%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWC094+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 : n014.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 08:56:48 AM UTC 2026
% Result : Theorem 34.23s 5.42s
% Output : CNFRefutation 34.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 3
% Syntax : Number of formulae : 26 ( 13 unt; 0 def)
% Number of atoms : 99 ( 47 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 120 ( 47 ~; 35 |; 29 &)
% ( 0 <=>; 9 =>; 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 : 40 ( 0 sgn 18 !; 10 ?)
% Comments :
%------------------------------------------------------------------------------
fof(ax28,axiom,
! [U] :
( ssList(U)
=> app(nil,U) = U ),
file('theBenchmark.p',ax28) ).
fof(co1,conjecture,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ! [X] :
( ssList(X)
=> ( ? [Y] :
( ? [Z] :
( ? [X1] :
( app(Y,X1) = V
& app(app(Y,Z),X1) = U
& ssList(X1) )
& ssList(Z) )
& ssList(Y) )
| X != 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)
=> ( ? [Y] :
( ? [Z] :
( ? [X1] :
( app(Y,X1) = V
& app(app(Y,Z),X1) = U
& ssList(X1) )
& ssList(Z) )
& ssList(Y) )
| X != W
| U != W
| V != X ) ) ) ) ),
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]) ).
fof(nnf_87,plain,
? [U] :
( ? [V] :
( ? [W] :
( ? [X] :
( ! [Y] :
( ! [Z] :
( ! [X1] :
( app(Y,X1) != V
| app(app(Y,Z),X1) != U
| ~ ssList(X1) )
| ~ ssList(Z) )
| ~ ssList(Y) )
& X = W
& 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,
( ! [Y] :
( ! [Z] :
( ! [X1] :
( app(Y,X1) != sK2
| app(app(Y,Z),X1) != sK0
| ~ ssList(X1) )
| ~ ssList(Z) )
| ~ ssList(Y) )
& sK1 = sK3
& sK3 = sK0
& sK1 = sK2
& ssList(sK1)
& ssList(sK3)
& ssList(sK2)
& ssList(sK0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK2,sK3,sK1]),skolemize(U,sK0),skolemize(V,sK2),skolemize(W,sK3),skolemize(X,sK1)],[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 = sK3
& 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,
sK1 = sK3,
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_4920,negated_conjecture,
sK2 = sK3,
inference(paramod,[status(thm)],[c_331,c_333]) ).
cnf(c_334,negated_conjecture,
sK2 = sK0,
inference(paramod,[status(thm)],[c_332,c_4920]) ).
cnf(c_335,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_336,negated_conjecture,
( app(A,C) != sK0
| app(app(A,B),C) != sK0
| ~ ssList(C)
| ~ ssList(B)
| ~ ssList(A) ),
inference(paramod,[status(thm)],[c_334,c_335]) ).
cnf(c_617,plain,
( app(A,B) != sK0
| app(app(A,A),B) != sK0
| ~ ssList(B)
| ~ ssList(A) ),
inference(factor,[status(thm)],[c_336]) ).
cnf(c_2646,plain,
app(nil,nil) = nil,
inference(resolve,[status(thm)],[c_245,c_231]) ).
cnf(c_2729,plain,
app(nil,sK0) = sK0,
inference(resolve,[status(thm)],[c_327,c_245]) ).
cnf(c_4921,plain,
( app(nil,A) != sK0
| app(app(nil,nil),A) != sK0
| ~ ssList(A) ),
inference(resolve,[status(thm)],[c_617,c_231]) ).
cnf(c_4922,plain,
( app(nil,A) != sK0
| app(nil,A) != sK0
| ~ ssList(A) ),
inference(paramod,[status(thm)],[c_2646,c_4921]) ).
cnf(c_4104,plain,
( app(nil,A) != sK0
| ~ ssList(A) ),
inference(copy,[status(thm)],[c_4922]) ).
cnf(c_4923,negated_conjecture,
app(nil,sK0) != sK0,
inference(resolve,[status(thm)],[c_4104,c_327]) ).
cnf(c_4924,negated_conjecture,
sK0 != sK0,
inference(paramod,[status(thm)],[c_2729,c_4923]) ).
cnf(c_4919,negated_conjecture,
$false,
inference(copy,[status(thm)],[c_4924]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SWC094+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.16/0.42 % Computer : n014.cluster.edu
% 0.16/0.42 % Model : x86_64 x86_64
% 0.16/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.42 % Memory : 8046.5625MB
% 0.16/0.42 % OS : Linux 6.8.0-71-generic
% 0.16/0.42 % CPULimit : 300
% 0.16/0.42 % WCLimit : 300
% 0.16/0.42 % DateTime : Sat Sep 26 12:13:47 UTC 2026
% 0.16/0.43 % CPUTime :
% 0.16/0.43 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.16/0.43 % Process 3113472 was started by sandbox on n014,
% 0.16/0.43 % Sat Sep 26 12:13:47 2026
% 0.16/0.43 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.16/0.47
% 0.16/0.47 % From the command line: assign(max_seconds, 300).
% 34.23/5.42
% 34.23/5.42 % given #500 (I,wt=27): 706 -ssList(A) | ssList(f36(A)) | -ssItem(B) | -ssItem(C) | -ssList(D) | -ssList(E) | app(app(D,cons(B,E)),cons(C,E)) != A | C != B. [factor(363,f,g)].
% 34.23/5.42
% 34.23/5.42 % given #1000 (I,wt=27): 1231 -ssList(A) | f34(A) = f33(A) | -ssItem(B) | -ssItem(C) | -ssList(D) | app(app(A,cons(B,D)),cons(C,D)) != A | C != B. [factor(721,e,f)].
% 34.23/5.42
% 34.23/5.42 % SZS status Theorem for theBenchmark
% 34.23/5.42
% 34.23/5.42 % Proof 1 at 4.51 (+ 0.38) seconds.
% 34.23/5.42 % Length of proof is 16.
% 34.23/5.42 % Level of proof is 6.
% 34.23/5.42 % Maximum clause weight is 18.000.
% 34.23/5.42 % Given clauses 1397.
% 34.23/5.42
% 34.23/5.42 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------