%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWC275+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 08:57:21 AM UTC 2026
% Result : Theorem 147.95s 20.34s
% Output : CNFRefutation 147.95s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 5
% Syntax : Number of formulae : 50 ( 20 unt; 0 def)
% Number of atoms : 148 ( 55 equ)
% Maximal formula atoms : 15 ( 2 avg)
% Number of connectives : 155 ( 57 ~; 54 |; 34 &)
% ( 1 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 6 con; 0-2 aty)
% Number of variables : 27 ( 0 sgn 13 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(ax15,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ( neq(U,V)
<=> U != V ) ) ),
file('theBenchmark.p',ax15) ).
fof(ax65,axiom,
! [U] :
( ssItem(U)
=> totalorderedP(cons(U,nil)) ),
file('theBenchmark.p',ax65) ).
fof(co1,conjecture,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ! [X] :
( ( neq(X,nil)
& ! [Y] :
( ~ memberP(X,Y)
| cons(Y,nil) != W
| ~ ssItem(Y) ) )
| ( nil = X
& nil != W )
| totalorderedP(U)
| 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] :
( ( neq(X,nil)
& ! [Y] :
( ~ memberP(X,Y)
| cons(Y,nil) != W
| ~ ssItem(Y) ) )
| ( nil = X
& nil != W )
| totalorderedP(U)
| U != W
| V != X
| ~ ssList(X) ) ) ) ),
inference(assume_negation,[status(cth)],[co1]) ).
fof(nnf_87,plain,
? [U] :
( ? [V] :
( ? [W] :
( ? [X] :
( ( ~ neq(X,nil)
| ? [Y] :
( memberP(X,Y)
& cons(Y,nil) = W
& ssItem(Y) ) )
& ( nil != X
| nil = W )
& ~ totalorderedP(U)
& 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,
( ( ~ neq(sK2,nil)
| ( memberP(sK2,sK0)
& cons(sK0,nil) = sK1
& ssItem(sK0) ) )
& ( nil != sK2
| nil = sK1 )
& ~ totalorderedP(sK3)
& sK1 = sK3
& sK2 = sK4
& ssList(sK2)
& ssList(sK1)
& ssList(sK4)
& ssList(sK3) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3,sK4,sK1,sK2,sK0]),skolemize(U,sK3),skolemize(V,sK4),skolemize(W,sK1),skolemize(X,sK2),skolemize(Y,sK0)],[nnf_87]) ).
fof(sk_co1_neg,plain,
( ( ~ neq(sK2,nil)
| memberP(sK2,sK0) )
& ( ~ neq(sK2,nil)
| cons(sK0,nil) = sK1 )
& ( ~ neq(sK2,nil)
| ssItem(sK0) )
& ( nil != sK2
| nil = sK1 )
& ~ totalorderedP(sK3)
& sK1 = sK3
& sK2 = sK4
& ssList(sK2)
& ssList(sK1)
& ssList(sK4)
& ssList(sK3) ),
inference(cnf_transformation,[status(thm)],[sk_co1_neg_sk]) ).
cnf(c_191,negated_conjecture,
( ~ neq(sK2,nil)
| cons(sK0,nil) = sK1 ),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_192,negated_conjecture,
( ~ neq(sK2,nil)
| ssItem(sK0) ),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_193,negated_conjecture,
( nil != sK2
| nil = sK1 ),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_8004,negated_conjecture,
( nil != sK2
| sK1 = nil ),
inference(copy,[status(thm)],[c_193]) ).
cnf(c_194,negated_conjecture,
( sK2 != nil
| sK1 = nil ),
inference(copy,[status(thm)],[c_8004]) ).
cnf(c_195,negated_conjecture,
~ totalorderedP(sK3),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_196,negated_conjecture,
sK1 = sK3,
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_197,negated_conjecture,
sK2 = sK4,
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_198,negated_conjecture,
ssList(sK2),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_199,negated_conjecture,
ssList(sK4),
inference(paramod,[status(thm)],[c_197,c_198]) ).
cnf(c_200,negated_conjecture,
ssList(sK1),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_201,negated_conjecture,
ssList(sK3),
inference(paramod,[status(thm)],[c_196,c_200]) ).
fof(ax66,axiom,
totalorderedP(nil),
file('theBenchmark.p',ax66) ).
cnf(c_240,plain,
totalorderedP(nil),
inference(clausify,[status(thm)],[ax66]) ).
cnf(c_241,plain,
( totalorderedP(cons(A,nil))
| ~ ssItem(A) ),
inference(clausify,[status(thm)],[ax65]) ).
fof(ax17,axiom,
ssList(nil),
file('theBenchmark.p',ax17) ).
cnf(c_297,plain,
ssList(nil),
inference(clausify,[status(thm)],[ax17]) ).
cnf(c_299,plain,
( B = A
| neq(A,B)
| ~ ssList(B)
| ~ ssList(A) ),
inference(clausify,[status(thm)],[ax15]) ).
cnf(c_300,plain,
( B != A
| ~ neq(A,B)
| ~ ssList(B)
| ~ ssList(A) ),
inference(clausify,[status(thm)],[ax15]) ).
cnf(c_8005,negated_conjecture,
( sK2 != nil
| sK3 = nil ),
inference(paramod,[status(thm)],[c_196,c_194]) ).
cnf(c_546,negated_conjecture,
( sK4 != nil
| sK3 = nil ),
inference(paramod,[status(thm)],[c_197,c_8005]) ).
cnf(c_8006,negated_conjecture,
( ~ neq(sK2,nil)
| cons(sK0,nil) = sK3 ),
inference(paramod,[status(thm)],[c_196,c_191]) ).
cnf(c_547,negated_conjecture,
( ~ neq(sK4,nil)
| cons(sK0,nil) = sK3 ),
inference(paramod,[status(thm)],[c_197,c_8006]) ).
cnf(c_548,negated_conjecture,
( ~ neq(sK4,nil)
| ssItem(sK0) ),
inference(paramod,[status(thm)],[c_197,c_192]) ).
cnf(c_8007,plain,
( A = nil
| neq(nil,A)
| ~ ssList(A) ),
inference(resolve,[status(thm)],[c_299,c_297]) ).
cnf(c_1762,plain,
( nil = A
| neq(nil,A)
| ~ ssList(A) ),
inference(copy,[status(thm)],[c_8007]) ).
cnf(c_8008,negated_conjecture,
( A = sK4
| neq(sK4,A)
| ~ ssList(A) ),
inference(resolve,[status(thm)],[c_299,c_199]) ).
cnf(c_1764,negated_conjecture,
( sK4 = A
| neq(sK4,A)
| ~ ssList(A) ),
inference(copy,[status(thm)],[c_8008]) ).
cnf(c_8009,negated_conjecture,
( nil = sK3
| neq(nil,sK3) ),
inference(resolve,[status(thm)],[c_1762,c_201]) ).
cnf(c_5009,negated_conjecture,
( sK3 = nil
| neq(nil,sK3) ),
inference(copy,[status(thm)],[c_8009]) ).
cnf(c_8010,plain,
( ~ totalorderedP(nil)
| neq(nil,sK3) ),
inference(paramod,[status(thm)],[c_5009,c_195]) ).
cnf(c_5014,plain,
neq(nil,sK3),
inference(resolve,[status(thm)],[c_240,c_8010]) ).
cnf(c_8011,plain,
( sK3 != nil
| ~ ssList(sK3)
| ~ ssList(nil) ),
inference(resolve,[status(thm)],[c_5014,c_300]) ).
cnf(c_8012,plain,
( sK3 != nil
| ~ ssList(sK3) ),
inference(resolve,[status(thm)],[c_297,c_8011]) ).
cnf(c_5016,negated_conjecture,
sK3 != nil,
inference(resolve,[status(thm)],[c_201,c_8012]) ).
cnf(c_5038,negated_conjecture,
sK4 != nil,
inference(resolve,[status(thm)],[c_5016,c_546]) ).
cnf(c_8013,plain,
( sK4 = nil
| neq(sK4,nil) ),
inference(resolve,[status(thm)],[c_1764,c_297]) ).
cnf(c_6608,negated_conjecture,
neq(sK4,nil),
inference(resolve,[status(thm)],[c_5038,c_8013]) ).
cnf(c_6611,negated_conjecture,
ssItem(sK0),
inference(resolve,[status(thm)],[c_6608,c_548]) ).
cnf(c_6612,negated_conjecture,
cons(sK0,nil) = sK3,
inference(resolve,[status(thm)],[c_6608,c_547]) ).
cnf(c_8014,negated_conjecture,
totalorderedP(cons(sK0,nil)),
inference(resolve,[status(thm)],[c_6611,c_241]) ).
cnf(c_8015,negated_conjecture,
totalorderedP(sK3),
inference(paramod,[status(thm)],[c_6612,c_8014]) ).
cnf(c_8003,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_195,c_8015]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SWC275+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.15/0.42 % Computer : n013.cluster.edu
% 0.15/0.42 % Model : x86_64 x86_64
% 0.15/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.42 % Memory : 8046.5625MB
% 0.15/0.42 % OS : Linux 6.8.0-71-generic
% 0.15/0.42 % CPULimit : 300
% 0.15/0.42 % WCLimit : 300
% 0.15/0.42 % DateTime : Sat Sep 26 12:39:51 UTC 2026
% 0.15/0.43 % CPUTime :
% 0.15/0.43 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.15/0.43 % Process 2763066 was started by sandbox2 on n013,
% 0.15/0.43 % Sat Sep 26 12:39:51 2026
% 0.15/0.43 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.15/0.47
% 0.15/0.47 % From the command line: assign(max_seconds, 300).
% 147.95/20.34
% 147.95/20.34 % given #500 (I,wt=52): 703 -ssList(A) | -ssItem(B) | -ssItem(C) | -ssList(D) | -ssList(E) | app(app(D,cons(B,E)),cons(C,E)) != A | C != B | ssList(f35(A)). [factor(363,e,f)].
% 147.95/20.34
% 147.95/20.34 % given #1000 (I,wt=70): 1228 -ssList(A) | -ssItem(B) | -ssList(C) | -ssList(D) | app(app(C,cons(B,D)),cons(B,C)) != A | app(app(f35(A),cons(f33(A),f36(A))),cons(f34(A),f37(A))) = A. [factor(721,c,e)].
% 147.95/20.34
% 147.95/20.34 % SZS status Theorem for theBenchmark
% 147.95/20.34
% 147.95/20.34 % Proof 1 at 3.41 (+ 0.28) seconds.
% 147.95/20.34 % Length of proof is 32.
% 147.95/20.34 % Level of proof is 9.
% 147.95/20.34 % Maximum clause weight is 18.000.
% 147.95/20.34 % Given clauses 1487.
% 147.95/20.34
% 147.95/20.34 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------