%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWC386+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 : n002.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 51.00s 7.16s
% Output : CNFRefutation 51.00s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 8
% Syntax : Number of formulae : 91 ( 18 unt; 0 def)
% Number of atoms : 298 ( 139 equ)
% Maximal formula atoms : 30 ( 3 avg)
% Number of connectives : 320 ( 113 ~; 138 |; 48 &)
% ( 3 <=>; 18 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 6 con; 0-2 aty)
% Number of variables : 45 ( 0 sgn 22 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(ax4,axiom,
! [U] :
( ssList(U)
=> ( singletonP(U)
<=> ? [V] :
( cons(V,nil) = U
& ssItem(V) ) ) ),
file('theBenchmark.p',ax4) ).
fof(ax15,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ( neq(U,V)
<=> U != V ) ) ),
file('theBenchmark.p',ax15) ).
fof(ax28,axiom,
! [U] :
( ssList(U)
=> app(nil,U) = U ),
file('theBenchmark.p',ax28) ).
fof(ax36,axiom,
! [U] :
( ssItem(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ( memberP(app(V,W),U)
<=> ( memberP(W,U)
| memberP(V,U) ) ) ) ) ),
file('theBenchmark.p',ax36) ).
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)
=> ( ( ( ? [Z] :
( memberP(V,Z)
& cons(Z,nil) = U
& ssItem(Z) )
| ~ neq(V,nil) )
& ( nil = U
| nil != V ) )
| ( ( nil != W
| nil != X )
& ! [Y] :
( ssItem(Y)
=> ( ~ 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)
=> ( ( ( ? [Z] :
( memberP(V,Z)
& cons(Z,nil) = U
& ssItem(Z) )
| ~ neq(V,nil) )
& ( nil = U
| nil != V ) )
| ( ( nil != W
| nil != X )
& ! [Y] :
( ssItem(Y)
=> ( ~ memberP(X,Y)
| cons(Y,nil) != W ) ) )
| U != W
| V != X ) ) ) ) ),
inference(assume_negation,[status(cth)],[co1]) ).
cnf(c_90,plain,
( B != A
| ~ neq(A,B)
| ~ ssList(B)
| ~ ssList(A) ),
inference(clausify,[status(thm)],[ax15]) ).
fof(nnf_87,plain,
? [U] :
( ? [V] :
( ? [W] :
( ? [X] :
( ( ( ! [Z] :
( ~ memberP(V,Z)
| cons(Z,nil) != U
| ~ ssItem(Z) )
& neq(V,nil) )
| ( nil != U
& nil = V ) )
& ( ( nil = W
& nil = X )
| ? [Y] :
( 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,
( ( ( ! [Z] :
( ~ memberP(sK1,Z)
| cons(Z,nil) != sK0
| ~ ssItem(Z) )
& neq(sK1,nil) )
| ( nil != sK0
& nil = sK1 ) )
& ( ( nil = sK3
& nil = sK2 )
| ( memberP(sK2,sK4)
& cons(sK4,nil) = sK3
& ssItem(sK4) ) )
& sK3 = sK0
& sK2 = sK1
& ssList(sK2)
& ssList(sK3)
& ssList(sK1)
& ssList(sK0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK3,sK2,sK4]),skolemize(U,sK0),skolemize(V,sK1),skolemize(W,sK3),skolemize(X,sK2),skolemize(Y,sK4)],[nnf_87]) ).
fof(sk_co1_neg,plain,
( ! [VAR_0] :
( ~ memberP(sK1,VAR_0)
| cons(VAR_0,nil) != sK0
| ~ ssItem(VAR_0)
| nil != sK0 )
& ( neq(sK1,nil)
| nil != sK0 )
& ! [VAR_0] :
( ~ memberP(sK1,VAR_0)
| cons(VAR_0,nil) != sK0
| ~ ssItem(VAR_0)
| nil = sK1 )
& ( neq(sK1,nil)
| nil = sK1 )
& ( nil = sK3
| memberP(sK2,sK4) )
& ( nil = sK2
| memberP(sK2,sK4) )
& ( nil = sK3
| cons(sK4,nil) = sK3 )
& ( nil = sK2
| cons(sK4,nil) = sK3 )
& ( nil = sK3
| ssItem(sK4) )
& ( nil = sK2
| ssItem(sK4) )
& sK3 = sK0
& sK2 = sK1
& ssList(sK2)
& ssList(sK3)
& ssList(sK1)
& ssList(sK0) ),
inference(cnf_transformation,[status(thm)],[sk_co1_neg_sk]) ).
cnf(c_93,negated_conjecture,
( neq(sK1,nil)
| nil != sK0 ),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_205,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_233,plain,
ssList(nil),
inference(clausify,[status(thm)],[ax17]) ).
cnf(c_247,plain,
( app(nil,A) = A
| ~ ssList(A) ),
inference(clausify,[status(thm)],[ax28]) ).
cnf(c_258,plain,
( ~ memberP(B,A)
| memberP(app(B,C),A)
| ~ ssList(C)
| ~ ssList(B)
| ~ ssItem(A) ),
inference(clausify,[status(thm)],[ax36]) ).
cnf(c_263,plain,
( ~ memberP(nil,A)
| ~ ssItem(A) ),
inference(clausify,[status(thm)],[ax38]) ).
fof(ax39,axiom,
~ singletonP(nil),
file('theBenchmark.p',ax39) ).
cnf(c_264,plain,
~ singletonP(nil),
inference(clausify,[status(thm)],[ax39]) ).
cnf(c_329,negated_conjecture,
ssList(sK0),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_330,negated_conjecture,
ssList(sK1),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_333,negated_conjecture,
sK2 = sK1,
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_334,negated_conjecture,
sK3 = sK0,
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_335,negated_conjecture,
( nil = sK2
| ssItem(sK4) ),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_6975,negated_conjecture,
( nil = sK1
| ssItem(sK4) ),
inference(paramod,[status(thm)],[c_333,c_335]) ).
cnf(c_336,negated_conjecture,
( sK1 = nil
| ssItem(sK4) ),
inference(copy,[status(thm)],[c_6975]) ).
cnf(c_337,negated_conjecture,
( nil = sK3
| ssItem(sK4) ),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_6976,negated_conjecture,
( nil = sK0
| ssItem(sK4) ),
inference(paramod,[status(thm)],[c_334,c_337]) ).
cnf(c_338,negated_conjecture,
( sK0 = nil
| ssItem(sK4) ),
inference(copy,[status(thm)],[c_6976]) ).
cnf(c_339,negated_conjecture,
( nil = sK2
| cons(sK4,nil) = sK3 ),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_6977,negated_conjecture,
( nil = sK2
| cons(sK4,nil) = sK0 ),
inference(paramod,[status(thm)],[c_334,c_339]) ).
cnf(c_6978,negated_conjecture,
( nil = sK1
| cons(sK4,nil) = sK0 ),
inference(paramod,[status(thm)],[c_333,c_6977]) ).
cnf(c_340,negated_conjecture,
( sK1 = nil
| cons(sK4,nil) = sK0 ),
inference(copy,[status(thm)],[c_6978]) ).
cnf(c_341,negated_conjecture,
( nil = sK3
| cons(sK4,nil) = sK3 ),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_6979,negated_conjecture,
( nil = sK3
| cons(sK4,nil) = sK0 ),
inference(paramod,[status(thm)],[c_334,c_341]) ).
cnf(c_6980,negated_conjecture,
( nil = sK0
| cons(sK4,nil) = sK0 ),
inference(paramod,[status(thm)],[c_334,c_6979]) ).
cnf(c_342,negated_conjecture,
( sK0 = nil
| cons(sK4,nil) = sK0 ),
inference(copy,[status(thm)],[c_6980]) ).
cnf(c_343,negated_conjecture,
( nil = sK2
| memberP(sK2,sK4) ),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_6981,negated_conjecture,
( nil = sK2
| memberP(sK1,sK4) ),
inference(paramod,[status(thm)],[c_333,c_343]) ).
cnf(c_6982,negated_conjecture,
( nil = sK1
| memberP(sK1,sK4) ),
inference(paramod,[status(thm)],[c_333,c_6981]) ).
cnf(c_344,negated_conjecture,
( sK1 = nil
| memberP(sK1,sK4) ),
inference(copy,[status(thm)],[c_6982]) ).
cnf(c_345,negated_conjecture,
( nil = sK3
| memberP(sK2,sK4) ),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_6983,negated_conjecture,
( nil = sK3
| memberP(sK1,sK4) ),
inference(paramod,[status(thm)],[c_333,c_345]) ).
cnf(c_6984,negated_conjecture,
( nil = sK0
| memberP(sK1,sK4) ),
inference(paramod,[status(thm)],[c_334,c_6983]) ).
cnf(c_346,negated_conjecture,
( sK0 = nil
| memberP(sK1,sK4) ),
inference(copy,[status(thm)],[c_6984]) ).
cnf(c_347,negated_conjecture,
( ~ memberP(sK1,A)
| cons(A,nil) != sK0
| ~ ssItem(A)
| nil = sK1 ),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_348,negated_conjecture,
( ~ memberP(sK1,A)
| cons(A,nil) != sK0
| ~ ssItem(A)
| sK1 = nil ),
inference(copy,[status(thm)],[c_347]) ).
cnf(c_349,negated_conjecture,
( ~ memberP(sK1,A)
| cons(A,nil) != sK0
| ~ ssItem(A)
| nil != sK0 ),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_350,negated_conjecture,
( ~ memberP(sK1,A)
| cons(A,nil) != sK0
| ~ ssItem(A)
| sK0 != nil ),
inference(copy,[status(thm)],[c_349]) ).
cnf(c_351,negated_conjecture,
( nil != sK1
| ~ ssList(nil)
| ~ ssList(sK1)
| nil != sK0 ),
inference(resolve,[status(thm)],[c_93,c_90]) ).
cnf(c_6985,negated_conjecture,
( nil != sK1
| ~ ssList(nil)
| ~ ssList(sK1)
| sK0 != nil ),
inference(copy,[status(thm)],[c_351]) ).
cnf(c_6986,negated_conjecture,
( sK1 != nil
| ~ ssList(nil)
| ~ ssList(sK1)
| sK0 != nil ),
inference(copy,[status(thm)],[c_6985]) ).
cnf(c_6987,negated_conjecture,
( sK1 != nil
| ~ ssList(nil)
| sK0 != nil ),
inference(resolve,[status(thm)],[c_330,c_6986]) ).
cnf(c_352,negated_conjecture,
( sK1 != nil
| sK0 != nil ),
inference(resolve,[status(thm)],[c_233,c_6987]) ).
cnf(c_602,plain,
( ~ memberP(B,A)
| memberP(app(B,B),A)
| ~ ssList(B)
| ~ ssItem(A) ),
inference(factor,[status(thm)],[c_258]) ).
cnf(c_1756,plain,
app(nil,nil) = nil,
inference(resolve,[status(thm)],[c_247,c_233]) ).
cnf(c_6988,negated_conjecture,
( ~ ssItem(sK4)
| singletonP(sK0)
| ~ ssList(sK0)
| sK1 = nil ),
inference(resolve,[status(thm)],[c_340,c_205]) ).
cnf(c_2592,negated_conjecture,
( ~ ssItem(sK4)
| singletonP(sK0)
| sK1 = nil ),
inference(resolve,[status(thm)],[c_329,c_6988]) ).
cnf(c_6989,negated_conjecture,
( ~ ssItem(sK4)
| singletonP(sK0)
| ~ ssList(sK0)
| sK0 = nil ),
inference(resolve,[status(thm)],[c_342,c_205]) ).
cnf(c_2632,negated_conjecture,
( ~ ssItem(sK4)
| singletonP(sK0)
| sK0 = nil ),
inference(resolve,[status(thm)],[c_329,c_6989]) ).
cnf(c_6990,negated_conjecture,
( sK1 = nil
| cons(sK4,nil) != sK0
| ~ ssItem(sK4)
| sK1 = nil ),
inference(resolve,[status(thm)],[c_348,c_344]) ).
cnf(c_2718,negated_conjecture,
( cons(sK4,nil) != sK0
| ~ ssItem(sK4)
| sK1 = nil ),
inference(copy,[status(thm)],[c_6990]) ).
cnf(c_2726,plain,
( ssItem(sK4)
| sK1 != nil ),
inference(resolve,[status(thm)],[c_352,c_338]) ).
cnf(c_6991,negated_conjecture,
( sK0 = nil
| memberP(app(sK1,sK1),sK4)
| ~ ssList(sK1)
| ~ ssItem(sK4) ),
inference(resolve,[status(thm)],[c_602,c_346]) ).
cnf(c_2888,negated_conjecture,
( sK0 = nil
| memberP(app(sK1,sK1),sK4)
| ~ ssItem(sK4) ),
inference(resolve,[status(thm)],[c_330,c_6991]) ).
cnf(c_6992,negated_conjecture,
( ssItem(sK4)
| ssItem(sK4) ),
inference(resolve,[status(thm)],[c_2726,c_336]) ).
cnf(c_5712,negated_conjecture,
ssItem(sK4),
inference(copy,[status(thm)],[c_6992]) ).
cnf(c_6106,negated_conjecture,
( sK0 = nil
| memberP(app(sK1,sK1),sK4) ),
inference(resolve,[status(thm)],[c_5712,c_2888]) ).
cnf(c_6142,negated_conjecture,
( cons(sK4,nil) != sK0
| sK1 = nil ),
inference(resolve,[status(thm)],[c_5712,c_2718]) ).
cnf(c_6175,negated_conjecture,
( singletonP(sK0)
| sK0 = nil ),
inference(resolve,[status(thm)],[c_5712,c_2632]) ).
cnf(c_6196,negated_conjecture,
( singletonP(sK0)
| sK1 = nil ),
inference(resolve,[status(thm)],[c_5712,c_2592]) ).
cnf(c_6375,plain,
( ~ memberP(sK1,sK4)
| cons(sK4,nil) != sK0
| sK0 != nil ),
inference(resolve,[status(thm)],[c_5712,c_350]) ).
cnf(c_6412,plain,
~ memberP(nil,sK4),
inference(resolve,[status(thm)],[c_5712,c_263]) ).
cnf(c_6703,plain,
( sK1 != nil
| singletonP(sK0) ),
inference(resolve,[status(thm)],[c_6175,c_352]) ).
cnf(c_6993,plain,
( singletonP(sK0)
| singletonP(sK0) ),
inference(resolve,[status(thm)],[c_6703,c_6196]) ).
cnf(c_6743,plain,
singletonP(sK0),
inference(copy,[status(thm)],[c_6993]) ).
cnf(c_6994,plain,
( singletonP(nil)
| cons(sK4,nil) = sK0 ),
inference(paramod,[status(thm)],[c_342,c_6743]) ).
cnf(c_6754,plain,
cons(sK4,nil) = sK0,
inference(resolve,[status(thm)],[c_264,c_6994]) ).
cnf(c_6995,plain,
( singletonP(nil)
| memberP(sK1,sK4) ),
inference(paramod,[status(thm)],[c_346,c_6743]) ).
cnf(c_6755,plain,
memberP(sK1,sK4),
inference(resolve,[status(thm)],[c_264,c_6995]) ).
cnf(c_6996,plain,
( ~ memberP(sK1,sK4)
| sK0 != sK0
| sK0 != nil ),
inference(paramod,[status(thm)],[c_6754,c_6375]) ).
cnf(c_6997,plain,
( ~ memberP(sK1,sK4)
| sK0 != nil ),
inference(copy,[status(thm)],[c_6996]) ).
cnf(c_6818,plain,
sK0 != nil,
inference(resolve,[status(thm)],[c_6755,c_6997]) ).
cnf(c_6998,negated_conjecture,
( sK0 != sK0
| sK1 = nil ),
inference(paramod,[status(thm)],[c_6754,c_6142]) ).
cnf(c_6823,negated_conjecture,
sK1 = nil,
inference(copy,[status(thm)],[c_6998]) ).
cnf(c_6999,negated_conjecture,
( sK0 = nil
| memberP(app(nil,sK1),sK4) ),
inference(paramod,[status(thm)],[c_6823,c_6106]) ).
cnf(c_7000,negated_conjecture,
( sK0 = nil
| memberP(app(nil,nil),sK4) ),
inference(paramod,[status(thm)],[c_6823,c_6999]) ).
cnf(c_7001,negated_conjecture,
( sK0 = nil
| memberP(nil,sK4) ),
inference(paramod,[status(thm)],[c_1756,c_7000]) ).
cnf(c_7002,negated_conjecture,
sK0 = nil,
inference(resolve,[status(thm)],[c_6412,c_7001]) ).
cnf(c_6974,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_6818,c_7002]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SWC386+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.16/0.64 % Computer : n002.cluster.edu
% 0.16/0.64 % Model : x86_64 x86_64
% 0.16/0.64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.64 % Memory : 8046.5625MB
% 0.16/0.64 % OS : Linux 6.8.0-71-generic
% 0.16/0.64 % CPULimit : 300
% 0.16/0.64 % WCLimit : 300
% 0.16/0.64 % DateTime : Sat Sep 26 12:58:54 UTC 2026
% 0.16/0.65 % CPUTime :
% 0.21/0.65 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.21/0.65 % Process 1779298 was started by sandbox on n002,
% 0.21/0.65 % Sat Sep 26 12:58:54 2026
% 0.21/0.65 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.21/0.69
% 0.21/0.69 % From the command line: assign(max_seconds, 300).
% 51.00/7.16
% 51.00/7.16 % given #500 (I,wt=37): 706 -ssList(A) | ssList(f35(A)) | -ssItem(B) | -ssItem(C) | -ssList(D) | -ssList(E) | app(app(A,cons(B,D)),cons(C,E)) != A | C != B. [factor(378,a,e)].
% 51.00/7.16
% 51.00/7.16 % given #1000 (I,wt=35): 1226 -ssList(A) | ssList(f37(A)) | -ssItem(B) | -ssItem(C) | -ssList(D) | app(app(D,cons(B,D)),cons(C,D)) != A | C != B. [factor(724,e,f)].
% 51.00/7.16
% 51.00/7.16 % SZS status Theorem for theBenchmark
% 51.00/7.16
% 51.00/7.16 % Proof 1 at 5.32 (+ 1.09) seconds.
% 51.00/7.16 % Length of proof is 57.
% 51.00/7.16 % Level of proof is 11.
% 51.00/7.16 % Maximum clause weight is 18.000.
% 51.00/7.16 % Given clauses 1466.
% 51.00/7.16
% 51.00/7.16 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------