%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWC359+1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/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 : Sun Sep 27 08:57:35 AM UTC 2026
% Result : Theorem 0.22s 5.72s
% Output : CNFRefutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 1
% Syntax : Number of formulae : 11 ( 7 unt; 0 def)
% Number of atoms : 67 ( 10 equ)
% Maximal formula atoms : 15 ( 6 avg)
% Number of connectives : 80 ( 24 ~; 20 |; 28 &)
% ( 0 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 8 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 5 con; 0-0 aty)
% Number of variables : 16 ( 0 sgn 10 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(co1,conjecture,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ! [X] :
( ssList(X)
=> ( segmentP(V,U)
| ? [Y] :
( equalelemsP(Y)
& segmentP(Y,W)
& segmentP(X,Y)
& neq(W,Y)
& ssList(Y) )
| ~ equalelemsP(W)
| ~ segmentP(X,W)
| ~ neq(V,nil)
| U != W
| V != X ) ) ) ) ),
file('theBenchmark.p',co1) ).
fof(co1_neg,negated_conjecture,
~ ! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ! [X] :
( ssList(X)
=> ( segmentP(V,U)
| ? [Y] :
( equalelemsP(Y)
& segmentP(Y,W)
& segmentP(X,Y)
& neq(W,Y)
& ssList(Y) )
| ~ equalelemsP(W)
| ~ segmentP(X,W)
| ~ neq(V,nil)
| U != W
| V != X ) ) ) ) ),
inference(assume_negation,[status(cth)],[co1]) ).
fof(nnf_87,plain,
? [U] :
( ? [V] :
( ? [W] :
( ? [X] :
( ~ segmentP(V,U)
& ! [Y] :
( ~ equalelemsP(Y)
| ~ segmentP(Y,W)
| ~ segmentP(X,Y)
| ~ neq(W,Y)
| ~ ssList(Y) )
& equalelemsP(W)
& segmentP(X,W)
& neq(V,nil)
& W = U
& X = V
& ssList(X) )
& ssList(W) )
& ssList(V) )
& ssList(U) ),
inference(fof_nnf,[status(thm)],[co1_neg]) ).
fof(sk_co1_neg,plain,
( ~ segmentP(sK0,sK1)
& ! [Y] :
( ~ equalelemsP(Y)
| ~ segmentP(Y,sK3)
| ~ segmentP(sK2,Y)
| ~ neq(sK3,Y)
| ~ ssList(Y) )
& equalelemsP(sK3)
& segmentP(sK2,sK3)
& neq(sK0,nil)
& sK3 = sK1
& sK2 = sK0
& ssList(sK2)
& ssList(sK3)
& ssList(sK0)
& ssList(sK1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK0,sK3,sK2]),skolemize(U,sK1),skolemize(V,sK0),skolemize(W,sK3),skolemize(X,sK2)],[nnf_87]) ).
cnf(c_208,negated_conjecture,
~ segmentP(sK0,sK1),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_209,negated_conjecture,
segmentP(sK2,sK3),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_211,negated_conjecture,
sK3 = sK1,
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_212,negated_conjecture,
sK2 = sK0,
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_565,negated_conjecture,
segmentP(sK0,sK3),
inference(paramod,[status(thm)],[c_212,c_209]) ).
cnf(c_566,negated_conjecture,
segmentP(sK0,sK1),
inference(paramod,[status(thm)],[c_211,c_565]) ).
cnf(c_564,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_208,c_566]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SWC359+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.16/5.44 % Computer : n007.cluster.edu
% 0.16/5.44 % Model : x86_64 x86_64
% 0.16/5.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/5.44 % Memory : 8046.5625MB
% 0.16/5.44 % OS : Linux 6.8.0-71-generic
% 0.16/5.44 % CPULimit : 300
% 0.16/5.44 % WCLimit : 300
% 0.16/5.44 % DateTime : Sat Sep 26 12:50:44 UTC 2026
% 0.16/5.45 % CPUTime :
% 0.16/5.45 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.16/5.45 % Process 3777061 was started by sandbox on n007,
% 0.16/5.45 % Sat Sep 26 12:50:44 2026
% 0.16/5.45 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.16/5.49
% 0.16/5.49 % From the command line: assign(max_seconds, 300).
% 0.22/5.72
% 0.22/5.72 % SZS status Theorem for theBenchmark
% 0.22/5.72
% 0.22/5.72 % Proof 1 at 0.22 (+ 0.01) seconds.
% 0.22/5.72 % Length of proof is 6.
% 0.22/5.72 % Level of proof is 2.
% 0.22/5.72 % Maximum clause weight is 5.000.
% 0.22/5.72 % Given clauses 0.
% 0.22/5.72
% 0.22/5.72 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------