%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWC096+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 08:56:48 AM UTC 2026
% Result : Theorem 29.33s 14.36s
% Output : CNFRefutation 29.33s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 1
% Syntax : Number of formulae : 29 ( 11 unt; 0 def)
% Number of atoms : 134 ( 50 equ)
% Maximal formula atoms : 20 ( 4 avg)
% Number of connectives : 169 ( 64 ~; 54 |; 43 &)
% ( 0 <=>; 8 =>; 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 : 36 ( 0 sgn 18 !; 10 ?)
% Comments :
%------------------------------------------------------------------------------
fof(co1,conjecture,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ! [X] :
( ( ( neq(X,nil)
| ~ neq(V,nil) )
& ( ! [X1] :
( ssItem(X1)
=> ! [X2] :
( app(X2,cons(X1,nil)) != X
| cons(X1,nil) != W
| ~ ssList(X2) ) )
| ? [Y] :
( ? [Z] :
( app(Z,cons(Y,nil)) = V
& cons(Y,nil) = U
& ssList(Z) )
& ssItem(Y) )
| ~ neq(V,nil) ) )
| 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] :
( ( ( neq(X,nil)
| ~ neq(V,nil) )
& ( ! [X1] :
( ssItem(X1)
=> ! [X2] :
( app(X2,cons(X1,nil)) != X
| cons(X1,nil) != W
| ~ ssList(X2) ) )
| ? [Y] :
( ? [Z] :
( app(Z,cons(Y,nil)) = V
& cons(Y,nil) = U
& ssList(Z) )
& ssItem(Y) )
| ~ neq(V,nil) ) )
| U != W
| V != X
| ~ ssList(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
& cons(X1,nil) = W
& ssList(X2) )
& ssItem(X1) )
& ! [Y] :
( ! [Z] :
( app(Z,cons(Y,nil)) != V
| cons(Y,nil) != 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
& cons(sK1,nil) = sK3
& ssList(sK0)
& ssItem(sK1)
& ! [Y] :
( ! [Z] :
( app(Z,cons(Y,nil)) != sK5
| cons(Y,nil) != 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)
| cons(sK1,nil) = 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
| cons(VAR_0,nil) != 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)
| cons(sK1,nil) = 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
| cons(A,nil) != 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_7543,plain,
( ~ neq(sK5,nil)
| app(sK0,cons(sK1,nil)) = sK2 ),
inference(paramod,[status(thm)],[c_197,c_190]) ).
cnf(c_1642,negated_conjecture,
app(sK0,cons(sK1,nil)) = sK2,
inference(resolve,[status(thm)],[c_195,c_7543]) ).
cnf(c_7544,plain,
( ~ neq(sK5,nil)
| cons(sK1,nil) = sK3 ),
inference(paramod,[status(thm)],[c_197,c_191]) ).
cnf(c_1643,negated_conjecture,
cons(sK1,nil) = sK3,
inference(resolve,[status(thm)],[c_195,c_7544]) ).
cnf(c_7545,plain,
( ~ neq(sK5,nil)
| ssList(sK0) ),
inference(paramod,[status(thm)],[c_197,c_192]) ).
cnf(c_1644,negated_conjecture,
ssList(sK0),
inference(resolve,[status(thm)],[c_195,c_7545]) ).
cnf(c_7546,plain,
( ~ neq(sK5,nil)
| ssItem(sK1) ),
inference(paramod,[status(thm)],[c_197,c_193]) ).
cnf(c_1645,negated_conjecture,
ssItem(sK1),
inference(resolve,[status(thm)],[c_195,c_7546]) ).
cnf(c_7547,plain,
( ~ neq(sK5,nil)
| app(B,cons(A,nil)) != sK5
| cons(A,nil) != sK4
| ~ ssList(B)
| ~ ssItem(A) ),
inference(paramod,[status(thm)],[c_197,c_194]) ).
cnf(c_1646,negated_conjecture,
( app(B,cons(A,nil)) != sK5
| cons(A,nil) != sK4
| ~ ssList(B)
| ~ ssItem(A) ),
inference(resolve,[status(thm)],[c_195,c_7547]) ).
cnf(c_4874,plain,
app(sK0,cons(sK1,nil)) = sK5,
inference(paramod,[status(thm)],[c_197,c_1642]) ).
cnf(c_4876,plain,
cons(sK1,nil) = sK4,
inference(paramod,[status(thm)],[c_196,c_1643]) ).
cnf(c_7548,plain,
( app(A,cons(sK1,nil)) != sK5
| cons(sK1,nil) != sK4
| ~ ssList(A) ),
inference(resolve,[status(thm)],[c_1646,c_1645]) ).
cnf(c_6341,plain,
( app(A,cons(sK1,nil)) != sK5
| ~ ssList(A) ),
inference(resolve,[status(thm)],[c_4876,c_7548]) ).
cnf(c_7549,plain,
app(sK0,cons(sK1,nil)) != sK5,
inference(resolve,[status(thm)],[c_6341,c_1644]) ).
cnf(c_7542,plain,
$false,
inference(resolve,[status(thm)],[c_4874,c_7549]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWC096+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/10.58 % Computer : n019.cluster.edu
% 0.08/10.58 % Model : x86_64 x86_64
% 0.08/10.58 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/10.58 % Memory : 8046.5625MB
% 0.08/10.58 % OS : Linux 6.8.0-71-generic
% 0.08/10.58 % CPULimit : 300
% 0.08/10.58 % WCLimit : 300
% 0.08/10.58 % DateTime : Sat Sep 26 12:15:02 UTC 2026
% 0.08/10.58 % CPUTime :
% 0.08/10.58 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.08/10.58 % Process 1268398 was started by sandbox on n019,
% 0.08/10.58 % Sat Sep 26 12:15:02 2026
% 0.08/10.58 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.12/10.61
% 0.12/10.61 % From the command line: assign(max_seconds, 300).
% 29.33/14.36
% 29.33/14.36 % given #500 (I,wt=44): 696 -ssList(A) | -ssItem(B) | -ssList(C) | -ssList(D) | -ssList(E) | app(app(C,cons(B,D)),cons(B,E)) != A | ssList(f35(A)). [factor(363,b,c),xx(g)].
% 29.33/14.36
% 29.33/14.36 % given #1000 (I,wt=60): 1221 -ssList(A) | -ssItem(B) | -ssList(C) | -ssList(D) | app(app(C,cons(B,D)),cons(B,A)) != A | app(app(f35(A),cons(f33(A),f36(A))),cons(f34(A),f37(A))) = A. [factor(716,b,c),xx(f)].
% 29.33/14.36
% 29.33/14.36 % given #1500 (F,wt=15): 7143 cons(c1,c4) != c6. [para(197(a,1),7087(a,1,2))].
% 29.33/14.36
% 29.33/14.36 % SZS status Theorem for theBenchmark
% 29.33/14.36
% 29.33/14.36 % Proof 1 at 3.42 (+ 0.30) seconds.
% 29.33/14.36 % Length of proof is 18.
% 29.33/14.36 % Level of proof is 5.
% 29.33/14.36 % Maximum clause weight is 34.000.
% 29.33/14.36 % Given clauses 1655.
% 29.33/14.36
% 29.33/14.36 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------