%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWC258+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 : n020.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 08:57:18 AM UTC 2026
% Result : Theorem 56.85s 7.69s
% Output : CNFRefutation 56.85s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 4
% Syntax : Number of formulae : 34 ( 10 unt; 0 def)
% Number of atoms : 142 ( 62 equ)
% Maximal formula atoms : 29 ( 4 avg)
% Number of connectives : 145 ( 37 ~; 52 |; 44 &)
% ( 0 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 5 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 : 25 ( 0 sgn 16 !; 7 ?)
% Comments :
%------------------------------------------------------------------------------
fof(ax38,axiom,
! [U] :
( ssItem(U)
=> ~ memberP(nil,U) ),
file('theBenchmark.p',ax38) ).
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] :
( ssList(X)
=> ( ( ( nil != W
| nil != X )
& ! [Y] :
( ssItem(Y)
=> ( ? [Z] :
( leq(Z,Y)
& memberP(X,Z)
& Y != Z
& ssItem(Z) )
| ~ memberP(X,Y)
| cons(Y,nil) != W ) ) )
| totalorderedP(U)
| 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 )
& ! [Y] :
( ssItem(Y)
=> ( ? [Z] :
( leq(Z,Y)
& memberP(X,Z)
& Y != Z
& ssItem(Z) )
| ~ memberP(X,Y)
| cons(Y,nil) != W ) ) )
| totalorderedP(U)
| U != W
| V != X ) ) ) ) ),
inference(assume_negation,[status(cth)],[co1]) ).
cnf(c_261,plain,
( ~ memberP(nil,A)
| ~ ssItem(A) ),
inference(clausify,[status(thm)],[ax38]) ).
cnf(c_287,plain,
( totalorderedP(cons(A,nil))
| ~ ssItem(A) ),
inference(clausify,[status(thm)],[ax65]) ).
fof(ax66,axiom,
totalorderedP(nil),
file('theBenchmark.p',ax66) ).
cnf(c_288,plain,
totalorderedP(nil),
inference(clausify,[status(thm)],[ax66]) ).
fof(nnf_87,plain,
? [U] :
( ? [V] :
( ? [W] :
( ? [X] :
( ( ( nil = W
& nil = X )
| ? [Y] :
( ! [Z] :
( ~ leq(Z,Y)
| ~ memberP(X,Z)
| Z = Y
| ~ ssItem(Z) )
& memberP(X,Y)
& cons(Y,nil) = W
& ssItem(Y) ) )
& ~ 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,
( ( ( nil = sK0
& nil = sK3 )
| ( ! [Z] :
( ~ leq(Z,sK2)
| ~ memberP(sK3,Z)
| Z = sK2
| ~ ssItem(Z) )
& memberP(sK3,sK2)
& cons(sK2,nil) = sK0
& ssItem(sK2) ) )
& ~ totalorderedP(sK1)
& sK0 = sK1
& sK3 = sK4
& ssList(sK3)
& ssList(sK0)
& ssList(sK4)
& ssList(sK1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK4,sK0,sK3,sK2]),skolemize(U,sK1),skolemize(V,sK4),skolemize(W,sK0),skolemize(X,sK3),skolemize(Y,sK2)],[nnf_87]) ).
fof(sk_co1_neg,plain,
( ! [VAR_0] :
( nil = sK0
| ~ leq(VAR_0,sK2)
| ~ memberP(sK3,VAR_0)
| VAR_0 = sK2
| ~ ssItem(VAR_0) )
& ! [VAR_0] :
( nil = sK3
| ~ leq(VAR_0,sK2)
| ~ memberP(sK3,VAR_0)
| VAR_0 = sK2
| ~ ssItem(VAR_0) )
& ( nil = sK0
| memberP(sK3,sK2) )
& ( nil = sK3
| memberP(sK3,sK2) )
& ( nil = sK0
| cons(sK2,nil) = sK0 )
& ( nil = sK3
| cons(sK2,nil) = sK0 )
& ( nil = sK0
| ssItem(sK2) )
& ( nil = sK3
| ssItem(sK2) )
& ~ totalorderedP(sK1)
& sK0 = sK1
& sK3 = sK4
& ssList(sK3)
& ssList(sK0)
& ssList(sK4)
& ssList(sK1) ),
inference(cnf_transformation,[status(thm)],[sk_co1_neg_sk]) ).
cnf(c_332,negated_conjecture,
sK0 = sK1,
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_333,negated_conjecture,
~ totalorderedP(sK1),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_334,negated_conjecture,
( nil = sK3
| ssItem(sK2) ),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_335,negated_conjecture,
( sK3 = nil
| ssItem(sK2) ),
inference(copy,[status(thm)],[c_334]) ).
cnf(c_336,negated_conjecture,
( nil = sK0
| ssItem(sK2) ),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_337,negated_conjecture,
( sK0 = nil
| ssItem(sK2) ),
inference(copy,[status(thm)],[c_336]) ).
cnf(c_338,negated_conjecture,
( nil = sK3
| cons(sK2,nil) = sK0 ),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_339,negated_conjecture,
( sK3 = nil
| cons(sK2,nil) = sK0 ),
inference(copy,[status(thm)],[c_338]) ).
cnf(c_344,negated_conjecture,
( nil = sK0
| memberP(sK3,sK2) ),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_345,negated_conjecture,
( sK0 = nil
| memberP(sK3,sK2) ),
inference(copy,[status(thm)],[c_344]) ).
cnf(c_3045,plain,
( totalorderedP(cons(sK2,nil))
| sK3 = nil ),
inference(resolve,[status(thm)],[c_335,c_287]) ).
cnf(c_28229,plain,
( totalorderedP(sK0)
| sK3 = nil
| sK3 = nil ),
inference(paramod,[status(thm)],[c_339,c_3045]) ).
cnf(c_27509,plain,
( totalorderedP(sK0)
| sK3 = nil ),
inference(copy,[status(thm)],[c_28229]) ).
cnf(c_28230,plain,
( totalorderedP(sK1)
| sK3 = nil ),
inference(paramod,[status(thm)],[c_332,c_27509]) ).
cnf(c_27510,negated_conjecture,
sK3 = nil,
inference(resolve,[status(thm)],[c_333,c_28230]) ).
cnf(c_27528,plain,
( sK0 = nil
| memberP(nil,sK2) ),
inference(paramod,[status(thm)],[c_27510,c_345]) ).
cnf(c_27871,plain,
( ~ ssItem(sK2)
| sK0 = nil ),
inference(resolve,[status(thm)],[c_27528,c_261]) ).
cnf(c_28231,negated_conjecture,
( sK0 = nil
| sK0 = nil ),
inference(resolve,[status(thm)],[c_27871,c_337]) ).
cnf(c_27872,negated_conjecture,
sK0 = nil,
inference(copy,[status(thm)],[c_28231]) ).
cnf(c_28232,plain,
nil = sK1,
inference(paramod,[status(thm)],[c_27872,c_332]) ).
cnf(c_27883,plain,
sK1 = nil,
inference(copy,[status(thm)],[c_28232]) ).
cnf(c_28233,plain,
~ totalorderedP(nil),
inference(paramod,[status(thm)],[c_27883,c_333]) ).
cnf(c_28228,plain,
$false,
inference(resolve,[status(thm)],[c_288,c_28233]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC258+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n020.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sat Sep 26 12:38:34 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.37 % Process 1585466 was started by sandbox2 on n020,
% 0.10/0.37 % Sat Sep 26 12:38:34 2026
% 0.10/0.37 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.14/0.41
% 0.14/0.41 % From the command line: assign(max_seconds, 300).
% 56.85/7.69
% 56.85/7.69 % given #500 (I,wt=49): 708 -ssList(A) | ssList(f35(A)) | -ssItem(B) | -ssItem(C) | -ssList(D) | -ssList(E) | app(app(D,cons(B,E)),cons(C,E)) != A | C != B. [factor(374,f,g)].
% 56.85/7.69
% 56.85/7.69 % given #1000 (I,wt=64): 1233 -ssList(A) | app(app(f35(A),cons(f33(A),f36(A))),cons(f34(A),f37(A))) = A | -ssItem(B) | -ssList(C) | -ssList(D) | app(app(C,cons(B,D)),cons(B,C)) != A. [factor(726,d,f)].
% 56.85/7.69
% 56.85/7.69 % given #1500 (W,wt=11): 3436 c5 = nil | leq(c7,c7). [resolve(337,a,248,a)].
% 56.85/7.69
% 56.85/7.69 % given #2000 (F,wt=22): 17616 cons(c2,f6(c5,c3)) != nil. [resolve(8947,a,2642,a)].
% 56.85/7.69
% 56.85/7.69 % given #2500 (T,wt=15): 20066 strictorderedP(c4) | ssItem(f28(c6)). [para(331(a,1),3002(a,1))].
% 56.85/7.69
% 56.85/7.69 % given #3000 (F,wt=21): 27635 cons(f24(c5),nil) != c6. [para(27510(a,1),22215(a,1,2))].
% 56.85/7.69
% 56.85/7.69 % SZS status Theorem for theBenchmark
% 56.85/7.69
% 56.85/7.69 % Proof 1 at 6.32 (+ 0.92) seconds.
% 56.85/7.69 % Length of proof is 24.
% 56.85/7.69 % Level of proof is 10.
% 56.85/7.69 % Maximum clause weight is 18.000.
% 56.85/7.69 % Given clauses 3019.
% 56.85/7.69
% 56.85/7.69 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------