%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWC254+1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n003.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 08:57:17 AM UTC 2026
% Result : Theorem 19.72s 2.93s
% Output : CNFRefutation 19.72s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 2
% Syntax : Number of formulae : 27 ( 10 unt; 0 def)
% Number of atoms : 113 ( 31 equ)
% Maximal formula atoms : 17 ( 4 avg)
% Number of connectives : 127 ( 41 ~; 34 |; 38 &)
% ( 1 <=>; 13 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 7 con; 0-2 aty)
% Number of variables : 24 ( 0 sgn 13 !; 7 ?)
% Comments :
%------------------------------------------------------------------------------
fof(ax4,axiom,
! [U] :
( ssList(U)
=> ( singletonP(U)
<=> ? [V] :
( cons(V,nil) = U
& ssItem(V) ) ) ),
file('theBenchmark.p',ax4) ).
fof(co1,conjecture,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ! [X] :
( ssList(X)
=> ( ( ( neq(X,nil)
| ~ neq(V,nil) )
& ( singletonP(U)
| ! [Y] :
( ssItem(Y)
=> ! [Z] :
( ssList(Z)
=> ( app(Z,cons(Y,nil)) != X
| cons(Y,nil) != W ) ) )
| ~ 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) )
& ( singletonP(U)
| ! [Y] :
( ssItem(Y)
=> ! [Z] :
( ssList(Z)
=> ( app(Z,cons(Y,nil)) != X
| cons(Y,nil) != W ) ) )
| ~ 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) )
| ( ~ singletonP(U)
& ? [Y] :
( ? [Z] :
( app(Z,cons(Y,nil)) = X
& cons(Y,nil) = W
& 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(sK1,nil)
& neq(sK4,nil) )
| ( ~ singletonP(sK0)
& app(sK5,cons(sK2,nil)) = sK1
& cons(sK2,nil) = sK3
& ssList(sK5)
& ssItem(sK2)
& neq(sK4,nil) ) )
& sK3 = sK0
& sK1 = sK4
& ssList(sK1)
& ssList(sK3)
& ssList(sK4)
& ssList(sK0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK4,sK3,sK1,sK2,sK5]),skolemize(U,sK0),skolemize(V,sK4),skolemize(W,sK3),skolemize(X,sK1),skolemize(Y,sK2),skolemize(Z,sK5)],[nnf_87]) ).
fof(sk_co1_neg,plain,
( ( ~ neq(sK1,nil)
| ~ singletonP(sK0) )
& ( ~ neq(sK1,nil)
| app(sK5,cons(sK2,nil)) = sK1 )
& ( ~ neq(sK1,nil)
| cons(sK2,nil) = sK3 )
& ( ~ neq(sK1,nil)
| ssList(sK5) )
& ( ~ neq(sK1,nil)
| ssItem(sK2) )
& neq(sK4,nil)
& sK3 = sK0
& sK1 = sK4
& ssList(sK1)
& ssList(sK3)
& ssList(sK4)
& ssList(sK0) ),
inference(cnf_transformation,[status(thm)],[sk_co1_neg_sk]) ).
cnf(c_190,negated_conjecture,
( ~ neq(sK1,nil)
| ~ singletonP(sK0) ),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_192,negated_conjecture,
( ~ neq(sK1,nil)
| cons(sK2,nil) = sK3 ),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_194,negated_conjecture,
( ~ neq(sK1,nil)
| ssItem(sK2) ),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_195,negated_conjecture,
neq(sK4,nil),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_196,negated_conjecture,
sK3 = sK0,
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_197,negated_conjecture,
sK1 = sK4,
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_200,negated_conjecture,
ssList(sK3),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_201,negated_conjecture,
ssList(sK0),
inference(paramod,[status(thm)],[c_196,c_200]) ).
cnf(c_327,plain,
( cons(B,nil) != A
| ~ ssItem(B)
| singletonP(A)
| ~ ssList(A) ),
inference(clausify,[status(thm)],[ax4]) ).
cnf(c_6722,negated_conjecture,
( ~ neq(sK1,nil)
| cons(sK2,nil) = sK0 ),
inference(paramod,[status(thm)],[c_196,c_192]) ).
cnf(c_6723,negated_conjecture,
( ~ neq(sK4,nil)
| cons(sK2,nil) = sK0 ),
inference(paramod,[status(thm)],[c_197,c_6722]) ).
cnf(c_546,negated_conjecture,
cons(sK2,nil) = sK0,
inference(resolve,[status(thm)],[c_195,c_6723]) ).
cnf(c_6724,negated_conjecture,
( ~ neq(sK4,nil)
| ssItem(sK2) ),
inference(paramod,[status(thm)],[c_197,c_194]) ).
cnf(c_547,negated_conjecture,
ssItem(sK2),
inference(resolve,[status(thm)],[c_195,c_6724]) ).
cnf(c_6725,negated_conjecture,
( ~ neq(sK4,nil)
| ~ singletonP(sK0) ),
inference(paramod,[status(thm)],[c_197,c_190]) ).
cnf(c_550,negated_conjecture,
~ singletonP(sK0),
inference(resolve,[status(thm)],[c_195,c_6725]) ).
cnf(c_6726,negated_conjecture,
( cons(sK2,nil) != A
| singletonP(A)
| ~ ssList(A) ),
inference(resolve,[status(thm)],[c_547,c_327]) ).
cnf(c_4350,negated_conjecture,
( sK0 != A
| singletonP(A)
| ~ ssList(A) ),
inference(paramod,[status(thm)],[c_546,c_6726]) ).
cnf(c_6727,negated_conjecture,
( sK0 != sK0
| singletonP(sK0) ),
inference(resolve,[status(thm)],[c_4350,c_201]) ).
cnf(c_6728,negated_conjecture,
singletonP(sK0),
inference(copy,[status(thm)],[c_6727]) ).
cnf(c_6721,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_550,c_6728]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWC254+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n003.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sat Sep 26 12:39:09 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 2886695 was started by sandbox2 on n003,
% 0.09/0.36 % Sat Sep 26 12:39:09 2026
% 0.09/0.36 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.09/0.39
% 0.09/0.39 % From the command line: assign(max_seconds, 300).
% 19.72/2.93
% 19.72/2.93 % given #500 (I,wt=47): 703 -ssList(A) | -ssItem(B) | -ssItem(C) | -ssList(D) | -ssList(E) | app(app(D,cons(B,E)),cons(C,D)) != A | C != B | ssList(f35(A)). [factor(363,d,f)].
% 19.72/2.93
% 19.72/2.93 % given #1000 (I,wt=60): 1228 -ssList(A) | -ssItem(B) | -ssList(C) | -ssList(D) | app(app(C,cons(B,C)),cons(B,D)) != A | app(app(f35(A),cons(f33(A),f36(A))),cons(f34(A),f37(A))) = A. [factor(722,c,d)].
% 19.72/2.93
% 19.72/2.93 % SZS status Theorem for theBenchmark
% 19.72/2.93
% 19.72/2.93 % Proof 1 at 2.27 (+ 0.22) seconds.
% 19.72/2.93 % Length of proof is 16.
% 19.72/2.93 % Level of proof is 4.
% 19.72/2.93 % Maximum clause weight is 21.000.
% 19.72/2.93 % Given clauses 1463.
% 19.72/2.93
% 19.72/2.93 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------