%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWC007+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 : 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 08:56:31 AM UTC 2026
% Result : Theorem 49.26s 7.55s
% Output : CNFRefutation 49.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 4
% Syntax : Number of formulae : 30 ( 13 unt; 0 def)
% Number of atoms : 112 ( 50 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 138 ( 56 ~; 43 |; 29 &)
% ( 0 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 5 con; 0-2 aty)
% Number of variables : 39 ( 0 sgn 19 !; 10 ?)
% Comments :
%------------------------------------------------------------------------------
fof(ax28,axiom,
! [U] :
( ssList(U)
=> app(nil,U) = U ),
file('theBenchmark.p',ax28) ).
fof(ax84,axiom,
! [U] :
( ssList(U)
=> app(U,nil) = U ),
file('theBenchmark.p',ax84) ).
fof(co1,conjecture,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ! [X] :
( ssList(X)
=> ( ? [Y] :
( ? [Z] :
( ? [X1] :
( app(Y,X1) = U
& app(app(Y,Z),X1) = V
& ssList(X1) )
& ssList(Z) )
& ssList(Y) )
| U != W
| V != X
| nil != W ) ) ) ) ),
file('theBenchmark.p',co1) ).
fof(co1_neg,negated_conjecture,
~ ! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ! [X] :
( ssList(X)
=> ( ? [Y] :
( ? [Z] :
( ? [X1] :
( app(Y,X1) = U
& app(app(Y,Z),X1) = V
& ssList(X1) )
& ssList(Z) )
& ssList(Y) )
| U != W
| V != X
| nil != W ) ) ) ) ),
inference(assume_negation,[status(cth)],[co1]) ).
fof(ax17,axiom,
ssList(nil),
file('theBenchmark.p',ax17) ).
cnf(c_231,plain,
ssList(nil),
inference(clausify,[status(thm)],[ax17]) ).
cnf(c_245,plain,
( app(nil,A) = A
| ~ ssList(A) ),
inference(clausify,[status(thm)],[ax28]) ).
cnf(c_314,plain,
( app(A,nil) = A
| ~ ssList(A) ),
inference(clausify,[status(thm)],[ax84]) ).
fof(nnf_87,plain,
? [U] :
( ? [V] :
( ? [W] :
( ? [X] :
( ! [Y] :
( ! [Z] :
( ! [X1] :
( app(Y,X1) != U
| app(app(Y,Z),X1) != V
| ~ ssList(X1) )
| ~ ssList(Z) )
| ~ ssList(Y) )
& W = U
& X = V
& nil = W
& ssList(X) )
& ssList(W) )
& ssList(V) )
& ssList(U) ),
inference(fof_nnf,[status(thm)],[co1_neg]) ).
fof(sk_co1_neg_sk,plain,
( ! [Y] :
( ! [Z] :
( ! [X1] :
( app(Y,X1) != sK2
| app(app(Y,Z),X1) != sK0
| ~ ssList(X1) )
| ~ ssList(Z) )
| ~ ssList(Y) )
& sK1 = sK2
& sK3 = sK0
& nil = sK1
& ssList(sK3)
& ssList(sK1)
& ssList(sK0)
& ssList(sK2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK0,sK1,sK3]),skolemize(U,sK2),skolemize(V,sK0),skolemize(W,sK1),skolemize(X,sK3)],[nnf_87]) ).
fof(sk_co1_neg,plain,
( ! [VAR_0,VAR_1,VAR_2] :
( app(VAR_0,VAR_2) != sK2
| app(app(VAR_0,VAR_1),VAR_2) != sK0
| ~ ssList(VAR_2)
| ~ ssList(VAR_1)
| ~ ssList(VAR_0) )
& sK1 = sK2
& sK3 = sK0
& nil = sK1
& ssList(sK3)
& ssList(sK1)
& ssList(sK0)
& ssList(sK2) ),
inference(cnf_transformation,[status(thm)],[sk_co1_neg_sk]) ).
cnf(c_328,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_334,negated_conjecture,
sK1 = sK2,
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_8157,negated_conjecture,
nil = sK2,
inference(paramod,[status(thm)],[c_332,c_334]) ).
cnf(c_335,negated_conjecture,
sK2 = nil,
inference(copy,[status(thm)],[c_8157]) ).
cnf(c_336,negated_conjecture,
( app(A,C) != sK2
| app(app(A,B),C) != sK0
| ~ ssList(C)
| ~ ssList(B)
| ~ ssList(A) ),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_337,negated_conjecture,
( app(A,C) != nil
| app(app(A,B),C) != sK0
| ~ ssList(C)
| ~ ssList(B)
| ~ ssList(A) ),
inference(paramod,[status(thm)],[c_335,c_336]) ).
cnf(c_618,plain,
( app(A,A) != nil
| app(app(A,B),A) != sK0
| ~ ssList(B)
| ~ ssList(A) ),
inference(factor,[status(thm)],[c_337]) ).
cnf(c_1744,plain,
app(nil,nil) = nil,
inference(resolve,[status(thm)],[c_245,c_231]) ).
cnf(c_1966,plain,
app(sK0,nil) = sK0,
inference(resolve,[status(thm)],[c_328,c_314]) ).
cnf(c_2044,plain,
app(nil,sK0) = sK0,
inference(resolve,[status(thm)],[c_328,c_245]) ).
cnf(c_8158,plain,
( app(nil,nil) != nil
| app(sK0,nil) != sK0
| ~ ssList(sK0)
| ~ ssList(nil) ),
inference(paramod,[status(thm)],[c_2044,c_618]) ).
cnf(c_8159,plain,
( app(nil,nil) != nil
| sK0 != sK0
| ~ ssList(sK0)
| ~ ssList(nil) ),
inference(paramod,[status(thm)],[c_1966,c_8158]) ).
cnf(c_8160,plain,
( nil != nil
| sK0 != sK0
| ~ ssList(sK0)
| ~ ssList(nil) ),
inference(paramod,[status(thm)],[c_1744,c_8159]) ).
cnf(c_8161,plain,
( nil != nil
| ~ ssList(sK0)
| ~ ssList(nil) ),
inference(copy,[status(thm)],[c_8160]) ).
cnf(c_8162,plain,
( ~ ssList(sK0)
| ~ ssList(nil) ),
inference(copy,[status(thm)],[c_8161]) ).
cnf(c_8163,plain,
~ ssList(sK0),
inference(resolve,[status(thm)],[c_231,c_8162]) ).
cnf(c_8156,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_328,c_8163]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC007+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.12/0.37 % Computer : n020.cluster.edu
% 0.12/0.37 % Model : x86_64 x86_64
% 0.12/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.37 % Memory : 8046.5625MB
% 0.12/0.37 % OS : Linux 6.8.0-71-generic
% 0.12/0.37 % CPULimit : 300
% 0.12/0.37 % WCLimit : 300
% 0.12/0.37 % DateTime : Sat Sep 26 12:03:48 UTC 2026
% 0.12/0.37 % CPUTime :
% 0.12/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.12/0.37 % Process 1486369 was started by sandbox on n020,
% 0.12/0.37 % Sat Sep 26 12:03:48 2026
% 0.12/0.37 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.12/0.39
% 0.12/0.39 % From the command line: assign(max_seconds, 300).
% 49.26/7.55
% 49.26/7.55 % given #500 (I,wt=37): 698 -ssList(A) | ssList(f35(A)) | -ssItem(B) | -ssItem(C) | -ssList(D) | -ssList(E) | app(app(D,cons(B,E)),cons(C,D)) != A | C != B. [factor(362,e,g)].
% 49.26/7.55
% 49.26/7.55 % given #1000 (I,wt=52): 1218 -ssList(A) | app(app(f35(A),cons(f33(A),f36(A))),cons(f34(A),f37(A))) = A | -ssItem(B) | -ssItem(C) | -ssList(D) | app(app(A,cons(B,D)),cons(C,D)) != A | C != B. [factor(714,e,f)].
% 49.26/7.55
% 49.26/7.55 % SZS status Theorem for theBenchmark
% 49.26/7.55
% 49.26/7.55 % Proof 1 at 5.60 (+ 1.48) seconds.
% 49.26/7.55 % Length of proof is 18.
% 49.26/7.55 % Level of proof is 6.
% 49.26/7.55 % Maximum clause weight is 26.000.
% 49.26/7.55 % Given clauses 1475.
% 49.26/7.55
% 49.26/7.55 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------