%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWC027+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 : n011.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 08:56:35 AM UTC 2026
% Result : Theorem 31.02s 9.34s
% Output : CNFRefutation 31.02s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 5
% Syntax : Number of formulae : 57 ( 13 unt; 0 def)
% Number of atoms : 206 ( 113 equ)
% Maximal formula atoms : 32 ( 3 avg)
% Number of connectives : 210 ( 61 ~; 84 |; 52 &)
% ( 1 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 6 con; 0-2 aty)
% Number of variables : 29 ( 0 sgn 16 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(ax4,axiom,
! [U] :
( ssList(U)
=> ( singletonP(U)
<=> ? [V] :
( cons(V,nil) = U
& ssItem(V) ) ) ),
file('theBenchmark.p',ax4) ).
fof(ax38,axiom,
! [U] :
( ssItem(U)
=> ~ memberP(nil,U) ),
file('theBenchmark.p',ax38) ).
fof(co1,conjecture,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ! [X] :
( ssList(X)
=> ( ( ( nil = V
| nil != U )
& ( nil = U
| nil != V ) )
| ( ( nil != W
| nil != X )
& ! [Y] :
( ssItem(Y)
=> ( ? [Z] :
( leq(Y,Z)
& memberP(X,Z)
& Y != Z
& ssItem(Z) )
| ~ memberP(X,Y)
| cons(Y,nil) != W ) ) )
| 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)
=> ( ( ( nil = V
| nil != U )
& ( nil = U
| nil != V ) )
| ( ( nil != W
| nil != X )
& ! [Y] :
( ssItem(Y)
=> ( ? [Z] :
( leq(Y,Z)
& memberP(X,Z)
& Y != Z
& ssItem(Z) )
| ~ memberP(X,Y)
| cons(Y,nil) != W ) ) )
| U != W
| V != X ) ) ) ) ),
inference(assume_negation,[status(cth)],[co1]) ).
cnf(c_203,plain,
( cons(B,nil) != A
| ~ ssItem(B)
| singletonP(A)
| ~ ssList(A) ),
inference(clausify,[status(thm)],[ax4]) ).
fof(ax17,axiom,
ssList(nil),
file('theBenchmark.p',ax17) ).
cnf(c_231,plain,
ssList(nil),
inference(clausify,[status(thm)],[ax17]) ).
cnf(c_261,plain,
( ~ memberP(nil,A)
| ~ ssItem(A) ),
inference(clausify,[status(thm)],[ax38]) ).
fof(ax39,axiom,
~ singletonP(nil),
file('theBenchmark.p',ax39) ).
cnf(c_262,plain,
~ singletonP(nil),
inference(clausify,[status(thm)],[ax39]) ).
fof(nnf_87,plain,
? [U] :
( ? [V] :
( ? [W] :
( ? [X] :
( ( ( nil != V
& nil = U )
| ( nil != U
& nil = V ) )
& ( ( nil = W
& nil = X )
| ? [Y] :
( ! [Z] :
( ~ leq(Y,Z)
| ~ memberP(X,Z)
| Z = Y
| ~ ssItem(Z) )
& memberP(X,Y)
& cons(Y,nil) = W
& 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,
( ( ( nil != sK1
& nil = sK3 )
| ( nil != sK3
& nil = sK1 ) )
& ( ( nil = sK2
& nil = sK0 )
| ( ! [Z] :
( ~ leq(sK4,Z)
| ~ memberP(sK0,Z)
| Z = sK4
| ~ ssItem(Z) )
& memberP(sK0,sK4)
& cons(sK4,nil) = sK2
& ssItem(sK4) ) )
& sK2 = sK3
& sK0 = sK1
& ssList(sK0)
& ssList(sK2)
& ssList(sK1)
& ssList(sK3) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3,sK1,sK2,sK0,sK4]),skolemize(U,sK3),skolemize(V,sK1),skolemize(W,sK2),skolemize(X,sK0),skolemize(Y,sK4)],[nnf_87]) ).
fof(sk_co1_neg,plain,
( ( nil != sK1
| nil != sK3 )
& ( nil = sK3
| nil = sK1 )
& ! [VAR_0] :
( nil = sK2
| ~ leq(sK4,VAR_0)
| ~ memberP(sK0,VAR_0)
| VAR_0 = sK4
| ~ ssItem(VAR_0) )
& ! [VAR_0] :
( nil = sK0
| ~ leq(sK4,VAR_0)
| ~ memberP(sK0,VAR_0)
| VAR_0 = sK4
| ~ ssItem(VAR_0) )
& ( nil = sK2
| memberP(sK0,sK4) )
& ( nil = sK0
| memberP(sK0,sK4) )
& ( nil = sK2
| cons(sK4,nil) = sK2 )
& ( nil = sK0
| cons(sK4,nil) = sK2 )
& ( nil = sK2
| ssItem(sK4) )
& ( nil = sK0
| ssItem(sK4) )
& sK2 = sK3
& sK0 = sK1
& ssList(sK0)
& ssList(sK2)
& ssList(sK1)
& ssList(sK3) ),
inference(cnf_transformation,[status(thm)],[sk_co1_neg_sk]) ).
cnf(c_331,negated_conjecture,
sK0 = sK1,
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_332,negated_conjecture,
sK2 = sK3,
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_333,negated_conjecture,
( nil = sK0
| ssItem(sK4) ),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_6540,negated_conjecture,
( nil = sK1
| ssItem(sK4) ),
inference(paramod,[status(thm)],[c_331,c_333]) ).
cnf(c_334,negated_conjecture,
( sK1 = nil
| ssItem(sK4) ),
inference(copy,[status(thm)],[c_6540]) ).
cnf(c_335,negated_conjecture,
( nil = sK2
| ssItem(sK4) ),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_6541,negated_conjecture,
( nil = sK3
| ssItem(sK4) ),
inference(paramod,[status(thm)],[c_332,c_335]) ).
cnf(c_336,negated_conjecture,
( sK3 = nil
| ssItem(sK4) ),
inference(copy,[status(thm)],[c_6541]) ).
cnf(c_337,negated_conjecture,
( nil = sK0
| cons(sK4,nil) = sK2 ),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_6542,negated_conjecture,
( nil = sK0
| cons(sK4,nil) = sK3 ),
inference(paramod,[status(thm)],[c_332,c_337]) ).
cnf(c_6543,negated_conjecture,
( nil = sK1
| cons(sK4,nil) = sK3 ),
inference(paramod,[status(thm)],[c_331,c_6542]) ).
cnf(c_338,negated_conjecture,
( sK1 = nil
| cons(sK4,nil) = sK3 ),
inference(copy,[status(thm)],[c_6543]) ).
cnf(c_341,negated_conjecture,
( nil = sK0
| memberP(sK0,sK4) ),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_6544,negated_conjecture,
( nil = sK0
| memberP(sK1,sK4) ),
inference(paramod,[status(thm)],[c_331,c_341]) ).
cnf(c_6545,negated_conjecture,
( nil = sK1
| memberP(sK1,sK4) ),
inference(paramod,[status(thm)],[c_331,c_6544]) ).
cnf(c_342,negated_conjecture,
( sK1 = nil
| memberP(sK1,sK4) ),
inference(copy,[status(thm)],[c_6545]) ).
cnf(c_343,negated_conjecture,
( nil = sK2
| memberP(sK0,sK4) ),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_6546,negated_conjecture,
( nil = sK2
| memberP(sK1,sK4) ),
inference(paramod,[status(thm)],[c_331,c_343]) ).
cnf(c_6547,negated_conjecture,
( nil = sK3
| memberP(sK1,sK4) ),
inference(paramod,[status(thm)],[c_332,c_6546]) ).
cnf(c_344,negated_conjecture,
( sK3 = nil
| memberP(sK1,sK4) ),
inference(copy,[status(thm)],[c_6547]) ).
cnf(c_349,negated_conjecture,
( nil = sK3
| nil = sK1 ),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_6548,negated_conjecture,
( nil = sK3
| sK1 = nil ),
inference(copy,[status(thm)],[c_349]) ).
cnf(c_350,negated_conjecture,
( sK3 = nil
| sK1 = nil ),
inference(copy,[status(thm)],[c_6548]) ).
cnf(c_351,negated_conjecture,
( nil != sK1
| nil != sK3 ),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_6549,negated_conjecture,
( nil != sK1
| sK3 != nil ),
inference(copy,[status(thm)],[c_351]) ).
cnf(c_352,negated_conjecture,
( sK1 != nil
| sK3 != nil ),
inference(copy,[status(thm)],[c_6549]) ).
cnf(c_6550,plain,
( cons(A,nil) != nil
| ~ ssItem(A)
| singletonP(nil) ),
inference(resolve,[status(thm)],[c_231,c_203]) ).
cnf(c_1708,plain,
( cons(A,nil) != nil
| ~ ssItem(A) ),
inference(resolve,[status(thm)],[c_262,c_6550]) ).
cnf(c_6551,plain,
( sK1 = nil
| cons(sK4,nil) = nil
| sK1 = nil ),
inference(paramod,[status(thm)],[c_350,c_338]) ).
cnf(c_2740,plain,
( cons(sK4,nil) = nil
| sK1 = nil ),
inference(copy,[status(thm)],[c_6551]) ).
cnf(c_6552,plain,
( sK3 = nil
| memberP(nil,sK4)
| sK3 = nil ),
inference(paramod,[status(thm)],[c_350,c_344]) ).
cnf(c_2741,plain,
( memberP(nil,sK4)
| sK3 = nil ),
inference(copy,[status(thm)],[c_6552]) ).
cnf(c_2748,plain,
( ssItem(sK4)
| sK1 != nil ),
inference(resolve,[status(thm)],[c_352,c_336]) ).
cnf(c_2749,plain,
( memberP(sK1,sK4)
| sK3 != nil ),
inference(resolve,[status(thm)],[c_352,c_342]) ).
cnf(c_6553,negated_conjecture,
( ssItem(sK4)
| ssItem(sK4) ),
inference(resolve,[status(thm)],[c_2748,c_334]) ).
cnf(c_5737,negated_conjecture,
ssItem(sK4),
inference(copy,[status(thm)],[c_6553]) ).
cnf(c_6234,plain,
cons(sK4,nil) != nil,
inference(resolve,[status(thm)],[c_5737,c_1708]) ).
cnf(c_6434,plain,
~ memberP(nil,sK4),
inference(resolve,[status(thm)],[c_5737,c_261]) ).
cnf(c_6475,plain,
sK1 = nil,
inference(resolve,[status(thm)],[c_6234,c_2740]) ).
cnf(c_6533,plain,
sK3 = nil,
inference(resolve,[status(thm)],[c_6434,c_2741]) ).
cnf(c_6554,plain,
( memberP(sK1,sK4)
| nil != nil ),
inference(paramod,[status(thm)],[c_6533,c_2749]) ).
cnf(c_6555,plain,
( memberP(nil,sK4)
| nil != nil ),
inference(paramod,[status(thm)],[c_6475,c_6554]) ).
cnf(c_6556,plain,
memberP(nil,sK4),
inference(copy,[status(thm)],[c_6555]) ).
cnf(c_6539,plain,
$false,
inference(resolve,[status(thm)],[c_6434,c_6556]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC027+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/5.38 % Computer : n011.cluster.edu
% 0.10/5.38 % Model : x86_64 x86_64
% 0.10/5.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/5.38 % Memory : 8046.5625MB
% 0.10/5.38 % OS : Linux 6.8.0-71-generic
% 0.10/5.38 % CPULimit : 300
% 0.10/5.38 % WCLimit : 300
% 0.10/5.38 % DateTime : Sat Sep 26 12:05:35 UTC 2026
% 0.10/5.38 % CPUTime :
% 0.10/5.38 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/5.38 % Process 454294 was started by sandbox2 on n011,
% 0.10/5.38 % Sat Sep 26 12:05:35 2026
% 0.10/5.38 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.14/5.41
% 0.14/5.41 % From the command line: assign(max_seconds, 300).
% 31.02/9.34
% 31.02/9.34 % given #500 (I,wt=37): 704 -ssList(A) | ssItem(f34(A)) | -ssItem(B) | -ssItem(C) | -ssList(D) | -ssList(E) | app(app(D,cons(B,E)),cons(C,E)) != A | C != B. [factor(375,f,g)].
% 31.02/9.34
% 31.02/9.34 % given #1000 (I,wt=32): 1224 -ssList(A) | ssList(f37(A)) | -ssItem(B) | -ssList(C) | -ssList(D) | app(app(C,cons(B,D)),cons(B,D)) != A. [factor(722,e,f)].
% 31.02/9.34
% 31.02/9.34 % SZS status Theorem for theBenchmark
% 31.02/9.34
% 31.02/9.34 % Proof 1 at 3.18 (+ 0.70) seconds.
% 31.02/9.34 % Length of proof is 34.
% 31.02/9.34 % Level of proof is 7.
% 31.02/9.34 % Maximum clause weight is 15.000.
% 31.02/9.34 % Given clauses 1446.
% 31.02/9.34
% 31.02/9.34 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------