%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWC389+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 : 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 08:57:41 AM UTC 2026
% Result : Theorem 232.91s 30.98s
% Output : CNFRefutation 232.91s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 6
% Syntax : Number of formulae : 84 ( 13 unt; 0 def)
% Number of atoms : 331 ( 129 equ)
% Maximal formula atoms : 46 ( 3 avg)
% Number of connectives : 367 ( 120 ~; 161 |; 66 &)
% ( 4 <=>; 16 =>; 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 : 51 ( 0 sgn 28 !; 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(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] :
( ( ( singletonP(U)
| ~ neq(V,nil) )
& 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] :
( ( ( singletonP(U)
| ~ neq(V,nil) )
& 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_90,plain,
( B != A
| ~ neq(A,B)
| ~ ssList(B)
| ~ ssList(A) ),
inference(clausify,[status(thm)],[ax15]) ).
fof(nnf_87,plain,
? [U] :
( ? [V] :
( ? [W] :
( ? [X] :
( ( ( ~ singletonP(U)
& neq(V,nil) )
| ~ 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,
( ( ( ~ singletonP(sK1)
& neq(sK0,nil) )
| ~ segmentP(sK0,sK1) )
& ( ( 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 = sK1
& sK2 = sK0
& ssList(sK2)
& ssList(sK3)
& ssList(sK0)
& ssList(sK1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK0,sK3,sK2,sK4,sK5,sK6]),skolemize(U,sK1),skolemize(V,sK0),skolemize(W,sK3),skolemize(X,sK2),skolemize(Y,sK4),skolemize(Z,sK5),skolemize(X1,sK6)],[nnf_87]) ).
fof(sk_co1_neg,plain,
( ( ~ singletonP(sK1)
| ~ segmentP(sK0,sK1) )
& ( neq(sK0,nil)
| ~ segmentP(sK0,sK1) )
& ! [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 = sK1
& sK2 = sK0
& ssList(sK2)
& ssList(sK3)
& ssList(sK0)
& ssList(sK1) ),
inference(cnf_transformation,[status(thm)],[sk_co1_neg_sk]) ).
cnf(c_92,negated_conjecture,
( neq(sK0,nil)
| ~ segmentP(sK0,sK1) ),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_204,plain,
( cons(B,nil) != A
| ~ ssItem(B)
| singletonP(A)
| ~ ssList(A) ),
inference(clausify,[status(thm)],[ax4]) ).
cnf(c_214,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_232,plain,
ssList(nil),
inference(clausify,[status(thm)],[ax17]) ).
cnf(c_287,plain,
( nil != A
| segmentP(nil,A)
| ~ ssList(A) ),
inference(clausify,[status(thm)],[ax58]) ).
cnf(c_328,negated_conjecture,
ssList(sK1),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_329,negated_conjecture,
ssList(sK0),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_332,negated_conjecture,
sK2 = sK0,
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_333,negated_conjecture,
sK3 = sK1,
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_334,negated_conjecture,
( nil = sK2
| ssItem(sK4) ),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_8986,negated_conjecture,
( nil = sK0
| ssItem(sK4) ),
inference(paramod,[status(thm)],[c_332,c_334]) ).
cnf(c_335,negated_conjecture,
( sK0 = nil
| ssItem(sK4) ),
inference(copy,[status(thm)],[c_8986]) ).
cnf(c_338,negated_conjecture,
( nil = sK2
| ssList(sK5) ),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_8987,negated_conjecture,
( nil = sK0
| ssList(sK5) ),
inference(paramod,[status(thm)],[c_332,c_338]) ).
cnf(c_339,negated_conjecture,
( sK0 = nil
| ssList(sK5) ),
inference(copy,[status(thm)],[c_8987]) ).
cnf(c_340,negated_conjecture,
( nil = sK3
| ssList(sK5) ),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_8988,negated_conjecture,
( nil = sK1
| ssList(sK5) ),
inference(paramod,[status(thm)],[c_333,c_340]) ).
cnf(c_341,negated_conjecture,
( sK1 = nil
| ssList(sK5) ),
inference(copy,[status(thm)],[c_8988]) ).
cnf(c_342,negated_conjecture,
( nil = sK2
| ssList(sK6) ),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_8989,negated_conjecture,
( nil = sK0
| ssList(sK6) ),
inference(paramod,[status(thm)],[c_332,c_342]) ).
cnf(c_343,negated_conjecture,
( sK0 = nil
| ssList(sK6) ),
inference(copy,[status(thm)],[c_8989]) ).
cnf(c_344,negated_conjecture,
( nil = sK3
| ssList(sK6) ),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_8990,negated_conjecture,
( nil = sK1
| ssList(sK6) ),
inference(paramod,[status(thm)],[c_333,c_344]) ).
cnf(c_345,negated_conjecture,
( sK1 = nil
| ssList(sK6) ),
inference(copy,[status(thm)],[c_8990]) ).
cnf(c_346,negated_conjecture,
( nil = sK2
| cons(sK4,nil) = sK3 ),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_8991,negated_conjecture,
( nil = sK2
| cons(sK4,nil) = sK1 ),
inference(paramod,[status(thm)],[c_333,c_346]) ).
cnf(c_8992,negated_conjecture,
( nil = sK0
| cons(sK4,nil) = sK1 ),
inference(paramod,[status(thm)],[c_332,c_8991]) ).
cnf(c_347,negated_conjecture,
( sK0 = nil
| cons(sK4,nil) = sK1 ),
inference(copy,[status(thm)],[c_8992]) ).
cnf(c_350,negated_conjecture,
( nil = sK2
| app(app(sK5,sK3),sK6) = sK2 ),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_8993,negated_conjecture,
( nil = sK2
| app(app(sK5,sK1),sK6) = sK2 ),
inference(paramod,[status(thm)],[c_333,c_350]) ).
cnf(c_8994,negated_conjecture,
( nil = sK2
| app(app(sK5,sK1),sK6) = sK0 ),
inference(paramod,[status(thm)],[c_332,c_8993]) ).
cnf(c_8995,negated_conjecture,
( nil = sK0
| app(app(sK5,sK1),sK6) = sK0 ),
inference(paramod,[status(thm)],[c_332,c_8994]) ).
cnf(c_351,negated_conjecture,
( sK0 = nil
| app(app(sK5,sK1),sK6) = sK0 ),
inference(copy,[status(thm)],[c_8995]) ).
cnf(c_352,negated_conjecture,
( nil = sK3
| app(app(sK5,sK3),sK6) = sK2 ),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_8996,negated_conjecture,
( nil = sK3
| app(app(sK5,sK1),sK6) = sK2 ),
inference(paramod,[status(thm)],[c_333,c_352]) ).
cnf(c_8997,negated_conjecture,
( nil = sK3
| app(app(sK5,sK1),sK6) = sK0 ),
inference(paramod,[status(thm)],[c_332,c_8996]) ).
cnf(c_8998,negated_conjecture,
( nil = sK1
| app(app(sK5,sK1),sK6) = sK0 ),
inference(paramod,[status(thm)],[c_333,c_8997]) ).
cnf(c_353,negated_conjecture,
( sK1 = nil
| app(app(sK5,sK1),sK6) = sK0 ),
inference(copy,[status(thm)],[c_8998]) ).
cnf(c_362,negated_conjecture,
( ~ singletonP(sK1)
| ~ segmentP(sK0,sK1) ),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_363,negated_conjecture,
( nil != sK0
| ~ ssList(nil)
| ~ ssList(sK0)
| ~ segmentP(sK0,sK1) ),
inference(resolve,[status(thm)],[c_92,c_90]) ).
cnf(c_8999,negated_conjecture,
( sK0 != nil
| ~ ssList(nil)
| ~ ssList(sK0)
| ~ segmentP(sK0,sK1) ),
inference(copy,[status(thm)],[c_363]) ).
cnf(c_9000,negated_conjecture,
( sK0 != nil
| ~ ssList(nil)
| ~ segmentP(sK0,sK1) ),
inference(resolve,[status(thm)],[c_329,c_8999]) ).
cnf(c_364,negated_conjecture,
( sK0 != nil
| ~ segmentP(sK0,sK1) ),
inference(resolve,[status(thm)],[c_232,c_9000]) ).
cnf(c_9001,negated_conjecture,
( nil != sK1
| segmentP(nil,sK1) ),
inference(resolve,[status(thm)],[c_328,c_287]) ).
cnf(c_1951,negated_conjecture,
( sK1 != nil
| segmentP(nil,sK1) ),
inference(copy,[status(thm)],[c_9001]) ).
cnf(c_9002,negated_conjecture,
( ~ ssItem(sK4)
| singletonP(sK1)
| ~ ssList(sK1)
| sK0 = nil ),
inference(resolve,[status(thm)],[c_347,c_204]) ).
cnf(c_2957,negated_conjecture,
( ~ ssItem(sK4)
| singletonP(sK1)
| sK0 = nil ),
inference(resolve,[status(thm)],[c_328,c_9002]) ).
cnf(c_9003,negated_conjecture,
( ~ ssList(sK6)
| ~ ssList(sK5)
| segmentP(sK0,sK1)
| ~ ssList(sK1)
| ~ ssList(sK0)
| sK0 = nil ),
inference(resolve,[status(thm)],[c_351,c_214]) ).
cnf(c_9004,negated_conjecture,
( ~ ssList(sK6)
| ~ ssList(sK5)
| segmentP(sK0,sK1)
| ~ ssList(sK1)
| sK0 = nil ),
inference(resolve,[status(thm)],[c_329,c_9003]) ).
cnf(c_2964,negated_conjecture,
( ~ ssList(sK6)
| ~ ssList(sK5)
| segmentP(sK0,sK1)
| sK0 = nil ),
inference(resolve,[status(thm)],[c_328,c_9004]) ).
cnf(c_9005,negated_conjecture,
( ~ ssList(sK6)
| ~ ssList(sK5)
| segmentP(sK0,sK1)
| ~ ssList(sK1)
| ~ ssList(sK0)
| sK1 = nil ),
inference(resolve,[status(thm)],[c_353,c_214]) ).
cnf(c_9006,negated_conjecture,
( ~ ssList(sK6)
| ~ ssList(sK5)
| segmentP(sK0,sK1)
| ~ ssList(sK1)
| sK1 = nil ),
inference(resolve,[status(thm)],[c_329,c_9005]) ).
cnf(c_2967,negated_conjecture,
( ~ ssList(sK6)
| ~ ssList(sK5)
| segmentP(sK0,sK1)
| sK1 = nil ),
inference(resolve,[status(thm)],[c_328,c_9006]) ).
cnf(c_9007,negated_conjecture,
( sK0 = nil
| singletonP(sK1)
| sK0 = nil ),
inference(resolve,[status(thm)],[c_2957,c_335]) ).
cnf(c_3657,negated_conjecture,
( singletonP(sK1)
| sK0 = nil ),
inference(copy,[status(thm)],[c_9007]) ).
cnf(c_3666,plain,
( ~ segmentP(sK0,sK1)
| sK0 = nil ),
inference(resolve,[status(thm)],[c_3657,c_362]) ).
cnf(c_9008,negated_conjecture,
( sK0 = nil
| ~ ssList(sK6)
| segmentP(sK0,sK1)
| sK0 = nil ),
inference(resolve,[status(thm)],[c_2964,c_339]) ).
cnf(c_8099,negated_conjecture,
( ~ ssList(sK6)
| segmentP(sK0,sK1)
| sK0 = nil ),
inference(copy,[status(thm)],[c_9008]) ).
cnf(c_9009,negated_conjecture,
( sK0 = nil
| segmentP(sK0,sK1)
| sK0 = nil ),
inference(resolve,[status(thm)],[c_8099,c_343]) ).
cnf(c_8103,negated_conjecture,
( segmentP(sK0,sK1)
| sK0 = nil ),
inference(copy,[status(thm)],[c_9009]) ).
cnf(c_9010,plain,
( sK0 = nil
| sK0 = nil ),
inference(resolve,[status(thm)],[c_8103,c_3666]) ).
cnf(c_8105,plain,
sK0 = nil,
inference(copy,[status(thm)],[c_9010]) ).
cnf(c_8108,negated_conjecture,
( ~ ssList(sK6)
| ~ ssList(sK5)
| segmentP(nil,sK1)
| sK1 = nil ),
inference(paramod,[status(thm)],[c_8105,c_2967]) ).
cnf(c_9011,negated_conjecture,
( sK0 != nil
| ~ segmentP(nil,sK1) ),
inference(paramod,[status(thm)],[c_8105,c_364]) ).
cnf(c_9012,negated_conjecture,
( nil != nil
| ~ segmentP(nil,sK1) ),
inference(paramod,[status(thm)],[c_8105,c_9011]) ).
cnf(c_8109,negated_conjecture,
~ segmentP(nil,sK1),
inference(copy,[status(thm)],[c_9012]) ).
cnf(c_8112,negated_conjecture,
( ~ ssList(sK6)
| ~ ssList(sK5)
| sK1 = nil ),
inference(resolve,[status(thm)],[c_8109,c_8108]) ).
cnf(c_8113,negated_conjecture,
sK1 != nil,
inference(resolve,[status(thm)],[c_8109,c_1951]) ).
cnf(c_8114,negated_conjecture,
( ~ ssList(sK6)
| ~ ssList(sK5) ),
inference(resolve,[status(thm)],[c_8113,c_8112]) ).
cnf(c_8900,negated_conjecture,
ssList(sK6),
inference(resolve,[status(thm)],[c_8113,c_345]) ).
cnf(c_8901,negated_conjecture,
ssList(sK5),
inference(resolve,[status(thm)],[c_8113,c_341]) ).
cnf(c_9013,negated_conjecture,
~ ssList(sK6),
inference(resolve,[status(thm)],[c_8901,c_8114]) ).
cnf(c_8985,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_8900,c_9013]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC389+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n004.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Sat Sep 26 12:56:36 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.09/0.35 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.35 % Process 1765631 was started by sandbox2 on n004,
% 0.09/0.35 % Sat Sep 26 12:56:36 2026
% 0.09/0.35 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.13/0.38
% 0.13/0.38 % From the command line: assign(max_seconds, 300).
% 232.91/30.98
% 232.91/30.98 % given #500 (I,wt=49): 711 -ssList(A) | ssItem(f34(A)) | -ssItem(B) | -ssItem(C) | -ssList(D) | -ssList(E) | app(app(A,cons(B,D)),cons(C,E)) != A | C != B. [factor(388,a,e)].
% 232.91/30.98
% 232.91/30.98 % given #1000 (I,wt=44): 1231 -ssList(A) | ssList(f37(A)) | -ssItem(B) | -ssList(C) | -ssList(D) | app(app(C,cons(B,A)),cons(B,D)) != A. [factor(733,c,d),xx(g)].
% 232.91/30.98
% 232.91/30.98 % given #1500 (T,wt=11): 2852 c3 = nil | rearsegP(c9,c9). [resolve(345,a,276,a)].
% 232.91/30.98
% 232.91/30.98 % SZS status Theorem for theBenchmark
% 232.91/30.98
% 232.91/30.98 % Proof 1 at 4.80 (+ 1.60) seconds.
% 232.91/30.98 % Length of proof is 51.
% 232.91/30.98 % Level of proof is 10.
% 232.91/30.98 % Maximum clause weight is 35.000.
% 232.91/30.98 % Given clauses 1903.
% 232.91/30.98
% 232.91/30.98 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------