%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWC010+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 : 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 08:56:31 AM UTC 2026
% Result : Theorem 18.48s 2.86s
% Output : CNFRefutation 18.48s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 1
% Syntax : Number of formulae : 34 ( 10 unt; 0 def)
% Number of atoms : 184 ( 53 equ)
% Maximal formula atoms : 28 ( 5 avg)
% Number of connectives : 241 ( 91 ~; 79 |; 57 &)
% ( 0 <=>; 14 =>; 0 <=; 0 <~>)
% Maximal formula depth : 27 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 8 con; 0-2 aty)
% Number of variables : 50 ( 0 sgn 26 !; 15 ?)
% 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)
=> ( ? [X5] :
( geq(X5,X2)
& memberP(X,X5)
& X2 != X5
& ssItem(X5) )
| app(X3,X4) != W
| app(app(X3,cons(X2,nil)),X4) != X ) ) ) )
| ? [Y] :
( ? [Z] :
( ? [X1] :
( app(Z,X1) = 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)
=> ( ? [X5] :
( geq(X5,X2)
& memberP(X,X5)
& X2 != X5
& ssItem(X5) )
| app(X3,X4) != W
| app(app(X3,cons(X2,nil)),X4) != X ) ) ) )
| ? [Y] :
( ? [Z] :
( ? [X1] :
( app(Z,X1) = 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] :
( ! [X5] :
( ~ geq(X5,X2)
| ~ memberP(X,X5)
| X5 = X2
| ~ ssItem(X5) )
& app(X3,X4) = W
& app(app(X3,cons(X2,nil)),X4) = X
& ssList(X4) )
& ssList(X3) )
& ssItem(X2) )
& ! [Y] :
( ! [Z] :
( ! [X1] :
( app(Z,X1) != 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(sK3,nil)
& neq(sK5,nil) )
| ( ! [X5] :
( ~ geq(X5,sK4)
| ~ memberP(sK3,X5)
| X5 = sK4
| ~ ssItem(X5) )
& app(sK0,sK1) = sK2
& app(app(sK0,cons(sK4,nil)),sK1) = sK3
& ssList(sK1)
& ssList(sK0)
& ssItem(sK4)
& ! [Y] :
( ! [Z] :
( ! [X1] :
( app(Z,X1) != sK6
| app(app(Z,cons(Y,nil)),X1) != sK5
| ~ ssList(X1) )
| ~ ssList(Z) )
| ~ ssItem(Y) )
& neq(sK5,nil) ) )
& sK2 = sK6
& sK3 = sK5
& ssList(sK3)
& ssList(sK2)
& ssList(sK5)
& ssList(sK6) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6,sK5,sK2,sK3,sK4,sK0,sK1]),skolemize(U,sK6),skolemize(V,sK5),skolemize(W,sK2),skolemize(X,sK3),skolemize(X2,sK4),skolemize(X3,sK0),skolemize(X4,sK1)],[nnf_87]) ).
fof(sk_co1_neg,plain,
( ! [VAR_0] :
( ~ neq(sK3,nil)
| ~ geq(VAR_0,sK4)
| ~ memberP(sK3,VAR_0)
| VAR_0 = sK4
| ~ ssItem(VAR_0) )
& ( ~ neq(sK3,nil)
| app(sK0,sK1) = sK2 )
& ( ~ neq(sK3,nil)
| app(app(sK0,cons(sK4,nil)),sK1) = sK3 )
& ( ~ neq(sK3,nil)
| ssList(sK1) )
& ( ~ neq(sK3,nil)
| ssList(sK0) )
& ( ~ neq(sK3,nil)
| ssItem(sK4) )
& ! [VAR_0,VAR_1,VAR_2] :
( ~ neq(sK3,nil)
| app(VAR_1,VAR_2) != sK6
| app(app(VAR_1,cons(VAR_0,nil)),VAR_2) != sK5
| ~ ssList(VAR_2)
| ~ ssList(VAR_1)
| ~ ssItem(VAR_0) )
& neq(sK5,nil)
& sK2 = sK6
& sK3 = sK5
& ssList(sK3)
& ssList(sK2)
& ssList(sK5)
& ssList(sK6) ),
inference(cnf_transformation,[status(thm)],[sk_co1_neg_sk]) ).
cnf(c_192,negated_conjecture,
( ~ neq(sK3,nil)
| app(sK0,sK1) = sK2 ),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_193,negated_conjecture,
( ~ neq(sK3,nil)
| app(app(sK0,cons(sK4,nil)),sK1) = sK3 ),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_194,negated_conjecture,
( ~ neq(sK3,nil)
| ssList(sK1) ),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_195,negated_conjecture,
( ~ neq(sK3,nil)
| ssList(sK0) ),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_196,negated_conjecture,
( ~ neq(sK3,nil)
| ssItem(sK4) ),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_197,negated_conjecture,
( ~ neq(sK3,nil)
| app(B,C) != 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_198,negated_conjecture,
neq(sK5,nil),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_199,negated_conjecture,
sK2 = sK6,
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_200,negated_conjecture,
sK3 = sK5,
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_2989,negated_conjecture,
( ~ neq(sK3,nil)
| app(sK0,sK1) = sK6 ),
inference(paramod,[status(thm)],[c_199,c_192]) ).
cnf(c_2990,negated_conjecture,
( ~ neq(sK5,nil)
| app(sK0,sK1) = sK6 ),
inference(paramod,[status(thm)],[c_200,c_2989]) ).
cnf(c_550,negated_conjecture,
app(sK0,sK1) = sK6,
inference(resolve,[status(thm)],[c_198,c_2990]) ).
cnf(c_2991,negated_conjecture,
( ~ neq(sK5,nil)
| app(B,C) != sK6
| app(app(B,cons(A,nil)),C) != sK5
| ~ ssList(C)
| ~ ssList(B)
| ~ ssItem(A) ),
inference(paramod,[status(thm)],[c_200,c_197]) ).
cnf(c_551,negated_conjecture,
( app(B,C) != sK6
| app(app(B,cons(A,nil)),C) != sK5
| ~ ssList(C)
| ~ ssList(B)
| ~ ssItem(A) ),
inference(resolve,[status(thm)],[c_198,c_2991]) ).
cnf(c_2992,negated_conjecture,
( ~ neq(sK5,nil)
| ssItem(sK4) ),
inference(paramod,[status(thm)],[c_200,c_196]) ).
cnf(c_552,negated_conjecture,
ssItem(sK4),
inference(resolve,[status(thm)],[c_198,c_2992]) ).
cnf(c_2993,negated_conjecture,
( ~ neq(sK5,nil)
| ssList(sK0) ),
inference(paramod,[status(thm)],[c_200,c_195]) ).
cnf(c_553,negated_conjecture,
ssList(sK0),
inference(resolve,[status(thm)],[c_198,c_2993]) ).
cnf(c_2994,negated_conjecture,
( ~ neq(sK5,nil)
| ssList(sK1) ),
inference(paramod,[status(thm)],[c_200,c_194]) ).
cnf(c_554,negated_conjecture,
ssList(sK1),
inference(resolve,[status(thm)],[c_198,c_2994]) ).
cnf(c_2995,negated_conjecture,
( ~ neq(sK3,nil)
| app(app(sK0,cons(sK4,nil)),sK1) = sK5 ),
inference(paramod,[status(thm)],[c_200,c_193]) ).
cnf(c_2996,negated_conjecture,
( ~ neq(sK5,nil)
| app(app(sK0,cons(sK4,nil)),sK1) = sK5 ),
inference(paramod,[status(thm)],[c_200,c_2995]) ).
cnf(c_555,negated_conjecture,
app(app(sK0,cons(sK4,nil)),sK1) = sK5,
inference(resolve,[status(thm)],[c_198,c_2996]) ).
cnf(c_2997,negated_conjecture,
( app(sK0,sK1) != sK6
| ~ ssList(sK1)
| ~ ssList(sK0)
| ~ ssItem(sK4) ),
inference(resolve,[status(thm)],[c_555,c_551]) ).
cnf(c_2998,negated_conjecture,
( sK6 != sK6
| ~ ssList(sK1)
| ~ ssList(sK0)
| ~ ssItem(sK4) ),
inference(paramod,[status(thm)],[c_550,c_2997]) ).
cnf(c_2999,negated_conjecture,
( ~ ssList(sK1)
| ~ ssList(sK0)
| ~ ssItem(sK4) ),
inference(copy,[status(thm)],[c_2998]) ).
cnf(c_3000,negated_conjecture,
( ~ ssList(sK1)
| ~ ssList(sK0) ),
inference(resolve,[status(thm)],[c_552,c_2999]) ).
cnf(c_3001,negated_conjecture,
~ ssList(sK1),
inference(resolve,[status(thm)],[c_553,c_3000]) ).
cnf(c_2988,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_554,c_3001]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SWC010+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.20/0.46 % Computer : n016.cluster.edu
% 0.20/0.46 % Model : x86_64 x86_64
% 0.20/0.46 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.20/0.46 % Memory : 8046.5625MB
% 0.20/0.46 % OS : Linux 6.8.0-71-generic
% 0.20/0.46 % CPULimit : 300
% 0.20/0.46 % WCLimit : 300
% 0.20/0.46 % DateTime : Sat Sep 26 12:08:15 UTC 2026
% 0.20/0.46 % CPUTime :
% 0.20/0.47 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.20/0.47 % Process 819198 was started by sandbox2 on n016,
% 0.20/0.47 % Sat Sep 26 12:08:15 2026
% 0.20/0.47 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.20/0.48
% 0.20/0.48 % From the command line: assign(max_seconds, 300).
% 18.48/2.86
% 18.48/2.86 % SZS status Theorem for theBenchmark
% 18.48/2.86
% 18.48/2.86 % Proof 1 at 1.89 (+ 0.23) seconds.
% 18.48/2.86 % Length of proof is 17.
% 18.48/2.86 % Level of proof is 3.
% 18.48/2.86 % Maximum clause weight is 33.000.
% 18.48/2.86 % Given clauses 358.
% 18.48/2.86
% 18.48/2.86 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------