%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWC406+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 : n015.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 08:57:43 AM UTC 2026
% Result : Theorem 6.49s 2.32s
% Output : CNFRefutation 6.49s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 1
% Syntax : Number of formulae : 16 ( 7 unt; 0 def)
% Number of atoms : 140 ( 22 equ)
% Maximal formula atoms : 34 ( 8 avg)
% Number of connectives : 182 ( 58 ~; 56 |; 56 &)
% ( 0 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 23 ( 8 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 5 con; 0-1 aty)
% Number of variables : 36 ( 0 sgn 23 !; 10 ?)
% Comments :
%------------------------------------------------------------------------------
fof(co1,conjecture,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ! [X] :
( ssList(X)
=> ( ! [X1] :
( ssItem(X1)
=> ( memberP(V,X1)
| ~ memberP(U,X1) ) )
| ? [Y] :
( ( ( ( ? [Z] :
( leq(Z,Y)
& memberP(X,Z)
& Y != Z
& ssItem(Z) )
| ~ memberP(X,Y) )
& memberP(W,Y) )
| ( memberP(X,Y)
& ! [Z] :
( ssItem(Z)
=> ( Y = Z
| ~ leq(Z,Y)
| ~ memberP(X,Z) ) )
& ~ memberP(W,Y) ) )
& ssItem(Y) )
| 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)
=> ( ! [X1] :
( ssItem(X1)
=> ( memberP(V,X1)
| ~ memberP(U,X1) ) )
| ? [Y] :
( ( ( ( ? [Z] :
( leq(Z,Y)
& memberP(X,Z)
& Y != Z
& ssItem(Z) )
| ~ memberP(X,Y) )
& memberP(W,Y) )
| ( memberP(X,Y)
& ! [Z] :
( ssItem(Z)
=> ( Y = Z
| ~ leq(Z,Y)
| ~ memberP(X,Z) ) )
& ~ memberP(W,Y) ) )
& ssItem(Y) )
| U != W
| V != X ) ) ) ) ),
inference(assume_negation,[status(cth)],[co1]) ).
fof(nnf_87,plain,
? [U] :
( ? [V] :
( ? [W] :
( ? [X] :
( ? [X1] :
( ~ memberP(V,X1)
& memberP(U,X1)
& ssItem(X1) )
& ! [Y] :
( ( ( ( ! [Z] :
( ~ leq(Z,Y)
| ~ memberP(X,Z)
| Z = Y
| ~ ssItem(Z) )
& memberP(X,Y) )
| ~ memberP(W,Y) )
& ( ~ memberP(X,Y)
| ? [X0] :
( X0 != Y
& leq(X0,Y)
& memberP(X,X0)
& ssItem(X0) )
| memberP(W,Y) ) )
| ~ ssItem(Y) )
& 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,
( ~ memberP(sK1,sK4)
& memberP(sK3,sK4)
& ssItem(sK4)
& ! [Y] :
( ( ( ( ! [Z] :
( ~ leq(Z,Y)
| ~ memberP(sK0,Z)
| Z = Y
| ~ ssItem(Z) )
& memberP(sK0,Y) )
| ~ memberP(sK2,Y) )
& ( ~ memberP(sK0,Y)
| ( sK5(Y) != Y
& leq(sK5(Y),Y)
& memberP(sK0,sK5(Y))
& ssItem(sK5(Y)) )
| memberP(sK2,Y) ) )
| ~ ssItem(Y) )
& sK2 = sK3
& sK0 = sK1
& ssList(sK0)
& ssList(sK2)
& ssList(sK1)
& ssList(sK3) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3,sK1,sK2,sK0,sK5,sK4]),skolemize(U,sK3),skolemize(V,sK1),skolemize(W,sK2),skolemize(X,sK0),skolemize(X0,sK5(Y)),skolemize(X1,sK4)],[nnf_87]) ).
fof(sk_co1_neg,plain,
( ~ memberP(sK1,sK4)
& memberP(sK3,sK4)
& ssItem(sK4)
& ! [VAR_0,VAR_1] :
( ~ leq(VAR_1,VAR_0)
| ~ memberP(sK0,VAR_1)
| VAR_1 = VAR_0
| ~ ssItem(VAR_1)
| ~ memberP(sK2,VAR_0)
| ~ ssItem(VAR_0) )
& ! [VAR_0] :
( memberP(sK0,VAR_0)
| ~ memberP(sK2,VAR_0)
| ~ ssItem(VAR_0) )
& ! [VAR_0] :
( ~ memberP(sK0,VAR_0)
| sK5(VAR_0) != VAR_0
| memberP(sK2,VAR_0)
| ~ ssItem(VAR_0) )
& ! [VAR_0] :
( ~ memberP(sK0,VAR_0)
| leq(sK5(VAR_0),VAR_0)
| memberP(sK2,VAR_0)
| ~ ssItem(VAR_0) )
& ! [VAR_0] :
( ~ memberP(sK0,VAR_0)
| memberP(sK0,sK5(VAR_0))
| memberP(sK2,VAR_0)
| ~ ssItem(VAR_0) )
& ! [VAR_0] :
( ~ memberP(sK0,VAR_0)
| ssItem(sK5(VAR_0))
| memberP(sK2,VAR_0)
| ~ ssItem(VAR_0) )
& sK2 = sK3
& sK0 = sK1
& ssList(sK0)
& ssList(sK2)
& ssList(sK1)
& ssList(sK3) ),
inference(cnf_transformation,[status(thm)],[sk_co1_neg_sk]) ).
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_341,negated_conjecture,
( memberP(sK0,A)
| ~ memberP(sK2,A)
| ~ ssItem(A) ),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_2386,negated_conjecture,
( memberP(sK0,A)
| ~ memberP(sK3,A)
| ~ ssItem(A) ),
inference(paramod,[status(thm)],[c_332,c_341]) ).
cnf(c_342,negated_conjecture,
( memberP(sK1,A)
| ~ memberP(sK3,A)
| ~ ssItem(A) ),
inference(paramod,[status(thm)],[c_331,c_2386]) ).
cnf(c_345,negated_conjecture,
ssItem(sK4),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_346,negated_conjecture,
memberP(sK3,sK4),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_347,negated_conjecture,
~ memberP(sK1,sK4),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_2387,negated_conjecture,
( memberP(sK1,sK4)
| ~ memberP(sK3,sK4) ),
inference(resolve,[status(thm)],[c_345,c_342]) ).
cnf(c_2388,negated_conjecture,
memberP(sK1,sK4),
inference(resolve,[status(thm)],[c_346,c_2387]) ).
cnf(c_2385,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_347,c_2388]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWC406+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.37 % Computer : n015.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Sat Sep 26 13:02:29 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.37 % Process 4121388 was started by sandbox on n015,
% 0.09/0.37 % Sat Sep 26 13:02:29 2026
% 0.09/0.37 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.09/0.40
% 0.09/0.40 % From the command line: assign(max_seconds, 300).
% 6.49/2.32
% 6.49/2.32 % SZS status Theorem for theBenchmark
% 6.49/2.32
% 6.49/2.32 % Proof 1 at 0.90 (+ 0.07) seconds.
% 6.49/2.32 % Length of proof is 9.
% 6.49/2.32 % Level of proof is 3.
% 6.49/2.32 % Maximum clause weight is 10.000.
% 6.49/2.32 % Given clauses 167.
% 6.49/2.32
% 6.49/2.32 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------