%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWC320+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 : n020.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 08:57:28 AM UTC 2026
% Result : Theorem 87.83s 12.51s
% Output : CNFRefutation 87.83s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 3
% Syntax : Number of formulae : 57 ( 13 unt; 0 def)
% Number of atoms : 219 ( 110 equ)
% Maximal formula atoms : 30 ( 3 avg)
% Number of connectives : 265 ( 103 ~; 99 |; 52 &)
% ( 1 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 7 con; 0-2 aty)
% Number of variables : 41 ( 0 sgn 22 !; 10 ?)
% Comments :
%------------------------------------------------------------------------------
fof(ax15,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ( neq(U,V)
<=> U != V ) ) ),
file('theBenchmark.p',ax15) ).
fof(co1,conjecture,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ! [X] :
( ( ( ? [X1] :
( ? [X2] :
( app(X2,cons(X1,nil)) = V
& app(cons(X1,nil),X2) = U
& ssList(X2) )
& ssItem(X1) )
| ~ neq(V,nil) )
& ( nil = U
| nil != V ) )
| ( neq(X,nil)
& ! [Y] :
( ssItem(Y)
=> ! [Z] :
( app(Z,cons(Y,nil)) != X
| app(cons(Y,nil),Z) != W
| ~ ssList(Z) ) ) )
| ( nil = X
& nil != W )
| U != W
| V != X
| ~ ssList(X) ) ) ) ),
file('theBenchmark.p',co1) ).
fof(co1_neg,negated_conjecture,
~ ! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ! [X] :
( ( ( ? [X1] :
( ? [X2] :
( app(X2,cons(X1,nil)) = V
& app(cons(X1,nil),X2) = U
& ssList(X2) )
& ssItem(X1) )
| ~ neq(V,nil) )
& ( nil = U
| nil != V ) )
| ( neq(X,nil)
& ! [Y] :
( ssItem(Y)
=> ! [Z] :
( app(Z,cons(Y,nil)) != X
| app(cons(Y,nil),Z) != W
| ~ ssList(Z) ) ) )
| ( nil = X
& nil != W )
| U != W
| V != X
| ~ ssList(X) ) ) ) ),
inference(assume_negation,[status(cth)],[co1]) ).
fof(nnf_87,plain,
? [U] :
( ? [V] :
( ? [W] :
( ? [X] :
( ( ( ! [X1] :
( ! [X2] :
( app(X2,cons(X1,nil)) != V
| app(cons(X1,nil),X2) != U
| ~ ssList(X2) )
| ~ ssItem(X1) )
& neq(V,nil) )
| ( nil != U
& nil = V ) )
& ( ~ neq(X,nil)
| ? [Y] :
( ? [Z] :
( app(Z,cons(Y,nil)) = X
& app(cons(Y,nil),Z) = W
& ssList(Z) )
& ssItem(Y) ) )
& ( nil != X
| nil = W )
& 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,
( ( ( ! [X1] :
( ! [X2] :
( app(X2,cons(X1,nil)) != sK1
| app(cons(X1,nil),X2) != sK0
| ~ ssList(X2) )
| ~ ssItem(X1) )
& neq(sK1,nil) )
| ( nil != sK0
& nil = sK1 ) )
& ( ~ neq(sK4,nil)
| ( app(sK2,cons(sK3,nil)) = sK4
& app(cons(sK3,nil),sK2) = sK5
& ssList(sK2)
& ssItem(sK3) ) )
& ( nil != sK4
| nil = sK5 )
& sK5 = sK0
& sK4 = sK1
& ssList(sK4)
& ssList(sK5)
& ssList(sK1)
& ssList(sK0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK5,sK4,sK3,sK2]),skolemize(U,sK0),skolemize(V,sK1),skolemize(W,sK5),skolemize(X,sK4),skolemize(Y,sK3),skolemize(Z,sK2)],[nnf_87]) ).
fof(sk_co1_neg,plain,
( ! [VAR_0,VAR_1] :
( app(VAR_1,cons(VAR_0,nil)) != sK1
| app(cons(VAR_0,nil),VAR_1) != sK0
| ~ ssList(VAR_1)
| ~ ssItem(VAR_0)
| nil != sK0 )
& ( neq(sK1,nil)
| nil != sK0 )
& ! [VAR_0,VAR_1] :
( app(VAR_1,cons(VAR_0,nil)) != sK1
| app(cons(VAR_0,nil),VAR_1) != sK0
| ~ ssList(VAR_1)
| ~ ssItem(VAR_0)
| nil = sK1 )
& ( neq(sK1,nil)
| nil = sK1 )
& ( ~ neq(sK4,nil)
| app(sK2,cons(sK3,nil)) = sK4 )
& ( ~ neq(sK4,nil)
| app(cons(sK3,nil),sK2) = sK5 )
& ( ~ neq(sK4,nil)
| ssList(sK2) )
& ( ~ neq(sK4,nil)
| ssItem(sK3) )
& ( nil != sK4
| nil = sK5 )
& sK5 = sK0
& sK4 = sK1
& ssList(sK4)
& ssList(sK5)
& ssList(sK1)
& ssList(sK0) ),
inference(cnf_transformation,[status(thm)],[sk_co1_neg_sk]) ).
cnf(c_192,negated_conjecture,
( neq(sK1,nil)
| nil != sK0 ),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_193,negated_conjecture,
( neq(sK1,nil)
| sK0 != nil ),
inference(copy,[status(thm)],[c_192]) ).
cnf(c_194,negated_conjecture,
( app(B,cons(A,nil)) != sK1
| app(cons(A,nil),B) != sK0
| ~ ssList(B)
| ~ ssItem(A)
| nil = sK1 ),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_195,negated_conjecture,
( app(B,cons(A,nil)) != sK1
| app(cons(A,nil),B) != sK0
| ~ ssList(B)
| ~ ssItem(A)
| sK1 = nil ),
inference(copy,[status(thm)],[c_194]) ).
cnf(c_196,negated_conjecture,
( neq(sK1,nil)
| nil = sK1 ),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_197,negated_conjecture,
( neq(sK1,nil)
| sK1 = nil ),
inference(copy,[status(thm)],[c_196]) ).
cnf(c_198,negated_conjecture,
( ~ neq(sK4,nil)
| app(sK2,cons(sK3,nil)) = sK4 ),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_199,negated_conjecture,
( ~ neq(sK4,nil)
| app(cons(sK3,nil),sK2) = sK5 ),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_200,negated_conjecture,
( ~ neq(sK4,nil)
| ssList(sK2) ),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_201,negated_conjecture,
( ~ neq(sK4,nil)
| ssItem(sK3) ),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_202,negated_conjecture,
( nil != sK4
| nil = sK5 ),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_10948,negated_conjecture,
( nil != sK4
| sK5 = nil ),
inference(copy,[status(thm)],[c_202]) ).
cnf(c_203,negated_conjecture,
( sK4 != nil
| sK5 = nil ),
inference(copy,[status(thm)],[c_10948]) ).
cnf(c_204,negated_conjecture,
sK5 = sK0,
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_205,negated_conjecture,
sK4 = sK1,
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_206,negated_conjecture,
ssList(sK4),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_207,negated_conjecture,
ssList(sK1),
inference(paramod,[status(thm)],[c_205,c_206]) ).
fof(ax17,axiom,
ssList(nil),
file('theBenchmark.p',ax17) ).
cnf(c_305,plain,
ssList(nil),
inference(clausify,[status(thm)],[ax17]) ).
cnf(c_308,plain,
( B != A
| ~ neq(A,B)
| ~ ssList(B)
| ~ ssList(A) ),
inference(clausify,[status(thm)],[ax15]) ).
cnf(c_10949,negated_conjecture,
( sK4 != nil
| sK0 = nil ),
inference(paramod,[status(thm)],[c_204,c_203]) ).
cnf(c_554,negated_conjecture,
( sK1 != nil
| sK0 = nil ),
inference(paramod,[status(thm)],[c_205,c_10949]) ).
cnf(c_10950,negated_conjecture,
( ~ neq(sK4,nil)
| app(cons(sK3,nil),sK2) = sK0 ),
inference(paramod,[status(thm)],[c_204,c_199]) ).
cnf(c_555,negated_conjecture,
( ~ neq(sK1,nil)
| app(cons(sK3,nil),sK2) = sK0 ),
inference(paramod,[status(thm)],[c_205,c_10950]) ).
cnf(c_556,negated_conjecture,
( ~ neq(sK1,nil)
| ssItem(sK3) ),
inference(paramod,[status(thm)],[c_205,c_201]) ).
cnf(c_557,negated_conjecture,
( ~ neq(sK1,nil)
| ssList(sK2) ),
inference(paramod,[status(thm)],[c_205,c_200]) ).
cnf(c_10951,negated_conjecture,
( ~ neq(sK4,nil)
| app(sK2,cons(sK3,nil)) = sK1 ),
inference(paramod,[status(thm)],[c_205,c_198]) ).
cnf(c_558,negated_conjecture,
( ~ neq(sK1,nil)
| app(sK2,cons(sK3,nil)) = sK1 ),
inference(paramod,[status(thm)],[c_205,c_10951]) ).
cnf(c_4148,plain,
( neq(sK1,nil)
| sK0 = nil ),
inference(resolve,[status(thm)],[c_554,c_197]) ).
cnf(c_4150,plain,
( sK1 = nil
| ssItem(sK3) ),
inference(resolve,[status(thm)],[c_556,c_197]) ).
cnf(c_4151,plain,
( sK1 = nil
| ssList(sK2) ),
inference(resolve,[status(thm)],[c_557,c_197]) ).
cnf(c_10952,negated_conjecture,
( app(A,cons(sK3,nil)) != sK1
| app(cons(sK3,nil),A) != sK0
| ~ ssList(A)
| sK1 = nil
| sK1 = nil ),
inference(resolve,[status(thm)],[c_4150,c_195]) ).
cnf(c_6277,negated_conjecture,
( app(A,cons(sK3,nil)) != sK1
| app(cons(sK3,nil),A) != sK0
| ~ ssList(A)
| sK1 = nil ),
inference(copy,[status(thm)],[c_10952]) ).
cnf(c_6443,plain,
( sK0 = nil
| ssList(sK2) ),
inference(resolve,[status(thm)],[c_4151,c_554]) ).
cnf(c_7857,plain,
( neq(sK1,nil)
| ssList(sK2) ),
inference(resolve,[status(thm)],[c_6443,c_193]) ).
cnf(c_10953,negated_conjecture,
( ssList(sK2)
| ssList(sK2) ),
inference(resolve,[status(thm)],[c_7857,c_557]) ).
cnf(c_10528,negated_conjecture,
ssList(sK2),
inference(copy,[status(thm)],[c_10953]) ).
cnf(c_10954,negated_conjecture,
( neq(sK1,nil)
| neq(sK1,nil) ),
inference(resolve,[status(thm)],[c_4148,c_193]) ).
cnf(c_10741,negated_conjecture,
neq(sK1,nil),
inference(copy,[status(thm)],[c_10954]) ).
cnf(c_10744,negated_conjecture,
app(sK2,cons(sK3,nil)) = sK1,
inference(resolve,[status(thm)],[c_10741,c_558]) ).
cnf(c_10745,negated_conjecture,
app(cons(sK3,nil),sK2) = sK0,
inference(resolve,[status(thm)],[c_10741,c_555]) ).
cnf(c_10955,plain,
( nil != sK1
| ~ ssList(nil)
| ~ ssList(sK1) ),
inference(resolve,[status(thm)],[c_10741,c_308]) ).
cnf(c_10956,plain,
( sK1 != nil
| ~ ssList(nil)
| ~ ssList(sK1) ),
inference(copy,[status(thm)],[c_10955]) ).
cnf(c_10957,negated_conjecture,
( sK1 != nil
| ~ ssList(nil) ),
inference(resolve,[status(thm)],[c_207,c_10956]) ).
cnf(c_10747,negated_conjecture,
sK1 != nil,
inference(resolve,[status(thm)],[c_305,c_10957]) ).
cnf(c_10764,negated_conjecture,
( app(A,cons(sK3,nil)) != sK1
| app(cons(sK3,nil),A) != sK0
| ~ ssList(A) ),
inference(resolve,[status(thm)],[c_10747,c_6277]) ).
cnf(c_10958,plain,
( app(sK2,cons(sK3,nil)) != sK1
| app(cons(sK3,nil),sK2) != sK0 ),
inference(resolve,[status(thm)],[c_10764,c_10528]) ).
cnf(c_10959,plain,
( app(sK2,cons(sK3,nil)) != sK1
| sK0 != sK0 ),
inference(paramod,[status(thm)],[c_10745,c_10958]) ).
cnf(c_10960,plain,
( sK1 != sK1
| sK0 != sK0 ),
inference(paramod,[status(thm)],[c_10744,c_10959]) ).
cnf(c_10961,plain,
sK1 != sK1,
inference(copy,[status(thm)],[c_10960]) ).
cnf(c_10947,plain,
$false,
inference(copy,[status(thm)],[c_10961]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC320+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n020.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Sat Sep 26 12:48:18 UTC 2026
% 0.13/0.36 % CPUTime :
% 0.13/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.13/0.36 % Process 1602317 was started by sandbox on n020,
% 0.13/0.36 % Sat Sep 26 12:48:18 2026
% 0.13/0.36 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.13/0.38
% 0.13/0.38 % From the command line: assign(max_seconds, 300).
% 87.83/12.51
% 87.83/12.51 % given #500 (I,wt=47): 708 -ssList(A) | -ssItem(B) | -ssItem(C) | -ssList(D) | -ssList(E) | app(app(D,cons(B,E)),cons(C,A)) != A | C != B | ssList(f35(A)). [factor(371,a,f)].
% 87.83/12.51
% 87.83/12.51 % given #1000 (I,wt=63): 1233 -ssList(A) | -ssItem(B) | -ssItem(C) | -ssList(D) | app(app(D,cons(B,A)),cons(C,D)) != A | C != B | app(app(f35(A),cons(f33(A),f36(A))),cons(f34(A),f37(A))) = A. [factor(728,d,e)].
% 87.83/12.51
% 87.83/12.51 % given #1500 (T,wt=11): 7828 c3 = nil | rearsegP(c8,nil). [resolve(6443,a,259,a)].
% 87.83/12.51
% 87.83/12.51 % SZS status Theorem for theBenchmark
% 87.83/12.51
% 87.83/12.51 % Proof 1 at 3.71 (+ 0.33) seconds.
% 87.83/12.51 % Length of proof is 38.
% 87.83/12.51 % Level of proof is 8.
% 87.83/12.51 % Maximum clause weight is 36.000.
% 87.83/12.51 % Given clauses 1575.
% 87.83/12.51
% 87.83/12.51 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------