%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWC095+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 : n002.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 15.92s 2.59s
% Output : CNFRefutation 15.92s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 1
% Syntax : Number of formulae : 21 ( 11 unt; 0 def)
% Number of atoms : 109 ( 40 equ)
% Maximal formula atoms : 16 ( 5 avg)
% Number of connectives : 135 ( 47 ~; 37 |; 41 &)
% ( 0 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 7 con; 0-2 aty)
% Number of variables : 39 ( 0 sgn 23 !; 13 ?)
% Comments :
%------------------------------------------------------------------------------
fof(co1,conjecture,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ! [X] :
( ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( app(X2,X4) != X
| app(app(X2,X3),X4) != W
| ~ ssList(X4) ) ) )
| ? [Y] :
( ? [Z] :
( ? [X1] :
( app(Y,X1) = V
& app(app(Y,Z),X1) = U
& ssList(X1) )
& ssList(Z) )
& ssList(Y) )
| U != W
| V != X
| ~ ssList(X) ) ) ) ),
file('theBenchmark.p',co1) ).
fof(co1_neg,negated_conjecture,
~ ! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ! [X] :
( ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( app(X2,X4) != X
| app(app(X2,X3),X4) != W
| ~ ssList(X4) ) ) )
| ? [Y] :
( ? [Z] :
( ? [X1] :
( app(Y,X1) = V
& app(app(Y,Z),X1) = U
& ssList(X1) )
& ssList(Z) )
& ssList(Y) )
| U != W
| V != X
| ~ ssList(X) ) ) ) ),
inference(assume_negation,[status(cth)],[co1]) ).
fof(nnf_87,plain,
? [U] :
( ? [V] :
( ? [W] :
( ? [X] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( app(X2,X4) = X
& app(app(X2,X3),X4) = W
& ssList(X4) )
& ssList(X3) )
& ssList(X2) )
& ! [Y] :
( ! [Z] :
( ! [X1] :
( app(Y,X1) != V
| app(app(Y,Z),X1) != U
| ~ ssList(X1) )
| ~ ssList(Z) )
| ~ 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,
( app(sK4,sK6) = sK0
& app(app(sK4,sK5),sK6) = sK2
& ssList(sK6)
& ssList(sK5)
& ssList(sK4)
& ! [Y] :
( ! [Z] :
( ! [X1] :
( app(Y,X1) != sK1
| app(app(Y,Z),X1) != sK3
| ~ ssList(X1) )
| ~ ssList(Z) )
| ~ ssList(Y) )
& sK2 = sK3
& sK0 = sK1
& ssList(sK0)
& ssList(sK2)
& ssList(sK1)
& ssList(sK3) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3,sK1,sK2,sK0,sK4,sK5,sK6]),skolemize(U,sK3),skolemize(V,sK1),skolemize(W,sK2),skolemize(X,sK0),skolemize(X2,sK4),skolemize(X3,sK5),skolemize(X4,sK6)],[nnf_87]) ).
fof(sk_co1_neg,plain,
( app(sK4,sK6) = sK0
& app(app(sK4,sK5),sK6) = sK2
& ssList(sK6)
& ssList(sK5)
& ssList(sK4)
& ! [VAR_0,VAR_1,VAR_2] :
( app(VAR_0,VAR_2) != sK1
| app(app(VAR_0,VAR_1),VAR_2) != sK3
| ~ ssList(VAR_2)
| ~ ssList(VAR_1)
| ~ ssList(VAR_0) )
& sK2 = sK3
& sK0 = sK1
& ssList(sK0)
& ssList(sK2)
& ssList(sK1)
& ssList(sK3) ),
inference(cnf_transformation,[status(thm)],[sk_co1_neg_sk]) ).
cnf(c_331,negated_conjecture,
sK0 = sK1,
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_332,negated_conjecture,
sK2 = sK3,
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_333,negated_conjecture,
( app(A,C) != sK1
| app(app(A,B),C) != sK3
| ~ ssList(C)
| ~ ssList(B)
| ~ ssList(A) ),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_334,negated_conjecture,
ssList(sK4),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_335,negated_conjecture,
ssList(sK5),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_336,negated_conjecture,
ssList(sK6),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_337,negated_conjecture,
app(app(sK4,sK5),sK6) = sK2,
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_338,negated_conjecture,
app(app(sK4,sK5),sK6) = sK3,
inference(paramod,[status(thm)],[c_332,c_337]) ).
cnf(c_339,negated_conjecture,
app(sK4,sK6) = sK0,
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_340,negated_conjecture,
app(sK4,sK6) = sK1,
inference(paramod,[status(thm)],[c_331,c_339]) ).
cnf(c_3007,negated_conjecture,
( app(sK4,sK6) != sK1
| ~ ssList(sK6)
| ~ ssList(sK5)
| ~ ssList(sK4) ),
inference(resolve,[status(thm)],[c_338,c_333]) ).
cnf(c_3008,negated_conjecture,
( sK1 != sK1
| ~ ssList(sK6)
| ~ ssList(sK5)
| ~ ssList(sK4) ),
inference(paramod,[status(thm)],[c_340,c_3007]) ).
cnf(c_3009,negated_conjecture,
( ~ ssList(sK6)
| ~ ssList(sK5)
| ~ ssList(sK4) ),
inference(copy,[status(thm)],[c_3008]) ).
cnf(c_3010,negated_conjecture,
( ~ ssList(sK6)
| ~ ssList(sK5) ),
inference(resolve,[status(thm)],[c_334,c_3009]) ).
cnf(c_3011,negated_conjecture,
~ ssList(sK6),
inference(resolve,[status(thm)],[c_335,c_3010]) ).
cnf(c_3006,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_336,c_3011]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SWC095+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.18/0.45 % Computer : n002.cluster.edu
% 0.18/0.45 % Model : x86_64 x86_64
% 0.18/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.45 % Memory : 8046.5625MB
% 0.18/0.45 % OS : Linux 6.8.0-71-generic
% 0.18/0.45 % CPULimit : 300
% 0.18/0.45 % WCLimit : 300
% 0.18/0.45 % DateTime : Sat Sep 26 12:16:37 UTC 2026
% 0.18/0.46 % CPUTime :
% 0.18/0.46 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.18/0.46 % Process 1694643 was started by sandbox on n002,
% 0.18/0.46 % Sat Sep 26 12:16:37 2026
% 0.18/0.46 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.18/0.50
% 0.18/0.50 % From the command line: assign(max_seconds, 300).
% 15.92/2.59
% 15.92/2.59 % SZS status Theorem for theBenchmark
% 15.92/2.59
% 15.92/2.59 % Proof 1 at 1.68 (+ 0.16) seconds.
% 15.92/2.59 % Length of proof is 12.
% 15.92/2.59 % Level of proof is 3.
% 15.92/2.59 % Maximum clause weight is 26.000.
% 15.92/2.59 % Given clauses 165.
% 15.92/2.59
% 15.92/2.59 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------