%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWC330+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 : n013.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 08:57:29 AM UTC 2026
% Result : Theorem 61.38s 8.23s
% Output : CNFRefutation 61.38s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 7
% Syntax : Number of formulae : 79 ( 22 unt; 0 def)
% Number of atoms : 287 ( 88 equ)
% Maximal formula atoms : 44 ( 3 avg)
% Number of connectives : 304 ( 96 ~; 128 |; 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 : 49 ( 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(ax73,axiom,
! [U] :
( ssItem(U)
=> equalelemsP(cons(U,nil)) ),
file('theBenchmark.p',ax73) ).
fof(co1,conjecture,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ! [X] :
( ( equalelemsP(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] :
( ( equalelemsP(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]) ).
fof(nnf_87,plain,
? [U] :
( ? [V] :
( ? [W] :
( ? [X] :
( ( ~ equalelemsP(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,
( ( ~ equalelemsP(sK1)
| ~ segmentP(sK0,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 = sK1
& sK5 = sK0
& ssList(sK5)
& ssList(sK3)
& ssList(sK0)
& ssList(sK1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK0,sK3,sK5,sK6,sK2,sK4]),skolemize(U,sK1),skolemize(V,sK0),skolemize(W,sK3),skolemize(X,sK5),skolemize(Y,sK6),skolemize(Z,sK2),skolemize(X1,sK4)],[nnf_87]) ).
fof(sk_co1_neg,plain,
( ( ~ equalelemsP(sK1)
| ~ segmentP(sK0,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 = sK1
& sK5 = sK0
& ssList(sK5)
& ssList(sK3)
& ssList(sK0)
& ssList(sK1) ),
inference(cnf_transformation,[status(thm)],[sk_co1_neg_sk]) ).
cnf(c_169,negated_conjecture,
( ~ equalelemsP(sK1)
| ~ segmentP(sK0,sK1) ),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_178,negated_conjecture,
( nil = sK3
| app(app(sK2,sK3),sK4) = sK5 ),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_179,negated_conjecture,
( sK3 = nil
| app(app(sK2,sK3),sK4) = sK5 ),
inference(copy,[status(thm)],[c_178]) ).
cnf(c_182,negated_conjecture,
( nil = sK3
| cons(sK6,nil) = sK3 ),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_183,negated_conjecture,
( sK3 = nil
| cons(sK6,nil) = sK3 ),
inference(copy,[status(thm)],[c_182]) ).
cnf(c_186,negated_conjecture,
( nil = sK3
| ssList(sK4) ),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_187,negated_conjecture,
( sK3 = nil
| ssList(sK4) ),
inference(copy,[status(thm)],[c_186]) ).
cnf(c_190,negated_conjecture,
( nil = sK3
| ssList(sK2) ),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_191,negated_conjecture,
( sK3 = nil
| ssList(sK2) ),
inference(copy,[status(thm)],[c_190]) ).
cnf(c_194,negated_conjecture,
( nil = sK3
| ssItem(sK6) ),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_195,negated_conjecture,
( sK3 = nil
| ssItem(sK6) ),
inference(copy,[status(thm)],[c_194]) ).
cnf(c_198,negated_conjecture,
sK3 = sK1,
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_199,negated_conjecture,
sK5 = sK0,
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_200,negated_conjecture,
ssList(sK5),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_201,negated_conjecture,
ssList(sK0),
inference(paramod,[status(thm)],[c_199,c_200]) ).
cnf(c_202,negated_conjecture,
ssList(sK3),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_203,negated_conjecture,
ssList(sK1),
inference(paramod,[status(thm)],[c_198,c_202]) ).
fof(ax74,axiom,
equalelemsP(nil),
file('theBenchmark.p',ax74) ).
cnf(c_232,plain,
equalelemsP(nil),
inference(clausify,[status(thm)],[ax74]) ).
cnf(c_233,plain,
( equalelemsP(cons(A,nil))
| ~ ssItem(A) ),
inference(clausify,[status(thm)],[ax73]) ).
cnf(c_248,plain,
( segmentP(A,nil)
| ~ ssList(A) ),
inference(clausify,[status(thm)],[ax57]) ).
fof(ax39,axiom,
~ singletonP(nil),
file('theBenchmark.p',ax39) ).
cnf(c_270,plain,
~ singletonP(nil),
inference(clausify,[status(thm)],[ax39]) ).
cnf(c_326,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_336,plain,
( cons(B,nil) != A
| ~ ssItem(B)
| singletonP(A)
| ~ ssList(A) ),
inference(clausify,[status(thm)],[ax4]) ).
cnf(c_511,negated_conjecture,
( sK1 = nil
| ssItem(sK6) ),
inference(paramod,[status(thm)],[c_198,c_195]) ).
cnf(c_512,negated_conjecture,
( sK1 = nil
| ssList(sK2) ),
inference(paramod,[status(thm)],[c_198,c_191]) ).
cnf(c_513,negated_conjecture,
( sK1 = nil
| ssList(sK4) ),
inference(paramod,[status(thm)],[c_198,c_187]) ).
cnf(c_8424,negated_conjecture,
( sK3 = nil
| cons(sK6,nil) = sK1 ),
inference(paramod,[status(thm)],[c_198,c_183]) ).
cnf(c_515,negated_conjecture,
( sK1 = nil
| cons(sK6,nil) = sK1 ),
inference(paramod,[status(thm)],[c_198,c_8424]) ).
cnf(c_8425,negated_conjecture,
( sK3 = nil
| app(app(sK2,sK1),sK4) = sK5 ),
inference(paramod,[status(thm)],[c_198,c_179]) ).
cnf(c_8426,negated_conjecture,
( sK3 = nil
| app(app(sK2,sK1),sK4) = sK0 ),
inference(paramod,[status(thm)],[c_199,c_8425]) ).
cnf(c_517,negated_conjecture,
( sK1 = nil
| app(app(sK2,sK1),sK4) = sK0 ),
inference(paramod,[status(thm)],[c_198,c_8426]) ).
cnf(c_1628,plain,
segmentP(sK0,nil),
inference(resolve,[status(thm)],[c_248,c_201]) ).
cnf(c_8427,plain,
( ~ equalelemsP(sK1)
| ~ segmentP(sK0,nil)
| ssItem(sK6) ),
inference(paramod,[status(thm)],[c_511,c_169]) ).
cnf(c_2483,plain,
( ~ equalelemsP(sK1)
| ssItem(sK6) ),
inference(resolve,[status(thm)],[c_1628,c_8427]) ).
cnf(c_8428,plain,
( ~ equalelemsP(sK1)
| ~ segmentP(sK0,nil)
| ssList(sK2) ),
inference(paramod,[status(thm)],[c_512,c_169]) ).
cnf(c_2673,plain,
( ~ equalelemsP(sK1)
| ssList(sK2) ),
inference(resolve,[status(thm)],[c_1628,c_8428]) ).
cnf(c_8429,plain,
( ~ equalelemsP(sK1)
| ~ segmentP(sK0,nil)
| ssList(sK4) ),
inference(paramod,[status(thm)],[c_513,c_169]) ).
cnf(c_2906,plain,
( ~ equalelemsP(sK1)
| ssList(sK4) ),
inference(resolve,[status(thm)],[c_1628,c_8429]) ).
cnf(c_8430,negated_conjecture,
( ~ ssItem(sK6)
| singletonP(sK1)
| ~ ssList(sK1)
| sK1 = nil ),
inference(resolve,[status(thm)],[c_515,c_336]) ).
cnf(c_3037,negated_conjecture,
( ~ ssItem(sK6)
| singletonP(sK1)
| sK1 = nil ),
inference(resolve,[status(thm)],[c_203,c_8430]) ).
cnf(c_8431,negated_conjecture,
( ~ ssList(sK4)
| ~ ssList(sK2)
| segmentP(sK0,sK1)
| ~ ssList(sK1)
| ~ ssList(sK0)
| sK1 = nil ),
inference(resolve,[status(thm)],[c_517,c_326]) ).
cnf(c_8432,negated_conjecture,
( ~ ssList(sK4)
| ~ ssList(sK2)
| segmentP(sK0,sK1)
| ~ ssList(sK1)
| sK1 = nil ),
inference(resolve,[status(thm)],[c_201,c_8431]) ).
cnf(c_3138,negated_conjecture,
( ~ ssList(sK4)
| ~ ssList(sK2)
| segmentP(sK0,sK1)
| sK1 = nil ),
inference(resolve,[status(thm)],[c_203,c_8432]) ).
cnf(c_8433,plain,
( ~ equalelemsP(nil)
| ssItem(sK6)
| ssItem(sK6) ),
inference(paramod,[status(thm)],[c_511,c_2483]) ).
cnf(c_8434,plain,
( ~ equalelemsP(nil)
| ssItem(sK6) ),
inference(copy,[status(thm)],[c_8433]) ).
cnf(c_6008,plain,
ssItem(sK6),
inference(resolve,[status(thm)],[c_232,c_8434]) ).
cnf(c_6404,negated_conjecture,
( singletonP(sK1)
| sK1 = nil ),
inference(resolve,[status(thm)],[c_6008,c_3037]) ).
cnf(c_6694,plain,
equalelemsP(cons(sK6,nil)),
inference(resolve,[status(thm)],[c_6008,c_233]) ).
cnf(c_8435,plain,
( ~ equalelemsP(nil)
| ssList(sK2)
| ssList(sK2) ),
inference(paramod,[status(thm)],[c_512,c_2673]) ).
cnf(c_8436,plain,
( ~ equalelemsP(nil)
| ssList(sK2) ),
inference(copy,[status(thm)],[c_8435]) ).
cnf(c_6950,plain,
ssList(sK2),
inference(resolve,[status(thm)],[c_232,c_8436]) ).
cnf(c_6954,negated_conjecture,
( ~ ssList(sK4)
| segmentP(sK0,sK1)
| sK1 = nil ),
inference(resolve,[status(thm)],[c_6950,c_3138]) ).
cnf(c_8437,plain,
( ~ equalelemsP(nil)
| ssList(sK4)
| ssList(sK4) ),
inference(paramod,[status(thm)],[c_513,c_2906]) ).
cnf(c_8438,plain,
( ~ equalelemsP(nil)
| ssList(sK4) ),
inference(copy,[status(thm)],[c_8437]) ).
cnf(c_7556,plain,
ssList(sK4),
inference(resolve,[status(thm)],[c_232,c_8438]) ).
cnf(c_7561,negated_conjecture,
( segmentP(sK0,sK1)
| sK1 = nil ),
inference(resolve,[status(thm)],[c_7556,c_6954]) ).
cnf(c_8439,plain,
( ~ equalelemsP(sK1)
| ~ segmentP(sK0,nil)
| singletonP(sK1) ),
inference(paramod,[status(thm)],[c_6404,c_169]) ).
cnf(c_8270,plain,
( ~ equalelemsP(sK1)
| singletonP(sK1) ),
inference(resolve,[status(thm)],[c_1628,c_8439]) ).
cnf(c_8440,plain,
( ~ equalelemsP(nil)
| singletonP(sK1)
| singletonP(sK1) ),
inference(paramod,[status(thm)],[c_6404,c_8270]) ).
cnf(c_8441,plain,
( ~ equalelemsP(nil)
| singletonP(sK1) ),
inference(copy,[status(thm)],[c_8440]) ).
cnf(c_8280,plain,
singletonP(sK1),
inference(resolve,[status(thm)],[c_232,c_8441]) ).
cnf(c_8442,plain,
( singletonP(nil)
| cons(sK6,nil) = sK1 ),
inference(paramod,[status(thm)],[c_515,c_8280]) ).
cnf(c_8283,plain,
cons(sK6,nil) = sK1,
inference(resolve,[status(thm)],[c_270,c_8442]) ).
cnf(c_8338,plain,
equalelemsP(sK1),
inference(paramod,[status(thm)],[c_8283,c_6694]) ).
cnf(c_8409,negated_conjecture,
~ segmentP(sK0,sK1),
inference(resolve,[status(thm)],[c_8338,c_169]) ).
cnf(c_8422,negated_conjecture,
sK1 = nil,
inference(resolve,[status(thm)],[c_8409,c_7561]) ).
cnf(c_8443,negated_conjecture,
~ segmentP(sK0,nil),
inference(paramod,[status(thm)],[c_8422,c_8409]) ).
cnf(c_8423,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_1628,c_8443]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC330+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.39 % Computer : n013.cluster.edu
% 0.10/0.39 % Model : x86_64 x86_64
% 0.10/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.39 % Memory : 8046.5625MB
% 0.10/0.39 % OS : Linux 6.8.0-71-generic
% 0.10/0.39 % CPULimit : 300
% 0.10/0.39 % WCLimit : 300
% 0.10/0.39 % DateTime : Sat Sep 26 12:48:22 UTC 2026
% 0.10/0.40 % CPUTime :
% 0.10/0.40 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.40 % Process 2780082 was started by sandbox2 on n013,
% 0.10/0.40 % Sat Sep 26 12:48:22 2026
% 0.10/0.40 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.10/0.42
% 0.10/0.42 % From the command line: assign(max_seconds, 300).
% 61.38/8.23
% 61.38/8.23 % given #500 (I,wt=57): 702 -ssList(A) | -ssItem(B) | -ssItem(C) | -ssList(D) | -ssList(E) | app(app(D,cons(B,A)),cons(C,E)) != A | lt(B,C) | lt(C,B) | app(app(f20(A),cons(f18(A),f21(A))),cons(f19(A),f22(A))) = A. [factor(376,a,e)].
% 61.38/8.23
% 61.38/8.23 % given #1000 (I,wt=37): 1202 -ssList(A) | -ssItem(B) | -ssList(C) | -ssList(D) | app(app(C,cons(B,D)),cons(B,D)) != A | lt(B,B) | -lt(f19(A),f18(A)). [factor(718,d,e)].
% 61.38/8.23
% 61.38/8.23 % SZS status Theorem for theBenchmark
% 61.38/8.23
% 61.38/8.23 % Proof 1 at 5.96 (+ 1.77) seconds.
% 61.38/8.23 % Length of proof is 53.
% 61.38/8.23 % Level of proof is 13.
% 61.38/8.23 % Maximum clause weight is 26.000.
% 61.38/8.23 % Given clauses 1482.
% 61.38/8.23
% 61.38/8.23 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------