%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWC387+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 : n012.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 08:57:40 AM UTC 2026
% Result : Theorem 14.86s 2.28s
% Output : CNFRefutation 14.86s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 3
% Syntax : Number of formulae : 53 ( 14 unt; 0 def)
% Number of atoms : 181 ( 80 equ)
% Maximal formula atoms : 19 ( 3 avg)
% Number of connectives : 207 ( 79 ~; 72 |; 43 &)
% ( 1 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 6 con; 0-2 aty)
% Number of variables : 31 ( 0 sgn 15 !; 7 ?)
% Comments :
%------------------------------------------------------------------------------
fof(ax15,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ( neq(U,V)
<=> U != V ) ) ),
file('theBenchmark.p',ax15) ).
fof(co1,conjecture,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ! [X] :
( ssList(X)
=> ( ( neq(X,nil)
& ! [Z] :
( ssItem(Z)
=> ( ~ memberP(X,Z)
| cons(Z,nil) != W ) ) )
| ( nil = U
& nil = V )
| ( nil = X
& nil != W )
| ? [Y] :
( memberP(V,Y)
& cons(Y,nil) = U
& 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)
=> ( ( neq(X,nil)
& ! [Z] :
( ssItem(Z)
=> ( ~ memberP(X,Z)
| cons(Z,nil) != W ) ) )
| ( nil = U
& nil = V )
| ( nil = X
& nil != W )
| ? [Y] :
( memberP(V,Y)
& cons(Y,nil) = U
& ssItem(Y) )
| U != W
| V != X ) ) ) ) ),
inference(assume_negation,[status(cth)],[co1]) ).
fof(nnf_87,plain,
? [U] :
( ? [V] :
( ? [W] :
( ? [X] :
( ( ~ neq(X,nil)
| ? [Z] :
( memberP(X,Z)
& cons(Z,nil) = W
& ssItem(Z) ) )
& ( nil != U
| nil != V )
& ( nil != X
| nil = W )
& ! [Y] :
( ~ memberP(V,Y)
| cons(Y,nil) != U
| ~ 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,
( ( ~ neq(sK0,nil)
| ( memberP(sK0,sK1)
& cons(sK1,nil) = sK2
& ssItem(sK1) ) )
& ( nil != sK4
| nil != sK3 )
& ( nil != sK0
| nil = sK2 )
& ! [Y] :
( ~ memberP(sK3,Y)
| cons(Y,nil) != sK4
| ~ ssItem(Y) )
& sK2 = sK4
& sK0 = sK3
& ssList(sK0)
& ssList(sK2)
& ssList(sK3)
& ssList(sK4) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4,sK3,sK2,sK0,sK1]),skolemize(U,sK4),skolemize(V,sK3),skolemize(W,sK2),skolemize(X,sK0),skolemize(Z,sK1)],[nnf_87]) ).
fof(sk_co1_neg,plain,
( ( ~ neq(sK0,nil)
| memberP(sK0,sK1) )
& ( ~ neq(sK0,nil)
| cons(sK1,nil) = sK2 )
& ( ~ neq(sK0,nil)
| ssItem(sK1) )
& ( nil != sK4
| nil != sK3 )
& ( nil != sK0
| nil = sK2 )
& ! [VAR_0] :
( ~ memberP(sK3,VAR_0)
| cons(VAR_0,nil) != sK4
| ~ ssItem(VAR_0) )
& sK2 = sK4
& sK0 = sK3
& ssList(sK0)
& ssList(sK2)
& ssList(sK3)
& ssList(sK4) ),
inference(cnf_transformation,[status(thm)],[sk_co1_neg_sk]) ).
cnf(c_190,negated_conjecture,
( ~ neq(sK0,nil)
| memberP(sK0,sK1) ),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_191,negated_conjecture,
( ~ neq(sK0,nil)
| cons(sK1,nil) = sK2 ),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_192,negated_conjecture,
( ~ neq(sK0,nil)
| ssItem(sK1) ),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_193,negated_conjecture,
( nil != sK4
| nil != sK3 ),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_6486,negated_conjecture,
( nil != sK4
| sK3 != nil ),
inference(copy,[status(thm)],[c_193]) ).
cnf(c_194,negated_conjecture,
( sK4 != nil
| sK3 != nil ),
inference(copy,[status(thm)],[c_6486]) ).
cnf(c_195,negated_conjecture,
( nil != sK0
| nil = sK2 ),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_6487,negated_conjecture,
( nil != sK0
| sK2 = nil ),
inference(copy,[status(thm)],[c_195]) ).
cnf(c_196,negated_conjecture,
( sK0 != nil
| sK2 = nil ),
inference(copy,[status(thm)],[c_6487]) ).
cnf(c_197,negated_conjecture,
( ~ memberP(sK3,A)
| cons(A,nil) != sK4
| ~ ssItem(A) ),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_198,negated_conjecture,
sK2 = sK4,
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_199,negated_conjecture,
sK0 = sK3,
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_200,negated_conjecture,
ssList(sK0),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_201,negated_conjecture,
ssList(sK3),
inference(paramod,[status(thm)],[c_199,c_200]) ).
fof(ax17,axiom,
ssList(nil),
file('theBenchmark.p',ax17) ).
cnf(c_299,plain,
ssList(nil),
inference(clausify,[status(thm)],[ax17]) ).
cnf(c_301,plain,
( B = A
| neq(A,B)
| ~ ssList(B)
| ~ ssList(A) ),
inference(clausify,[status(thm)],[ax15]) ).
cnf(c_302,plain,
( B != A
| ~ neq(A,B)
| ~ ssList(B)
| ~ ssList(A) ),
inference(clausify,[status(thm)],[ax15]) ).
cnf(c_6488,negated_conjecture,
( sK0 != nil
| sK4 = nil ),
inference(paramod,[status(thm)],[c_198,c_196]) ).
cnf(c_548,negated_conjecture,
( sK3 != nil
| sK4 = nil ),
inference(paramod,[status(thm)],[c_199,c_6488]) ).
cnf(c_6489,negated_conjecture,
( ~ neq(sK0,nil)
| cons(sK1,nil) = sK4 ),
inference(paramod,[status(thm)],[c_198,c_191]) ).
cnf(c_549,negated_conjecture,
( ~ neq(sK3,nil)
| cons(sK1,nil) = sK4 ),
inference(paramod,[status(thm)],[c_199,c_6489]) ).
cnf(c_550,negated_conjecture,
( ~ neq(sK3,nil)
| ssItem(sK1) ),
inference(paramod,[status(thm)],[c_199,c_192]) ).
cnf(c_6490,negated_conjecture,
( ~ neq(sK0,nil)
| memberP(sK3,sK1) ),
inference(paramod,[status(thm)],[c_199,c_190]) ).
cnf(c_551,negated_conjecture,
( ~ neq(sK3,nil)
| memberP(sK3,sK1) ),
inference(paramod,[status(thm)],[c_199,c_6490]) ).
cnf(c_6491,plain,
( A = nil
| neq(nil,A)
| ~ ssList(A) ),
inference(resolve,[status(thm)],[c_301,c_299]) ).
cnf(c_1764,plain,
( nil = A
| neq(nil,A)
| ~ ssList(A) ),
inference(copy,[status(thm)],[c_6491]) ).
cnf(c_6492,negated_conjecture,
( A = sK3
| neq(sK3,A)
| ~ ssList(A) ),
inference(resolve,[status(thm)],[c_301,c_201]) ).
cnf(c_1766,negated_conjecture,
( sK3 = A
| neq(sK3,A)
| ~ ssList(A) ),
inference(copy,[status(thm)],[c_6492]) ).
cnf(c_6493,negated_conjecture,
( nil = sK3
| neq(nil,sK3) ),
inference(resolve,[status(thm)],[c_1764,c_201]) ).
cnf(c_5018,negated_conjecture,
( sK3 = nil
| neq(nil,sK3) ),
inference(copy,[status(thm)],[c_6493]) ).
cnf(c_5025,plain,
( sK4 = nil
| neq(nil,sK3) ),
inference(resolve,[status(thm)],[c_5018,c_548]) ).
cnf(c_5026,plain,
( sK4 != nil
| neq(nil,sK3) ),
inference(resolve,[status(thm)],[c_5018,c_194]) ).
cnf(c_6494,plain,
( neq(nil,sK3)
| neq(nil,sK3) ),
inference(resolve,[status(thm)],[c_5026,c_5025]) ).
cnf(c_5082,plain,
neq(nil,sK3),
inference(copy,[status(thm)],[c_6494]) ).
cnf(c_6495,plain,
( sK3 != nil
| ~ ssList(sK3)
| ~ ssList(nil) ),
inference(resolve,[status(thm)],[c_5082,c_302]) ).
cnf(c_6496,plain,
( sK3 != nil
| ~ ssList(sK3) ),
inference(resolve,[status(thm)],[c_299,c_6495]) ).
cnf(c_5096,negated_conjecture,
sK3 != nil,
inference(resolve,[status(thm)],[c_201,c_6496]) ).
cnf(c_6497,plain,
( sK3 = nil
| neq(sK3,nil) ),
inference(resolve,[status(thm)],[c_1766,c_299]) ).
cnf(c_5164,plain,
neq(sK3,nil),
inference(resolve,[status(thm)],[c_5096,c_6497]) ).
cnf(c_5166,negated_conjecture,
memberP(sK3,sK1),
inference(resolve,[status(thm)],[c_5164,c_551]) ).
cnf(c_5167,negated_conjecture,
ssItem(sK1),
inference(resolve,[status(thm)],[c_5164,c_550]) ).
cnf(c_5168,negated_conjecture,
cons(sK1,nil) = sK4,
inference(resolve,[status(thm)],[c_5164,c_549]) ).
cnf(c_6498,negated_conjecture,
( cons(sK1,nil) != sK4
| ~ ssItem(sK1) ),
inference(resolve,[status(thm)],[c_5166,c_197]) ).
cnf(c_6499,negated_conjecture,
( sK4 != sK4
| ~ ssItem(sK1) ),
inference(paramod,[status(thm)],[c_5168,c_6498]) ).
cnf(c_6500,negated_conjecture,
~ ssItem(sK1),
inference(copy,[status(thm)],[c_6499]) ).
cnf(c_6485,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_5167,c_6500]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SWC387+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.02 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.04/0.29 % Computer : n012.cluster.edu
% 0.04/0.29 % Model : x86_64 x86_64
% 0.04/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.04/0.29 % Memory : 8046.5625MB
% 0.04/0.29 % OS : Linux 6.8.0-71-generic
% 0.04/0.29 % CPULimit : 300
% 0.04/0.29 % WCLimit : 300
% 0.04/0.29 % DateTime : Sat Sep 26 12:56:19 UTC 2026
% 0.04/0.30 % CPUTime :
% 0.04/0.30 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.04/0.30 % Process 652891 was started by sandbox on n012,
% 0.04/0.30 % Sat Sep 26 12:56:19 2026
% 0.04/0.30 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.04/0.31
% 0.04/0.31 % From the command line: assign(max_seconds, 300).
% 14.86/2.28
% 14.86/2.28 % given #500 (I,wt=47): 704 -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(365,d,f)].
% 14.86/2.28
% 14.86/2.28 % given #1000 (I,wt=60): 1229 -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(723,c,d)].
% 14.86/2.28
% 14.86/2.28 % given #1500 (T,wt=7): 6414 strictorderedP(c3). [resolve(5167,a,237,a),rewrite([5168(3)])].
% 14.86/2.28
% 14.86/2.28 % SZS status Theorem for theBenchmark
% 14.86/2.28
% 14.86/2.28 % Proof 1 at 1.75 (+ 0.19) seconds.
% 14.86/2.28 % Length of proof is 33.
% 14.86/2.28 % Level of proof is 9.
% 14.86/2.28 % Maximum clause weight is 20.000.
% 14.86/2.28 % Given clauses 1502.
% 14.86/2.28
% 14.86/2.28 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------