%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWC109+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 : n004.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 08:56:51 AM UTC 2026
% Result : Theorem 231.05s 40.75s
% Output : CNFRefutation 231.05s
% Verified :
% SZS Type : Refutation
% Derivation depth : 33
% Number of leaves : 10
% Syntax : Number of formulae : 112 ( 16 unt; 0 def)
% Number of atoms : 434 ( 170 equ)
% Maximal formula atoms : 52 ( 3 avg)
% Number of connectives : 473 ( 151 ~; 220 |; 74 &)
% ( 4 <=>; 24 =>; 0 <=; 0 <~>)
% Maximal formula depth : 27 ( 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 : 73 ( 0 sgn 34 !; 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(ax15,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ( neq(U,V)
<=> U != V ) ) ),
file('theBenchmark.p',ax15) ).
fof(ax53,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ( ( segmentP(V,W)
& segmentP(U,V) )
=> segmentP(U,W) ) ) ) ),
file('theBenchmark.p',ax53) ).
fof(ax54,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ( ( segmentP(V,U)
& segmentP(U,V) )
=> U = V ) ) ),
file('theBenchmark.p',ax54) ).
fof(ax57,axiom,
! [U] :
( ssList(U)
=> segmentP(U,nil) ),
file('theBenchmark.p',ax57) ).
fof(ax58,axiom,
! [U] :
( ssList(U)
=> ( segmentP(nil,U)
<=> nil = U ) ),
file('theBenchmark.p',ax58) ).
fof(co1,conjecture,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ! [X] :
( ( ( ( segmentP(V,U)
& neq(U,nil) )
| ~ neq(V,nil) )
& ( nil = U
| nil != V ) )
| ( ( 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] :
( ( ( ( segmentP(V,U)
& neq(U,nil) )
| ~ neq(V,nil) )
& ( nil = U
| nil != V ) )
| ( ( 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]) ).
fof(nnf_87,plain,
? [U] :
( ? [V] :
( ? [W] :
( ? [X] :
( ( ( ( ~ segmentP(V,U)
| ~ neq(U,nil) )
& neq(V,nil) )
| ( nil != U
& nil = V ) )
& ( ( 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,
( ( ( ( ~ segmentP(sK1,sK0)
| ~ neq(sK0,nil) )
& neq(sK1,nil) )
| ( nil != sK0
& nil = sK1 ) )
& ( ( nil = sK3
& nil = sK5 )
| ( ! [X3] :
( ~ lt(X3,sK6)
| ~ memberP(sK4,X3)
| ~ ssItem(X3) )
& ! [X2] :
( ~ lt(sK6,X2)
| ~ memberP(sK2,X2)
| ~ ssItem(X2) )
& app(app(sK2,sK3),sK4) = sK5
& cons(sK6,nil) = sK3
& ssList(sK4)
& ssList(sK2)
& ssItem(sK6) ) )
& sK3 = sK0
& sK5 = sK1
& ssList(sK5)
& ssList(sK3)
& ssList(sK1)
& ssList(sK0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK3,sK5,sK6,sK2,sK4]),skolemize(U,sK0),skolemize(V,sK1),skolemize(W,sK3),skolemize(X,sK5),skolemize(Y,sK6),skolemize(Z,sK2),skolemize(X1,sK4)],[nnf_87]) ).
fof(sk_co1_neg,plain,
( ( ~ segmentP(sK1,sK0)
| ~ neq(sK0,nil)
| nil != sK0 )
& ( neq(sK1,nil)
| nil != sK0 )
& ( ~ segmentP(sK1,sK0)
| ~ neq(sK0,nil)
| nil = sK1 )
& ( neq(sK1,nil)
| nil = sK1 )
& ! [VAR_0] :
( nil = sK3
| ~ lt(VAR_0,sK6)
| ~ memberP(sK4,VAR_0)
| ~ ssItem(VAR_0) )
& ! [VAR_0] :
( nil = sK5
| ~ lt(VAR_0,sK6)
| ~ memberP(sK4,VAR_0)
| ~ ssItem(VAR_0) )
& ! [VAR_0] :
( nil = sK3
| ~ lt(sK6,VAR_0)
| ~ memberP(sK2,VAR_0)
| ~ ssItem(VAR_0) )
& ! [VAR_0] :
( nil = sK5
| ~ lt(sK6,VAR_0)
| ~ memberP(sK2,VAR_0)
| ~ ssItem(VAR_0) )
& ( nil = sK3
| app(app(sK2,sK3),sK4) = sK5 )
& ( nil = sK5
| app(app(sK2,sK3),sK4) = sK5 )
& ( nil = sK3
| cons(sK6,nil) = sK3 )
& ( nil = sK5
| cons(sK6,nil) = sK3 )
& ( nil = sK3
| ssList(sK4) )
& ( nil = sK5
| ssList(sK4) )
& ( nil = sK3
| ssList(sK2) )
& ( nil = sK5
| ssList(sK2) )
& ( nil = sK3
| ssItem(sK6) )
& ( nil = sK5
| ssItem(sK6) )
& sK3 = sK0
& sK5 = sK1
& ssList(sK5)
& ssList(sK3)
& ssList(sK1)
& ssList(sK0) ),
inference(cnf_transformation,[status(thm)],[sk_co1_neg_sk]) ).
cnf(c_192,negated_conjecture,
( neq(sK1,nil)
| nil != sK0 ),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_193,negated_conjecture,
( neq(sK1,nil)
| sK0 != nil ),
inference(copy,[status(thm)],[c_192]) ).
cnf(c_194,negated_conjecture,
( ~ segmentP(sK1,sK0)
| ~ neq(sK0,nil)
| nil = sK1 ),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_195,negated_conjecture,
( ~ segmentP(sK1,sK0)
| ~ neq(sK0,nil)
| sK1 = nil ),
inference(copy,[status(thm)],[c_194]) ).
cnf(c_206,negated_conjecture,
( nil = sK3
| app(app(sK2,sK3),sK4) = sK5 ),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_207,negated_conjecture,
( sK3 = nil
| app(app(sK2,sK3),sK4) = sK5 ),
inference(copy,[status(thm)],[c_206]) ).
cnf(c_208,negated_conjecture,
( nil = sK5
| app(app(sK2,sK3),sK4) = sK5 ),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_209,negated_conjecture,
( sK5 = nil
| app(app(sK2,sK3),sK4) = sK5 ),
inference(copy,[status(thm)],[c_208]) ).
cnf(c_212,negated_conjecture,
( nil = sK5
| cons(sK6,nil) = sK3 ),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_213,negated_conjecture,
( sK5 = nil
| cons(sK6,nil) = sK3 ),
inference(copy,[status(thm)],[c_212]) ).
cnf(c_214,negated_conjecture,
( nil = sK3
| ssList(sK4) ),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_215,negated_conjecture,
( sK3 = nil
| ssList(sK4) ),
inference(copy,[status(thm)],[c_214]) ).
cnf(c_216,negated_conjecture,
( nil = sK5
| ssList(sK4) ),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_217,negated_conjecture,
( sK5 = nil
| ssList(sK4) ),
inference(copy,[status(thm)],[c_216]) ).
cnf(c_218,negated_conjecture,
( nil = sK3
| ssList(sK2) ),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_219,negated_conjecture,
( sK3 = nil
| ssList(sK2) ),
inference(copy,[status(thm)],[c_218]) ).
cnf(c_220,negated_conjecture,
( nil = sK5
| ssList(sK2) ),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_221,negated_conjecture,
( sK5 = nil
| ssList(sK2) ),
inference(copy,[status(thm)],[c_220]) ).
cnf(c_224,negated_conjecture,
( nil = sK5
| ssItem(sK6) ),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_225,negated_conjecture,
( sK5 = nil
| ssItem(sK6) ),
inference(copy,[status(thm)],[c_224]) ).
cnf(c_226,negated_conjecture,
sK3 = sK0,
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_227,negated_conjecture,
sK5 = sK1,
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_228,negated_conjecture,
ssList(sK5),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_229,negated_conjecture,
ssList(sK1),
inference(paramod,[status(thm)],[c_227,c_228]) ).
cnf(c_230,negated_conjecture,
ssList(sK3),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_231,negated_conjecture,
ssList(sK0),
inference(paramod,[status(thm)],[c_226,c_230]) ).
cnf(c_272,plain,
( nil != A
| segmentP(nil,A)
| ~ ssList(A) ),
inference(clausify,[status(thm)],[ax58]) ).
cnf(c_274,plain,
( segmentP(A,nil)
| ~ ssList(A) ),
inference(clausify,[status(thm)],[ax57]) ).
cnf(c_277,plain,
( B = A
| ~ segmentP(B,A)
| ~ segmentP(A,B)
| ~ ssList(B)
| ~ ssList(A) ),
inference(clausify,[status(thm)],[ax54]) ).
cnf(c_278,plain,
( segmentP(A,C)
| ~ segmentP(B,C)
| ~ segmentP(A,B)
| ~ ssList(C)
| ~ ssList(B)
| ~ ssList(A) ),
inference(clausify,[status(thm)],[ax53]) ).
fof(ax39,axiom,
~ singletonP(nil),
file('theBenchmark.p',ax39) ).
cnf(c_296,plain,
~ singletonP(nil),
inference(clausify,[status(thm)],[ax39]) ).
fof(ax17,axiom,
ssList(nil),
file('theBenchmark.p',ax17) ).
cnf(c_327,plain,
ssList(nil),
inference(clausify,[status(thm)],[ax17]) ).
cnf(c_329,plain,
( B = A
| neq(A,B)
| ~ ssList(B)
| ~ ssList(A) ),
inference(clausify,[status(thm)],[ax15]) ).
cnf(c_330,plain,
( B != A
| ~ neq(A,B)
| ~ ssList(B)
| ~ ssList(A) ),
inference(clausify,[status(thm)],[ax15]) ).
cnf(c_347,plain,
( app(app(C,B),D) != A
| ~ ssList(D)
| ~ ssList(C)
| segmentP(A,B)
| ~ ssList(B)
| ~ ssList(A) ),
inference(clausify,[status(thm)],[ax7]) ).
cnf(c_357,plain,
( cons(B,nil) != A
| ~ ssItem(B)
| singletonP(A)
| ~ ssList(A) ),
inference(clausify,[status(thm)],[ax4]) ).
cnf(c_577,negated_conjecture,
( sK0 = nil
| ssList(sK2) ),
inference(paramod,[status(thm)],[c_226,c_219]) ).
cnf(c_578,negated_conjecture,
( sK0 = nil
| ssList(sK4) ),
inference(paramod,[status(thm)],[c_226,c_215]) ).
cnf(c_8567,negated_conjecture,
( sK5 = nil
| cons(sK6,nil) = sK0 ),
inference(paramod,[status(thm)],[c_226,c_213]) ).
cnf(c_579,negated_conjecture,
( sK1 = nil
| cons(sK6,nil) = sK0 ),
inference(paramod,[status(thm)],[c_227,c_8567]) ).
cnf(c_8568,negated_conjecture,
( sK5 = nil
| app(app(sK2,sK0),sK4) = sK5 ),
inference(paramod,[status(thm)],[c_226,c_209]) ).
cnf(c_8569,negated_conjecture,
( sK5 = nil
| app(app(sK2,sK0),sK4) = sK1 ),
inference(paramod,[status(thm)],[c_227,c_8568]) ).
cnf(c_581,negated_conjecture,
( sK1 = nil
| app(app(sK2,sK0),sK4) = sK1 ),
inference(paramod,[status(thm)],[c_227,c_8569]) ).
cnf(c_8570,negated_conjecture,
( sK3 = nil
| app(app(sK2,sK0),sK4) = sK5 ),
inference(paramod,[status(thm)],[c_226,c_207]) ).
cnf(c_8571,negated_conjecture,
( sK3 = nil
| app(app(sK2,sK0),sK4) = sK1 ),
inference(paramod,[status(thm)],[c_227,c_8570]) ).
cnf(c_582,negated_conjecture,
( sK0 = nil
| app(app(sK2,sK0),sK4) = sK1 ),
inference(paramod,[status(thm)],[c_226,c_8571]) ).
cnf(c_585,negated_conjecture,
( sK1 = nil
| ssItem(sK6) ),
inference(paramod,[status(thm)],[c_227,c_225]) ).
cnf(c_586,negated_conjecture,
( sK1 = nil
| ssList(sK2) ),
inference(paramod,[status(thm)],[c_227,c_221]) ).
cnf(c_587,negated_conjecture,
( sK1 = nil
| ssList(sK4) ),
inference(paramod,[status(thm)],[c_227,c_217]) ).
cnf(c_8572,plain,
( A != A
| ~ neq(A,A)
| ~ ssList(A) ),
inference(factor,[status(thm)],[c_330]) ).
cnf(c_630,plain,
( ~ neq(A,A)
| ~ ssList(A) ),
inference(copy,[status(thm)],[c_8572]) ).
cnf(c_8573,negated_conjecture,
( nil != sK1
| segmentP(nil,sK1) ),
inference(resolve,[status(thm)],[c_272,c_229]) ).
cnf(c_1751,negated_conjecture,
( sK1 != nil
| segmentP(nil,sK1) ),
inference(copy,[status(thm)],[c_8573]) ).
cnf(c_1755,plain,
segmentP(sK0,nil),
inference(resolve,[status(thm)],[c_274,c_231]) ).
cnf(c_8574,negated_conjecture,
( A = sK0
| ~ segmentP(A,sK0)
| ~ segmentP(sK0,A)
| ~ ssList(A) ),
inference(resolve,[status(thm)],[c_277,c_231]) ).
cnf(c_1759,negated_conjecture,
( sK0 = A
| ~ segmentP(A,sK0)
| ~ segmentP(sK0,A)
| ~ ssList(A) ),
inference(copy,[status(thm)],[c_8574]) ).
cnf(c_1765,plain,
( segmentP(A,sK0)
| ~ segmentP(B,sK0)
| ~ segmentP(A,B)
| ~ ssList(B)
| ~ ssList(A) ),
inference(resolve,[status(thm)],[c_278,c_231]) ).
cnf(c_8575,negated_conjecture,
( A = sK0
| neq(sK0,A)
| ~ ssList(A) ),
inference(resolve,[status(thm)],[c_329,c_231]) ).
cnf(c_1965,negated_conjecture,
( sK0 = A
| neq(sK0,A)
| ~ ssList(A) ),
inference(copy,[status(thm)],[c_8575]) ).
cnf(c_8576,negated_conjecture,
( ~ ssItem(sK6)
| singletonP(sK0)
| ~ ssList(sK0)
| sK1 = nil ),
inference(resolve,[status(thm)],[c_579,c_357]) ).
cnf(c_2638,negated_conjecture,
( ~ ssItem(sK6)
| singletonP(sK0)
| sK1 = nil ),
inference(resolve,[status(thm)],[c_231,c_8576]) ).
cnf(c_8577,negated_conjecture,
( ~ ssList(sK4)
| ~ ssList(sK2)
| segmentP(sK1,sK0)
| ~ ssList(sK0)
| ~ ssList(sK1)
| sK1 = nil ),
inference(resolve,[status(thm)],[c_581,c_347]) ).
cnf(c_8578,negated_conjecture,
( ~ ssList(sK4)
| ~ ssList(sK2)
| segmentP(sK1,sK0)
| ~ ssList(sK0)
| sK1 = nil ),
inference(resolve,[status(thm)],[c_229,c_8577]) ).
cnf(c_2655,negated_conjecture,
( ~ ssList(sK4)
| ~ ssList(sK2)
| segmentP(sK1,sK0)
| sK1 = nil ),
inference(resolve,[status(thm)],[c_231,c_8578]) ).
cnf(c_8579,negated_conjecture,
( ~ ssList(sK4)
| ~ ssList(sK2)
| segmentP(sK1,sK0)
| ~ ssList(sK0)
| ~ ssList(sK1)
| sK0 = nil ),
inference(resolve,[status(thm)],[c_582,c_347]) ).
cnf(c_8580,negated_conjecture,
( ~ ssList(sK4)
| ~ ssList(sK2)
| segmentP(sK1,sK0)
| ~ ssList(sK0)
| sK0 = nil ),
inference(resolve,[status(thm)],[c_229,c_8579]) ).
cnf(c_2658,negated_conjecture,
( ~ ssList(sK4)
| ~ ssList(sK2)
| segmentP(sK1,sK0)
| sK0 = nil ),
inference(resolve,[status(thm)],[c_231,c_8580]) ).
cnf(c_3231,plain,
~ neq(nil,nil),
inference(resolve,[status(thm)],[c_630,c_327]) ).
cnf(c_8581,negated_conjecture,
( sK1 = nil
| singletonP(sK0)
| sK1 = nil ),
inference(resolve,[status(thm)],[c_2638,c_585]) ).
cnf(c_3714,negated_conjecture,
( singletonP(sK0)
| sK1 = nil ),
inference(copy,[status(thm)],[c_8581]) ).
cnf(c_3742,plain,
( sK0 = nil
| neq(sK0,nil) ),
inference(resolve,[status(thm)],[c_1965,c_327]) ).
cnf(c_3744,plain,
( ~ segmentP(sK1,sK0)
| sK1 = nil
| sK0 = nil ),
inference(resolve,[status(thm)],[c_3742,c_195]) ).
cnf(c_8582,negated_conjecture,
( sK1 = nil
| ~ ssList(sK4)
| segmentP(sK1,sK0)
| sK1 = nil ),
inference(resolve,[status(thm)],[c_2655,c_586]) ).
cnf(c_7728,negated_conjecture,
( ~ ssList(sK4)
| segmentP(sK1,sK0)
| sK1 = nil ),
inference(copy,[status(thm)],[c_8582]) ).
cnf(c_8583,negated_conjecture,
( sK1 = nil
| segmentP(sK1,sK0)
| sK1 = nil ),
inference(resolve,[status(thm)],[c_7728,c_587]) ).
cnf(c_7730,negated_conjecture,
( segmentP(sK1,sK0)
| sK1 = nil ),
inference(copy,[status(thm)],[c_8583]) ).
cnf(c_8584,plain,
( sK1 = nil
| sK0 = nil
| sK1 = nil ),
inference(resolve,[status(thm)],[c_7730,c_3744]) ).
cnf(c_7731,plain,
( sK0 = nil
| sK1 = nil ),
inference(copy,[status(thm)],[c_8584]) ).
cnf(c_7751,plain,
( segmentP(nil,sK1)
| sK0 = nil ),
inference(resolve,[status(thm)],[c_7731,c_1751]) ).
cnf(c_8585,negated_conjecture,
( sK0 = nil
| ~ ssList(sK4)
| segmentP(sK1,sK0)
| sK0 = nil ),
inference(resolve,[status(thm)],[c_2658,c_577]) ).
cnf(c_7941,negated_conjecture,
( ~ ssList(sK4)
| segmentP(sK1,sK0)
| sK0 = nil ),
inference(copy,[status(thm)],[c_8585]) ).
cnf(c_8586,negated_conjecture,
( sK0 = nil
| segmentP(sK1,sK0)
| sK0 = nil ),
inference(resolve,[status(thm)],[c_7941,c_578]) ).
cnf(c_7943,negated_conjecture,
( segmentP(sK1,sK0)
| sK0 = nil ),
inference(copy,[status(thm)],[c_8586]) ).
cnf(c_8587,plain,
( sK0 = nil
| segmentP(nil,sK0)
| ~ segmentP(sK1,sK0)
| ~ ssList(sK1)
| ~ ssList(nil) ),
inference(resolve,[status(thm)],[c_1765,c_7751]) ).
cnf(c_8588,plain,
( sK0 = nil
| segmentP(nil,sK0)
| ~ segmentP(sK1,sK0)
| ~ ssList(sK1) ),
inference(resolve,[status(thm)],[c_327,c_8587]) ).
cnf(c_8460,negated_conjecture,
( sK0 = nil
| segmentP(nil,sK0)
| ~ segmentP(sK1,sK0) ),
inference(resolve,[status(thm)],[c_229,c_8588]) ).
cnf(c_8589,plain,
( sK0 = nil
| sK0 = nil
| segmentP(nil,sK0) ),
inference(resolve,[status(thm)],[c_8460,c_7943]) ).
cnf(c_8486,plain,
( sK0 = nil
| segmentP(nil,sK0) ),
inference(copy,[status(thm)],[c_8589]) ).
cnf(c_8590,plain,
( sK0 = nil
| ~ segmentP(sK0,nil)
| ~ ssList(nil)
| sK0 = nil ),
inference(resolve,[status(thm)],[c_8486,c_1759]) ).
cnf(c_8591,plain,
( ~ segmentP(sK0,nil)
| ~ ssList(nil)
| sK0 = nil ),
inference(copy,[status(thm)],[c_8590]) ).
cnf(c_8592,plain,
( ~ segmentP(sK0,nil)
| sK0 = nil ),
inference(resolve,[status(thm)],[c_327,c_8591]) ).
cnf(c_8489,plain,
sK0 = nil,
inference(resolve,[status(thm)],[c_1755,c_8592]) ).
cnf(c_8593,negated_conjecture,
( singletonP(nil)
| sK1 = nil ),
inference(paramod,[status(thm)],[c_8489,c_3714]) ).
cnf(c_8564,negated_conjecture,
sK1 = nil,
inference(resolve,[status(thm)],[c_296,c_8593]) ).
cnf(c_8594,negated_conjecture,
( neq(sK1,nil)
| nil != nil ),
inference(paramod,[status(thm)],[c_8489,c_193]) ).
cnf(c_8595,negated_conjecture,
( neq(nil,nil)
| nil != nil ),
inference(paramod,[status(thm)],[c_8564,c_8594]) ).
cnf(c_8596,negated_conjecture,
neq(nil,nil),
inference(copy,[status(thm)],[c_8595]) ).
cnf(c_8566,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_3231,c_8596]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SWC109+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.17/10.45 % Computer : n004.cluster.edu
% 0.17/10.45 % Model : x86_64 x86_64
% 0.17/10.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/10.45 % Memory : 8046.5625MB
% 0.17/10.45 % OS : Linux 6.8.0-71-generic
% 0.17/10.45 % CPULimit : 300
% 0.17/10.45 % WCLimit : 300
% 0.17/10.45 % DateTime : Sat Sep 26 12:16:17 UTC 2026
% 0.17/10.45 % CPUTime :
% 0.17/10.45 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.17/10.45 % Process 1672773 was started by sandbox on n004,
% 0.17/10.45 % Sat Sep 26 12:16:17 2026
% 0.17/10.45 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.17/10.49
% 0.17/10.49 % From the command line: assign(max_seconds, 300).
% 231.05/40.75
% 231.05/40.75 % given #500 (I,wt=47): 722 -ssItem(A) | -ssItem(B) | -ssList(C) | -ssList(D) | app(app(C,cons(A,D)),cons(B,D)) != nil | leq(A,B) | leq(B,A). [factor(387,d,e)].
% 231.05/40.75
% 231.05/40.75 % given #1000 (I,wt=44): 1242 -ssList(A) | -ssItem(B) | -ssList(C) | -ssList(D) | app(app(C,cons(B,D)),cons(B,C)) != A | ssList(f36(A)). [factor(747,c,e)].
% 231.05/40.75
% 231.05/40.75 % given #1500 (F,wt=11): 3642 -leq(c1,c2) | -lt(c2,c1). [resolve(3051,a,365,a)].
% 231.05/40.75
% 231.05/40.75 % given #2000 (W,wt=15): 1996 totalorderedP(c3) | ssList(f25(c3)). [resolve(343,a,231,a)].
% 231.05/40.75
% 231.05/40.75 % SZS status Theorem for theBenchmark
% 231.05/40.75
% 231.05/40.75 % Proof 1 at 4.60 (+ 1.51) seconds.
% 231.05/40.75 % Length of proof is 76.
% 231.05/40.75 % Level of proof is 13.
% 231.05/40.75 % Maximum clause weight is 35.000.
% 231.05/40.75 % Given clauses 2118.
% 231.05/40.75
% 231.05/40.75 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------