%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SWC060+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 02:39:48 PM UTC 2026
% Result : Theorem 0.09s 5.40s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 9
% Syntax : Number of formulae : 77 ( 12 unt; 2 def)
% Number of atoms : 293 ( 80 equ)
% Maximal formula atoms : 17 ( 3 avg)
% Number of connectives : 351 ( 135 ~; 143 |; 52 &)
% ( 6 <=>; 15 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 5 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 5 con; 0-0 aty)
% Number of variables : 82 ( 72 !; 10 ?)
% 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(f53,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ( ( segmentP(V,W)
& segmentP(U,V) )
=> segmentP(U,W) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f55,axiom,
! [U] :
( ssList(U)
=> segmentP(U,U) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f57,axiom,
! [U] :
( ssList(U)
=> segmentP(U,nil) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f58,axiom,
! [U] :
( ssList(U)
=> ( segmentP(nil,U)
<=> nil = U ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f96,conjecture,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ! [X] :
( ( ( ~ segmentP(X,W)
| ~ neq(W,nil) )
& ( nil != W
| nil != X ) )
| ( ( ? [Y] :
( segmentP(U,Y)
& segmentP(V,Y)
& neq(Y,nil)
& ssList(Y) )
| ~ neq(V,nil) )
& ( nil = U
| nil != V ) )
| U != W
| V != X
| ~ ssList(X) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f97,negated_conjecture,
~ ! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ! [X] :
( ( ( ~ segmentP(X,W)
| ~ neq(W,nil) )
& ( nil != W
| nil != X ) )
| ( ( ? [Y] :
( segmentP(U,Y)
& segmentP(V,Y)
& neq(Y,nil)
& ssList(Y) )
| ~ neq(V,nil) )
& ( nil = U
| nil != V ) )
| U != W
| V != X
| ~ ssList(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(f314,plain,
! [U] :
( ! [V] :
( ! [W] :
( segmentP(U,W)
| ~ segmentP(V,W)
| ~ segmentP(U,V)
| ~ ssList(W) )
| ~ ssList(V) )
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f53]) ).
fof(f315,plain,
! [X0,X1,X2] :
( segmentP(X0,X2)
| ~ segmentP(X1,X2)
| ~ segmentP(X0,X1)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f314]) ).
fof(f318,plain,
! [U] :
( segmentP(U,U)
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f55]) ).
fof(f319,plain,
! [X0] :
( segmentP(X0,X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f318]) ).
fof(f322,plain,
! [U] :
( segmentP(U,nil)
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f57]) ).
fof(f323,plain,
! [X0] :
( segmentP(X0,nil)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f322]) ).
fof(f324,plain,
! [U] :
( ( segmentP(nil,U)
<=> nil = U )
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f58]) ).
fof(f325,plain,
! [U] :
( ( ( nil != U
| segmentP(nil,U) )
& ( nil = U
| ~ segmentP(nil,U) ) )
| ~ ssList(U) ),
inference(NNF_transformation,[status(thm)],[f324]) ).
fof(f326,plain,
! [X0] :
( nil = X0
| ~ segmentP(nil,X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f325]) ).
fof(f415,plain,
? [U] :
( ? [V] :
( ? [W] :
( ? [X] :
( ( ( segmentP(X,W)
& neq(W,nil) )
| ( nil = W
& nil = X ) )
& ( ( ! [Y] :
( ~ segmentP(U,Y)
| ~ segmentP(V,Y)
| ~ neq(Y,nil)
| ~ ssList(Y) )
& neq(V,nil) )
| ( nil != U
& nil = V ) )
& U = W
& V = X
& ssList(X) )
& ssList(W) )
& ssList(V) )
& ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f97]) ).
fof(f416,definition,
! [U,V] :
( sP0_prd(V,U)
<=> ( nil != U
& nil = V ) ),
introduced(definition,[new_symbols(definition,[sP0_prd])],[]) ).
fof(f417,definition,
! [W,X] :
( sP1_prd(X,W)
<=> ( nil = W
& nil = X ) ),
introduced(definition,[new_symbols(definition,[sP1_prd])],[]) ).
fof(f418,plain,
? [U] :
( ? [V] :
( ? [W] :
( ? [X] :
( ( ( segmentP(X,W)
& neq(W,nil) )
| sP1_prd(X,W) )
& ( ( ! [Y] :
( ~ segmentP(U,Y)
| ~ segmentP(V,Y)
| ~ neq(Y,nil)
| ~ ssList(Y) )
& neq(V,nil) )
| sP0_prd(V,U) )
& U = W
& V = X
& ssList(X) )
& ssList(W) )
& ssList(V) )
& ssList(U) ),
inference(formula_renaming,[status(thm)],[f415,f417,f416]) ).
fof(f419,plain,
( ( ( segmentP(sK50_skl,sK49_skl)
& neq(sK49_skl,nil) )
| sP1_prd(sK50_skl,sK49_skl) )
& ( ( ! [Y] :
( ~ segmentP(sK47_skl,Y)
| ~ segmentP(sK48_skl,Y)
| ~ neq(Y,nil)
| ~ ssList(Y) )
& neq(sK48_skl,nil) )
| sP0_prd(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]),skolemize(U,sK47_skl),skolemize(V,sK48_skl),skolemize(W,sK49_skl),skolemize(X,sK50_skl)],[f418]) ).
fof(f421,plain,
ssList(sK48_skl),
inference(cnf_transformation,[status(thm)],[f419]) ).
fof(f422,plain,
ssList(sK49_skl),
inference(cnf_transformation,[status(thm)],[f419]) ).
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,
( neq(sK48_skl,nil)
| sP0_prd(sK48_skl,sK47_skl) ),
inference(cnf_transformation,[status(thm)],[f419]) ).
fof(f427,plain,
! [X0] :
( ~ segmentP(sK47_skl,X0)
| ~ segmentP(sK48_skl,X0)
| ~ neq(X0,nil)
| ~ ssList(X0)
| sP0_prd(sK48_skl,sK47_skl) ),
inference(cnf_transformation,[status(thm)],[f419]) ).
fof(f428,plain,
( neq(sK49_skl,nil)
| sP1_prd(sK50_skl,sK49_skl) ),
inference(cnf_transformation,[status(thm)],[f419]) ).
fof(f429,plain,
( segmentP(sK50_skl,sK49_skl)
| sP1_prd(sK50_skl,sK49_skl) ),
inference(cnf_transformation,[status(thm)],[f419]) ).
fof(f430,plain,
! [U,V] :
( ( nil = U
| nil != V
| sP0_prd(V,U) )
& ( ( nil != U
& nil = V )
| ~ sP0_prd(V,U) ) ),
inference(NNF_transformation,[status(thm)],[f416]) ).
fof(f431,plain,
( ! [U,V] :
( nil = U
| nil != V
| sP0_prd(V,U) )
& ! [U,V] :
( ( nil != U
& nil = V )
| ~ sP0_prd(V,U) ) ),
inference(miniscoping,[status(thm)],[f430]) ).
fof(f432,plain,
! [X0,X1] :
( nil = X0
| ~ sP0_prd(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f431]) ).
fof(f433,plain,
! [X0,X1] :
( nil != X1
| ~ sP0_prd(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f431]) ).
fof(f435,plain,
! [W,X] :
( ( nil != W
| nil != X
| sP1_prd(X,W) )
& ( ( nil = W
& nil = X )
| ~ sP1_prd(X,W) ) ),
inference(NNF_transformation,[status(thm)],[f417]) ).
fof(f436,plain,
( ! [W,X] :
( nil != W
| nil != X
| sP1_prd(X,W) )
& ! [W,X] :
( ( nil = W
& nil = X )
| ~ sP1_prd(X,W) ) ),
inference(miniscoping,[status(thm)],[f435]) ).
fof(f437,plain,
! [X0,X1] :
( nil = X0
| ~ sP1_prd(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f436]) ).
fof(f438,plain,
! [X0,X1] :
( nil = X1
| ~ sP1_prd(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f436]) ).
fof(f455,plain,
! [X1] :
( ~ neq(X1,X1)
| ~ ssList(X1)
| ~ ssList(X1) ),
inference(destructive_equality_resolution,[status(thm)],[f219]) ).
fof(f456,plain,
! [X0] :
( ~ neq(X0,X0)
| ~ ssList(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f455]) ).
fof(f470,plain,
! [X0] : ~ sP0_prd(X0,nil),
inference(destructive_equality_resolution,[status(thm)],[f433]) ).
fof(f478,plain,
( neq(sK48_skl,nil)
| sP0_prd(sK48_skl,sK49_skl) ),
inference(forward_demodulation,[status(thm)],[f425,f426]) ).
fof(f494,plain,
( neq(sK49_skl,nil)
| sP1_prd(sK48_skl,sK49_skl) ),
inference(forward_demodulation,[status(thm)],[f424,f428]) ).
fof(f496,plain,
( nil = sK48_skl
| neq(sK49_skl,nil) ),
inference(resolution,[status(thm)],[f494,f437]) ).
fof(f497,plain,
! [X0] :
( ~ segmentP(sK47_skl,X0)
| ~ segmentP(sK48_skl,X0)
| ~ neq(X0,nil)
| ~ ssList(X0)
| sP0_prd(sK48_skl,sK49_skl) ),
inference(forward_demodulation,[status(thm)],[f425,f427]) ).
fof(f498,plain,
! [X0] :
( ~ segmentP(sK49_skl,X0)
| ~ segmentP(sK48_skl,X0)
| ~ neq(X0,nil)
| ~ ssList(X0)
| sP0_prd(sK48_skl,sK49_skl) ),
inference(forward_demodulation,[status(thm)],[f425,f497]) ).
fof(f499,plain,
! [X0] :
( nil = sK48_skl
| ~ segmentP(sK49_skl,X0)
| ~ segmentP(sK48_skl,X0)
| ~ neq(X0,nil)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f498,f432]) ).
fof(f505,plain,
( segmentP(sK50_skl,sK49_skl)
| sP1_prd(sK48_skl,sK49_skl) ),
inference(forward_demodulation,[status(thm)],[f424,f429]) ).
fof(f506,plain,
( segmentP(sK48_skl,sK49_skl)
| sP1_prd(sK48_skl,sK49_skl) ),
inference(forward_demodulation,[status(thm)],[f424,f505]) ).
fof(f507,plain,
( nil = sK49_skl
| segmentP(sK48_skl,sK49_skl) ),
inference(resolution,[status(thm)],[f506,f438]) ).
fof(f508,plain,
( nil = sK48_skl
| segmentP(sK48_skl,sK49_skl) ),
inference(resolution,[status(thm)],[f506,f437]) ).
fof(f509,plain,
! [X0] :
( segmentP(X0,sK49_skl)
| ~ segmentP(X0,sK48_skl)
| ~ ssList(sK49_skl)
| ~ ssList(sK48_skl)
| ~ ssList(X0)
| nil = sK49_skl ),
inference(resolution,[status(thm)],[f507,f315]) ).
fof(f510,plain,
! [X0] :
( segmentP(X0,sK49_skl)
| ~ segmentP(X0,sK48_skl)
| ~ ssList(sK49_skl)
| ~ ssList(X0)
| nil = sK49_skl ),
inference(forward_subsumption_resolution,[status(thm)],[f509,f421]) ).
fof(f549,plain,
! [X0] :
( segmentP(X0,sK49_skl)
| ~ segmentP(X0,sK48_skl)
| ~ ssList(X0)
| nil = sK49_skl ),
inference(forward_subsumption_resolution,[status(thm)],[f510,f422]) ).
fof(f551,plain,
( nil = sK49_skl
| ~ ssList(sK49_skl)
| ~ segmentP(nil,sK48_skl)
| ~ ssList(nil)
| nil = sK49_skl ),
inference(resolution,[status(thm)],[f549,f326]) ).
fof(f555,plain,
( ~ ssList(sK49_skl)
| ~ segmentP(nil,sK48_skl)
| ~ ssList(nil)
| nil = sK49_skl ),
inference(duplicate_literals_removal,[status(thm)],[f551]) ).
fof(f556,plain,
( ~ ssList(sK49_skl)
| ~ segmentP(nil,sK48_skl)
| nil = sK49_skl ),
inference(forward_subsumption_resolution,[status(thm)],[f555,f223]) ).
fof(f561,plain,
( nil = sK48_skl
| nil = sK48_skl
| ~ segmentP(sK49_skl,sK49_skl)
| ~ segmentP(sK48_skl,sK49_skl)
| ~ ssList(sK49_skl) ),
inference(resolution,[status(thm)],[f499,f496]) ).
fof(f566,plain,
( nil = sK48_skl
| ~ segmentP(sK49_skl,sK49_skl)
| ~ segmentP(sK48_skl,sK49_skl)
| ~ ssList(sK49_skl) ),
inference(duplicate_literals_removal,[status(thm)],[f561]) ).
fof(f567,plain,
( nil = sK48_skl
| ~ segmentP(sK49_skl,sK49_skl)
| ~ segmentP(sK48_skl,sK49_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f566,f422]) ).
fof(f573,plain,
( ~ segmentP(nil,sK48_skl)
| nil = sK49_skl ),
inference(forward_subsumption_resolution,[status(thm)],[f556,f422]) ).
fof(f576,plain,
( nil = sK48_skl
| ~ segmentP(sK49_skl,sK49_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f567,f508]) ).
fof(f579,plain,
( ~ ssList(sK49_skl)
| nil = sK48_skl ),
inference(resolution,[status(thm)],[f576,f319]) ).
fof(f583,plain,
nil = sK48_skl,
inference(forward_subsumption_resolution,[status(thm)],[f579,f422]) ).
fof(f585,plain,
( ~ segmentP(nil,nil)
| nil = sK49_skl ),
inference(backward_demodulation,[status(thm)],[f583,f573]) ).
fof(f597,plain,
( neq(nil,nil)
| sP0_prd(sK48_skl,sK49_skl) ),
inference(backward_demodulation,[status(thm)],[f583,f478]) ).
fof(f605,plain,
( neq(nil,nil)
| sP0_prd(nil,sK49_skl) ),
inference(forward_demodulation,[status(thm)],[f583,f597]) ).
fof(f606,plain,
( ~ ssList(nil)
| nil = sK49_skl ),
inference(resolution,[status(thm)],[f585,f323]) ).
fof(f609,plain,
nil = sK49_skl,
inference(forward_subsumption_resolution,[status(thm)],[f606,f223]) ).
fof(f630,plain,
( neq(nil,nil)
| sP0_prd(nil,nil) ),
inference(forward_demodulation,[status(thm)],[f609,f605]) ).
fof(f631,plain,
neq(nil,nil),
inference(forward_subsumption_resolution,[status(thm)],[f630,f470]) ).
fof(f633,plain,
~ ssList(nil),
inference(resolution,[status(thm)],[f631,f456]) ).
fof(f636,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f633,f223]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWC060+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/5.36 % Computer : n005.cluster.edu
% 0.09/5.36 % Model : x86_64 x86_64
% 0.09/5.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/5.36 % Memory : 8046.5625MB
% 0.09/5.36 % OS : Linux 6.8.0-71-generic
% 0.09/5.36 % CPULimit : 300
% 0.09/5.36 % WCLimit : 300
% 0.09/5.36 % DateTime : Mon Sep 21 07:51:53 UTC 2026
% 0.09/5.36 % CPUTime :
% 0.09/5.38 % Drodi V4.1.1
% 0.09/5.40 % Refutation found
% 0.09/5.40 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.09/5.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/5.42 % Elapsed time: 0.055524 seconds
% 0.13/5.42 % CPU time: 0.185844 seconds
% 0.13/5.42 % Total memory used: 83.687 MB
% 0.13/5.42 % Net memory used: 83.530 MB
%------------------------------------------------------------------------------