%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWC405+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 : n017.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 19.32s 3.20s
% Output : CNFRefutation 19.32s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 1
% Syntax : Number of formulae : 16 ( 7 unt; 0 def)
% Number of atoms : 89 ( 12 equ)
% Maximal formula atoms : 15 ( 5 avg)
% Number of connectives : 105 ( 32 ~; 27 |; 36 &)
% ( 0 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 6 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 : 24 ( 0 sgn 14 !; 7 ?)
% Comments :
%------------------------------------------------------------------------------
fof(co1,conjecture,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ! [X] :
( ssList(X)
=> ( ! [Z] :
( ssItem(Z)
=> ( memberP(V,Z)
| ~ memberP(U,Z) ) )
| ? [Y] :
( ( ( memberP(X,Y)
& ~ memberP(W,Y) )
| ( memberP(W,Y)
& ~ memberP(X,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)
=> ( ! [Z] :
( ssItem(Z)
=> ( memberP(V,Z)
| ~ memberP(U,Z) ) )
| ? [Y] :
( ( ( memberP(X,Y)
& ~ memberP(W,Y) )
| ( memberP(W,Y)
& ~ memberP(X,Y) ) )
& ssItem(Y) )
| U != W
| V != X ) ) ) ) ),
inference(assume_negation,[status(cth)],[co1]) ).
fof(nnf_87,plain,
? [U] :
( ? [V] :
( ? [W] :
( ? [X] :
( ? [Z] :
( ~ memberP(V,Z)
& memberP(U,Z)
& ssItem(Z) )
& ! [Y] :
( ( ( ~ memberP(X,Y)
| memberP(W,Y) )
& ( ~ memberP(W,Y)
| memberP(X,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] :
( ( ( ~ memberP(sK0,Y)
| memberP(sK2,Y) )
& ( ~ memberP(sK2,Y)
| memberP(sK0,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,sK4]),skolemize(U,sK3),skolemize(V,sK1),skolemize(W,sK2),skolemize(X,sK0),skolemize(Z,sK4)],[nnf_87]) ).
fof(sk_co1_neg,plain,
( ~ memberP(sK1,sK4)
& memberP(sK3,sK4)
& ssItem(sK4)
& ! [VAR_0] :
( ~ memberP(sK0,VAR_0)
| memberP(sK2,VAR_0)
| ~ ssItem(VAR_0) )
& ! [VAR_0] :
( ~ memberP(sK2,VAR_0)
| memberP(sK0,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_333,negated_conjecture,
( ~ memberP(sK2,A)
| memberP(sK0,A)
| ~ ssItem(A) ),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_3364,negated_conjecture,
( ~ memberP(sK2,A)
| memberP(sK1,A)
| ~ ssItem(A) ),
inference(paramod,[status(thm)],[c_331,c_333]) ).
cnf(c_334,negated_conjecture,
( ~ memberP(sK3,A)
| memberP(sK1,A)
| ~ ssItem(A) ),
inference(paramod,[status(thm)],[c_332,c_3364]) ).
cnf(c_337,negated_conjecture,
ssItem(sK4),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_338,negated_conjecture,
memberP(sK3,sK4),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_339,negated_conjecture,
~ memberP(sK1,sK4),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_3365,negated_conjecture,
( memberP(sK1,sK4)
| ~ ssItem(sK4) ),
inference(resolve,[status(thm)],[c_338,c_334]) ).
cnf(c_3366,negated_conjecture,
memberP(sK1,sK4),
inference(resolve,[status(thm)],[c_337,c_3365]) ).
cnf(c_3363,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_339,c_3366]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SWC405+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.14/0.41 % Computer : n017.cluster.edu
% 0.14/0.41 % Model : x86_64 x86_64
% 0.14/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.41 % Memory : 8046.5625MB
% 0.14/0.41 % OS : Linux 6.8.0-71-generic
% 0.14/0.41 % CPULimit : 300
% 0.14/0.41 % WCLimit : 300
% 0.14/0.41 % DateTime : Sat Sep 26 12:54:33 UTC 2026
% 0.14/0.41 % CPUTime :
% 0.14/0.42 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.14/0.42 % Process 762255 was started by sandbox on n017,
% 0.14/0.42 % Sat Sep 26 12:54:33 2026
% 0.14/0.42 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.14/0.46
% 0.14/0.46 % From the command line: assign(max_seconds, 300).
% 19.32/3.20
% 19.32/3.20 % SZS status Theorem for theBenchmark
% 19.32/3.20
% 19.32/3.20 % Proof 1 at 2.53 (+ 0.20) seconds.
% 19.32/3.20 % Length of proof is 9.
% 19.32/3.20 % Level of proof is 3.
% 19.32/3.20 % Maximum clause weight is 8.000.
% 19.32/3.20 % Given clauses 164.
% 19.32/3.20
% 19.32/3.20 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------