%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWC408+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 : n017.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 08:57:44 AM UTC 2026
% Result : Theorem 18.53s 2.88s
% Output : CNFRefutation 18.53s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 2
% Syntax : Number of formulae : 22 ( 12 unt; 0 def)
% Number of atoms : 75 ( 18 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 77 ( 24 ~; 21 |; 18 &)
% ( 1 <=>; 13 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 5 con; 0-2 aty)
% Number of variables : 23 ( 0 sgn 13 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(ax36,axiom,
! [U] :
( ssItem(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ( memberP(app(V,W),U)
<=> ( memberP(W,U)
| memberP(V,U) ) ) ) ) ),
file('theBenchmark.p',ax36) ).
fof(co1,conjecture,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ! [X] :
( ssList(X)
=> ( ! [Y] :
( ssItem(Y)
=> ( memberP(U,Y)
| ~ memberP(V,Y) ) )
| U != W
| V != X
| app(X,X) != W ) ) ) ) ),
file('theBenchmark.p',co1) ).
fof(co1_neg,negated_conjecture,
~ ! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ! [X] :
( ssList(X)
=> ( ! [Y] :
( ssItem(Y)
=> ( memberP(U,Y)
| ~ memberP(V,Y) ) )
| U != W
| V != X
| app(X,X) != W ) ) ) ) ),
inference(assume_negation,[status(cth)],[co1]) ).
cnf(c_256,plain,
( ~ memberP(B,A)
| memberP(app(B,C),A)
| ~ ssList(C)
| ~ ssList(B)
| ~ ssItem(A) ),
inference(clausify,[status(thm)],[ax36]) ).
fof(nnf_87,plain,
? [U] :
( ? [V] :
( ? [W] :
( ? [X] :
( ? [Y] :
( ~ memberP(U,Y)
& memberP(V,Y)
& ssItem(Y) )
& W = U
& X = V
& app(X,X) = W
& ssList(X) )
& ssList(W) )
& ssList(V) )
& ssList(U) ),
inference(fof_nnf,[status(thm)],[co1_neg]) ).
fof(sk_co1_neg,plain,
( ~ memberP(sK3,sK4)
& memberP(sK0,sK4)
& ssItem(sK4)
& sK2 = sK3
& sK1 = sK0
& app(sK1,sK1) = sK2
& ssList(sK1)
& ssList(sK2)
& ssList(sK0)
& ssList(sK3) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3,sK0,sK2,sK1,sK4]),skolemize(U,sK3),skolemize(V,sK0),skolemize(W,sK2),skolemize(X,sK1),skolemize(Y,sK4)],[nnf_87]) ).
cnf(c_328,negated_conjecture,
ssList(sK0),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_331,negated_conjecture,
app(sK1,sK1) = sK2,
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_332,negated_conjecture,
sK1 = sK0,
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_333,negated_conjecture,
sK2 = sK3,
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_334,negated_conjecture,
ssItem(sK4),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_335,negated_conjecture,
memberP(sK0,sK4),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_336,negated_conjecture,
~ memberP(sK3,sK4),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_585,plain,
( ~ memberP(B,A)
| memberP(app(B,B),A)
| ~ ssList(B)
| ~ ssItem(A) ),
inference(factor,[status(thm)],[c_256]) ).
cnf(c_2567,negated_conjecture,
app(sK0,sK1) = sK2,
inference(paramod,[status(thm)],[c_332,c_331]) ).
cnf(c_2568,negated_conjecture,
app(sK0,sK0) = sK2,
inference(paramod,[status(thm)],[c_332,c_2567]) ).
cnf(c_616,negated_conjecture,
app(sK0,sK0) = sK3,
inference(paramod,[status(thm)],[c_333,c_2568]) ).
cnf(c_2569,negated_conjecture,
( memberP(app(sK0,sK0),sK4)
| ~ ssList(sK0)
| ~ ssItem(sK4) ),
inference(resolve,[status(thm)],[c_585,c_335]) ).
cnf(c_2570,negated_conjecture,
( memberP(sK3,sK4)
| ~ ssList(sK0)
| ~ ssItem(sK4) ),
inference(paramod,[status(thm)],[c_616,c_2569]) ).
cnf(c_2571,negated_conjecture,
( memberP(sK3,sK4)
| ~ ssList(sK0) ),
inference(resolve,[status(thm)],[c_334,c_2570]) ).
cnf(c_2572,negated_conjecture,
memberP(sK3,sK4),
inference(resolve,[status(thm)],[c_328,c_2571]) ).
cnf(c_2566,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_336,c_2572]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SWC408+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.18/0.43 % Computer : n017.cluster.edu
% 0.18/0.43 % Model : x86_64 x86_64
% 0.18/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.43 % Memory : 8046.5625MB
% 0.18/0.43 % OS : Linux 6.8.0-71-generic
% 0.18/0.43 % CPULimit : 300
% 0.18/0.43 % WCLimit : 300
% 0.18/0.43 % DateTime : Sat Sep 26 12:54:49 UTC 2026
% 0.18/0.43 % CPUTime :
% 0.18/0.43 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.18/0.43 % Process 762636 was started by sandbox on n017,
% 0.18/0.43 % Sat Sep 26 12:54:49 2026
% 0.18/0.43 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.18/0.47
% 0.18/0.47 % From the command line: assign(max_seconds, 300).
% 18.53/2.88
% 18.53/2.88 % SZS status Theorem for theBenchmark
% 18.53/2.88
% 18.53/2.88 % Proof 1 at 1.95 (+ 0.22) seconds.
% 18.53/2.88 % Length of proof is 13.
% 18.53/2.88 % Level of proof is 3.
% 18.53/2.88 % Maximum clause weight is 18.000.
% 18.53/2.88 % Given clauses 390.
% 18.53/2.88
% 18.53/2.88 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------