%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWC032+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 : n001.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 08:56:36 AM UTC 2026
% Result : Theorem 9.57s 1.66s
% Output : CNFRefutation 9.57s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 2
% Syntax : Number of formulae : 37 ( 11 unt; 0 def)
% Number of atoms : 173 ( 106 equ)
% Maximal formula atoms : 22 ( 4 avg)
% Number of connectives : 210 ( 74 ~; 68 |; 55 &)
% ( 1 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 27 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 6 con; 0-2 aty)
% Number of variables : 39 ( 0 sgn 24 !; 13 ?)
% Comments :
%------------------------------------------------------------------------------
fof(ax83,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ( nil = app(U,V)
<=> ( nil = U
& nil = V ) ) ) ),
file('theBenchmark.p',ax83) ).
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] :
( ssList(Y)
=> ( ? [Z] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( lt(X2,Z)
& app(X3,cons(X2,nil)) = W
& ssList(X3) )
& ssItem(X2) )
& app(cons(Z,nil),X1) = Y
& ssList(X1) )
& ssItem(Z) )
| ~ strictorderedP(W)
| app(W,Y) != X ) )
| 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] :
( ssList(Y)
=> ( ? [Z] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( lt(X2,Z)
& app(X3,cons(X2,nil)) = W
& ssList(X3) )
& ssItem(X2) )
& app(cons(Z,nil),X1) = Y
& ssList(X1) )
& ssItem(Z) )
| ~ strictorderedP(W)
| app(W,Y) != X ) )
| U != W
| V != X ) ) ) ) ),
inference(assume_negation,[status(cth)],[co1]) ).
cnf(c_312,plain,
( nil = A
| app(A,B) != nil
| ~ ssList(B)
| ~ ssList(A) ),
inference(clausify,[status(thm)],[ax83]) ).
fof(nnf_87,plain,
? [U] :
( ? [V] :
( ? [W] :
( ? [X] :
( ( ( nil != V
& nil = U )
| ( nil != U
& nil = V ) )
& ( nil != W
| nil = X )
& ? [Y] :
( ! [Z] :
( ! [X1] :
( ! [X2] :
( ! [X3] :
( ~ lt(X2,Z)
| app(X3,cons(X2,nil)) != W
| ~ ssList(X3) )
| ~ ssItem(X2) )
| app(cons(Z,nil),X1) != Y
| ~ ssList(X1) )
| ~ ssItem(Z) )
& strictorderedP(W)
& app(W,Y) = X
& ssList(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 != sK2
& nil = sK0 )
| ( nil != sK0
& nil = sK2 ) )
& ( nil != sK3
| nil = sK1 )
& ! [Z] :
( ! [X1] :
( ! [X2] :
( ! [X3] :
( ~ lt(X2,Z)
| app(X3,cons(X2,nil)) != sK3
| ~ ssList(X3) )
| ~ ssItem(X2) )
| app(cons(Z,nil),X1) != sK4
| ~ ssList(X1) )
| ~ ssItem(Z) )
& strictorderedP(sK3)
& app(sK3,sK4) = sK1
& ssList(sK4)
& sK3 = sK0
& sK1 = sK2
& ssList(sK1)
& ssList(sK3)
& ssList(sK2)
& ssList(sK0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK2,sK3,sK1,sK4]),skolemize(U,sK0),skolemize(V,sK2),skolemize(W,sK3),skolemize(X,sK1),skolemize(Y,sK4)],[nnf_87]) ).
fof(sk_co1_neg,plain,
( ( nil != sK2
| nil != sK0 )
& ( nil = sK0
| nil = sK2 )
& ( nil != sK3
| nil = sK1 )
& ! [VAR_0,VAR_1,VAR_2,VAR_3] :
( ~ lt(VAR_2,VAR_0)
| app(VAR_3,cons(VAR_2,nil)) != sK3
| ~ ssList(VAR_3)
| ~ ssItem(VAR_2)
| app(cons(VAR_0,nil),VAR_1) != sK4
| ~ ssList(VAR_1)
| ~ ssItem(VAR_0) )
& strictorderedP(sK3)
& app(sK3,sK4) = sK1
& ssList(sK4)
& sK3 = sK0
& sK1 = sK2
& ssList(sK1)
& ssList(sK3)
& ssList(sK2)
& ssList(sK0) ),
inference(cnf_transformation,[status(thm)],[sk_co1_neg_sk]) ).
cnf(c_327,negated_conjecture,
ssList(sK0),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_331,negated_conjecture,
sK1 = sK2,
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_332,negated_conjecture,
sK3 = sK0,
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_333,negated_conjecture,
ssList(sK4),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_334,negated_conjecture,
app(sK3,sK4) = sK1,
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_2607,negated_conjecture,
app(sK0,sK4) = sK1,
inference(paramod,[status(thm)],[c_332,c_334]) ).
cnf(c_335,negated_conjecture,
app(sK0,sK4) = sK2,
inference(paramod,[status(thm)],[c_331,c_2607]) ).
cnf(c_340,negated_conjecture,
( nil != sK3
| nil = sK1 ),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_2608,negated_conjecture,
( nil != sK3
| nil = sK2 ),
inference(paramod,[status(thm)],[c_331,c_340]) ).
cnf(c_2609,negated_conjecture,
( nil != sK0
| nil = sK2 ),
inference(paramod,[status(thm)],[c_332,c_2608]) ).
cnf(c_2610,negated_conjecture,
( nil != sK0
| sK2 = nil ),
inference(copy,[status(thm)],[c_2609]) ).
cnf(c_341,negated_conjecture,
( sK0 != nil
| sK2 = nil ),
inference(copy,[status(thm)],[c_2610]) ).
cnf(c_342,negated_conjecture,
( nil = sK0
| nil = sK2 ),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_2611,negated_conjecture,
( nil = sK0
| sK2 = nil ),
inference(copy,[status(thm)],[c_342]) ).
cnf(c_343,negated_conjecture,
( sK0 = nil
| sK2 = nil ),
inference(copy,[status(thm)],[c_2611]) ).
cnf(c_344,negated_conjecture,
( nil != sK2
| nil != sK0 ),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_2612,negated_conjecture,
( nil != sK2
| sK0 != nil ),
inference(copy,[status(thm)],[c_344]) ).
cnf(c_345,negated_conjecture,
( sK2 != nil
| sK0 != nil ),
inference(copy,[status(thm)],[c_2612]) ).
cnf(c_2613,plain,
( nil = sK0
| sK2 != nil
| ~ ssList(sK4)
| ~ ssList(sK0) ),
inference(paramod,[status(thm)],[c_335,c_312]) ).
cnf(c_2614,plain,
( sK0 = nil
| sK2 != nil
| ~ ssList(sK4)
| ~ ssList(sK0) ),
inference(copy,[status(thm)],[c_2613]) ).
cnf(c_2615,negated_conjecture,
( sK0 = nil
| sK2 != nil
| ~ ssList(sK4) ),
inference(resolve,[status(thm)],[c_327,c_2614]) ).
cnf(c_2571,negated_conjecture,
( sK0 = nil
| sK2 != nil ),
inference(resolve,[status(thm)],[c_333,c_2615]) ).
cnf(c_2616,negated_conjecture,
( sK2 = nil
| sK2 = nil ),
inference(resolve,[status(thm)],[c_343,c_341]) ).
cnf(c_2602,negated_conjecture,
sK2 = nil,
inference(copy,[status(thm)],[c_2616]) ).
cnf(c_2617,negated_conjecture,
( sK0 = nil
| nil != nil ),
inference(paramod,[status(thm)],[c_2602,c_2571]) ).
cnf(c_2604,negated_conjecture,
sK0 = nil,
inference(copy,[status(thm)],[c_2617]) ).
cnf(c_2618,negated_conjecture,
( sK2 != nil
| nil != nil ),
inference(paramod,[status(thm)],[c_2604,c_345]) ).
cnf(c_2619,negated_conjecture,
( nil != nil
| nil != nil ),
inference(paramod,[status(thm)],[c_2602,c_2618]) ).
cnf(c_2620,negated_conjecture,
nil != nil,
inference(copy,[status(thm)],[c_2619]) ).
cnf(c_2606,negated_conjecture,
$false,
inference(copy,[status(thm)],[c_2620]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC032+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n001.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Sat Sep 26 12:11:43 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.09/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.36 % Process 1749359 was started by sandbox on n001,
% 0.09/0.36 % Sat Sep 26 12:11:43 2026
% 0.09/0.36 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.13/0.38
% 0.13/0.38 % From the command line: assign(max_seconds, 300).
% 9.57/1.66
% 9.57/1.66 % SZS status Theorem for theBenchmark
% 9.57/1.66
% 9.57/1.66 % Proof 1 at 1.07 (+ 0.11) seconds.
% 9.57/1.66 % Length of proof is 19.
% 9.57/1.66 % Level of proof is 5.
% 9.57/1.66 % Maximum clause weight is 16.000.
% 9.57/1.66 % Given clauses 166.
% 9.57/1.66
% 9.57/1.66 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------