(sK53_skl(X0,sK51_skl,X1))
| ~ ssItem(X0)
| ~ sP0_prd(X0,sK51_skl,X1) ),
inference(resolution,[status(thm)],[f438,f481]) ).
fof(f487,plain,
! [X0,X1,X2] :
( app(X2,cons(X0,nil)) != sK47_skl
| ~ ssList(X2)
| ~ ssList(sK53_skl(X0,sK51_skl,X1))
| ~ sP0_prd(X0,sK51_skl,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f486,f436]) ).
fof(f488,plain,
! [X0] :
( nil = sK47_skl
| sP0_prd(sK52_skl(X0),X0,sK47_skl)
| app(sK47_skl,X0) != sK48_skl
| ~ ssList(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f431,f475]) ).
fof(f541,plain,
! [X0] :
( nil != sK48_skl
| sP0_prd(sK52_skl(X0),X0,sK47_skl)
| app(sK47_skl,X0) != sK48_skl
| ~ ssList(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f432,f475]) ).
fof(f596,plain,
! [X0,X1,X2] :
( app(X2,cons(X0,nil)) != sK47_skl
| ~ ssList(X2)
| ~ sP0_prd(X0,sK51_skl,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f487,f437]) ).
fof(f597,plain,
! [X0,X1,X2] :
( ~ sP0_prd(X0,X2,sK47_skl)
| ~ ssList(sK54_skl(X0,X2,sK47_skl))
| ~ sP0_prd(X0,sK51_skl,X1) ),
inference(resolution,[status(thm)],[f596,f440]) ).
fof(f598,plain,
! [X0,X1,X2] :
( ~ sP0_prd(X0,X2,sK47_skl)
| ~ sP0_prd(X0,sK51_skl,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f597,f439]) ).
fof(f599,plain,
! [X0] :
( nil != sK48_skl
| app(sK47_skl,sK51_skl) != sK48_skl
| ~ ssList(sK51_skl)
| ~ sP0_prd(sK52_skl(sK51_skl),X0,sK47_skl) ),
inference(resolution,[status(thm)],[f598,f541]) ).
fof(f601,plain,
! [X0] :
( nil != sK48_skl
| sK48_skl != sK48_skl
| ~ ssList(sK51_skl)
| ~ sP0_prd(sK52_skl(sK51_skl),X0,sK47_skl) ),
inference(forward_demodulation,[status(thm)],[f478,f599]) ).
fof(f602,plain,
! [X0] :
( nil != sK48_skl
| ~ ssList(sK51_skl)
| ~ sP0_prd(sK52_skl(sK51_skl),X0,sK47_skl) ),
inference(trivial_equality_resolution,[status(thm)],[f601]) ).
fof(f603,plain,
! [X0] :
( nil != sK48_skl
| ~ sP0_prd(sK52_skl(sK51_skl),X0,sK47_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f602,f426]) ).
fof(f607,plain,
( nil != sK48_skl
| app(sK47_skl,sK51_skl) != sK48_skl
| ~ ssList(sK51_skl)
| nil != sK48_skl ),
inference(resolution,[status(thm)],[f603,f541]) ).
fof(f609,plain,
( nil != sK48_skl
| sK48_skl != sK48_skl
| ~ ssList(sK51_skl)
| nil != sK48_skl ),
inference(forward_demodulation,[status(thm)],[f478,f607]) ).
fof(f610,plain,
( sK48_skl != sK48_skl
| ~ ssList(sK51_skl)
| nil != sK48_skl ),
inference(duplicate_literals_removal,[status(thm)],[f609]) ).
fof(f611,plain,
( ~ ssList(sK51_skl)
| nil != sK48_skl ),
inference(trivial_equality_resolution,[status(thm)],[f610]) ).
fof(f612,plain,
nil != sK48_skl,
inference(forward_subsumption_resolution,[status(thm)],[f611,f426]) ).
fof(f615,plain,
nil != sK47_skl,
inference(backward_subsumption_resolution,[status(thm)],[f480,f612]) ).
fof(f618,plain,
! [X0] :
( sP0_prd(sK52_skl(X0),X0,sK47_skl)
| app(sK47_skl,X0) != sK48_skl
| ~ ssList(X0) ),
inference(backward_subsumption_resolution,[status(thm)],[f488,f615]) ).
fof(f619,plain,
! [X0] :
( ~ sP0_prd(sK52_skl(sK51_skl),X0,sK47_skl)
| app(sK47_skl,sK51_skl) != sK48_skl
| ~ ssList(sK51_skl) ),
inference(resolution,[status(thm)],[f618,f598]) ).
fof(f621,plain,
! [X0] :
( ~ sP0_prd(sK52_skl(sK51_skl),X0,sK47_skl)
| sK48_skl != sK48_skl
| ~ ssList(sK51_skl) ),
inference(forward_demodulation,[status(thm)],[f478,f619]) ).
fof(f622,plain,
! [X0] :
( ~ sP0_prd(sK52_skl(sK51_skl),X0,sK47_skl)
| ~ ssList(sK51_skl) ),
inference(trivial_equality_resolution,[status(thm)],[f621]) ).
fof(f623,plain,
! [X0] : ~ sP0_prd(sK52_skl(sK51_skl),X0,sK47_skl),
inference(forward_subsumption_resolution,[status(thm)],[f622,f426]) ).
fof(f624,plain,
( app(sK47_skl,sK51_skl) != sK48_skl
| ~ ssList(sK51_skl) ),
inference(resolution,[status(thm)],[f623,f618]) ).
fof(f625,plain,
( sK48_skl != sK48_skl
| ~ ssList(sK51_skl) ),
inference(forward_demodulation,[status(thm)],[f478,f624]) ).
fof(f626,plain,
~ ssList(sK51_skl),
inference(trivial_equality_resolution,[status(thm)],[f625]) ).
fof(f627,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f626,f426]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SWC327+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.16/0.43 % Computer : n001.cluster.edu
% 0.16/0.43 % Model : x86_64 x86_64
% 0.16/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.43 % Memory : 8046.5625MB
% 0.16/0.43 % OS : Linux 6.8.0-71-generic
% 0.16/0.43 % CPULimit : 300
% 0.16/0.43 % WCLimit : 300
% 0.16/0.43 % DateTime : Mon Sep 21 08:21:44 UTC 2026
% 0.16/0.43 % CPUTime :
% 0.16/0.45 % Drodi V4.1.1
% 0.16/0.46 % Refutation found
% 0.16/0.46 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.16/0.46 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.22/0.50 % Elapsed time: 0.065205 seconds
% 0.22/0.50 % CPU time: 0.136205 seconds
% 0.22/0.50 % Total memory used: 25.233 MB
% 0.22/0.50 % Net memory used: 25.139 MB
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