%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWC071+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 : 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 08:56:44 AM UTC 2026
% Result : Theorem 222.41s 29.47s
% Output : CNFRefutation 222.41s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 7
% Syntax : Number of formulae : 71 ( 15 unt; 0 def)
% Number of atoms : 303 ( 123 equ)
% Maximal formula atoms : 48 ( 4 avg)
% Number of connectives : 338 ( 106 ~; 137 |; 72 &)
% ( 3 <=>; 20 =>; 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 : 59 ( 0 sgn 31 !; 16 ?)
% 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(ax55,axiom,
! [U] :
( ssList(U)
=> segmentP(U,U) ),
file('theBenchmark.p',ax55) ).
fof(co1,conjecture,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ! [X] :
( ssList(X)
=> ( ( ( nil != W
| nil != X )
& ! [Z] :
( ssItem(Z)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( ? [X4] :
( lt(X4,Z)
& memberP(X2,X4)
& ssItem(X4) )
| ? [X3] :
( lt(Z,X3)
& memberP(X1,X3)
& ssItem(X3) )
| app(app(X1,W),X2) != X
| cons(Z,nil) != W ) ) ) ) )
| ( nil = U
& nil = V )
| ? [Y] :
( segmentP(U,Y)
& segmentP(V,Y)
& neq(Y,nil)
& ssList(Y) )
| 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)
=> ( ( ( nil != W
| nil != X )
& ! [Z] :
( ssItem(Z)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( ? [X4] :
( lt(X4,Z)
& memberP(X2,X4)
& ssItem(X4) )
| ? [X3] :
( lt(Z,X3)
& memberP(X1,X3)
& ssItem(X3) )
| app(app(X1,W),X2) != X
| cons(Z,nil) != W ) ) ) ) )
| ( nil = U
& nil = V )
| ? [Y] :
( segmentP(U,Y)
& segmentP(V,Y)
& neq(Y,nil)
& ssList(Y) )
| U != W
| V != X ) ) ) ) ),
inference(assume_negation,[status(cth)],[co1]) ).
fof(nnf_87,plain,
? [U] :
( ? [V] :
( ? [W] :
( ? [X] :
( ( ( nil = W
& nil = X )
| ? [Z] :
( ? [X1] :
( ? [X2] :
( ! [X4] :
( ~ lt(X4,Z)
| ~ memberP(X2,X4)
| ~ ssItem(X4) )
& ! [X3] :
( ~ lt(Z,X3)
| ~ memberP(X1,X3)
| ~ ssItem(X3) )
& app(app(X1,W),X2) = X
& cons(Z,nil) = W
& ssList(X2) )
& ssList(X1) )
& ssItem(Z) ) )
& ( nil != U
| nil != V )
& ! [Y] :
( ~ segmentP(U,Y)
| ~ segmentP(V,Y)
| ~ neq(Y,nil)
| ~ 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,
( ( ( nil = sK1
& nil = sK3 )
| ( ! [X4] :
( ~ lt(X4,sK4)
| ~ memberP(sK2,X4)
| ~ ssItem(X4) )
& ! [X3] :
( ~ lt(sK4,X3)
| ~ memberP(sK0,X3)
| ~ ssItem(X3) )
& app(app(sK0,sK1),sK2) = sK3
& cons(sK4,nil) = sK1
& ssList(sK2)
& ssList(sK0)
& ssItem(sK4) ) )
& ( nil != sK6
| nil != sK5 )
& ! [Y] :
( ~ segmentP(sK6,Y)
| ~ segmentP(sK5,Y)
| ~ neq(Y,nil)
| ~ ssList(Y) )
& sK1 = sK6
& sK3 = sK5
& ssList(sK3)
& ssList(sK1)
& ssList(sK5)
& ssList(sK6) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6,sK5,sK1,sK3,sK4,sK0,sK2]),skolemize(U,sK6),skolemize(V,sK5),skolemize(W,sK1),skolemize(X,sK3),skolemize(Z,sK4),skolemize(X1,sK0),skolemize(X2,sK2)],[nnf_87]) ).
fof(sk_co1_neg,plain,
( ! [VAR_0] :
( nil = sK1
| ~ lt(VAR_0,sK4)
| ~ memberP(sK2,VAR_0)
| ~ ssItem(VAR_0) )
& ! [VAR_0] :
( nil = sK3
| ~ lt(VAR_0,sK4)
| ~ memberP(sK2,VAR_0)
| ~ ssItem(VAR_0) )
& ! [VAR_0] :
( nil = sK1
| ~ lt(sK4,VAR_0)
| ~ memberP(sK0,VAR_0)
| ~ ssItem(VAR_0) )
& ! [VAR_0] :
( nil = sK3
| ~ lt(sK4,VAR_0)
| ~ memberP(sK0,VAR_0)
| ~ ssItem(VAR_0) )
& ( nil = sK1
| app(app(sK0,sK1),sK2) = sK3 )
& ( nil = sK3
| app(app(sK0,sK1),sK2) = sK3 )
& ( nil = sK1
| cons(sK4,nil) = sK1 )
& ( nil = sK3
| cons(sK4,nil) = sK1 )
& ( nil = sK1
| ssList(sK2) )
& ( nil = sK3
| ssList(sK2) )
& ( nil = sK1
| ssList(sK0) )
& ( nil = sK3
| ssList(sK0) )
& ( nil = sK1
| ssItem(sK4) )
& ( nil = sK3
| ssItem(sK4) )
& ( nil != sK6
| nil != sK5 )
& ! [VAR_0] :
( ~ segmentP(sK6,VAR_0)
| ~ segmentP(sK5,VAR_0)
| ~ neq(VAR_0,nil)
| ~ ssList(VAR_0) )
& sK1 = sK6
& sK3 = sK5
& ssList(sK3)
& ssList(sK1)
& ssList(sK5)
& ssList(sK6) ),
inference(cnf_transformation,[status(thm)],[sk_co1_neg_sk]) ).
cnf(c_198,negated_conjecture,
( nil = sK1
| app(app(sK0,sK1),sK2) = sK3 ),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_199,negated_conjecture,
( sK1 = nil
| app(app(sK0,sK1),sK2) = sK3 ),
inference(copy,[status(thm)],[c_198]) ).
cnf(c_204,negated_conjecture,
( nil = sK3
| cons(sK4,nil) = sK1 ),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_205,negated_conjecture,
( sK3 = nil
| cons(sK4,nil) = sK1 ),
inference(copy,[status(thm)],[c_204]) ).
cnf(c_206,negated_conjecture,
( nil = sK1
| ssList(sK2) ),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_207,negated_conjecture,
( sK1 = nil
| ssList(sK2) ),
inference(copy,[status(thm)],[c_206]) ).
cnf(c_210,negated_conjecture,
( nil = sK1
| ssList(sK0) ),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_211,negated_conjecture,
( sK1 = nil
| ssList(sK0) ),
inference(copy,[status(thm)],[c_210]) ).
cnf(c_216,negated_conjecture,
( nil = sK3
| ssItem(sK4) ),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_217,negated_conjecture,
( sK3 = nil
| ssItem(sK4) ),
inference(copy,[status(thm)],[c_216]) ).
cnf(c_218,negated_conjecture,
( nil != sK6
| nil != sK5 ),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_8011,negated_conjecture,
( nil != sK6
| sK5 != nil ),
inference(copy,[status(thm)],[c_218]) ).
cnf(c_219,negated_conjecture,
( sK6 != nil
| sK5 != nil ),
inference(copy,[status(thm)],[c_8011]) ).
cnf(c_220,negated_conjecture,
( ~ segmentP(sK6,A)
| ~ segmentP(sK5,A)
| ~ neq(A,nil)
| ~ ssList(A) ),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_221,negated_conjecture,
sK1 = sK6,
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_222,negated_conjecture,
sK3 = sK5,
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_223,negated_conjecture,
ssList(sK3),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_224,negated_conjecture,
ssList(sK5),
inference(paramod,[status(thm)],[c_222,c_223]) ).
cnf(c_225,negated_conjecture,
ssList(sK1),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_226,negated_conjecture,
ssList(sK6),
inference(paramod,[status(thm)],[c_221,c_225]) ).
cnf(c_271,plain,
( segmentP(A,A)
| ~ ssList(A) ),
inference(clausify,[status(thm)],[ax55]) ).
fof(ax39,axiom,
~ singletonP(nil),
file('theBenchmark.p',ax39) ).
cnf(c_291,plain,
~ singletonP(nil),
inference(clausify,[status(thm)],[ax39]) ).
fof(ax17,axiom,
ssList(nil),
file('theBenchmark.p',ax17) ).
cnf(c_322,plain,
ssList(nil),
inference(clausify,[status(thm)],[ax17]) ).
cnf(c_324,plain,
( B = A
| neq(A,B)
| ~ ssList(B)
| ~ ssList(A) ),
inference(clausify,[status(thm)],[ax15]) ).
cnf(c_342,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_352,plain,
( cons(B,nil) != A
| ~ ssItem(B)
| singletonP(A)
| ~ ssList(A) ),
inference(clausify,[status(thm)],[ax4]) ).
cnf(c_572,negated_conjecture,
( sK6 = nil
| ssList(sK0) ),
inference(paramod,[status(thm)],[c_221,c_211]) ).
cnf(c_573,negated_conjecture,
( sK6 = nil
| ssList(sK2) ),
inference(paramod,[status(thm)],[c_221,c_207]) ).
cnf(c_8012,negated_conjecture,
( sK3 = nil
| cons(sK4,nil) = sK6 ),
inference(paramod,[status(thm)],[c_221,c_205]) ).
cnf(c_574,negated_conjecture,
( sK5 = nil
| cons(sK4,nil) = sK6 ),
inference(paramod,[status(thm)],[c_222,c_8012]) ).
cnf(c_8013,negated_conjecture,
( sK1 = nil
| app(app(sK0,sK6),sK2) = sK3 ),
inference(paramod,[status(thm)],[c_221,c_199]) ).
cnf(c_8014,negated_conjecture,
( sK1 = nil
| app(app(sK0,sK6),sK2) = sK5 ),
inference(paramod,[status(thm)],[c_222,c_8013]) ).
cnf(c_577,negated_conjecture,
( sK6 = nil
| app(app(sK0,sK6),sK2) = sK5 ),
inference(paramod,[status(thm)],[c_221,c_8014]) ).
cnf(c_580,negated_conjecture,
( sK5 = nil
| ssItem(sK4) ),
inference(paramod,[status(thm)],[c_222,c_217]) ).
cnf(c_1682,plain,
( ~ segmentP(sK6,sK6)
| ~ segmentP(sK5,sK6)
| ~ neq(sK6,nil) ),
inference(resolve,[status(thm)],[c_226,c_220]) ).
cnf(c_1754,plain,
segmentP(sK6,sK6),
inference(resolve,[status(thm)],[c_271,c_226]) ).
cnf(c_1756,plain,
( ~ segmentP(sK5,sK6)
| ~ neq(sK6,nil) ),
inference(resolve,[status(thm)],[c_1754,c_1682]) ).
cnf(c_8015,negated_conjecture,
( A = sK6
| neq(sK6,A)
| ~ ssList(A) ),
inference(resolve,[status(thm)],[c_324,c_226]) ).
cnf(c_1965,negated_conjecture,
( sK6 = A
| neq(sK6,A)
| ~ ssList(A) ),
inference(copy,[status(thm)],[c_8015]) ).
cnf(c_8016,negated_conjecture,
( ~ ssItem(sK4)
| singletonP(sK6)
| ~ ssList(sK6)
| sK5 = nil ),
inference(resolve,[status(thm)],[c_574,c_352]) ).
cnf(c_2640,negated_conjecture,
( ~ ssItem(sK4)
| singletonP(sK6)
| sK5 = nil ),
inference(resolve,[status(thm)],[c_226,c_8016]) ).
cnf(c_8017,negated_conjecture,
( ~ ssList(sK2)
| ~ ssList(sK0)
| segmentP(sK5,sK6)
| ~ ssList(sK6)
| ~ ssList(sK5)
| sK6 = nil ),
inference(resolve,[status(thm)],[c_577,c_342]) ).
cnf(c_8018,negated_conjecture,
( ~ ssList(sK2)
| ~ ssList(sK0)
| segmentP(sK5,sK6)
| ~ ssList(sK6)
| sK6 = nil ),
inference(resolve,[status(thm)],[c_224,c_8017]) ).
cnf(c_2660,negated_conjecture,
( ~ ssList(sK2)
| ~ ssList(sK0)
| segmentP(sK5,sK6)
| sK6 = nil ),
inference(resolve,[status(thm)],[c_226,c_8018]) ).
cnf(c_8019,negated_conjecture,
( sK5 = nil
| singletonP(sK6)
| sK5 = nil ),
inference(resolve,[status(thm)],[c_2640,c_580]) ).
cnf(c_3711,negated_conjecture,
( singletonP(sK6)
| sK5 = nil ),
inference(copy,[status(thm)],[c_8019]) ).
cnf(c_3743,plain,
( sK6 = nil
| neq(sK6,nil) ),
inference(resolve,[status(thm)],[c_1965,c_322]) ).
cnf(c_3745,plain,
( ~ segmentP(sK5,sK6)
| sK6 = nil ),
inference(resolve,[status(thm)],[c_3743,c_1756]) ).
cnf(c_8020,negated_conjecture,
( sK6 = nil
| ~ ssList(sK2)
| segmentP(sK5,sK6)
| sK6 = nil ),
inference(resolve,[status(thm)],[c_2660,c_572]) ).
cnf(c_7964,negated_conjecture,
( ~ ssList(sK2)
| segmentP(sK5,sK6)
| sK6 = nil ),
inference(copy,[status(thm)],[c_8020]) ).
cnf(c_8021,negated_conjecture,
( sK6 = nil
| segmentP(sK5,sK6)
| sK6 = nil ),
inference(resolve,[status(thm)],[c_7964,c_573]) ).
cnf(c_7966,negated_conjecture,
( segmentP(sK5,sK6)
| sK6 = nil ),
inference(copy,[status(thm)],[c_8021]) ).
cnf(c_8022,plain,
( sK6 = nil
| sK6 = nil ),
inference(resolve,[status(thm)],[c_7966,c_3745]) ).
cnf(c_7968,plain,
sK6 = nil,
inference(copy,[status(thm)],[c_8022]) ).
cnf(c_8023,negated_conjecture,
( singletonP(nil)
| sK5 = nil ),
inference(paramod,[status(thm)],[c_7968,c_3711]) ).
cnf(c_8007,negated_conjecture,
sK5 = nil,
inference(resolve,[status(thm)],[c_291,c_8023]) ).
cnf(c_8024,negated_conjecture,
( sK6 != nil
| nil != nil ),
inference(paramod,[status(thm)],[c_8007,c_219]) ).
cnf(c_8025,negated_conjecture,
( nil != nil
| nil != nil ),
inference(paramod,[status(thm)],[c_7968,c_8024]) ).
cnf(c_8026,negated_conjecture,
nil != nil,
inference(copy,[status(thm)],[c_8025]) ).
cnf(c_8010,negated_conjecture,
$false,
inference(copy,[status(thm)],[c_8026]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SWC071+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.02 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.05/0.30 % Computer : n012.cluster.edu
% 0.05/0.30 % Model : x86_64 x86_64
% 0.05/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.05/0.30 % Memory : 8046.5625MB
% 0.05/0.30 % OS : Linux 6.8.0-71-generic
% 0.05/0.30 % CPULimit : 300
% 0.05/0.30 % WCLimit : 300
% 0.05/0.30 % DateTime : Sat Sep 26 12:10:50 UTC 2026
% 0.05/0.30 % CPUTime :
% 0.05/0.30 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.05/0.30 % Process 549029 was started by sandbox on n012,
% 0.05/0.30 % Sat Sep 26 12:10:50 2026
% 0.05/0.30 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.05/0.31
% 0.05/0.31 % From the command line: assign(max_seconds, 300).
% 222.41/29.47
% 222.41/29.47 % given #500 (I,wt=49): 719 -ssList(A) | -ssItem(B) | -ssItem(C) | -ssList(D) | -ssList(E) | app(app(D,cons(B,A)),cons(C,E)) != A | C != B | ssItem(f33(A)). [factor(384,a,e)].
% 222.41/29.47
% 222.41/29.47 % given #1000 (I,wt=47): 1239 -ssList(A) | -ssItem(B) | -ssItem(C) | -ssList(D) | app(app(D,cons(B,D)),cons(C,D)) != A | C != B | ssList(f36(A)). [factor(743,d,e)].
% 222.41/29.47
% 222.41/29.47 % given #1500 (T,wt=11): 2836 c4 = nil | rearsegP(c8,nil). [resolve(581,a,276,a)].
% 222.41/29.47
% 222.41/29.47 % given #2000 (W,wt=15): 1994 totalorderedP(c3) | ssList(f26(c3)). [resolve(337,a,226,a)].
% 222.41/29.47
% 222.41/29.47 % SZS status Theorem for theBenchmark
% 222.41/29.47
% 222.41/29.47 % Proof 1 at 3.73 (+ 1.23) seconds.
% 222.41/29.47 % Length of proof is 49.
% 222.41/29.47 % Level of proof is 9.
% 222.41/29.47 % Maximum clause weight is 35.000.
% 222.41/29.47 % Given clauses 2054.
% 222.41/29.47
% 222.41/29.47 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------