%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWC375+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 08:57:38 AM UTC 2026
% Result : Theorem 1.92s 0.73s
% Output : CNFRefutation 1.92s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 1
% Syntax : Number of formulae : 16 ( 8 unt; 0 def)
% Number of atoms : 64 ( 17 equ)
% Maximal formula atoms : 12 ( 4 avg)
% Number of connectives : 68 ( 20 ~; 16 |; 22 &)
% ( 0 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 5 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 5 con; 0-0 aty)
% Number of variables : 15 ( 0 sgn 10 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(co1,conjecture,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ! [X] :
( ssList(X)
=> ( ! [Y] :
( ssItem(Y)
=> ( ( memberP(U,Y)
& memberP(V,Y) )
| ( ~ memberP(U,Y)
& ~ memberP(V,Y) ) ) )
| X != W
| 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)
=> ( ! [Y] :
( ssItem(Y)
=> ( ( memberP(U,Y)
& memberP(V,Y) )
| ( ~ memberP(U,Y)
& ~ memberP(V,Y) ) ) )
| X != W
| U != W
| V != X ) ) ) ) ),
inference(assume_negation,[status(cth)],[co1]) ).
fof(nnf_87,plain,
? [U] :
( ? [V] :
( ? [W] :
( ? [X] :
( ? [Y] :
( ( ~ memberP(U,Y)
| ~ memberP(V,Y) )
& ( memberP(U,Y)
| memberP(V,Y) )
& ssItem(Y) )
& X = W
& W = U
& X = V
& ssList(X) )
& ssList(W) )
& ssList(V) )
& ssList(U) ),
inference(fof_nnf,[status(thm)],[co1_neg]) ).
fof(sk_co1_neg,plain,
( ( ~ memberP(sK3,sK4)
| ~ memberP(sK1,sK4) )
& ( memberP(sK3,sK4)
| memberP(sK1,sK4) )
& ssItem(sK4)
& sK0 = sK2
& sK2 = sK3
& sK0 = sK1
& ssList(sK0)
& ssList(sK2)
& ssList(sK1)
& ssList(sK3) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3,sK1,sK2,sK0,sK4]),skolemize(U,sK3),skolemize(V,sK1),skolemize(W,sK2),skolemize(X,sK0),skolemize(Y,sK4)],[nnf_87]) ).
cnf(c_331,negated_conjecture,
sK0 = sK1,
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_332,negated_conjecture,
sK2 = sK3,
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_333,negated_conjecture,
sK0 = sK2,
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_340,negated_conjecture,
sK1 = sK2,
inference(paramod,[status(thm)],[c_331,c_333]) ).
cnf(c_334,negated_conjecture,
sK1 = sK3,
inference(paramod,[status(thm)],[c_332,c_340]) ).
cnf(c_336,negated_conjecture,
( memberP(sK3,sK4)
| memberP(sK1,sK4) ),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_341,negated_conjecture,
( memberP(sK3,sK4)
| memberP(sK3,sK4) ),
inference(paramod,[status(thm)],[c_334,c_336]) ).
cnf(c_337,negated_conjecture,
memberP(sK3,sK4),
inference(copy,[status(thm)],[c_341]) ).
cnf(c_338,negated_conjecture,
( ~ memberP(sK3,sK4)
| ~ memberP(sK1,sK4) ),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_342,negated_conjecture,
( ~ memberP(sK3,sK4)
| ~ memberP(sK3,sK4) ),
inference(paramod,[status(thm)],[c_334,c_338]) ).
cnf(c_343,negated_conjecture,
~ memberP(sK3,sK4),
inference(copy,[status(thm)],[c_342]) ).
cnf(c_339,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_337,c_343]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SWC375+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.15/0.43 % Computer : n009.cluster.edu
% 0.15/0.43 % Model : x86_64 x86_64
% 0.15/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.43 % Memory : 8046.5625MB
% 0.15/0.43 % OS : Linux 6.8.0-71-generic
% 0.15/0.43 % CPULimit : 300
% 0.15/0.43 % WCLimit : 300
% 0.15/0.43 % DateTime : Sat Sep 26 12:54:29 UTC 2026
% 0.15/0.43 % CPUTime :
% 0.15/0.44 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.15/0.44 % Process 177383 was started by sandbox on n009,
% 0.15/0.44 % Sat Sep 26 12:54:29 2026
% 0.15/0.44 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.15/0.47
% 0.15/0.47 % From the command line: assign(max_seconds, 300).
% 1.92/0.73
% 1.92/0.73 % SZS status Theorem for theBenchmark
% 1.92/0.73
% 1.92/0.73 % Proof 1 at 0.24 (+ 0.01) seconds.
% 1.92/0.73 % Length of proof is 9.
% 1.92/0.73 % Level of proof is 4.
% 1.92/0.73 % Maximum clause weight is 8.000.
% 1.92/0.73 % Given clauses 0.
% 1.92/0.73
% 1.92/0.73 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------