%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWC042+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 : n010.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 08:56:38 AM UTC 2026
% Result : Theorem 8.15s 2.70s
% Output : CNFRefutation 8.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 2
% Syntax : Number of formulae : 24 ( 14 unt; 0 def)
% Number of atoms : 131 ( 64 equ)
% Maximal formula atoms : 20 ( 5 avg)
% Number of connectives : 157 ( 50 ~; 43 |; 51 &)
% ( 1 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 29 ( 7 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 = W
& nil != X )
| ! [Y] :
( ssList(Y)
=> ( ? [Z] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( leq(X2,Z)
& app(X3,cons(X2,nil)) = W
& ssList(X3) )
& ssItem(X2) )
& app(cons(Z,nil),X1) = Y
& ssList(X1) )
& ssItem(Z) )
| ~ totalorderedP(W)
| app(W,Y) != X ) )
| nil = U
| U != W
| V != X
| nil != V ) ) ) ) ),
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] :
( ssList(Y)
=> ( ? [Z] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( leq(X2,Z)
& app(X3,cons(X2,nil)) = W
& ssList(X3) )
& ssItem(X2) )
& app(cons(Z,nil),X1) = Y
& ssList(X1) )
& ssItem(Z) )
| ~ totalorderedP(W)
| app(W,Y) != X ) )
| nil = U
| U != W
| V != X
| nil != V ) ) ) ) ),
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 != W
| nil = X )
& ? [Y] :
( ! [Z] :
( ! [X1] :
( ! [X2] :
( ! [X3] :
( ~ leq(X2,Z)
| app(X3,cons(X2,nil)) != W
| ~ ssList(X3) )
| ~ ssItem(X2) )
| app(cons(Z,nil),X1) != Y
| ~ ssList(X1) )
| ~ ssItem(Z) )
& totalorderedP(W)
& app(W,Y) = X
& ssList(Y) )
& nil != U
& W = U
& X = V
& nil = V
& ssList(X) )
& ssList(W) )
& ssList(V) )
& ssList(U) ),
inference(fof_nnf,[status(thm)],[co1_neg]) ).
fof(sk_co1_neg_sk,plain,
( ( nil != sK3
| nil = sK2 )
& ! [Z] :
( ! [X1] :
( ! [X2] :
( ! [X3] :
( ~ leq(X2,Z)
| app(X3,cons(X2,nil)) != sK3
| ~ ssList(X3) )
| ~ ssItem(X2) )
| app(cons(Z,nil),X1) != sK4
| ~ ssList(X1) )
| ~ ssItem(Z) )
& totalorderedP(sK3)
& app(sK3,sK4) = sK2
& ssList(sK4)
& nil != sK0
& sK3 = sK0
& sK2 = sK1
& nil = 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,
( ( nil != sK3
| nil = sK2 )
& ! [VAR_0,VAR_1,VAR_2,VAR_3] :
( ~ leq(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) )
& totalorderedP(sK3)
& app(sK3,sK4) = sK2
& ssList(sK4)
& nil != sK0
& sK3 = sK0
& sK2 = sK1
& nil = sK1
& ssList(sK2)
& ssList(sK3)
& ssList(sK1)
& 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,
nil = sK1,
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_332,negated_conjecture,
sK1 = nil,
inference(copy,[status(thm)],[c_331]) ).
cnf(c_333,negated_conjecture,
sK2 = sK1,
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_334,negated_conjecture,
sK2 = nil,
inference(paramod,[status(thm)],[c_332,c_333]) ).
cnf(c_335,negated_conjecture,
sK3 = sK0,
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_336,negated_conjecture,
nil != sK0,
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_337,negated_conjecture,
sK0 != nil,
inference(copy,[status(thm)],[c_336]) ).
cnf(c_338,negated_conjecture,
ssList(sK4),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_339,negated_conjecture,
app(sK3,sK4) = sK2,
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_2354,negated_conjecture,
app(sK0,sK4) = sK2,
inference(paramod,[status(thm)],[c_335,c_339]) ).
cnf(c_340,negated_conjecture,
app(sK0,sK4) = nil,
inference(paramod,[status(thm)],[c_334,c_2354]) ).
cnf(c_2355,negated_conjecture,
( nil = sK0
| ~ ssList(sK4)
| ~ ssList(sK0) ),
inference(resolve,[status(thm)],[c_340,c_312]) ).
cnf(c_2356,negated_conjecture,
( sK0 = nil
| ~ ssList(sK4)
| ~ ssList(sK0) ),
inference(copy,[status(thm)],[c_2355]) ).
cnf(c_2357,negated_conjecture,
( sK0 = nil
| ~ ssList(sK4) ),
inference(resolve,[status(thm)],[c_327,c_2356]) ).
cnf(c_2358,negated_conjecture,
sK0 = nil,
inference(resolve,[status(thm)],[c_338,c_2357]) ).
cnf(c_2353,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_337,c_2358]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWC042+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.37 % Computer : n010.cluster.edu
% 0.08/0.37 % Model : x86_64 x86_64
% 0.08/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.37 % Memory : 8046.5625MB
% 0.08/0.37 % OS : Linux 6.8.0-71-generic
% 0.08/0.37 % CPULimit : 300
% 0.08/0.37 % WCLimit : 300
% 0.08/0.37 % DateTime : Sat Sep 26 12:07:45 UTC 2026
% 0.08/0.37 % CPUTime :
% 0.08/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.08/0.37 % Process 3250186 was started by sandbox on n010,
% 0.08/0.37 % Sat Sep 26 12:07:45 2026
% 0.08/0.37 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.11/0.39
% 0.11/0.39 % From the command line: assign(max_seconds, 300).
% 8.15/2.70
% 8.15/2.70 % SZS status Theorem for theBenchmark
% 8.15/2.70
% 8.15/2.70 % Proof 1 at 1.07 (+ 0.09) seconds.
% 8.15/2.70 % Length of proof is 15.
% 8.15/2.70 % Level of proof is 5.
% 8.15/2.70 % Maximum clause weight is 16.000.
% 8.15/2.70 % Given clauses 163.
% 8.15/2.70
% 8.15/2.70 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------