%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWC422+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 : n004.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 08:57:46 AM UTC 2026
% Result : Theorem 8.52s 1.60s
% Output : CNFRefutation 8.52s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 1
% Syntax : Number of formulae : 34 ( 10 unt; 0 def)
% Number of atoms : 163 ( 48 equ)
% Maximal formula atoms : 23 ( 4 avg)
% Number of connectives : 208 ( 79 ~; 67 |; 48 &)
% ( 0 <=>; 14 =>; 0 <=; 0 <~>)
% Maximal formula depth : 23 ( 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 : 45 ( 0 sgn 23 !; 13 ?)
% Comments :
%------------------------------------------------------------------------------
fof(co1,conjecture,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ! [X] :
( ssList(X)
=> ( ( ( neq(X,nil)
| ~ neq(V,nil) )
& ( ! [X2] :
( ssItem(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( app(app(X4,cons(X2,nil)),X3) != W
| app(app(X3,cons(X2,nil)),X4) != X ) ) ) )
| ? [Y] :
( ? [Z] :
( ? [X1] :
( app(app(X1,cons(Y,nil)),Z) = U
& app(app(Z,cons(Y,nil)),X1) = V
& ssList(X1) )
& 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) )
& ( ! [X2] :
( ssItem(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( app(app(X4,cons(X2,nil)),X3) != W
| app(app(X3,cons(X2,nil)),X4) != X ) ) ) )
| ? [Y] :
( ? [Z] :
( ? [X1] :
( app(app(X1,cons(Y,nil)),Z) = U
& app(app(Z,cons(Y,nil)),X1) = V
& ssList(X1) )
& 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) )
| ( ? [X2] :
( ? [X3] :
( ? [X4] :
( app(app(X4,cons(X2,nil)),X3) = W
& app(app(X3,cons(X2,nil)),X4) = X
& ssList(X4) )
& ssList(X3) )
& ssItem(X2) )
& ! [Y] :
( ! [Z] :
( ! [X1] :
( app(app(X1,cons(Y,nil)),Z) != U
| app(app(Z,cons(Y,nil)),X1) != V
| ~ ssList(X1) )
| ~ 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(sK4,nil)
& neq(sK5,nil) )
| ( app(app(sK0,cons(sK1,nil)),sK2) = sK3
& app(app(sK2,cons(sK1,nil)),sK0) = sK4
& ssList(sK0)
& ssList(sK2)
& ssItem(sK1)
& ! [Y] :
( ! [Z] :
( ! [X1] :
( app(app(X1,cons(Y,nil)),Z) != sK6
| app(app(Z,cons(Y,nil)),X1) != sK5
| ~ ssList(X1) )
| ~ ssList(Z) )
| ~ ssItem(Y) )
& neq(sK5,nil) ) )
& sK3 = sK6
& sK4 = sK5
& ssList(sK4)
& ssList(sK3)
& ssList(sK5)
& ssList(sK6) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6,sK5,sK3,sK4,sK1,sK2,sK0]),skolemize(U,sK6),skolemize(V,sK5),skolemize(W,sK3),skolemize(X,sK4),skolemize(X2,sK1),skolemize(X3,sK2),skolemize(X4,sK0)],[nnf_87]) ).
fof(sk_co1_neg,plain,
( ( ~ neq(sK4,nil)
| app(app(sK0,cons(sK1,nil)),sK2) = sK3 )
& ( ~ neq(sK4,nil)
| app(app(sK2,cons(sK1,nil)),sK0) = sK4 )
& ( ~ neq(sK4,nil)
| ssList(sK0) )
& ( ~ neq(sK4,nil)
| ssList(sK2) )
& ( ~ neq(sK4,nil)
| ssItem(sK1) )
& ! [VAR_0,VAR_1,VAR_2] :
( ~ neq(sK4,nil)
| app(app(VAR_2,cons(VAR_0,nil)),VAR_1) != sK6
| app(app(VAR_1,cons(VAR_0,nil)),VAR_2) != sK5
| ~ ssList(VAR_2)
| ~ ssList(VAR_1)
| ~ ssItem(VAR_0) )
& neq(sK5,nil)
& sK3 = sK6
& sK4 = sK5
& ssList(sK4)
& ssList(sK3)
& ssList(sK5)
& ssList(sK6) ),
inference(cnf_transformation,[status(thm)],[sk_co1_neg_sk]) ).
cnf(c_190,negated_conjecture,
( ~ neq(sK4,nil)
| app(app(sK0,cons(sK1,nil)),sK2) = sK3 ),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_191,negated_conjecture,
( ~ neq(sK4,nil)
| app(app(sK2,cons(sK1,nil)),sK0) = sK4 ),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_192,negated_conjecture,
( ~ neq(sK4,nil)
| ssList(sK0) ),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_193,negated_conjecture,
( ~ neq(sK4,nil)
| ssList(sK2) ),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_194,negated_conjecture,
( ~ neq(sK4,nil)
| ssItem(sK1) ),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_195,negated_conjecture,
( ~ neq(sK4,nil)
| app(app(C,cons(A,nil)),B) != sK6
| app(app(B,cons(A,nil)),C) != sK5
| ~ ssList(C)
| ~ ssList(B)
| ~ ssItem(A) ),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_196,negated_conjecture,
neq(sK5,nil),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_197,negated_conjecture,
sK3 = sK6,
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_198,negated_conjecture,
sK4 = sK5,
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_2454,negated_conjecture,
( ~ neq(sK4,nil)
| app(app(sK0,cons(sK1,nil)),sK2) = sK6 ),
inference(paramod,[status(thm)],[c_197,c_190]) ).
cnf(c_2455,negated_conjecture,
( ~ neq(sK5,nil)
| app(app(sK0,cons(sK1,nil)),sK2) = sK6 ),
inference(paramod,[status(thm)],[c_198,c_2454]) ).
cnf(c_548,negated_conjecture,
app(app(sK0,cons(sK1,nil)),sK2) = sK6,
inference(resolve,[status(thm)],[c_196,c_2455]) ).
cnf(c_2456,negated_conjecture,
( ~ neq(sK5,nil)
| app(app(C,cons(A,nil)),B) != sK6
| app(app(B,cons(A,nil)),C) != sK5
| ~ ssList(C)
| ~ ssList(B)
| ~ ssItem(A) ),
inference(paramod,[status(thm)],[c_198,c_195]) ).
cnf(c_549,negated_conjecture,
( app(app(C,cons(A,nil)),B) != sK6
| app(app(B,cons(A,nil)),C) != sK5
| ~ ssList(C)
| ~ ssList(B)
| ~ ssItem(A) ),
inference(resolve,[status(thm)],[c_196,c_2456]) ).
cnf(c_2457,negated_conjecture,
( ~ neq(sK5,nil)
| ssItem(sK1) ),
inference(paramod,[status(thm)],[c_198,c_194]) ).
cnf(c_550,negated_conjecture,
ssItem(sK1),
inference(resolve,[status(thm)],[c_196,c_2457]) ).
cnf(c_2458,negated_conjecture,
( ~ neq(sK5,nil)
| ssList(sK2) ),
inference(paramod,[status(thm)],[c_198,c_193]) ).
cnf(c_551,negated_conjecture,
ssList(sK2),
inference(resolve,[status(thm)],[c_196,c_2458]) ).
cnf(c_2459,negated_conjecture,
( ~ neq(sK5,nil)
| ssList(sK0) ),
inference(paramod,[status(thm)],[c_198,c_192]) ).
cnf(c_552,negated_conjecture,
ssList(sK0),
inference(resolve,[status(thm)],[c_196,c_2459]) ).
cnf(c_2460,negated_conjecture,
( ~ neq(sK4,nil)
| app(app(sK2,cons(sK1,nil)),sK0) = sK5 ),
inference(paramod,[status(thm)],[c_198,c_191]) ).
cnf(c_2461,negated_conjecture,
( ~ neq(sK5,nil)
| app(app(sK2,cons(sK1,nil)),sK0) = sK5 ),
inference(paramod,[status(thm)],[c_198,c_2460]) ).
cnf(c_553,negated_conjecture,
app(app(sK2,cons(sK1,nil)),sK0) = sK5,
inference(resolve,[status(thm)],[c_196,c_2461]) ).
cnf(c_2462,negated_conjecture,
( app(app(sK2,cons(sK1,nil)),sK0) != sK5
| ~ ssList(sK0)
| ~ ssList(sK2)
| ~ ssItem(sK1) ),
inference(resolve,[status(thm)],[c_549,c_548]) ).
cnf(c_2463,negated_conjecture,
( sK5 != sK5
| ~ ssList(sK0)
| ~ ssList(sK2)
| ~ ssItem(sK1) ),
inference(paramod,[status(thm)],[c_553,c_2462]) ).
cnf(c_2464,negated_conjecture,
( ~ ssList(sK0)
| ~ ssList(sK2)
| ~ ssItem(sK1) ),
inference(copy,[status(thm)],[c_2463]) ).
cnf(c_2465,negated_conjecture,
( ~ ssList(sK0)
| ~ ssList(sK2) ),
inference(resolve,[status(thm)],[c_550,c_2464]) ).
cnf(c_2466,negated_conjecture,
~ ssList(sK0),
inference(resolve,[status(thm)],[c_551,c_2465]) ).
cnf(c_2453,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_552,c_2466]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWC422+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 : n004.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 13:01:36 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.36 % Process 1771148 was started by sandbox on n004,
% 0.09/0.36 % Sat Sep 26 13:01:36 2026
% 0.09/0.36 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.09/0.38
% 0.09/0.38 % From the command line: assign(max_seconds, 300).
% 8.52/1.60
% 8.52/1.60 % SZS status Theorem for theBenchmark
% 8.52/1.60
% 8.52/1.60 % Proof 1 at 1.06 (+ 0.12) seconds.
% 8.52/1.60 % Length of proof is 17.
% 8.52/1.60 % Level of proof is 3.
% 8.52/1.60 % Maximum clause weight is 39.000.
% 8.52/1.60 % Given clauses 354.
% 8.52/1.60
% 8.52/1.60 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------