%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWC279+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 : n020.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 08:57:21 AM UTC 2026
% Result : Theorem 214.88s 34.00s
% Output : CNFRefutation 214.88s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 1
% Syntax : Number of formulae : 39 ( 11 unt; 0 def)
% Number of atoms : 227 ( 27 equ)
% Maximal formula atoms : 33 ( 5 avg)
% Number of connectives : 298 ( 110 ~; 110 |; 62 &)
% ( 0 <=>; 16 =>; 0 <=; 0 <~>)
% Maximal formula depth : 25 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 9 con; 0-2 aty)
% Number of variables : 72 ( 0 sgn 32 !; 16 ?)
% Comments :
%------------------------------------------------------------------------------
fof(co1,conjecture,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ! [X] :
( ssList(X)
=> ( ! [X3] :
( ssItem(X3)
=> ! [X4] :
( ssList(X4)
=> ! [X5] :
( ssList(X5)
=> ( ! [X6] :
( ssItem(X6)
=> ( ( leq(X3,X6)
| ~ memberP(X5,X6) )
& ( leq(X6,X3)
| ~ memberP(X4,X6) ) ) )
| app(app(X4,cons(X3,nil)),X5) != U ) ) ) )
| ? [Y] :
( ? [Z] :
( ? [X1] :
( ? [X2] :
( ( ( memberP(Z,X2)
& ~ leq(X2,Y) )
| ( memberP(X1,X2)
& ~ leq(Y,X2) ) )
& ssItem(X2) )
& app(app(Z,cons(Y,nil)),X1) = W
& ssList(X1) )
& ssList(Z) )
& ssItem(Y) )
| 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)
=> ( ! [X3] :
( ssItem(X3)
=> ! [X4] :
( ssList(X4)
=> ! [X5] :
( ssList(X5)
=> ( ! [X6] :
( ssItem(X6)
=> ( ( leq(X3,X6)
| ~ memberP(X5,X6) )
& ( leq(X6,X3)
| ~ memberP(X4,X6) ) ) )
| app(app(X4,cons(X3,nil)),X5) != U ) ) ) )
| ? [Y] :
( ? [Z] :
( ? [X1] :
( ? [X2] :
( ( ( memberP(Z,X2)
& ~ leq(X2,Y) )
| ( memberP(X1,X2)
& ~ leq(Y,X2) ) )
& ssItem(X2) )
& app(app(Z,cons(Y,nil)),X1) = W
& ssList(X1) )
& ssList(Z) )
& ssItem(Y) )
| U != W
| V != X ) ) ) ) ),
inference(assume_negation,[status(cth)],[co1]) ).
fof(nnf_87,plain,
? [U] :
( ? [V] :
( ? [W] :
( ? [X] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( ? [X6] :
( ( ( ~ leq(X3,X6)
& memberP(X5,X6) )
| ( ~ leq(X6,X3)
& memberP(X4,X6) ) )
& ssItem(X6) )
& app(app(X4,cons(X3,nil)),X5) = U
& ssList(X5) )
& ssList(X4) )
& ssItem(X3) )
& ! [Y] :
( ! [Z] :
( ! [X1] :
( ! [X2] :
( ( ( ~ memberP(Z,X2)
| leq(X2,Y) )
& ( ~ memberP(X1,X2)
| leq(Y,X2) ) )
| ~ ssItem(X2) )
| app(app(Z,cons(Y,nil)),X1) != W
| ~ ssList(X1) )
| ~ ssList(Z) )
| ~ ssItem(Y) )
& 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,
( ( ( ~ leq(sK2,sK5)
& memberP(sK4,sK5) )
| ( ~ leq(sK5,sK2)
& memberP(sK3,sK5) ) )
& ssItem(sK5)
& app(app(sK3,cons(sK2,nil)),sK4) = sK1
& ssList(sK4)
& ssList(sK3)
& ssItem(sK2)
& ! [Y] :
( ! [Z] :
( ! [X1] :
( ! [X2] :
( ( ( ~ memberP(Z,X2)
| leq(X2,Y) )
& ( ~ memberP(X1,X2)
| leq(Y,X2) ) )
| ~ ssItem(X2) )
| app(app(Z,cons(Y,nil)),X1) != sK0
| ~ ssList(X1) )
| ~ ssList(Z) )
| ~ ssItem(Y) )
& sK0 = sK1
& sK7 = sK6
& ssList(sK7)
& ssList(sK0)
& ssList(sK6)
& ssList(sK1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK6,sK0,sK7,sK2,sK3,sK4,sK5]),skolemize(U,sK1),skolemize(V,sK6),skolemize(W,sK0),skolemize(X,sK7),skolemize(X3,sK2),skolemize(X4,sK3),skolemize(X5,sK4),skolemize(X6,sK5)],[nnf_87]) ).
fof(sk_co1_neg,plain,
( ( ~ leq(sK2,sK5)
| ~ leq(sK5,sK2) )
& ( memberP(sK4,sK5)
| ~ leq(sK5,sK2) )
& ( ~ leq(sK2,sK5)
| memberP(sK3,sK5) )
& ( memberP(sK4,sK5)
| memberP(sK3,sK5) )
& ssItem(sK5)
& app(app(sK3,cons(sK2,nil)),sK4) = sK1
& ssList(sK4)
& ssList(sK3)
& ssItem(sK2)
& ! [VAR_0,VAR_1,VAR_2,VAR_3] :
( ~ memberP(VAR_1,VAR_3)
| leq(VAR_3,VAR_0)
| ~ ssItem(VAR_3)
| app(app(VAR_1,cons(VAR_0,nil)),VAR_2) != sK0
| ~ ssList(VAR_2)
| ~ ssList(VAR_1)
| ~ ssItem(VAR_0) )
& ! [VAR_0,VAR_1,VAR_2,VAR_3] :
( ~ memberP(VAR_2,VAR_3)
| leq(VAR_0,VAR_3)
| ~ ssItem(VAR_3)
| app(app(VAR_1,cons(VAR_0,nil)),VAR_2) != sK0
| ~ ssList(VAR_2)
| ~ ssList(VAR_1)
| ~ ssItem(VAR_0) )
& sK0 = sK1
& sK7 = sK6
& ssList(sK7)
& ssList(sK0)
& ssList(sK6)
& ssList(sK1) ),
inference(cnf_transformation,[status(thm)],[sk_co1_neg_sk]) ).
cnf(c_332,negated_conjecture,
sK0 = sK1,
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_333,negated_conjecture,
( ~ memberP(C,D)
| leq(A,D)
| ~ ssItem(D)
| app(app(B,cons(A,nil)),C) != sK0
| ~ ssList(C)
| ~ ssList(B)
| ~ ssItem(A) ),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_334,negated_conjecture,
( ~ memberP(C,D)
| leq(A,D)
| ~ ssItem(D)
| app(app(B,cons(A,nil)),C) != sK1
| ~ ssList(C)
| ~ ssList(B)
| ~ ssItem(A) ),
inference(paramod,[status(thm)],[c_332,c_333]) ).
cnf(c_335,negated_conjecture,
( ~ memberP(B,D)
| leq(D,A)
| ~ ssItem(D)
| app(app(B,cons(A,nil)),C) != sK0
| ~ ssList(C)
| ~ ssList(B)
| ~ ssItem(A) ),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_336,negated_conjecture,
( ~ memberP(B,D)
| leq(D,A)
| ~ ssItem(D)
| app(app(B,cons(A,nil)),C) != sK1
| ~ ssList(C)
| ~ ssList(B)
| ~ ssItem(A) ),
inference(paramod,[status(thm)],[c_332,c_335]) ).
cnf(c_337,negated_conjecture,
ssItem(sK2),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_338,negated_conjecture,
ssList(sK3),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_339,negated_conjecture,
ssList(sK4),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_340,negated_conjecture,
app(app(sK3,cons(sK2,nil)),sK4) = sK1,
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_341,negated_conjecture,
ssItem(sK5),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_342,negated_conjecture,
( memberP(sK4,sK5)
| memberP(sK3,sK5) ),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_343,negated_conjecture,
( ~ leq(sK2,sK5)
| memberP(sK3,sK5) ),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_344,negated_conjecture,
( memberP(sK4,sK5)
| ~ leq(sK5,sK2) ),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_345,negated_conjecture,
( ~ leq(sK2,sK5)
| ~ leq(sK5,sK2) ),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_3378,negated_conjecture,
( ~ memberP(sK3,A)
| leq(A,sK2)
| ~ ssItem(A)
| ~ ssList(sK4)
| ~ ssList(sK3)
| ~ ssItem(sK2) ),
inference(resolve,[status(thm)],[c_340,c_336]) ).
cnf(c_3379,negated_conjecture,
( ~ memberP(sK3,A)
| leq(A,sK2)
| ~ ssItem(A)
| ~ ssList(sK4)
| ~ ssList(sK3) ),
inference(resolve,[status(thm)],[c_337,c_3378]) ).
cnf(c_3380,negated_conjecture,
( ~ memberP(sK3,A)
| leq(A,sK2)
| ~ ssItem(A)
| ~ ssList(sK4) ),
inference(resolve,[status(thm)],[c_338,c_3379]) ).
cnf(c_2577,negated_conjecture,
( ~ memberP(sK3,A)
| leq(A,sK2)
| ~ ssItem(A) ),
inference(resolve,[status(thm)],[c_339,c_3380]) ).
cnf(c_3381,negated_conjecture,
( ~ memberP(sK4,A)
| leq(sK2,A)
| ~ ssItem(A)
| ~ ssList(sK4)
| ~ ssList(sK3)
| ~ ssItem(sK2) ),
inference(resolve,[status(thm)],[c_340,c_334]) ).
cnf(c_3382,negated_conjecture,
( ~ memberP(sK4,A)
| leq(sK2,A)
| ~ ssItem(A)
| ~ ssList(sK4)
| ~ ssList(sK3) ),
inference(resolve,[status(thm)],[c_337,c_3381]) ).
cnf(c_3383,negated_conjecture,
( ~ memberP(sK4,A)
| leq(sK2,A)
| ~ ssItem(A)
| ~ ssList(sK4) ),
inference(resolve,[status(thm)],[c_338,c_3382]) ).
cnf(c_2578,negated_conjecture,
( ~ memberP(sK4,A)
| leq(sK2,A)
| ~ ssItem(A) ),
inference(resolve,[status(thm)],[c_339,c_3383]) ).
cnf(c_3340,plain,
( ~ memberP(sK3,sK5)
| leq(sK5,sK2) ),
inference(resolve,[status(thm)],[c_2577,c_341]) ).
cnf(c_3343,plain,
( ~ memberP(sK4,sK5)
| leq(sK2,sK5) ),
inference(resolve,[status(thm)],[c_2578,c_341]) ).
cnf(c_3384,negated_conjecture,
( memberP(sK3,sK5)
| leq(sK2,sK5)
| ~ ssItem(sK5) ),
inference(resolve,[status(thm)],[c_2578,c_342]) ).
cnf(c_3346,negated_conjecture,
( memberP(sK3,sK5)
| leq(sK2,sK5) ),
inference(resolve,[status(thm)],[c_341,c_3384]) ).
cnf(c_3350,plain,
( leq(sK5,sK2)
| leq(sK2,sK5) ),
inference(resolve,[status(thm)],[c_3346,c_3340]) ).
cnf(c_3358,plain,
( memberP(sK4,sK5)
| leq(sK2,sK5) ),
inference(resolve,[status(thm)],[c_3350,c_344]) ).
cnf(c_3385,plain,
( leq(sK2,sK5)
| leq(sK2,sK5) ),
inference(resolve,[status(thm)],[c_3358,c_3343]) ).
cnf(c_3371,plain,
leq(sK2,sK5),
inference(copy,[status(thm)],[c_3385]) ).
cnf(c_3374,negated_conjecture,
~ leq(sK5,sK2),
inference(resolve,[status(thm)],[c_3371,c_345]) ).
cnf(c_3375,negated_conjecture,
memberP(sK3,sK5),
inference(resolve,[status(thm)],[c_3371,c_343]) ).
cnf(c_3386,negated_conjecture,
~ memberP(sK3,sK5),
inference(resolve,[status(thm)],[c_3374,c_3340]) ).
cnf(c_3377,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_3375,c_3386]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC279+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/5.39 % Computer : n020.cluster.edu
% 0.11/5.39 % Model : x86_64 x86_64
% 0.11/5.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/5.39 % Memory : 8046.5625MB
% 0.11/5.39 % OS : Linux 6.8.0-71-generic
% 0.11/5.39 % CPULimit : 300
% 0.11/5.39 % WCLimit : 300
% 0.11/5.39 % DateTime : Sat Sep 26 12:41:54 UTC 2026
% 0.11/5.39 % CPUTime :
% 0.11/5.39 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.11/5.39 % Process 1589856 was started by sandbox2 on n020,
% 0.11/5.39 % Sat Sep 26 12:41:54 2026
% 0.11/5.39 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.15/5.42
% 0.15/5.42 % From the command line: assign(max_seconds, 300).
% 214.88/34.00
% 214.88/34.00 % given #500 (I,wt=46): 696 -ssList(A) | ssItem(f34(A)) | -ssItem(B) | -ssList(C) | -ssList(D) | -ssList(E) | app(app(C,cons(B,D)),cons(B,E)) != A. [factor(368,c,d),xx(h)].
% 214.88/34.00
% 214.88/34.00 % given #1000 (I,wt=47): 1216 -ssList(A) | ssList(f37(A)) | -ssItem(B) | -ssItem(C) | -ssList(D) | app(app(D,cons(B,D)),cons(C,A)) != A | C != B. [factor(716,e,f)].
% 214.88/34.00
% 214.88/34.00 % given #1500 (F,wt=13): 2205 -ssItem(A) | -lt(c7,A) | c7 != A. [resolve(337,a,323,a),flip(c)].
% 214.88/34.00
% 214.88/34.00 % SZS status Theorem for theBenchmark
% 214.88/34.00
% 214.88/34.00 % Proof 1 at 3.67 (+ 0.65) seconds.
% 214.88/34.00 % Length of proof is 26.
% 214.88/34.00 % Level of proof is 9.
% 214.88/34.00 % Maximum clause weight is 45.000.
% 214.88/34.00 % Given clauses 1689.
% 214.88/34.00
% 214.88/34.00 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------