%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWC317+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 : n019.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 08:57:27 AM UTC 2026
% Result : Theorem 14.69s 7.61s
% Output : CNFRefutation 14.69s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 1
% Syntax : Number of formulae : 30 ( 9 unt; 0 def)
% Number of atoms : 139 ( 48 equ)
% Maximal formula atoms : 20 ( 4 avg)
% Number of connectives : 174 ( 65 ~; 54 |; 43 &)
% ( 0 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 5 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 : 34 ( 0 sgn 18 !; 10 ?)
% Comments :
%------------------------------------------------------------------------------
fof(co1,conjecture,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ! [X] :
( ssList(X)
=> ( ( ( neq(X,nil)
| ~ neq(V,nil) )
& ( ! [X1] :
( ssItem(X1)
=> ! [X2] :
( ssList(X2)
=> ( app(X2,cons(X1,nil)) != X
| app(cons(X1,nil),X2) != W ) ) )
| ? [Y] :
( ? [Z] :
( app(Z,cons(Y,nil)) = V
& app(cons(Y,nil),Z) = U
& ssList(Z) )
& 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) )
& ( ! [X1] :
( ssItem(X1)
=> ! [X2] :
( ssList(X2)
=> ( app(X2,cons(X1,nil)) != X
| app(cons(X1,nil),X2) != W ) ) )
| ? [Y] :
( ? [Z] :
( app(Z,cons(Y,nil)) = V
& app(cons(Y,nil),Z) = U
& ssList(Z) )
& 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) )
| ( ? [X1] :
( ? [X2] :
( app(X2,cons(X1,nil)) = X
& app(cons(X1,nil),X2) = W
& ssList(X2) )
& ssItem(X1) )
& ! [Y] :
( ! [Z] :
( app(Z,cons(Y,nil)) != V
| app(cons(Y,nil),Z) != U
| ~ ssList(Z) )
| ~ 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(sK5,nil) )
| ( app(sK0,cons(sK1,nil)) = sK2
& app(cons(sK1,nil),sK0) = sK3
& ssList(sK0)
& ssItem(sK1)
& ! [Y] :
( ! [Z] :
( app(Z,cons(Y,nil)) != sK5
| app(cons(Y,nil),Z) != sK4
| ~ ssList(Z) )
| ~ ssItem(Y) )
& neq(sK5,nil) ) )
& sK3 = sK4
& sK2 = sK5
& ssList(sK2)
& ssList(sK3)
& ssList(sK5)
& ssList(sK4) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4,sK5,sK3,sK2,sK1,sK0]),skolemize(U,sK4),skolemize(V,sK5),skolemize(W,sK3),skolemize(X,sK2),skolemize(X1,sK1),skolemize(X2,sK0)],[nnf_87]) ).
fof(sk_co1_neg,plain,
( ( ~ neq(sK2,nil)
| app(sK0,cons(sK1,nil)) = sK2 )
& ( ~ neq(sK2,nil)
| app(cons(sK1,nil),sK0) = sK3 )
& ( ~ neq(sK2,nil)
| ssList(sK0) )
& ( ~ neq(sK2,nil)
| ssItem(sK1) )
& ! [VAR_0,VAR_1] :
( ~ neq(sK2,nil)
| app(VAR_1,cons(VAR_0,nil)) != sK5
| app(cons(VAR_0,nil),VAR_1) != sK4
| ~ ssList(VAR_1)
| ~ ssItem(VAR_0) )
& neq(sK5,nil)
& sK3 = sK4
& sK2 = sK5
& ssList(sK2)
& ssList(sK3)
& ssList(sK5)
& ssList(sK4) ),
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)
| app(cons(sK1,nil),sK0) = sK3 ),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_192,negated_conjecture,
( ~ neq(sK2,nil)
| ssList(sK0) ),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_193,negated_conjecture,
( ~ neq(sK2,nil)
| ssItem(sK1) ),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_194,negated_conjecture,
( ~ neq(sK2,nil)
| app(B,cons(A,nil)) != sK5
| app(cons(A,nil),B) != sK4
| ~ ssList(B)
| ~ ssItem(A) ),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_195,negated_conjecture,
neq(sK5,nil),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_196,negated_conjecture,
sK3 = sK4,
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_197,negated_conjecture,
sK2 = sK5,
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_2456,negated_conjecture,
( ~ neq(sK2,nil)
| app(cons(sK1,nil),sK0) = sK4 ),
inference(paramod,[status(thm)],[c_196,c_191]) ).
cnf(c_2457,negated_conjecture,
( ~ neq(sK5,nil)
| app(cons(sK1,nil),sK0) = sK4 ),
inference(paramod,[status(thm)],[c_197,c_2456]) ).
cnf(c_546,negated_conjecture,
app(cons(sK1,nil),sK0) = sK4,
inference(resolve,[status(thm)],[c_195,c_2457]) ).
cnf(c_2458,negated_conjecture,
( ~ neq(sK5,nil)
| app(B,cons(A,nil)) != sK5
| app(cons(A,nil),B) != sK4
| ~ ssList(B)
| ~ ssItem(A) ),
inference(paramod,[status(thm)],[c_197,c_194]) ).
cnf(c_547,negated_conjecture,
( app(B,cons(A,nil)) != sK5
| app(cons(A,nil),B) != sK4
| ~ ssList(B)
| ~ ssItem(A) ),
inference(resolve,[status(thm)],[c_195,c_2458]) ).
cnf(c_2459,negated_conjecture,
( ~ neq(sK5,nil)
| ssItem(sK1) ),
inference(paramod,[status(thm)],[c_197,c_193]) ).
cnf(c_548,negated_conjecture,
ssItem(sK1),
inference(resolve,[status(thm)],[c_195,c_2459]) ).
cnf(c_2460,negated_conjecture,
( ~ neq(sK5,nil)
| ssList(sK0) ),
inference(paramod,[status(thm)],[c_197,c_192]) ).
cnf(c_549,negated_conjecture,
ssList(sK0),
inference(resolve,[status(thm)],[c_195,c_2460]) ).
cnf(c_2461,negated_conjecture,
( ~ neq(sK2,nil)
| app(sK0,cons(sK1,nil)) = sK5 ),
inference(paramod,[status(thm)],[c_197,c_190]) ).
cnf(c_2462,negated_conjecture,
( ~ neq(sK5,nil)
| app(sK0,cons(sK1,nil)) = sK5 ),
inference(paramod,[status(thm)],[c_197,c_2461]) ).
cnf(c_550,negated_conjecture,
app(sK0,cons(sK1,nil)) = sK5,
inference(resolve,[status(thm)],[c_195,c_2462]) ).
cnf(c_2463,negated_conjecture,
( app(sK0,cons(sK1,nil)) != sK5
| ~ ssList(sK0)
| ~ ssItem(sK1) ),
inference(resolve,[status(thm)],[c_547,c_546]) ).
cnf(c_2464,negated_conjecture,
( sK5 != sK5
| ~ ssList(sK0)
| ~ ssItem(sK1) ),
inference(paramod,[status(thm)],[c_550,c_2463]) ).
cnf(c_2465,negated_conjecture,
( ~ ssList(sK0)
| ~ ssItem(sK1) ),
inference(copy,[status(thm)],[c_2464]) ).
cnf(c_2466,negated_conjecture,
~ ssList(sK0),
inference(resolve,[status(thm)],[c_548,c_2465]) ).
cnf(c_2455,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_549,c_2466]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SWC317+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.07 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.18/5.45 % Computer : n019.cluster.edu
% 0.18/5.45 % Model : x86_64 x86_64
% 0.18/5.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/5.45 % Memory : 8046.5625MB
% 0.18/5.45 % OS : Linux 6.8.0-71-generic
% 0.18/5.45 % CPULimit : 300
% 0.18/5.45 % WCLimit : 300
% 0.18/5.45 % DateTime : Sat Sep 26 12:46:54 UTC 2026
% 0.18/5.45 % CPUTime :
% 0.18/5.46 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.18/5.46 % Process 1339661 was started by sandbox on n019,
% 0.18/5.46 % Sat Sep 26 12:46:54 2026
% 0.18/5.46 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.22/5.50
% 0.22/5.50 % From the command line: assign(max_seconds, 300).
% 14.69/7.61
% 14.69/7.61 % SZS status Theorem for theBenchmark
% 14.69/7.61
% 14.69/7.61 % Proof 1 at 1.88 (+ 0.20) seconds.
% 14.69/7.61 % Length of proof is 15.
% 14.69/7.61 % Level of proof is 3.
% 14.69/7.61 % Maximum clause weight is 27.000.
% 14.69/7.61 % Given clauses 353.
% 14.69/7.61
% 14.69/7.61 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------