%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWC336+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 : n012.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 29.10s 4.51s
% Output : CNFRefutation 29.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 8
% Syntax : Number of formulae : 86 ( 24 unt; 0 def)
% Number of atoms : 303 ( 94 equ)
% Maximal formula atoms : 44 ( 3 avg)
% Number of connectives : 322 ( 105 ~; 137 |; 63 &)
% ( 2 <=>; 15 =>; 0 <=; 0 <~>)
% Maximal formula depth : 26 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 8 con; 0-2 aty)
% Number of variables : 54 ( 0 sgn 27 !; 14 ?)
% Comments :
%------------------------------------------------------------------------------
fof(ax4,axiom,
! [U] :
( ssList(U)
=> ( singletonP(U)
<=> ? [V] :
( cons(V,nil) = U
& ssItem(V) ) ) ),
file('theBenchmark.p',ax4) ).
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(ax57,axiom,
! [U] :
( ssList(U)
=> segmentP(U,nil) ),
file('theBenchmark.p',ax57) ).
fof(ax65,axiom,
! [U] :
( ssItem(U)
=> totalorderedP(cons(U,nil)) ),
file('theBenchmark.p',ax65) ).
fof(co1,conjecture,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ! [X] :
( ( totalorderedP(U)
& segmentP(V,U) )
| ( ( nil != W
| nil != X )
& ! [Y] :
( ssItem(Y)
=> ! [Z] :
( ssList(Z)
=> ! [X1] :
( ? [X3] :
( lt(X3,Y)
& memberP(X1,X3)
& ssItem(X3) )
| ? [X2] :
( lt(Y,X2)
& memberP(Z,X2)
& ssItem(X2) )
| app(app(Z,W),X1) != X
| cons(Y,nil) != W
| ~ ssList(X1) ) ) ) )
| 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] :
( ( totalorderedP(U)
& segmentP(V,U) )
| ( ( nil != W
| nil != X )
& ! [Y] :
( ssItem(Y)
=> ! [Z] :
( ssList(Z)
=> ! [X1] :
( ? [X3] :
( lt(X3,Y)
& memberP(X1,X3)
& ssItem(X3) )
| ? [X2] :
( lt(Y,X2)
& memberP(Z,X2)
& ssItem(X2) )
| app(app(Z,W),X1) != X
| cons(Y,nil) != W
| ~ ssList(X1) ) ) ) )
| U != W
| V != X
| ~ ssList(X) ) ) ) ),
inference(assume_negation,[status(cth)],[co1]) ).
cnf(c_203,plain,
( cons(B,nil) != A
| ~ ssItem(B)
| singletonP(A)
| ~ ssList(A) ),
inference(clausify,[status(thm)],[ax4]) ).
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(ax17,axiom,
ssList(nil),
file('theBenchmark.p',ax17) ).
cnf(c_231,plain,
ssList(nil),
inference(clausify,[status(thm)],[ax17]) ).
fof(ax39,axiom,
~ singletonP(nil),
file('theBenchmark.p',ax39) ).
cnf(c_262,plain,
~ singletonP(nil),
inference(clausify,[status(thm)],[ax39]) ).
cnf(c_284,plain,
( segmentP(A,nil)
| ~ ssList(A) ),
inference(clausify,[status(thm)],[ax57]) ).
cnf(c_287,plain,
( totalorderedP(cons(A,nil))
| ~ ssItem(A) ),
inference(clausify,[status(thm)],[ax65]) ).
fof(ax66,axiom,
totalorderedP(nil),
file('theBenchmark.p',ax66) ).
cnf(c_288,plain,
totalorderedP(nil),
inference(clausify,[status(thm)],[ax66]) ).
fof(nnf_87,plain,
? [U] :
( ? [V] :
( ? [W] :
( ? [X] :
( ( ~ totalorderedP(U)
| ~ segmentP(V,U) )
& ( ( nil = W
& nil = X )
| ? [Y] :
( ? [Z] :
( ? [X1] :
( ! [X3] :
( ~ lt(X3,Y)
| ~ memberP(X1,X3)
| ~ ssItem(X3) )
& ! [X2] :
( ~ lt(Y,X2)
| ~ memberP(Z,X2)
| ~ ssItem(X2) )
& app(app(Z,W),X1) = X
& cons(Y,nil) = W
& ssList(X1) )
& ssList(Z) )
& ssItem(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 )
| ( ! [X3] :
( ~ lt(X3,sK4)
| ~ memberP(sK6,X3)
| ~ ssItem(X3) )
& ! [X2] :
( ~ lt(sK4,X2)
| ~ memberP(sK5,X2)
| ~ ssItem(X2) )
& app(app(sK5,sK3),sK6) = sK2
& cons(sK4,nil) = sK3
& ssList(sK6)
& ssList(sK5)
& ssItem(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,sK6]),skolemize(U,sK0),skolemize(V,sK1),skolemize(W,sK3),skolemize(X,sK2),skolemize(Y,sK4),skolemize(Z,sK5),skolemize(X1,sK6)],[nnf_87]) ).
fof(sk_co1_neg,plain,
( ( ~ totalorderedP(sK0)
| ~ segmentP(sK1,sK0) )
& ! [VAR_0] :
( nil = sK3
| ~ lt(VAR_0,sK4)
| ~ memberP(sK6,VAR_0)
| ~ ssItem(VAR_0) )
& ! [VAR_0] :
( nil = sK2
| ~ lt(VAR_0,sK4)
| ~ memberP(sK6,VAR_0)
| ~ ssItem(VAR_0) )
& ! [VAR_0] :
( nil = sK3
| ~ lt(sK4,VAR_0)
| ~ memberP(sK5,VAR_0)
| ~ ssItem(VAR_0) )
& ! [VAR_0] :
( nil = sK2
| ~ lt(sK4,VAR_0)
| ~ memberP(sK5,VAR_0)
| ~ ssItem(VAR_0) )
& ( nil = sK3
| app(app(sK5,sK3),sK6) = sK2 )
& ( nil = sK2
| app(app(sK5,sK3),sK6) = sK2 )
& ( nil = sK3
| cons(sK4,nil) = sK3 )
& ( nil = sK2
| cons(sK4,nil) = sK3 )
& ( nil = sK3
| ssList(sK6) )
& ( nil = sK2
| ssList(sK6) )
& ( nil = sK3
| ssList(sK5) )
& ( nil = sK2
| ssList(sK5) )
& ( nil = sK3
| ssItem(sK4) )
& ( nil = sK2
| ssItem(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_335,negated_conjecture,
( nil = sK3
| ssItem(sK4) ),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_8927,negated_conjecture,
( nil = sK0
| ssItem(sK4) ),
inference(paramod,[status(thm)],[c_332,c_335]) ).
cnf(c_336,negated_conjecture,
( sK0 = nil
| ssItem(sK4) ),
inference(copy,[status(thm)],[c_8927]) ).
cnf(c_339,negated_conjecture,
( nil = sK3
| ssList(sK5) ),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_8928,negated_conjecture,
( nil = sK0
| ssList(sK5) ),
inference(paramod,[status(thm)],[c_332,c_339]) ).
cnf(c_340,negated_conjecture,
( sK0 = nil
| ssList(sK5) ),
inference(copy,[status(thm)],[c_8928]) ).
cnf(c_343,negated_conjecture,
( nil = sK3
| ssList(sK6) ),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_8929,negated_conjecture,
( nil = sK0
| ssList(sK6) ),
inference(paramod,[status(thm)],[c_332,c_343]) ).
cnf(c_344,negated_conjecture,
( sK0 = nil
| ssList(sK6) ),
inference(copy,[status(thm)],[c_8929]) ).
cnf(c_347,negated_conjecture,
( nil = sK3
| cons(sK4,nil) = sK3 ),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_8930,negated_conjecture,
( nil = sK3
| cons(sK4,nil) = sK0 ),
inference(paramod,[status(thm)],[c_332,c_347]) ).
cnf(c_8931,negated_conjecture,
( nil = sK0
| cons(sK4,nil) = sK0 ),
inference(paramod,[status(thm)],[c_332,c_8930]) ).
cnf(c_348,negated_conjecture,
( sK0 = nil
| cons(sK4,nil) = sK0 ),
inference(copy,[status(thm)],[c_8931]) ).
cnf(c_351,negated_conjecture,
( nil = sK3
| app(app(sK5,sK3),sK6) = sK2 ),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_8932,negated_conjecture,
( nil = sK3
| app(app(sK5,sK0),sK6) = sK2 ),
inference(paramod,[status(thm)],[c_332,c_351]) ).
cnf(c_8933,negated_conjecture,
( nil = sK3
| app(app(sK5,sK0),sK6) = sK1 ),
inference(paramod,[status(thm)],[c_331,c_8932]) ).
cnf(c_8934,negated_conjecture,
( nil = sK0
| app(app(sK5,sK0),sK6) = sK1 ),
inference(paramod,[status(thm)],[c_332,c_8933]) ).
cnf(c_352,negated_conjecture,
( sK0 = nil
| app(app(sK5,sK0),sK6) = sK1 ),
inference(copy,[status(thm)],[c_8934]) ).
cnf(c_361,negated_conjecture,
( ~ totalorderedP(sK0)
| ~ segmentP(sK1,sK0) ),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_1688,plain,
( ~ ssList(C)
| ~ ssList(A)
| segmentP(app(app(A,B),C),B)
| ~ ssList(B)
| ~ ssList(app(app(A,B),C)) ),
inference(xxres,[status(thm)],[c_213]) ).
cnf(c_8935,plain,
( cons(A,nil) != nil
| ~ ssItem(A)
| singletonP(nil) ),
inference(resolve,[status(thm)],[c_231,c_203]) ).
cnf(c_1717,plain,
( cons(A,nil) != nil
| ~ ssItem(A) ),
inference(resolve,[status(thm)],[c_262,c_8935]) ).
cnf(c_2218,plain,
segmentP(sK1,nil),
inference(resolve,[status(thm)],[c_328,c_284]) ).
cnf(c_8936,negated_conjecture,
( ~ ssItem(sK4)
| singletonP(sK0)
| ~ ssList(sK0)
| sK0 = nil ),
inference(resolve,[status(thm)],[c_348,c_203]) ).
cnf(c_3520,negated_conjecture,
( ~ ssItem(sK4)
| singletonP(sK0)
| sK0 = nil ),
inference(resolve,[status(thm)],[c_327,c_8936]) ).
cnf(c_8937,plain,
( ~ totalorderedP(sK0)
| ~ segmentP(sK1,nil)
| ssItem(sK4) ),
inference(paramod,[status(thm)],[c_336,c_361]) ).
cnf(c_3634,plain,
( ~ totalorderedP(sK0)
| ssItem(sK4) ),
inference(resolve,[status(thm)],[c_2218,c_8937]) ).
cnf(c_8938,plain,
( ~ totalorderedP(sK0)
| ~ segmentP(sK1,nil)
| ssList(sK5) ),
inference(paramod,[status(thm)],[c_340,c_361]) ).
cnf(c_3637,plain,
( ~ totalorderedP(sK0)
| ssList(sK5) ),
inference(resolve,[status(thm)],[c_2218,c_8938]) ).
cnf(c_8939,plain,
( ~ totalorderedP(sK0)
| ~ segmentP(sK1,nil)
| ssList(sK6) ),
inference(paramod,[status(thm)],[c_344,c_361]) ).
cnf(c_3640,plain,
( ~ totalorderedP(sK0)
| ssList(sK6) ),
inference(resolve,[status(thm)],[c_2218,c_8939]) ).
cnf(c_8940,plain,
( ~ totalorderedP(nil)
| ssItem(sK4)
| ssItem(sK4) ),
inference(paramod,[status(thm)],[c_336,c_3634]) ).
cnf(c_8941,plain,
( ~ totalorderedP(nil)
| ssItem(sK4) ),
inference(copy,[status(thm)],[c_8940]) ).
cnf(c_6216,plain,
ssItem(sK4),
inference(resolve,[status(thm)],[c_288,c_8941]) ).
cnf(c_6661,negated_conjecture,
( singletonP(sK0)
| sK0 = nil ),
inference(resolve,[status(thm)],[c_6216,c_3520]) ).
cnf(c_6922,plain,
totalorderedP(cons(sK4,nil)),
inference(resolve,[status(thm)],[c_6216,c_287]) ).
cnf(c_8942,plain,
( ~ totalorderedP(nil)
| ssList(sK5)
| ssList(sK5) ),
inference(paramod,[status(thm)],[c_340,c_3637]) ).
cnf(c_8943,plain,
( ~ totalorderedP(nil)
| ssList(sK5) ),
inference(copy,[status(thm)],[c_8942]) ).
cnf(c_7212,plain,
ssList(sK5),
inference(resolve,[status(thm)],[c_288,c_8943]) ).
cnf(c_8944,plain,
( ~ totalorderedP(nil)
| ssList(sK6)
| ssList(sK6) ),
inference(paramod,[status(thm)],[c_344,c_3640]) ).
cnf(c_8945,plain,
( ~ totalorderedP(nil)
| ssList(sK6) ),
inference(copy,[status(thm)],[c_8944]) ).
cnf(c_7833,plain,
ssList(sK6),
inference(resolve,[status(thm)],[c_288,c_8945]) ).
cnf(c_8516,plain,
cons(sK4,nil) != nil,
inference(resolve,[status(thm)],[c_1717,c_6216]) ).
cnf(c_8946,plain,
( ~ ssList(sK6)
| ~ ssList(sK5)
| segmentP(app(app(sK5,sK0),sK6),sK0)
| ~ ssList(sK0)
| ~ ssList(sK1)
| sK0 = nil ),
inference(paramod,[status(thm)],[c_352,c_1688]) ).
cnf(c_8947,negated_conjecture,
( ~ ssList(sK6)
| ~ ssList(sK5)
| segmentP(app(app(sK5,sK0),sK6),sK0)
| ~ ssList(sK0)
| sK0 = nil ),
inference(resolve,[status(thm)],[c_328,c_8946]) ).
cnf(c_8948,negated_conjecture,
( ~ ssList(sK6)
| ~ ssList(sK5)
| segmentP(app(app(sK5,sK0),sK6),sK0)
| sK0 = nil ),
inference(resolve,[status(thm)],[c_327,c_8947]) ).
cnf(c_8949,negated_conjecture,
( ~ ssList(sK6)
| segmentP(app(app(sK5,sK0),sK6),sK0)
| sK0 = nil ),
inference(resolve,[status(thm)],[c_7212,c_8948]) ).
cnf(c_8541,negated_conjecture,
( segmentP(app(app(sK5,sK0),sK6),sK0)
| sK0 = nil ),
inference(resolve,[status(thm)],[c_7833,c_8949]) ).
cnf(c_8950,plain,
( ~ totalorderedP(sK0)
| ~ segmentP(sK1,nil)
| singletonP(sK0) ),
inference(paramod,[status(thm)],[c_6661,c_361]) ).
cnf(c_8580,plain,
( ~ totalorderedP(sK0)
| singletonP(sK0) ),
inference(resolve,[status(thm)],[c_2218,c_8950]) ).
cnf(c_8951,plain,
( ~ totalorderedP(nil)
| singletonP(sK0)
| singletonP(sK0) ),
inference(paramod,[status(thm)],[c_6661,c_8580]) ).
cnf(c_8952,plain,
( ~ totalorderedP(nil)
| singletonP(sK0) ),
inference(copy,[status(thm)],[c_8951]) ).
cnf(c_8585,plain,
singletonP(sK0),
inference(resolve,[status(thm)],[c_288,c_8952]) ).
cnf(c_8953,plain,
( singletonP(nil)
| cons(sK4,nil) = sK0 ),
inference(paramod,[status(thm)],[c_348,c_8585]) ).
cnf(c_8588,plain,
cons(sK4,nil) = sK0,
inference(resolve,[status(thm)],[c_262,c_8953]) ).
cnf(c_8954,plain,
( singletonP(nil)
| app(app(sK5,sK0),sK6) = sK1 ),
inference(paramod,[status(thm)],[c_352,c_8585]) ).
cnf(c_8589,plain,
app(app(sK5,sK0),sK6) = sK1,
inference(resolve,[status(thm)],[c_262,c_8954]) ).
cnf(c_8590,plain,
sK0 != nil,
inference(paramod,[status(thm)],[c_8588,c_8516]) ).
cnf(c_8623,plain,
totalorderedP(sK0),
inference(paramod,[status(thm)],[c_8588,c_6922]) ).
cnf(c_8955,negated_conjecture,
( segmentP(sK1,sK0)
| sK0 = nil ),
inference(paramod,[status(thm)],[c_8589,c_8541]) ).
cnf(c_8688,negated_conjecture,
segmentP(sK1,sK0),
inference(resolve,[status(thm)],[c_8590,c_8955]) ).
cnf(c_8956,negated_conjecture,
~ totalorderedP(sK0),
inference(resolve,[status(thm)],[c_8688,c_361]) ).
cnf(c_8926,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_8623,c_8956]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SWC336+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.02 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.03/0.29 % Computer : n012.cluster.edu
% 0.03/0.29 % Model : x86_64 x86_64
% 0.03/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.03/0.29 % Memory : 8046.5625MB
% 0.03/0.29 % OS : Linux 6.8.0-71-generic
% 0.03/0.30 % CPULimit : 300
% 0.03/0.30 % WCLimit : 300
% 0.03/0.30 % DateTime : Sat Sep 26 12:49:20 UTC 2026
% 0.03/0.30 % CPUTime :
% 0.03/0.30 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.03/0.30 % Process 635829 was started by sandbox2 on n012,
% 0.03/0.30 % Sat Sep 26 12:49:20 2026
% 0.03/0.30 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.03/0.31
% 0.03/0.31 % From the command line: assign(max_seconds, 300).
% 29.10/4.51
% 29.10/4.51 % given #500 (I,wt=37): 708 -ssList(A) | ssItem(f34(A)) | -ssItem(B) | -ssItem(C) | -ssList(D) | -ssList(E) | app(app(D,cons(B,A)),cons(C,E)) != A | C != B. [factor(384,a,f)].
% 29.10/4.51
% 29.10/4.51 % given #1000 (I,wt=35): 1228 -ssList(A) | ssList(f37(A)) | -ssItem(B) | -ssItem(C) | -ssList(D) | app(app(D,cons(B,A)),cons(C,D)) != A | C != B. [factor(729,e,f)].
% 29.10/4.51
% 29.10/4.51 % given #1500 (A,wt=17): 1684 -ssList(app(A,B)) | -ssList(A) | frontsegP(app(A,B),A) | -ssList(B). [xx_res(206,e)].
% 29.10/4.51
% 29.10/4.51 % SZS status Theorem for theBenchmark
% 29.10/4.51
% 29.10/4.51 % Proof 1 at 3.23 (+ 0.91) seconds.
% 29.10/4.51 % Length of proof is 49.
% 29.10/4.51 % Level of proof is 11.
% 29.10/4.51 % Maximum clause weight is 29.000.
% 29.10/4.51 % Given clauses 1529.
% 29.10/4.51
% 29.10/4.51 % SZS output start CNFRefutation for theBenchmark
% See solution above
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