%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWC082+1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/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 : Sun Sep 27 08:56:46 AM UTC 2026
% Result : Theorem 13.48s 2.42s
% Output : CNFRefutation 13.48s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 1
% Syntax : Number of formulae : 27 ( 9 unt; 0 def)
% Number of atoms : 131 ( 22 equ)
% Maximal formula atoms : 21 ( 4 avg)
% Number of connectives : 160 ( 56 ~; 48 |; 46 &)
% ( 0 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 5 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 6 con; 0-0 aty)
% Number of variables : 21 ( 0 sgn 13 !; 7 ?)
% Comments :
%------------------------------------------------------------------------------
fof(co1,conjecture,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ! [X] :
( ssList(X)
=> ( ( neq(X,nil)
& ! [Z] :
( ssList(Z)
=> ( ~ segmentP(W,Z)
| ~ segmentP(X,Z)
| ~ neq(Z,nil) ) ) )
| ( nil = X
& nil != W )
| ? [Y] :
( segmentP(U,Y)
& segmentP(V,Y)
& neq(Y,nil)
& ssList(Y) )
| ~ 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)
=> ( ( neq(X,nil)
& ! [Z] :
( ssList(Z)
=> ( ~ segmentP(W,Z)
| ~ segmentP(X,Z)
| ~ neq(Z,nil) ) ) )
| ( nil = X
& nil != W )
| ? [Y] :
( segmentP(U,Y)
& segmentP(V,Y)
& neq(Y,nil)
& ssList(Y) )
| ~ neq(V,nil)
| U != W
| V != X ) ) ) ) ),
inference(assume_negation,[status(cth)],[co1]) ).
fof(nnf_87,plain,
? [U] :
( ? [V] :
( ? [W] :
( ? [X] :
( ( ~ neq(X,nil)
| ? [Z] :
( segmentP(W,Z)
& segmentP(X,Z)
& neq(Z,nil)
& ssList(Z) ) )
& ( nil != X
| nil = W )
& ! [Y] :
( ~ segmentP(U,Y)
| ~ segmentP(V,Y)
| ~ neq(Y,nil)
| ~ ssList(Y) )
& 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_sk,plain,
( ( ~ neq(sK2,nil)
| ( segmentP(sK0,sK1)
& segmentP(sK2,sK1)
& neq(sK1,nil)
& ssList(sK1) ) )
& ( nil != sK2
| nil = sK0 )
& ! [Y] :
( ~ segmentP(sK4,Y)
| ~ segmentP(sK3,Y)
| ~ neq(Y,nil)
| ~ ssList(Y) )
& neq(sK3,nil)
& sK0 = sK4
& sK2 = sK3
& ssList(sK2)
& ssList(sK0)
& ssList(sK3)
& ssList(sK4) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4,sK3,sK0,sK2,sK1]),skolemize(U,sK4),skolemize(V,sK3),skolemize(W,sK0),skolemize(X,sK2),skolemize(Z,sK1)],[nnf_87]) ).
fof(sk_co1_neg,plain,
( ( ~ neq(sK2,nil)
| segmentP(sK0,sK1) )
& ( ~ neq(sK2,nil)
| segmentP(sK2,sK1) )
& ( ~ neq(sK2,nil)
| neq(sK1,nil) )
& ( ~ neq(sK2,nil)
| ssList(sK1) )
& ( nil != sK2
| nil = sK0 )
& ! [VAR_0] :
( ~ segmentP(sK4,VAR_0)
| ~ segmentP(sK3,VAR_0)
| ~ neq(VAR_0,nil)
| ~ ssList(VAR_0) )
& neq(sK3,nil)
& sK0 = sK4
& sK2 = sK3
& ssList(sK2)
& ssList(sK0)
& ssList(sK3)
& ssList(sK4) ),
inference(cnf_transformation,[status(thm)],[sk_co1_neg_sk]) ).
cnf(c_190,negated_conjecture,
( ~ neq(sK2,nil)
| segmentP(sK0,sK1) ),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_191,negated_conjecture,
( ~ neq(sK2,nil)
| segmentP(sK2,sK1) ),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_192,negated_conjecture,
( ~ neq(sK2,nil)
| neq(sK1,nil) ),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_193,negated_conjecture,
( ~ neq(sK2,nil)
| ssList(sK1) ),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_196,negated_conjecture,
( ~ segmentP(sK4,A)
| ~ segmentP(sK3,A)
| ~ neq(A,nil)
| ~ ssList(A) ),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_197,negated_conjecture,
neq(sK3,nil),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_198,negated_conjecture,
sK0 = sK4,
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_199,negated_conjecture,
sK2 = sK3,
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_2449,negated_conjecture,
( ~ neq(sK2,nil)
| segmentP(sK4,sK1) ),
inference(paramod,[status(thm)],[c_198,c_190]) ).
cnf(c_2450,negated_conjecture,
( ~ neq(sK3,nil)
| segmentP(sK4,sK1) ),
inference(paramod,[status(thm)],[c_199,c_2449]) ).
cnf(c_549,negated_conjecture,
segmentP(sK4,sK1),
inference(resolve,[status(thm)],[c_197,c_2450]) ).
cnf(c_2451,negated_conjecture,
( ~ neq(sK3,nil)
| ssList(sK1) ),
inference(paramod,[status(thm)],[c_199,c_193]) ).
cnf(c_550,negated_conjecture,
ssList(sK1),
inference(resolve,[status(thm)],[c_197,c_2451]) ).
cnf(c_2452,negated_conjecture,
( ~ neq(sK3,nil)
| neq(sK1,nil) ),
inference(paramod,[status(thm)],[c_199,c_192]) ).
cnf(c_551,negated_conjecture,
neq(sK1,nil),
inference(resolve,[status(thm)],[c_197,c_2452]) ).
cnf(c_2453,negated_conjecture,
( ~ neq(sK2,nil)
| segmentP(sK3,sK1) ),
inference(paramod,[status(thm)],[c_199,c_191]) ).
cnf(c_2454,negated_conjecture,
( ~ neq(sK3,nil)
| segmentP(sK3,sK1) ),
inference(paramod,[status(thm)],[c_199,c_2453]) ).
cnf(c_552,negated_conjecture,
segmentP(sK3,sK1),
inference(resolve,[status(thm)],[c_197,c_2454]) ).
cnf(c_2455,negated_conjecture,
( ~ segmentP(sK3,sK1)
| ~ neq(sK1,nil)
| ~ ssList(sK1) ),
inference(resolve,[status(thm)],[c_549,c_196]) ).
cnf(c_2456,negated_conjecture,
( ~ segmentP(sK3,sK1)
| ~ neq(sK1,nil) ),
inference(resolve,[status(thm)],[c_550,c_2455]) ).
cnf(c_2457,negated_conjecture,
~ segmentP(sK3,sK1),
inference(resolve,[status(thm)],[c_551,c_2456]) ).
cnf(c_2448,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_552,c_2457]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SWC082+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.16/0.41 % Computer : n005.cluster.edu
% 0.16/0.41 % Model : x86_64 x86_64
% 0.16/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.41 % Memory : 8046.5625MB
% 0.16/0.41 % OS : Linux 6.8.0-71-generic
% 0.16/0.41 % CPULimit : 300
% 0.16/0.41 % WCLimit : 300
% 0.16/0.41 % DateTime : Sat Sep 26 12:12:16 UTC 2026
% 0.16/0.42 % CPUTime :
% 0.16/0.42 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.16/0.42 % Process 2095566 was started by sandbox2 on n005,
% 0.16/0.42 % Sat Sep 26 12:12:16 2026
% 0.16/0.42 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.16/0.46
% 0.16/0.46 % From the command line: assign(max_seconds, 300).
% 13.48/2.42
% 13.48/2.42 % SZS status Theorem for theBenchmark
% 13.48/2.42
% 13.48/2.42 % Proof 1 at 1.72 (+ 0.20) seconds.
% 13.48/2.42 % Length of proof is 14.
% 13.48/2.42 % Level of proof is 3.
% 13.48/2.42 % Maximum clause weight is 13.000.
% 13.48/2.42 % Given clauses 353.
% 13.48/2.42
% 13.48/2.42 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------