%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWC097+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 : 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 08:56:49 AM UTC 2026
% Result : Theorem 15.15s 12.39s
% Output : CNFRefutation 15.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 1
% Syntax : Number of formulae : 22 ( 8 unt; 0 def)
% Number of atoms : 94 ( 32 equ)
% Maximal formula atoms : 14 ( 4 avg)
% Number of connectives : 110 ( 38 ~; 29 |; 33 &)
% ( 0 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 6 con; 0-2 aty)
% Number of variables : 23 ( 0 sgn 13 !; 7 ?)
% Comments :
%------------------------------------------------------------------------------
fof(co1,conjecture,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ! [X] :
( ssList(X)
=> ( ( ( neq(X,nil)
| ~ neq(V,nil) )
& ( ! [Z] :
( ssItem(Z)
=> app(W,cons(Z,nil)) != X )
| ? [Y] :
( app(U,cons(Y,nil)) = V
& ssItem(Y) )
| ~ neq(V,nil) ) )
| 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)
=> ( ( ( neq(X,nil)
| ~ neq(V,nil) )
& ( ! [Z] :
( ssItem(Z)
=> app(W,cons(Z,nil)) != X )
| ? [Y] :
( app(U,cons(Y,nil)) = V
& ssItem(Y) )
| ~ neq(V,nil) ) )
| U != W
| V != X ) ) ) ) ),
inference(assume_negation,[status(cth)],[co1]) ).
fof(nnf_87,plain,
? [U] :
( ? [V] :
( ? [W] :
( ? [X] :
( ( ( ~ neq(X,nil)
& neq(V,nil) )
| ( ? [Z] :
( app(W,cons(Z,nil)) = X
& ssItem(Z) )
& ! [Y] :
( app(U,cons(Y,nil)) != V
| ~ ssItem(Y) )
& neq(V,nil) ) )
& 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,
( ( ( ~ neq(sK2,nil)
& neq(sK4,nil) )
| ( app(sK0,cons(sK1,nil)) = sK2
& ssItem(sK1)
& ! [Y] :
( app(sK3,cons(Y,nil)) != sK4
| ~ ssItem(Y) )
& neq(sK4,nil) ) )
& sK0 = sK3
& sK2 = sK4
& ssList(sK2)
& ssList(sK0)
& ssList(sK4)
& ssList(sK3) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3,sK4,sK0,sK2,sK1]),skolemize(U,sK3),skolemize(V,sK4),skolemize(W,sK0),skolemize(X,sK2),skolemize(Z,sK1)],[nnf_87]) ).
fof(sk_co1_neg,plain,
( ( ~ neq(sK2,nil)
| app(sK0,cons(sK1,nil)) = sK2 )
& ( ~ neq(sK2,nil)
| ssItem(sK1) )
& ! [VAR_0] :
( ~ neq(sK2,nil)
| app(sK3,cons(VAR_0,nil)) != sK4
| ~ ssItem(VAR_0) )
& neq(sK4,nil)
& sK0 = sK3
& sK2 = sK4
& ssList(sK2)
& ssList(sK0)
& ssList(sK4)
& ssList(sK3) ),
inference(cnf_transformation,[status(thm)],[sk_co1_neg_sk]) ).
cnf(c_190,negated_conjecture,
( ~ neq(sK2,nil)
| app(sK0,cons(sK1,nil)) = sK2 ),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_191,negated_conjecture,
( ~ neq(sK2,nil)
| ssItem(sK1) ),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_192,negated_conjecture,
( ~ neq(sK2,nil)
| app(sK3,cons(A,nil)) != sK4
| ~ ssItem(A) ),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_193,negated_conjecture,
neq(sK4,nil),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_194,negated_conjecture,
sK0 = sK3,
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_195,negated_conjecture,
sK2 = sK4,
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_4151,negated_conjecture,
( ~ neq(sK2,nil)
| app(sK3,cons(sK1,nil)) = sK2 ),
inference(paramod,[status(thm)],[c_194,c_190]) ).
cnf(c_4152,negated_conjecture,
( ~ neq(sK2,nil)
| app(sK3,cons(sK1,nil)) = sK4 ),
inference(paramod,[status(thm)],[c_195,c_4151]) ).
cnf(c_4153,negated_conjecture,
( ~ neq(sK4,nil)
| app(sK3,cons(sK1,nil)) = sK4 ),
inference(paramod,[status(thm)],[c_195,c_4152]) ).
cnf(c_544,negated_conjecture,
app(sK3,cons(sK1,nil)) = sK4,
inference(resolve,[status(thm)],[c_193,c_4153]) ).
cnf(c_4154,negated_conjecture,
( ~ neq(sK4,nil)
| app(sK3,cons(A,nil)) != sK4
| ~ ssItem(A) ),
inference(paramod,[status(thm)],[c_195,c_192]) ).
cnf(c_545,negated_conjecture,
( app(sK3,cons(A,nil)) != sK4
| ~ ssItem(A) ),
inference(resolve,[status(thm)],[c_193,c_4154]) ).
cnf(c_4155,negated_conjecture,
( ~ neq(sK4,nil)
| ssItem(sK1) ),
inference(paramod,[status(thm)],[c_195,c_191]) ).
cnf(c_546,negated_conjecture,
ssItem(sK1),
inference(resolve,[status(thm)],[c_193,c_4155]) ).
cnf(c_4156,negated_conjecture,
app(sK3,cons(sK1,nil)) != sK4,
inference(resolve,[status(thm)],[c_546,c_545]) ).
cnf(c_4157,negated_conjecture,
sK4 != sK4,
inference(paramod,[status(thm)],[c_544,c_4156]) ).
cnf(c_4150,negated_conjecture,
$false,
inference(copy,[status(thm)],[c_4157]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC097+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/10.37 % Computer : n016.cluster.edu
% 0.09/10.37 % Model : x86_64 x86_64
% 0.09/10.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/10.37 % Memory : 8046.5625MB
% 0.09/10.37 % OS : Linux 6.8.0-71-generic
% 0.09/10.37 % CPULimit : 300
% 0.09/10.37 % WCLimit : 300
% 0.09/10.37 % DateTime : Sat Sep 26 12:19:56 UTC 2026
% 0.09/10.37 % CPUTime :
% 0.09/10.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/10.37 % Process 848062 was started by sandbox on n016,
% 0.09/10.37 % Sat Sep 26 12:19:56 2026
% 0.09/10.37 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.13/10.40
% 0.13/10.40 % From the command line: assign(max_seconds, 300).
% 15.15/12.39
% 15.15/12.39 % SZS status Theorem for theBenchmark
% 15.15/12.39
% 15.15/12.39 % Proof 1 at 1.80 (+ 0.17) seconds.
% 15.15/12.39 % Length of proof is 11.
% 15.15/12.39 % Level of proof is 3.
% 15.15/12.39 % Maximum clause weight is 27.000.
% 15.15/12.39 % Given clauses 350.
% 15.15/12.39
% 15.15/12.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------