%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWC339+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 : n010.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 08:57:31 AM UTC 2026
% Result : Theorem 7.28s 1.32s
% Output : CNFRefutation 7.28s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 2
% Syntax : Number of formulae : 26 ( 14 unt; 0 def)
% Number of atoms : 182 ( 52 equ)
% Maximal formula atoms : 28 ( 7 avg)
% Number of connectives : 238 ( 82 ~; 72 |; 69 &)
% ( 1 <=>; 14 =>; 0 <=; 0 <~>)
% Maximal formula depth : 30 ( 7 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 7 con; 0-2 aty)
% Number of variables : 66 ( 0 sgn 38 !; 24 ?)
% Comments :
%------------------------------------------------------------------------------
fof(ax7,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ( segmentP(U,V)
<=> ? [W] :
( ? [X] :
( app(app(W,V),X) = U
& ssList(X) )
& ssList(W) ) ) ) ),
file('theBenchmark.p',ax7) ).
fof(co1,conjecture,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ! [X] :
( ssList(X)
=> ( ( totalorderedP(U)
& segmentP(V,U) )
| ( nil = W
& nil != X )
| ! [Y] :
( ssList(Y)
=> ! [Z] :
( ssList(Z)
=> ( ? [X5] :
( ? [X6] :
( ? [X7] :
( ? [X8] :
( leq(X7,X5)
& app(X8,cons(X7,nil)) = W
& ssList(X8) )
& ssItem(X7) )
& app(cons(X5,nil),X6) = Z
& ssList(X6) )
& ssItem(X5) )
| ? [X1] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( leq(X1,X3)
& app(cons(X3,nil),X4) = W
& ssList(X4) )
& ssItem(X3) )
& app(X2,cons(X1,nil)) = Y
& ssList(X2) )
& ssItem(X1) )
| ~ totalorderedP(W)
| app(app(Y,W),Z) != X ) ) )
| 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)
=> ( ( totalorderedP(U)
& segmentP(V,U) )
| ( nil = W
& nil != X )
| ! [Y] :
( ssList(Y)
=> ! [Z] :
( ssList(Z)
=> ( ? [X5] :
( ? [X6] :
( ? [X7] :
( ? [X8] :
( leq(X7,X5)
& app(X8,cons(X7,nil)) = W
& ssList(X8) )
& ssItem(X7) )
& app(cons(X5,nil),X6) = Z
& ssList(X6) )
& ssItem(X5) )
| ? [X1] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( leq(X1,X3)
& app(cons(X3,nil),X4) = W
& ssList(X4) )
& ssItem(X3) )
& app(X2,cons(X1,nil)) = Y
& ssList(X2) )
& ssItem(X1) )
| ~ totalorderedP(W)
| app(app(Y,W),Z) != X ) ) )
| U != W
| V != X ) ) ) ) ),
inference(assume_negation,[status(cth)],[co1]) ).
cnf(c_213,plain,
( app(app(C,B),D) != A
| ~ ssList(D)
| ~ ssList(C)
| segmentP(A,B)
| ~ ssList(B)
| ~ ssList(A) ),
inference(clausify,[status(thm)],[ax7]) ).
fof(nnf_87,plain,
? [U] :
( ? [V] :
( ? [W] :
( ? [X] :
( ( ~ totalorderedP(U)
| ~ segmentP(V,U) )
& ( nil != W
| nil = X )
& ? [Y] :
( ? [Z] :
( ! [X5] :
( ! [X6] :
( ! [X7] :
( ! [X8] :
( ~ leq(X7,X5)
| app(X8,cons(X7,nil)) != W
| ~ ssList(X8) )
| ~ ssItem(X7) )
| app(cons(X5,nil),X6) != Z
| ~ ssList(X6) )
| ~ ssItem(X5) )
& ! [X1] :
( ! [X2] :
( ! [X3] :
( ! [X4] :
( ~ leq(X1,X3)
| app(cons(X3,nil),X4) != W
| ~ ssList(X4) )
| ~ ssItem(X3) )
| app(X2,cons(X1,nil)) != Y
| ~ ssList(X2) )
| ~ ssItem(X1) )
& totalorderedP(W)
& app(app(Y,W),Z) = X
& 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,
( ( ~ totalorderedP(sK0)
| ~ segmentP(sK1,sK0) )
& ( nil != sK3
| nil = sK2 )
& ! [X5] :
( ! [X6] :
( ! [X7] :
( ! [X8] :
( ~ leq(X7,X5)
| app(X8,cons(X7,nil)) != sK3
| ~ ssList(X8) )
| ~ ssItem(X7) )
| app(cons(X5,nil),X6) != sK5
| ~ ssList(X6) )
| ~ ssItem(X5) )
& ! [X1] :
( ! [X2] :
( ! [X3] :
( ! [X4] :
( ~ leq(X1,X3)
| app(cons(X3,nil),X4) != sK3
| ~ ssList(X4) )
| ~ ssItem(X3) )
| app(X2,cons(X1,nil)) != sK4
| ~ ssList(X2) )
| ~ ssItem(X1) )
& totalorderedP(sK3)
& app(app(sK4,sK3),sK5) = sK2
& ssList(sK5)
& ssList(sK4)
& sK3 = sK0
& sK2 = sK1
& ssList(sK2)
& ssList(sK3)
& ssList(sK1)
& ssList(sK0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK3,sK2,sK4,sK5]),skolemize(U,sK0),skolemize(V,sK1),skolemize(W,sK3),skolemize(X,sK2),skolemize(Y,sK4),skolemize(Z,sK5)],[nnf_87]) ).
fof(sk_co1_neg,plain,
( ( ~ totalorderedP(sK0)
| ~ segmentP(sK1,sK0) )
& ( nil != sK3
| nil = sK2 )
& ! [VAR_0,VAR_1,VAR_2,VAR_3] :
( ~ leq(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) != sK5
| ~ ssList(VAR_1)
| ~ ssItem(VAR_0) )
& ! [VAR_0,VAR_1,VAR_2,VAR_3] :
( ~ leq(VAR_0,VAR_2)
| app(cons(VAR_2,nil),VAR_3) != sK3
| ~ ssList(VAR_3)
| ~ ssItem(VAR_2)
| app(VAR_1,cons(VAR_0,nil)) != sK4
| ~ ssList(VAR_1)
| ~ ssItem(VAR_0) )
& totalorderedP(sK3)
& app(app(sK4,sK3),sK5) = sK2
& ssList(sK5)
& ssList(sK4)
& sK3 = sK0
& sK2 = sK1
& ssList(sK2)
& ssList(sK3)
& ssList(sK1)
& 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_328,negated_conjecture,
ssList(sK1),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_331,negated_conjecture,
sK2 = sK1,
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,
ssList(sK4),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_334,negated_conjecture,
ssList(sK5),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_335,negated_conjecture,
app(app(sK4,sK3),sK5) = sK2,
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_2770,negated_conjecture,
app(app(sK4,sK0),sK5) = sK2,
inference(paramod,[status(thm)],[c_332,c_335]) ).
cnf(c_336,negated_conjecture,
app(app(sK4,sK0),sK5) = sK1,
inference(paramod,[status(thm)],[c_331,c_2770]) ).
cnf(c_337,negated_conjecture,
totalorderedP(sK3),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_338,negated_conjecture,
totalorderedP(sK0),
inference(paramod,[status(thm)],[c_332,c_337]) ).
cnf(c_345,negated_conjecture,
( ~ totalorderedP(sK0)
| ~ segmentP(sK1,sK0) ),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_346,negated_conjecture,
~ segmentP(sK1,sK0),
inference(resolve,[status(thm)],[c_338,c_345]) ).
cnf(c_2771,negated_conjecture,
( ~ ssList(sK5)
| ~ ssList(sK4)
| segmentP(sK1,sK0)
| ~ ssList(sK0)
| ~ ssList(sK1) ),
inference(resolve,[status(thm)],[c_336,c_213]) ).
cnf(c_2772,negated_conjecture,
( ~ ssList(sK5)
| ~ ssList(sK4)
| segmentP(sK1,sK0)
| ~ ssList(sK0) ),
inference(resolve,[status(thm)],[c_328,c_2771]) ).
cnf(c_2773,negated_conjecture,
( ~ ssList(sK5)
| ~ ssList(sK4)
| segmentP(sK1,sK0) ),
inference(resolve,[status(thm)],[c_327,c_2772]) ).
cnf(c_2774,negated_conjecture,
( ~ ssList(sK5)
| ~ ssList(sK4) ),
inference(resolve,[status(thm)],[c_346,c_2773]) ).
cnf(c_2775,negated_conjecture,
~ ssList(sK5),
inference(resolve,[status(thm)],[c_333,c_2774]) ).
cnf(c_2769,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_334,c_2775]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC339+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n010.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sat Sep 26 12:50:15 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.14/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.14/0.37 % Process 3357015 was started by sandbox on n010,
% 0.14/0.37 % Sat Sep 26 12:50:15 2026
% 0.14/0.37 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.14/0.38
% 0.14/0.38 % From the command line: assign(max_seconds, 300).
% 7.28/1.32
% 7.28/1.32 % SZS status Theorem for theBenchmark
% 7.28/1.32
% 7.28/1.32 % Proof 1 at 0.82 (+ 0.10) seconds.
% 7.28/1.32 % Length of proof is 16.
% 7.28/1.32 % Level of proof is 4.
% 7.28/1.32 % Maximum clause weight is 26.000.
% 7.28/1.32 % Given clauses 163.
% 7.28/1.32
% 7.28/1.32 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------