%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWC333+1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n019.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 08:57:30 AM UTC 2026
% Result : Theorem 14.83s 2.43s
% Output : CNFRefutation 14.83s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 1
% Syntax : Number of formulae : 36 ( 14 unt; 0 def)
% Number of atoms : 176 ( 12 equ)
% Maximal formula atoms : 28 ( 4 avg)
% Number of connectives : 231 ( 91 ~; 79 |; 51 &)
% ( 0 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 5 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 5 con; 0-0 aty)
% Number of variables : 24 ( 0 sgn 13 !; 7 ?)
% Comments :
%------------------------------------------------------------------------------
fof(co1,conjecture,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ! [X] :
( ssList(X)
=> ( ( totalorderedP(U)
& segmentP(V,U)
& ! [Z] :
( ssList(Z)
=> ( ~ totalorderedP(Z)
| ~ segmentP(Z,U)
| ~ segmentP(V,Z)
| ~ neq(U,Z) ) ) )
| ? [Y] :
( totalorderedP(Y)
& segmentP(Y,W)
& segmentP(X,Y)
& neq(W,Y)
& ssList(Y) )
| ~ totalorderedP(W)
| ~ segmentP(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)
=> ( ( totalorderedP(U)
& segmentP(V,U)
& ! [Z] :
( ssList(Z)
=> ( ~ totalorderedP(Z)
| ~ segmentP(Z,U)
| ~ segmentP(V,Z)
| ~ neq(U,Z) ) ) )
| ? [Y] :
( totalorderedP(Y)
& segmentP(Y,W)
& segmentP(X,Y)
& neq(W,Y)
& ssList(Y) )
| ~ totalorderedP(W)
| ~ segmentP(X,W)
| U != W
| V != X ) ) ) ) ),
inference(assume_negation,[status(cth)],[co1]) ).
fof(nnf_87,plain,
? [U] :
( ? [V] :
( ? [W] :
( ? [X] :
( ( ~ totalorderedP(U)
| ~ segmentP(V,U)
| ? [Z] :
( totalorderedP(Z)
& segmentP(Z,U)
& segmentP(V,Z)
& neq(U,Z)
& ssList(Z) ) )
& ! [Y] :
( ~ totalorderedP(Y)
| ~ segmentP(Y,W)
| ~ segmentP(X,Y)
| ~ neq(W,Y)
| ~ ssList(Y) )
& totalorderedP(W)
& segmentP(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,
( ( ~ totalorderedP(sK2)
| ~ segmentP(sK1,sK2)
| ( totalorderedP(sK0)
& segmentP(sK0,sK2)
& segmentP(sK1,sK0)
& neq(sK2,sK0)
& ssList(sK0) ) )
& ! [Y] :
( ~ totalorderedP(Y)
| ~ segmentP(Y,sK3)
| ~ segmentP(sK4,Y)
| ~ neq(sK3,Y)
| ~ ssList(Y) )
& totalorderedP(sK3)
& segmentP(sK4,sK3)
& sK3 = sK2
& sK4 = sK1
& ssList(sK4)
& ssList(sK3)
& ssList(sK1)
& ssList(sK2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK1,sK3,sK4,sK0]),skolemize(U,sK2),skolemize(V,sK1),skolemize(W,sK3),skolemize(X,sK4),skolemize(Z,sK0)],[nnf_87]) ).
fof(sk_co1_neg,plain,
( ( ~ totalorderedP(sK2)
| ~ segmentP(sK1,sK2)
| totalorderedP(sK0) )
& ( ~ totalorderedP(sK2)
| ~ segmentP(sK1,sK2)
| segmentP(sK0,sK2) )
& ( ~ totalorderedP(sK2)
| ~ segmentP(sK1,sK2)
| segmentP(sK1,sK0) )
& ( ~ totalorderedP(sK2)
| ~ segmentP(sK1,sK2)
| neq(sK2,sK0) )
& ( ~ totalorderedP(sK2)
| ~ segmentP(sK1,sK2)
| ssList(sK0) )
& ! [VAR_0] :
( ~ totalorderedP(VAR_0)
| ~ segmentP(VAR_0,sK3)
| ~ segmentP(sK4,VAR_0)
| ~ neq(sK3,VAR_0)
| ~ ssList(VAR_0) )
& totalorderedP(sK3)
& segmentP(sK4,sK3)
& sK3 = sK2
& sK4 = sK1
& ssList(sK4)
& ssList(sK3)
& ssList(sK1)
& ssList(sK2) ),
inference(cnf_transformation,[status(thm)],[sk_co1_neg_sk]) ).
cnf(c_190,negated_conjecture,
( ~ totalorderedP(sK2)
| ~ segmentP(sK1,sK2)
| totalorderedP(sK0) ),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_191,negated_conjecture,
( ~ totalorderedP(sK2)
| ~ segmentP(sK1,sK2)
| segmentP(sK0,sK2) ),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_192,negated_conjecture,
( ~ totalorderedP(sK2)
| ~ segmentP(sK1,sK2)
| segmentP(sK1,sK0) ),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_193,negated_conjecture,
( ~ totalorderedP(sK2)
| ~ segmentP(sK1,sK2)
| neq(sK2,sK0) ),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_194,negated_conjecture,
( ~ totalorderedP(sK2)
| ~ segmentP(sK1,sK2)
| ssList(sK0) ),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_195,negated_conjecture,
( ~ totalorderedP(A)
| ~ segmentP(A,sK3)
| ~ segmentP(sK4,A)
| ~ neq(sK3,A)
| ~ ssList(A) ),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_196,negated_conjecture,
totalorderedP(sK3),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_197,negated_conjecture,
segmentP(sK4,sK3),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_198,negated_conjecture,
sK3 = sK2,
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_199,negated_conjecture,
sK4 = sK1,
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_3130,negated_conjecture,
segmentP(sK1,sK3),
inference(paramod,[status(thm)],[c_199,c_197]) ).
cnf(c_548,negated_conjecture,
segmentP(sK1,sK2),
inference(paramod,[status(thm)],[c_198,c_3130]) ).
cnf(c_549,negated_conjecture,
totalorderedP(sK2),
inference(paramod,[status(thm)],[c_198,c_196]) ).
cnf(c_3131,negated_conjecture,
( ~ totalorderedP(A)
| ~ segmentP(A,sK3)
| ~ segmentP(sK4,A)
| ~ neq(sK2,A)
| ~ ssList(A) ),
inference(paramod,[status(thm)],[c_198,c_195]) ).
cnf(c_3132,negated_conjecture,
( ~ totalorderedP(A)
| ~ segmentP(A,sK3)
| ~ segmentP(sK1,A)
| ~ neq(sK2,A)
| ~ ssList(A) ),
inference(paramod,[status(thm)],[c_199,c_3131]) ).
cnf(c_550,negated_conjecture,
( ~ totalorderedP(A)
| ~ segmentP(A,sK2)
| ~ segmentP(sK1,A)
| ~ neq(sK2,A)
| ~ ssList(A) ),
inference(paramod,[status(thm)],[c_198,c_3132]) ).
cnf(c_3133,negated_conjecture,
( ~ totalorderedP(sK2)
| ssList(sK0) ),
inference(resolve,[status(thm)],[c_548,c_194]) ).
cnf(c_1042,negated_conjecture,
ssList(sK0),
inference(resolve,[status(thm)],[c_549,c_3133]) ).
cnf(c_3134,negated_conjecture,
( ~ totalorderedP(sK2)
| neq(sK2,sK0) ),
inference(resolve,[status(thm)],[c_548,c_193]) ).
cnf(c_1043,negated_conjecture,
neq(sK2,sK0),
inference(resolve,[status(thm)],[c_549,c_3134]) ).
cnf(c_3135,negated_conjecture,
( ~ totalorderedP(sK2)
| segmentP(sK1,sK0) ),
inference(resolve,[status(thm)],[c_548,c_192]) ).
cnf(c_1044,negated_conjecture,
segmentP(sK1,sK0),
inference(resolve,[status(thm)],[c_549,c_3135]) ).
cnf(c_3136,negated_conjecture,
( ~ totalorderedP(sK2)
| segmentP(sK0,sK2) ),
inference(resolve,[status(thm)],[c_548,c_191]) ).
cnf(c_1045,negated_conjecture,
segmentP(sK0,sK2),
inference(resolve,[status(thm)],[c_549,c_3136]) ).
cnf(c_3137,negated_conjecture,
( ~ totalorderedP(sK2)
| totalorderedP(sK0) ),
inference(resolve,[status(thm)],[c_548,c_190]) ).
cnf(c_1046,negated_conjecture,
totalorderedP(sK0),
inference(resolve,[status(thm)],[c_549,c_3137]) ).
cnf(c_3138,negated_conjecture,
( ~ totalorderedP(sK0)
| ~ segmentP(sK0,sK2)
| ~ segmentP(sK1,sK0)
| ~ neq(sK2,sK0) ),
inference(resolve,[status(thm)],[c_1042,c_550]) ).
cnf(c_3139,negated_conjecture,
( ~ totalorderedP(sK0)
| ~ segmentP(sK0,sK2)
| ~ segmentP(sK1,sK0) ),
inference(resolve,[status(thm)],[c_1043,c_3138]) ).
cnf(c_3140,negated_conjecture,
( ~ totalorderedP(sK0)
| ~ segmentP(sK0,sK2) ),
inference(resolve,[status(thm)],[c_1044,c_3139]) ).
cnf(c_3141,negated_conjecture,
~ totalorderedP(sK0),
inference(resolve,[status(thm)],[c_1045,c_3140]) ).
cnf(c_3129,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_1046,c_3141]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC333+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.37 % Computer : n019.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Sat Sep 26 12:49:18 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.37 % Process 1347842 was started by sandbox2 on n019,
% 0.09/0.37 % Sat Sep 26 12:49:18 2026
% 0.09/0.37 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.09/0.40
% 0.09/0.40 % From the command line: assign(max_seconds, 300).
% 14.83/2.43
% 14.83/2.43 % given #500 (I,wt=37): 698 -ssList(A) | -ssItem(B) | -ssItem(C) | -ssList(D) | -ssList(E) | app(app(A,cons(B,D)),cons(C,E)) != A | C != B | ssList(f35(A)). [factor(365,a,d)].
% 14.83/2.43
% 14.83/2.43 % SZS status Theorem for theBenchmark
% 14.83/2.43
% 14.83/2.43 % Proof 1 at 1.44 (+ 0.22) seconds.
% 14.83/2.43 % Length of proof is 20.
% 14.83/2.43 % Level of proof is 4.
% 14.83/2.43 % Maximum clause weight is 15.000.
% 14.83/2.43 % Given clauses 824.
% 14.83/2.43
% 14.83/2.43 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------