%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWC179+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 08:57:04 AM UTC 2026
% Result : Theorem 13.16s 7.32s
% Output : CNFRefutation 13.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 3
% Syntax : Number of formulae : 25 ( 8 unt; 0 def)
% Number of atoms : 155 ( 61 equ)
% Maximal formula atoms : 43 ( 6 avg)
% Number of connectives : 174 ( 44 ~; 57 |; 58 &)
% ( 0 <=>; 15 =>; 0 <=; 0 <~>)
% Maximal formula depth : 26 ( 6 avg)
% Maximal term depth : 3 ( 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 : 35 ( 0 sgn 23 !; 11 ?)
% Comments :
%------------------------------------------------------------------------------
fof(ax71,axiom,
! [U] :
( ssItem(U)
=> duplicatefreeP(cons(U,nil)) ),
file('theBenchmark.p',ax71) ).
fof(co1,conjecture,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ! [X] :
( ssList(X)
=> ( ( ( nil != W
| nil != X )
& ! [Y] :
( ssItem(Y)
=> ! [Z] :
( ssList(Z)
=> ! [X1] :
( ssList(X1)
=> ( ? [X3] :
( lt(X3,Y)
& memberP(X1,X3)
& ssItem(X3) )
| ? [X2] :
( lt(Y,X2)
& memberP(Z,X2)
& ssItem(X2) )
| app(app(Z,W),X1) != X
| cons(Y,nil) != W ) ) ) ) )
| duplicatefreeP(U)
| 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 != W
| nil != X )
& ! [Y] :
( ssItem(Y)
=> ! [Z] :
( ssList(Z)
=> ! [X1] :
( ssList(X1)
=> ( ? [X3] :
( lt(X3,Y)
& memberP(X1,X3)
& ssItem(X3) )
| ? [X2] :
( lt(Y,X2)
& memberP(Z,X2)
& ssItem(X2) )
| app(app(Z,W),X1) != X
| cons(Y,nil) != W ) ) ) ) )
| duplicatefreeP(U)
| U != W
| V != X ) ) ) ) ),
inference(assume_negation,[status(cth)],[co1]) ).
fof(nnf_87,plain,
? [U] :
( ? [V] :
( ? [W] :
( ? [X] :
( ( ( nil = W
& nil = X )
| ? [Y] :
( ? [Z] :
( ? [X1] :
( ! [X3] :
( ~ lt(X3,Y)
| ~ memberP(X1,X3)
| ~ ssItem(X3) )
& ! [X2] :
( ~ lt(Y,X2)
| ~ memberP(Z,X2)
| ~ ssItem(X2) )
& app(app(Z,W),X1) = X
& cons(Y,nil) = W
& ssList(X1) )
& ssList(Z) )
& ssItem(Y) ) )
& ~ duplicatefreeP(U)
& 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 = sK4 )
| ( ! [X3] :
( ~ lt(X3,sK0)
| ~ memberP(sK6,X3)
| ~ ssItem(X3) )
& ! [X2] :
( ~ lt(sK0,X2)
| ~ memberP(sK5,X2)
| ~ ssItem(X2) )
& app(app(sK5,sK1),sK6) = sK4
& cons(sK0,nil) = sK1
& ssList(sK6)
& ssList(sK5)
& ssItem(sK0) ) )
& ~ duplicatefreeP(sK2)
& sK1 = sK2
& sK4 = sK3
& ssList(sK4)
& ssList(sK1)
& ssList(sK3)
& ssList(sK2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3,sK1,sK4,sK0,sK5,sK6]),skolemize(U,sK2),skolemize(V,sK3),skolemize(W,sK1),skolemize(X,sK4),skolemize(Y,sK0),skolemize(Z,sK5),skolemize(X1,sK6)],[nnf_87]) ).
fof(sk_co1_neg,plain,
( ! [VAR_0] :
( nil = sK1
| ~ lt(VAR_0,sK0)
| ~ memberP(sK6,VAR_0)
| ~ ssItem(VAR_0) )
& ! [VAR_0] :
( nil = sK4
| ~ lt(VAR_0,sK0)
| ~ memberP(sK6,VAR_0)
| ~ ssItem(VAR_0) )
& ! [VAR_0] :
( nil = sK1
| ~ lt(sK0,VAR_0)
| ~ memberP(sK5,VAR_0)
| ~ ssItem(VAR_0) )
& ! [VAR_0] :
( nil = sK4
| ~ lt(sK0,VAR_0)
| ~ memberP(sK5,VAR_0)
| ~ ssItem(VAR_0) )
& ( nil = sK1
| app(app(sK5,sK1),sK6) = sK4 )
& ( nil = sK4
| app(app(sK5,sK1),sK6) = sK4 )
& ( nil = sK1
| cons(sK0,nil) = sK1 )
& ( nil = sK4
| cons(sK0,nil) = sK1 )
& ( nil = sK1
| ssList(sK6) )
& ( nil = sK4
| ssList(sK6) )
& ( nil = sK1
| ssList(sK5) )
& ( nil = sK4
| ssList(sK5) )
& ( nil = sK1
| ssItem(sK0) )
& ( nil = sK4
| ssItem(sK0) )
& ~ duplicatefreeP(sK2)
& sK1 = sK2
& sK4 = sK3
& ssList(sK4)
& ssList(sK1)
& ssList(sK3)
& ssList(sK2) ),
inference(cnf_transformation,[status(thm)],[sk_co1_neg_sk]) ).
cnf(c_178,negated_conjecture,
( nil = sK1
| cons(sK0,nil) = sK1 ),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_179,negated_conjecture,
( sK1 = nil
| cons(sK0,nil) = sK1 ),
inference(copy,[status(thm)],[c_178]) ).
cnf(c_190,negated_conjecture,
( nil = sK1
| ssItem(sK0) ),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_191,negated_conjecture,
( sK1 = nil
| ssItem(sK0) ),
inference(copy,[status(thm)],[c_190]) ).
cnf(c_194,negated_conjecture,
~ duplicatefreeP(sK2),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_195,negated_conjecture,
sK1 = sK2,
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
fof(ax72,axiom,
duplicatefreeP(nil),
file('theBenchmark.p',ax72) ).
cnf(c_229,plain,
duplicatefreeP(nil),
inference(clausify,[status(thm)],[ax72]) ).
cnf(c_230,plain,
( duplicatefreeP(cons(A,nil))
| ~ ssItem(A) ),
inference(clausify,[status(thm)],[ax71]) ).
cnf(c_471,negated_conjecture,
( sK2 = nil
| ssItem(sK0) ),
inference(paramod,[status(thm)],[c_195,c_191]) ).
cnf(c_2865,negated_conjecture,
( sK1 = nil
| cons(sK0,nil) = sK2 ),
inference(paramod,[status(thm)],[c_195,c_179]) ).
cnf(c_475,negated_conjecture,
( sK2 = nil
| cons(sK0,nil) = sK2 ),
inference(paramod,[status(thm)],[c_195,c_2865]) ).
cnf(c_2203,plain,
( duplicatefreeP(cons(sK0,nil))
| sK2 = nil ),
inference(resolve,[status(thm)],[c_471,c_230]) ).
cnf(c_2866,plain,
( ~ duplicatefreeP(nil)
| cons(sK0,nil) = sK2 ),
inference(paramod,[status(thm)],[c_475,c_194]) ).
cnf(c_2798,plain,
cons(sK0,nil) = sK2,
inference(resolve,[status(thm)],[c_229,c_2866]) ).
cnf(c_2867,plain,
( duplicatefreeP(sK2)
| sK2 = nil ),
inference(paramod,[status(thm)],[c_2798,c_2203]) ).
cnf(c_2829,negated_conjecture,
sK2 = nil,
inference(resolve,[status(thm)],[c_194,c_2867]) ).
cnf(c_2868,negated_conjecture,
~ duplicatefreeP(nil),
inference(paramod,[status(thm)],[c_2829,c_194]) ).
cnf(c_2864,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_229,c_2868]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC179+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/5.38 % Computer : n020.cluster.edu
% 0.11/5.38 % Model : x86_64 x86_64
% 0.11/5.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/5.38 % Memory : 8046.5625MB
% 0.11/5.38 % OS : Linux 6.8.0-71-generic
% 0.11/5.38 % CPULimit : 300
% 0.11/5.38 % WCLimit : 300
% 0.11/5.38 % DateTime : Sat Sep 26 12:27:39 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 1557539 was started by sandbox2 on n020,
% 0.11/5.39 % Sat Sep 26 12:27:39 2026
% 0.11/5.39 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.16/5.43
% 0.16/5.43 % From the command line: assign(max_seconds, 300).
% 13.16/7.32
% 13.16/7.32 % SZS status Theorem for theBenchmark
% 13.16/7.32
% 13.16/7.32 % Proof 1 at 1.64 (+ 0.22) seconds.
% 13.16/7.32 % Length of proof is 16.
% 13.16/7.32 % Level of proof is 6.
% 13.16/7.32 % Maximum clause weight is 12.000.
% 13.16/7.32 % Given clauses 276.
% 13.16/7.32
% 13.16/7.32 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------