%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWC185+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 : n016.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 08:57:06 AM UTC 2026
% Result : Theorem 0.14s 20.90s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 1
% Syntax : Number of formulae : 25 ( 9 unt; 0 def)
% Number of atoms : 143 ( 27 equ)
% Maximal formula atoms : 22 ( 5 avg)
% Number of connectives : 191 ( 73 ~; 58 |; 46 &)
% ( 0 <=>; 14 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 8 con; 0-2 aty)
% Number of variables : 51 ( 0 sgn 26 !; 13 ?)
% Comments :
%------------------------------------------------------------------------------
fof(co1,conjecture,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ! [X] :
( ssList(X)
=> ( ! [X2] :
( ssItem(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( ( ~ memberP(X4,X2)
& ~ memberP(X3,X2) )
| app(app(X3,cons(X2,nil)),X4) != U ) ) ) )
| ? [Y] :
( ? [Z] :
( ? [X1] :
( ( memberP(X1,Y)
| memberP(Z,Y) )
& app(app(Z,cons(Y,nil)),X1) = W
& ssList(X1) )
& ssList(Z) )
& 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)
=> ( ! [X2] :
( ssItem(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( ( ~ memberP(X4,X2)
& ~ memberP(X3,X2) )
| app(app(X3,cons(X2,nil)),X4) != U ) ) ) )
| ? [Y] :
( ? [Z] :
( ? [X1] :
( ( memberP(X1,Y)
| memberP(Z,Y) )
& app(app(Z,cons(Y,nil)),X1) = W
& ssList(X1) )
& ssList(Z) )
& ssItem(Y) )
| U != W
| V != X ) ) ) ) ),
inference(assume_negation,[status(cth)],[co1]) ).
fof(nnf_87,plain,
? [U] :
( ? [V] :
( ? [W] :
( ? [X] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ( memberP(X4,X2)
| memberP(X3,X2) )
& app(app(X3,cons(X2,nil)),X4) = U
& ssList(X4) )
& ssList(X3) )
& ssItem(X2) )
& ! [Y] :
( ! [Z] :
( ! [X1] :
( ( ~ memberP(X1,Y)
& ~ memberP(Z,Y) )
| app(app(Z,cons(Y,nil)),X1) != W
| ~ ssList(X1) )
| ~ ssList(Z) )
| ~ 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(sK4,sK2)
| memberP(sK3,sK2) )
& app(app(sK3,cons(sK2,nil)),sK4) = sK1
& ssList(sK4)
& ssList(sK3)
& ssItem(sK2)
& ! [Y] :
( ! [Z] :
( ! [X1] :
( ( ~ memberP(X1,Y)
& ~ memberP(Z,Y) )
| app(app(Z,cons(Y,nil)),X1) != sK0
| ~ ssList(X1) )
| ~ ssList(Z) )
| ~ ssItem(Y) )
& sK0 = sK1
& sK6 = sK5
& ssList(sK6)
& ssList(sK0)
& ssList(sK5)
& ssList(sK1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK5,sK0,sK6,sK2,sK3,sK4]),skolemize(U,sK1),skolemize(V,sK5),skolemize(W,sK0),skolemize(X,sK6),skolemize(X2,sK2),skolemize(X3,sK3),skolemize(X4,sK4)],[nnf_87]) ).
fof(sk_co1_neg,plain,
( ( memberP(sK4,sK2)
| memberP(sK3,sK2) )
& app(app(sK3,cons(sK2,nil)),sK4) = sK1
& ssList(sK4)
& ssList(sK3)
& ssItem(sK2)
& ! [VAR_0,VAR_1,VAR_2] :
( ~ memberP(VAR_2,VAR_0)
| app(app(VAR_1,cons(VAR_0,nil)),VAR_2) != sK0
| ~ ssList(VAR_2)
| ~ ssList(VAR_1)
| ~ ssItem(VAR_0) )
& ! [VAR_0,VAR_1,VAR_2] :
( ~ memberP(VAR_1,VAR_0)
| app(app(VAR_1,cons(VAR_0,nil)),VAR_2) != sK0
| ~ ssList(VAR_2)
| ~ ssList(VAR_1)
| ~ ssItem(VAR_0) )
& sK0 = sK1
& sK6 = sK5
& ssList(sK6)
& ssList(sK0)
& ssList(sK5)
& ssList(sK1) ),
inference(cnf_transformation,[status(thm)],[sk_co1_neg_sk]) ).
cnf(c_332,negated_conjecture,
sK0 = sK1,
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_333,negated_conjecture,
( ~ memberP(B,A)
| app(app(B,cons(A,nil)),C) != sK0
| ~ ssList(C)
| ~ ssList(B)
| ~ ssItem(A) ),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_334,negated_conjecture,
( ~ memberP(B,A)
| app(app(B,cons(A,nil)),C) != sK1
| ~ ssList(C)
| ~ ssList(B)
| ~ ssItem(A) ),
inference(paramod,[status(thm)],[c_332,c_333]) ).
cnf(c_335,negated_conjecture,
( ~ memberP(C,A)
| app(app(B,cons(A,nil)),C) != sK0
| ~ ssList(C)
| ~ ssList(B)
| ~ ssItem(A) ),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_336,negated_conjecture,
( ~ memberP(C,A)
| app(app(B,cons(A,nil)),C) != sK1
| ~ ssList(C)
| ~ ssList(B)
| ~ ssItem(A) ),
inference(paramod,[status(thm)],[c_332,c_335]) ).
cnf(c_337,negated_conjecture,
ssItem(sK2),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_338,negated_conjecture,
ssList(sK3),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_339,negated_conjecture,
ssList(sK4),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_340,negated_conjecture,
app(app(sK3,cons(sK2,nil)),sK4) = sK1,
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_341,negated_conjecture,
( memberP(sK4,sK2)
| memberP(sK3,sK2) ),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_2900,negated_conjecture,
( ~ memberP(sK4,sK2)
| ~ ssList(sK4)
| ~ ssList(sK3)
| ~ ssItem(sK2) ),
inference(resolve,[status(thm)],[c_340,c_336]) ).
cnf(c_2901,negated_conjecture,
( ~ memberP(sK4,sK2)
| ~ ssList(sK4)
| ~ ssList(sK3) ),
inference(resolve,[status(thm)],[c_337,c_2900]) ).
cnf(c_2902,negated_conjecture,
( ~ memberP(sK4,sK2)
| ~ ssList(sK4) ),
inference(resolve,[status(thm)],[c_338,c_2901]) ).
cnf(c_2885,negated_conjecture,
~ memberP(sK4,sK2),
inference(resolve,[status(thm)],[c_339,c_2902]) ).
cnf(c_2903,negated_conjecture,
( ~ memberP(sK3,sK2)
| ~ ssList(sK4)
| ~ ssList(sK3)
| ~ ssItem(sK2) ),
inference(resolve,[status(thm)],[c_340,c_334]) ).
cnf(c_2904,negated_conjecture,
( ~ memberP(sK3,sK2)
| ~ ssList(sK4)
| ~ ssList(sK3) ),
inference(resolve,[status(thm)],[c_337,c_2903]) ).
cnf(c_2905,negated_conjecture,
( ~ memberP(sK3,sK2)
| ~ ssList(sK4) ),
inference(resolve,[status(thm)],[c_338,c_2904]) ).
cnf(c_2886,negated_conjecture,
~ memberP(sK3,sK2),
inference(resolve,[status(thm)],[c_339,c_2905]) ).
cnf(c_2906,negated_conjecture,
memberP(sK4,sK2),
inference(resolve,[status(thm)],[c_2886,c_341]) ).
cnf(c_2899,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_2885,c_2906]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SWC185+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.02 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/5.38 % Computer : n016.cluster.edu
% 0.09/5.38 % Model : x86_64 x86_64
% 0.09/5.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/5.38 % Memory : 8046.5625MB
% 0.09/5.38 % OS : Linux 6.8.0-71-generic
% 0.02/20.23 % CPULimit : 300
% 0.02/20.23 % WCLimit : 300
% 0.02/20.23 % DateTime : Sat Sep 26 12:27:30 UTC 2026
% 0.02/20.23 % CPUTime :
% 0.02/20.23 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.02/20.23 % Process 589356 was started by sandbox2 on n012,
% 0.02/20.23 % Sat Sep 26 12:27:30 2026
% 0.02/20.23 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.02/20.25
% 0.02/20.25 % From the command line: assign(max_seconds, 300).
% 0.14/20.90
% 0.14/20.90 % SZS status Theorem for theBenchmark
% 0.14/20.90
% 0.14/20.90 % Proof 1 at 0.58 (+ 0.07) seconds.
% 0.14/20.90 % Length of proof is 14.
% 0.14/20.90 % Level of proof is 4.
% 0.14/20.90 % Maximum clause weight is 28.000.
% 0.14/20.90 % Given clauses 166.
% 0.14/20.90
% 0.14/20.90 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------