%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWC067+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 : n009.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 08:56:43 AM UTC 2026
% Result : Theorem 199.13s 31.79s
% Output : CNFRefutation 199.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 7
% Syntax : Number of formulae : 73 ( 20 unt; 0 def)
% Number of atoms : 338 ( 108 equ)
% Maximal formula atoms : 40 ( 4 avg)
% Number of connectives : 423 ( 158 ~; 157 |; 83 &)
% ( 3 <=>; 22 =>; 0 <=; 0 <~>)
% Maximal formula depth : 30 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 7 con; 0-2 aty)
% Number of variables : 98 ( 0 sgn 49 !; 26 ?)
% 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(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(ax55,axiom,
! [U] :
( ssList(U)
=> segmentP(U,U) ),
file('theBenchmark.p',ax55) ).
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] :
( ssList(X)
=> ( ( ( ? [X9] :
( segmentP(U,X9)
& segmentP(V,X9)
& neq(X9,nil)
& ssList(X9) )
| ~ neq(V,nil) )
& ( nil = U
| nil != V ) )
| ( nil = W
& nil != X )
| ! [Y] :
( ssList(Y)
=> ! [Z] :
( ssList(Z)
=> ( ? [X5] :
( ? [X6] :
( ? [X7] :
( ? [X8] :
( lt(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] :
( lt(X1,X3)
& app(cons(X3,nil),X4) = W
& ssList(X4) )
& ssItem(X3) )
& app(X2,cons(X1,nil)) = Y
& ssList(X2) )
& ssItem(X1) )
| ~ strictorderedP(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)
=> ( ( ( ? [X9] :
( segmentP(U,X9)
& segmentP(V,X9)
& neq(X9,nil)
& ssList(X9) )
| ~ neq(V,nil) )
& ( nil = U
| nil != V ) )
| ( nil = W
& nil != X )
| ! [Y] :
( ssList(Y)
=> ! [Z] :
( ssList(Z)
=> ( ? [X5] :
( ? [X6] :
( ? [X7] :
( ? [X8] :
( lt(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] :
( lt(X1,X3)
& app(cons(X3,nil),X4) = W
& ssList(X4) )
& ssItem(X3) )
& app(X2,cons(X1,nil)) = Y
& ssList(X2) )
& ssItem(X1) )
| ~ strictorderedP(W)
| app(app(Y,W),Z) != X ) ) )
| U != W
| V != X ) ) ) ) ),
inference(assume_negation,[status(cth)],[co1]) ).
fof(nnf_87,plain,
? [U] :
( ? [V] :
( ? [W] :
( ? [X] :
( ( ( ! [X9] :
( ~ segmentP(U,X9)
| ~ segmentP(V,X9)
| ~ neq(X9,nil)
| ~ ssList(X9) )
& neq(V,nil) )
| ( nil != U
& nil = V ) )
& ( nil != W
| nil = X )
& ? [Y] :
( ? [Z] :
( ! [X5] :
( ! [X6] :
( ! [X7] :
( ! [X8] :
( ~ lt(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] :
( ~ lt(X1,X3)
| app(cons(X3,nil),X4) != W
| ~ ssList(X4) )
| ~ ssItem(X3) )
| app(X2,cons(X1,nil)) != Y
| ~ ssList(X2) )
| ~ ssItem(X1) )
& strictorderedP(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,
( ( ( ! [X9] :
( ~ segmentP(sK0,X9)
| ~ segmentP(sK1,X9)
| ~ neq(X9,nil)
| ~ ssList(X9) )
& neq(sK1,nil) )
| ( nil != sK0
& nil = sK1 ) )
& ( nil != sK3
| nil = sK2 )
& ! [X5] :
( ! [X6] :
( ! [X7] :
( ! [X8] :
( ~ lt(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] :
( ~ lt(X1,X3)
| app(cons(X3,nil),X4) != sK3
| ~ ssList(X4) )
| ~ ssItem(X3) )
| app(X2,cons(X1,nil)) != sK4
| ~ ssList(X2) )
| ~ ssItem(X1) )
& strictorderedP(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,
( ! [VAR_0] :
( ~ segmentP(sK0,VAR_0)
| ~ segmentP(sK1,VAR_0)
| ~ neq(VAR_0,nil)
| ~ ssList(VAR_0)
| nil != sK0 )
& ( neq(sK1,nil)
| nil != sK0 )
& ! [VAR_0] :
( ~ segmentP(sK0,VAR_0)
| ~ segmentP(sK1,VAR_0)
| ~ neq(VAR_0,nil)
| ~ ssList(VAR_0)
| nil = sK1 )
& ( neq(sK1,nil)
| nil = sK1 )
& ( nil != sK3
| nil = sK2 )
& ! [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) != sK5
| ~ ssList(VAR_1)
| ~ ssItem(VAR_0) )
& ! [VAR_0,VAR_1,VAR_2,VAR_3] :
( ~ lt(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) )
& strictorderedP(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_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(sK0,A)
| ~ segmentP(sK1,A)
| ~ neq(A,nil)
| ~ ssList(A)
| nil = sK1 ),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_195,negated_conjecture,
( ~ segmentP(sK0,A)
| ~ segmentP(sK1,A)
| ~ neq(A,nil)
| ~ ssList(A)
| sK1 = nil ),
inference(copy,[status(thm)],[c_194]) ).
cnf(c_198,negated_conjecture,
( nil != sK3
| nil = sK2 ),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_3325,negated_conjecture,
( nil != sK3
| sK2 = nil ),
inference(copy,[status(thm)],[c_198]) ).
cnf(c_199,negated_conjecture,
( sK3 != nil
| sK2 = nil ),
inference(copy,[status(thm)],[c_3325]) ).
cnf(c_203,negated_conjecture,
app(app(sK4,sK3),sK5) = sK2,
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_204,negated_conjecture,
ssList(sK5),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_205,negated_conjecture,
ssList(sK4),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_206,negated_conjecture,
sK3 = sK0,
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_207,negated_conjecture,
sK2 = sK1,
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_208,negated_conjecture,
ssList(sK2),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_209,negated_conjecture,
ssList(sK1),
inference(paramod,[status(thm)],[c_207,c_208]) ).
cnf(c_210,negated_conjecture,
ssList(sK3),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_211,negated_conjecture,
ssList(sK0),
inference(paramod,[status(thm)],[c_206,c_210]) ).
cnf(c_252,plain,
( nil != A
| segmentP(nil,A)
| ~ ssList(A) ),
inference(clausify,[status(thm)],[ax58]) ).
cnf(c_253,plain,
( nil = A
| ~ segmentP(nil,A)
| ~ ssList(A) ),
inference(clausify,[status(thm)],[ax58]) ).
cnf(c_256,plain,
( segmentP(A,A)
| ~ ssList(A) ),
inference(clausify,[status(thm)],[ax55]) ).
cnf(c_258,plain,
( segmentP(A,C)
| ~ segmentP(B,C)
| ~ segmentP(A,B)
| ~ ssList(C)
| ~ ssList(B)
| ~ ssList(A) ),
inference(clausify,[status(thm)],[ax53]) ).
fof(ax17,axiom,
ssList(nil),
file('theBenchmark.p',ax17) ).
cnf(c_307,plain,
ssList(nil),
inference(clausify,[status(thm)],[ax17]) ).
cnf(c_309,plain,
( B = A
| neq(A,B)
| ~ ssList(B)
| ~ ssList(A) ),
inference(clausify,[status(thm)],[ax15]) ).
cnf(c_310,plain,
( B != A
| ~ neq(A,B)
| ~ ssList(B)
| ~ ssList(A) ),
inference(clausify,[status(thm)],[ax15]) ).
cnf(c_327,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_3326,negated_conjecture,
app(app(sK4,sK0),sK5) = sK2,
inference(paramod,[status(thm)],[c_206,c_203]) ).
cnf(c_558,negated_conjecture,
app(app(sK4,sK0),sK5) = sK1,
inference(paramod,[status(thm)],[c_207,c_3326]) ).
cnf(c_3327,negated_conjecture,
( sK3 != nil
| sK1 = nil ),
inference(paramod,[status(thm)],[c_207,c_199]) ).
cnf(c_562,negated_conjecture,
( sK0 != nil
| sK1 = nil ),
inference(paramod,[status(thm)],[c_206,c_3327]) ).
cnf(c_3328,plain,
( A != A
| ~ neq(A,A)
| ~ ssList(A) ),
inference(factor,[status(thm)],[c_310]) ).
cnf(c_603,plain,
( ~ neq(A,A)
| ~ ssList(A) ),
inference(copy,[status(thm)],[c_3328]) ).
cnf(c_1665,plain,
( ~ segmentP(sK0,sK0)
| ~ segmentP(sK1,sK0)
| ~ neq(sK0,nil)
| sK1 = nil ),
inference(resolve,[status(thm)],[c_211,c_195]) ).
cnf(c_3329,negated_conjecture,
( nil != sK1
| segmentP(nil,sK1) ),
inference(resolve,[status(thm)],[c_252,c_209]) ).
cnf(c_1793,negated_conjecture,
( sK1 != nil
| segmentP(nil,sK1) ),
inference(copy,[status(thm)],[c_3329]) ).
cnf(c_3330,negated_conjecture,
( nil = sK0
| ~ segmentP(nil,sK0) ),
inference(resolve,[status(thm)],[c_253,c_211]) ).
cnf(c_1797,negated_conjecture,
( sK0 = nil
| ~ segmentP(nil,sK0) ),
inference(copy,[status(thm)],[c_3330]) ).
cnf(c_1805,plain,
segmentP(sK0,sK0),
inference(resolve,[status(thm)],[c_256,c_211]) ).
cnf(c_1810,plain,
( ~ segmentP(sK1,sK0)
| ~ neq(sK0,nil)
| sK1 = nil ),
inference(resolve,[status(thm)],[c_1805,c_1665]) ).
cnf(c_3331,negated_conjecture,
( A = sK0
| neq(sK0,A)
| ~ ssList(A) ),
inference(resolve,[status(thm)],[c_309,c_211]) ).
cnf(c_2167,negated_conjecture,
( sK0 = A
| neq(sK0,A)
| ~ ssList(A) ),
inference(copy,[status(thm)],[c_3331]) ).
cnf(c_3332,negated_conjecture,
( ~ ssList(sK5)
| ~ ssList(sK4)
| segmentP(sK1,sK0)
| ~ ssList(sK0)
| ~ ssList(sK1) ),
inference(resolve,[status(thm)],[c_558,c_327]) ).
cnf(c_3333,negated_conjecture,
( ~ ssList(sK5)
| ~ ssList(sK4)
| segmentP(sK1,sK0)
| ~ ssList(sK0) ),
inference(resolve,[status(thm)],[c_209,c_3332]) ).
cnf(c_3334,negated_conjecture,
( ~ ssList(sK5)
| ~ ssList(sK4)
| segmentP(sK1,sK0) ),
inference(resolve,[status(thm)],[c_211,c_3333]) ).
cnf(c_3335,negated_conjecture,
( ~ ssList(sK5)
| segmentP(sK1,sK0) ),
inference(resolve,[status(thm)],[c_205,c_3334]) ).
cnf(c_2541,negated_conjecture,
segmentP(sK1,sK0),
inference(resolve,[status(thm)],[c_204,c_3335]) ).
cnf(c_2542,plain,
( ~ neq(sK0,nil)
| sK1 = nil ),
inference(resolve,[status(thm)],[c_2541,c_1810]) ).
cnf(c_2654,plain,
~ neq(nil,nil),
inference(resolve,[status(thm)],[c_603,c_307]) ).
cnf(c_3336,plain,
( segmentP(A,sK0)
| ~ segmentP(A,sK1)
| ~ ssList(sK0)
| ~ ssList(sK1)
| ~ ssList(A) ),
inference(resolve,[status(thm)],[c_2541,c_258]) ).
cnf(c_3337,negated_conjecture,
( segmentP(A,sK0)
| ~ segmentP(A,sK1)
| ~ ssList(sK0)
| ~ ssList(A) ),
inference(resolve,[status(thm)],[c_209,c_3336]) ).
cnf(c_2991,negated_conjecture,
( segmentP(A,sK0)
| ~ segmentP(A,sK1)
| ~ ssList(A) ),
inference(resolve,[status(thm)],[c_211,c_3337]) ).
cnf(c_3016,plain,
( sK0 = nil
| neq(sK0,nil) ),
inference(resolve,[status(thm)],[c_2167,c_307]) ).
cnf(c_3021,plain,
( sK1 = nil
| sK0 = nil ),
inference(resolve,[status(thm)],[c_3016,c_2542]) ).
cnf(c_3026,plain,
( segmentP(nil,sK1)
| sK0 = nil ),
inference(resolve,[status(thm)],[c_3021,c_1793]) ).
cnf(c_3338,plain,
( sK0 = nil
| segmentP(nil,sK0)
| ~ ssList(nil) ),
inference(resolve,[status(thm)],[c_2991,c_3026]) ).
cnf(c_3286,plain,
( sK0 = nil
| segmentP(nil,sK0) ),
inference(resolve,[status(thm)],[c_307,c_3338]) ).
cnf(c_3339,plain,
( sK0 = nil
| sK0 = nil ),
inference(resolve,[status(thm)],[c_3286,c_1797]) ).
cnf(c_3315,plain,
sK0 = nil,
inference(copy,[status(thm)],[c_3339]) ).
cnf(c_3340,negated_conjecture,
( nil != nil
| sK1 = nil ),
inference(paramod,[status(thm)],[c_3315,c_562]) ).
cnf(c_3321,negated_conjecture,
sK1 = nil,
inference(copy,[status(thm)],[c_3340]) ).
cnf(c_3341,negated_conjecture,
( neq(sK1,nil)
| nil != nil ),
inference(paramod,[status(thm)],[c_3315,c_193]) ).
cnf(c_3342,negated_conjecture,
( neq(nil,nil)
| nil != nil ),
inference(paramod,[status(thm)],[c_3321,c_3341]) ).
cnf(c_3343,negated_conjecture,
neq(nil,nil),
inference(copy,[status(thm)],[c_3342]) ).
cnf(c_3324,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_2654,c_3343]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SWC067+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.17/5.45 % Computer : n009.cluster.edu
% 0.17/5.45 % Model : x86_64 x86_64
% 0.17/5.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/5.45 % Memory : 8046.5625MB
% 0.17/5.45 % OS : Linux 6.8.0-71-generic
% 0.17/5.45 % CPULimit : 300
% 0.17/5.45 % WCLimit : 300
% 0.17/5.45 % DateTime : Sat Sep 26 12:10:35 UTC 2026
% 0.17/5.45 % CPUTime :
% 0.17/5.45 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.17/5.45 % Process 60647 was started by sandbox2 on n009,
% 0.17/5.45 % Sat Sep 26 12:10:35 2026
% 0.17/5.45 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.17/5.49
% 0.17/5.49 % From the command line: assign(max_seconds, 300).
% 199.13/31.79
% 199.13/31.79 % given #500 (I,wt=49): 700 -ssList(A) | -ssItem(B) | -ssItem(C) | -ssList(D) | -ssList(E) | app(app(D,cons(B,D)),cons(C,E)) != A | C != B | ssItem(f33(A)). [factor(369,d,e)].
% 199.13/31.79
% 199.13/31.79 % given #1000 (I,wt=44): 1220 -ssList(A) | -ssItem(B) | -ssList(C) | -ssList(D) | app(app(A,cons(B,C)),cons(B,D)) != A | ssList(f37(A)). [factor(724,b,c),xx(f)].
% 199.13/31.79
% 199.13/31.79 % given #1500 (T,wt=11): 2542 c4 = nil | -neq(c3,nil). [back_unit_del(1810),unit_del(c,2541)].
% 199.13/31.79
% 199.13/31.79 % SZS status Theorem for theBenchmark
% 199.13/31.79
% 199.13/31.79 % Proof 1 at 1.77 (+ 0.29) seconds.
% 199.13/31.79 % Length of proof is 49.
% 199.13/31.79 % Level of proof is 11.
% 199.13/31.79 % Maximum clause weight is 35.000.
% 199.13/31.79 % Given clauses 1714.
% 199.13/31.79
% 199.13/31.79 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------