%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SWC277+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 : n007.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 02:40:37 PM UTC 2026
% Result : Theorem 0.13s 5.40s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 7
% Syntax : Number of formulae : 53 ( 17 unt; 0 def)
% Number of atoms : 161 ( 43 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 168 ( 60 ~; 63 |; 26 &)
% ( 6 <=>; 13 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 5 con; 0-2 aty)
% Number of variables : 40 ( 33 !; 7 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f4,axiom,
! [U] :
( ssList(U)
=> ( singletonP(U)
<=> ? [V] :
( cons(V,nil) = U
& ssItem(V) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f15,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ( neq(U,V)
<=> U != V ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f17,axiom,
ssList(nil),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f58,axiom,
! [U] :
( ssList(U)
=> ( segmentP(nil,U)
<=> nil = U ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f65,axiom,
! [U] :
( ssItem(U)
=> totalorderedP(cons(U,nil)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f66,axiom,
totalorderedP(nil),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f96,conjecture,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ! [X] :
( ssList(X)
=> ( ( neq(X,nil)
& ~ singletonP(W) )
| totalorderedP(U)
| ~ segmentP(X,W)
| 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)
=> ( ( neq(X,nil)
& ~ singletonP(W) )
| totalorderedP(U)
| ~ segmentP(X,W)
| U != W
| V != X ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f96]) ).
fof(f113,plain,
! [U] :
( ( singletonP(U)
<=> ? [V] :
( cons(V,nil) = U
& ssItem(V) ) )
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f4]) ).
fof(f114,plain,
! [U] :
( ( ( ! [V] :
( cons(V,nil) != U
| ~ ssItem(V) )
| singletonP(U) )
& ( ? [V] :
( cons(V,nil) = U
& ssItem(V) )
| ~ singletonP(U) ) )
| ~ ssList(U) ),
inference(NNF_transformation,[status(thm)],[f113]) ).
fof(f115,plain,
! [U] :
( ( ( ! [V] :
( cons(V,nil) != U
| ~ ssItem(V) )
| singletonP(U) )
& ( ( cons(sK4_skl(U),nil) = U
& ssItem(sK4_skl(U)) )
| ~ singletonP(U) ) )
| ~ ssList(U) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4_skl]),skolemize(V,sK4_skl(U))],[f114]) ).
fof(f116,plain,
! [X0] :
( ssItem(sK4_skl(X0))
| ~ singletonP(X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f115]) ).
fof(f117,plain,
! [X0] :
( cons(sK4_skl(X0),nil) = X0
| ~ singletonP(X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f115]) ).
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(f220,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(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(f337,plain,
! [U] :
( totalorderedP(cons(U,nil))
| ~ ssItem(U) ),
inference(pre_NNF_transformation,[status(thm)],[f65]) ).
fof(f338,plain,
! [X0] :
( totalorderedP(cons(X0,nil))
| ~ ssItem(X0) ),
inference(cnf_transformation,[status(thm)],[f337]) ).
fof(f339,plain,
totalorderedP(nil),
inference(cnf_transformation,[status(thm)],[f66]) ).
fof(f415,plain,
? [U] :
( ? [V] :
( ? [W] :
( ? [X] :
( ( ~ neq(X,nil)
| singletonP(W) )
& ~ totalorderedP(U)
& segmentP(X,W)
& U = W
& V = X
& ssList(X) )
& ssList(W) )
& ssList(V) )
& ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f97]) ).
fof(f416,plain,
( ( ~ neq(sK50_skl,nil)
| singletonP(sK49_skl) )
& ~ totalorderedP(sK47_skl)
& segmentP(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]),skolemize(U,sK47_skl),skolemize(V,sK48_skl),skolemize(W,sK49_skl),skolemize(X,sK50_skl)],[f415]) ).
fof(f417,plain,
ssList(sK47_skl),
inference(cnf_transformation,[status(thm)],[f416]) ).
fof(f418,plain,
ssList(sK48_skl),
inference(cnf_transformation,[status(thm)],[f416]) ).
fof(f421,plain,
sK48_skl = sK50_skl,
inference(cnf_transformation,[status(thm)],[f416]) ).
fof(f422,plain,
sK47_skl = sK49_skl,
inference(cnf_transformation,[status(thm)],[f416]) ).
fof(f423,plain,
segmentP(sK50_skl,sK49_skl),
inference(cnf_transformation,[status(thm)],[f416]) ).
fof(f424,plain,
~ totalorderedP(sK47_skl),
inference(cnf_transformation,[status(thm)],[f416]) ).
fof(f425,plain,
( ~ neq(sK50_skl,nil)
| singletonP(sK49_skl) ),
inference(cnf_transformation,[status(thm)],[f416]) ).
fof(f462,plain,
segmentP(sK48_skl,sK49_skl),
inference(forward_demodulation,[status(thm)],[f421,f423]) ).
fof(f463,plain,
segmentP(sK48_skl,sK47_skl),
inference(forward_demodulation,[status(thm)],[f422,f462]) ).
fof(f464,plain,
( ~ neq(sK50_skl,nil)
| singletonP(sK47_skl) ),
inference(forward_demodulation,[status(thm)],[f422,f425]) ).
fof(f465,plain,
( ~ neq(sK48_skl,nil)
| singletonP(sK47_skl) ),
inference(forward_demodulation,[status(thm)],[f421,f464]) ).
fof(f468,plain,
( singletonP(sK47_skl)
| sK48_skl = nil
| ~ ssList(nil)
| ~ ssList(sK48_skl) ),
inference(resolution,[status(thm)],[f220,f465]) ).
fof(f472,plain,
( singletonP(sK47_skl)
| sK48_skl = nil
| ~ ssList(nil) ),
inference(forward_subsumption_resolution,[status(thm)],[f468,f418]) ).
fof(f480,plain,
( singletonP(sK47_skl)
| sK48_skl = nil ),
inference(forward_subsumption_resolution,[status(thm)],[f472,f223]) ).
fof(f481,plain,
( cons(sK4_skl(sK47_skl),nil) = sK47_skl
| ~ ssList(sK47_skl)
| sK48_skl = nil ),
inference(resolution,[status(thm)],[f480,f117]) ).
fof(f482,plain,
( ssItem(sK4_skl(sK47_skl))
| ~ ssList(sK47_skl)
| sK48_skl = nil ),
inference(resolution,[status(thm)],[f480,f116]) ).
fof(f483,plain,
( cons(sK4_skl(sK47_skl),nil) = sK47_skl
| sK48_skl = nil ),
inference(forward_subsumption_resolution,[status(thm)],[f481,f417]) ).
fof(f484,plain,
( ssItem(sK4_skl(sK47_skl))
| sK48_skl = nil ),
inference(forward_subsumption_resolution,[status(thm)],[f482,f417]) ).
fof(f488,plain,
( sK48_skl = nil
| totalorderedP(sK47_skl)
| ~ ssItem(sK4_skl(sK47_skl)) ),
inference(paramodulation,[status(thm)],[f483,f338]) ).
fof(f493,plain,
( sK48_skl = nil
| totalorderedP(sK47_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f488,f484]) ).
fof(f505,plain,
! [X0] :
( sK48_skl = X0
| ~ segmentP(nil,X0)
| ~ ssList(X0) ),
inference(backward_demodulation,[status(thm)],[f520,f326]) ).
fof(f517,plain,
totalorderedP(sK48_skl),
inference(backward_demodulation,[status(thm)],[f520,f339]) ).
fof(f520,plain,
sK48_skl = nil,
inference(forward_subsumption_resolution,[status(thm)],[f493,f424]) ).
fof(f521,plain,
! [X0] :
( sK48_skl = X0
| ~ segmentP(sK48_skl,X0)
| ~ ssList(X0) ),
inference(forward_demodulation,[status(thm)],[f520,f505]) ).
fof(f621,plain,
( sK48_skl = sK47_skl
| ~ ssList(sK47_skl) ),
inference(resolution,[status(thm)],[f521,f463]) ).
fof(f625,plain,
sK48_skl = sK47_skl,
inference(forward_subsumption_resolution,[status(thm)],[f621,f417]) ).
fof(f632,plain,
~ totalorderedP(sK48_skl),
inference(backward_demodulation,[status(thm)],[f625,f424]) ).
fof(f639,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f632,f517]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWC277+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/5.36 % Computer : n007.cluster.edu
% 0.10/5.36 % Model : x86_64 x86_64
% 0.10/5.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/5.36 % Memory : 8046.5625MB
% 0.10/5.36 % OS : Linux 6.8.0-71-generic
% 0.10/5.36 % CPULimit : 300
% 0.10/5.36 % WCLimit : 300
% 0.10/5.36 % DateTime : Mon Sep 21 08:09:11 UTC 2026
% 0.10/5.36 % CPUTime :
% 0.10/5.38 % Drodi V4.1.1
% 0.13/5.40 % Refutation found
% 0.13/5.40 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.13/5.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/5.42 % Elapsed time: 0.053936 seconds
% 0.13/5.42 % CPU time: 0.157086 seconds
% 0.13/5.42 % Total memory used: 79.574 MB
% 0.13/5.42 % Net memory used: 79.474 MB
%------------------------------------------------------------------------------