%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWC351+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 08:57:33 AM UTC 2026
% Result : Theorem 8.85s 6.59s
% Output : CNFRefutation 8.85s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 2
% Syntax : Number of formulae : 21 ( 11 unt; 0 def)
% Number of atoms : 130 ( 42 equ)
% Maximal formula atoms : 20 ( 6 avg)
% Number of connectives : 161 ( 52 ~; 45 |; 51 &)
% ( 1 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 28 ( 8 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 6 con; 0-2 aty)
% Number of variables : 41 ( 0 sgn 24 !; 14 ?)
% Comments :
%------------------------------------------------------------------------------
fof(ax5,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ( frontsegP(U,V)
<=> ? [W] :
( app(V,W) = U
& ssList(W) ) ) ) ),
file('theBenchmark.p',ax5) ).
fof(co1,conjecture,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ! [X] :
( ssList(X)
=> ( ( nil = W
& nil != X )
| frontsegP(V,U)
| ! [Y] :
( ssList(Y)
=> ( ? [Z] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( lt(X2,Z)
& app(X3,cons(X2,nil)) = W
& ssList(X3) )
& ssItem(X2) )
& app(cons(Z,nil),X1) = Y
& ssList(X1) )
& ssItem(Z) )
| ~ strictorderedP(W)
| app(W,Y) != X ) )
| ~ neq(V,nil)
| 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)
=> ( ( nil = W
& nil != X )
| frontsegP(V,U)
| ! [Y] :
( ssList(Y)
=> ( ? [Z] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( lt(X2,Z)
& app(X3,cons(X2,nil)) = W
& ssList(X3) )
& ssItem(X2) )
& app(cons(Z,nil),X1) = Y
& ssList(X1) )
& ssItem(Z) )
| ~ strictorderedP(W)
| app(W,Y) != X ) )
| ~ neq(V,nil)
| U != W
| V != X ) ) ) ) ),
inference(assume_negation,[status(cth)],[co1]) ).
cnf(c_207,plain,
( app(B,C) != A
| ~ ssList(C)
| frontsegP(A,B)
| ~ ssList(B)
| ~ ssList(A) ),
inference(clausify,[status(thm)],[ax5]) ).
fof(nnf_87,plain,
? [U] :
( ? [V] :
( ? [W] :
( ? [X] :
( ( nil != W
| nil = X )
& ~ frontsegP(V,U)
& ? [Y] :
( ! [Z] :
( ! [X1] :
( ! [X2] :
( ! [X3] :
( ~ lt(X2,Z)
| app(X3,cons(X2,nil)) != W
| ~ ssList(X3) )
| ~ ssItem(X2) )
| app(cons(Z,nil),X1) != Y
| ~ ssList(X1) )
| ~ ssItem(Z) )
& strictorderedP(W)
& app(W,Y) = X
& ssList(Y) )
& neq(V,nil)
& 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,
( ( nil != sK3
| nil = sK2 )
& ~ frontsegP(sK1,sK0)
& ! [Z] :
( ! [X1] :
( ! [X2] :
( ! [X3] :
( ~ lt(X2,Z)
| app(X3,cons(X2,nil)) != sK3
| ~ ssList(X3) )
| ~ ssItem(X2) )
| app(cons(Z,nil),X1) != sK4
| ~ ssList(X1) )
| ~ ssItem(Z) )
& strictorderedP(sK3)
& app(sK3,sK4) = sK2
& ssList(sK4)
& neq(sK1,nil)
& sK3 = sK0
& sK2 = 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 )
& ~ frontsegP(sK1,sK0)
& ! [VAR_0,VAR_1,VAR_2,VAR_3] :
( ~ lt(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) )
& strictorderedP(sK3)
& app(sK3,sK4) = sK2
& ssList(sK4)
& neq(sK1,nil)
& sK3 = sK0
& sK2 = sK1
& ssList(sK2)
& ssList(sK3)
& ssList(sK1)
& ssList(sK0) ),
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_329,negated_conjecture,
ssList(sK1),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_332,negated_conjecture,
sK2 = sK1,
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_333,negated_conjecture,
sK3 = sK0,
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,
app(sK3,sK4) = sK2,
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_2546,negated_conjecture,
app(sK0,sK4) = sK2,
inference(paramod,[status(thm)],[c_333,c_335]) ).
cnf(c_336,negated_conjecture,
app(sK0,sK4) = sK1,
inference(paramod,[status(thm)],[c_332,c_2546]) ).
cnf(c_341,negated_conjecture,
~ frontsegP(sK1,sK0),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_2547,negated_conjecture,
( ~ ssList(sK4)
| frontsegP(sK1,sK0)
| ~ ssList(sK0)
| ~ ssList(sK1) ),
inference(resolve,[status(thm)],[c_336,c_207]) ).
cnf(c_2548,negated_conjecture,
( ~ ssList(sK4)
| frontsegP(sK1,sK0)
| ~ ssList(sK0) ),
inference(resolve,[status(thm)],[c_329,c_2547]) ).
cnf(c_2549,negated_conjecture,
( ~ ssList(sK4)
| frontsegP(sK1,sK0) ),
inference(resolve,[status(thm)],[c_328,c_2548]) ).
cnf(c_2550,negated_conjecture,
~ ssList(sK4),
inference(resolve,[status(thm)],[c_341,c_2549]) ).
cnf(c_2545,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_334,c_2550]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC351+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/5.36 % Computer : n017.cluster.edu
% 0.09/5.36 % Model : x86_64 x86_64
% 0.09/5.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/5.36 % Memory : 8046.5625MB
% 0.09/5.36 % OS : Linux 6.8.0-71-generic
% 0.09/5.36 % CPULimit : 300
% 0.09/5.36 % WCLimit : 300
% 0.09/5.36 % DateTime : Sat Sep 26 12:47:26 UTC 2026
% 0.09/5.36 % CPUTime :
% 0.09/5.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/5.37 % Process 748998 was started by sandbox on n017,
% 0.09/5.37 % Sat Sep 26 12:47:26 2026
% 0.09/5.37 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.09/5.39
% 0.09/5.39 % From the command line: assign(max_seconds, 300).
% 8.85/6.59
% 8.85/6.59 % SZS status Theorem for theBenchmark
% 8.85/6.59
% 8.85/6.59 % Proof 1 at 1.07 (+ 0.10) seconds.
% 8.85/6.59 % Length of proof is 12.
% 8.85/6.59 % Level of proof is 3.
% 8.85/6.59 % Maximum clause weight is 18.000.
% 8.85/6.59 % Given clauses 162.
% 8.85/6.59
% 8.85/6.59 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------