%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWC385+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 : n009.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 08:57:40 AM UTC 2026
% Result : Theorem 5.18s 6.16s
% Output : CNFRefutation 5.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 1
% Syntax : Number of formulae : 17 ( 9 unt; 0 def)
% Number of atoms : 65 ( 10 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 71 ( 23 ~; 18 |; 22 &)
% ( 0 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 5 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 : 12 ( 0 sgn 8 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(co1,conjecture,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ! [X] :
( ssList(X)
=> ( ( segmentP(V,U)
& singletonP(U) )
| ( neq(X,nil)
& ~ singletonP(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)
& singletonP(U) )
| ( neq(X,nil)
& ~ singletonP(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)
| ~ singletonP(U) )
& ( ~ neq(X,nil)
| singletonP(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(sK1,sK0)
| ~ singletonP(sK0) )
& ( ~ neq(sK3,nil)
| singletonP(sK2) )
& segmentP(sK3,sK2)
& neq(sK1,nil)
& sK2 = sK0
& sK3 = sK1
& ssList(sK3)
& ssList(sK2)
& ssList(sK1)
& ssList(sK0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3]),skolemize(U,sK0),skolemize(V,sK1),skolemize(W,sK2),skolemize(X,sK3)],[nnf_87]) ).
cnf(c_190,negated_conjecture,
( ~ segmentP(sK1,sK0)
| ~ singletonP(sK0) ),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_191,negated_conjecture,
( ~ neq(sK3,nil)
| singletonP(sK2) ),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_192,negated_conjecture,
segmentP(sK3,sK2),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_193,negated_conjecture,
neq(sK1,nil),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_194,negated_conjecture,
sK2 = sK0,
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_195,negated_conjecture,
sK3 = sK1,
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_1038,negated_conjecture,
segmentP(sK1,sK2),
inference(paramod,[status(thm)],[c_195,c_192]) ).
cnf(c_544,negated_conjecture,
segmentP(sK1,sK0),
inference(paramod,[status(thm)],[c_194,c_1038]) ).
cnf(c_1039,negated_conjecture,
( ~ neq(sK3,nil)
| singletonP(sK0) ),
inference(paramod,[status(thm)],[c_194,c_191]) ).
cnf(c_1040,negated_conjecture,
( ~ neq(sK1,nil)
| singletonP(sK0) ),
inference(paramod,[status(thm)],[c_195,c_1039]) ).
cnf(c_545,negated_conjecture,
singletonP(sK0),
inference(resolve,[status(thm)],[c_193,c_1040]) ).
cnf(c_1041,negated_conjecture,
~ segmentP(sK1,sK0),
inference(resolve,[status(thm)],[c_545,c_190]) ).
cnf(c_1037,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_544,c_1041]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWC385+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.13/5.40 % Computer : n009.cluster.edu
% 0.13/5.40 % Model : x86_64 x86_64
% 0.13/5.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/5.40 % Memory : 8046.5625MB
% 0.13/5.40 % OS : Linux 6.8.0-71-generic
% 0.13/5.40 % CPULimit : 300
% 0.13/5.40 % WCLimit : 300
% 0.13/5.40 % DateTime : Sat Sep 26 12:55:50 UTC 2026
% 0.13/5.41 % CPUTime :
% 0.13/5.41 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.13/5.41 % Process 179416 was started by sandbox on n009,
% 0.13/5.41 % Sat Sep 26 12:55:50 2026
% 0.13/5.41 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.13/5.45
% 0.13/5.45 % From the command line: assign(max_seconds, 300).
% 5.18/6.16
% 5.18/6.16 % SZS status Theorem for theBenchmark
% 5.18/6.16
% 5.18/6.16 % Proof 1 at 0.66 (+ 0.04) seconds.
% 5.18/6.16 % Length of proof is 10.
% 5.18/6.16 % Level of proof is 3.
% 5.18/6.16 % Maximum clause weight is 5.000.
% 5.18/6.16 % Given clauses 0.
% 5.18/6.16
% 5.18/6.16 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------