%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWC348+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 : n016.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 08:57:32 AM UTC 2026
% Result : Theorem 176.04s 24.10s
% Output : CNFRefutation 176.04s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 8
% Syntax : Number of formulae : 70 ( 27 unt; 0 def)
% Number of atoms : 192 ( 43 equ)
% Maximal formula atoms : 11 ( 2 avg)
% Number of connectives : 201 ( 79 ~; 76 |; 28 &)
% ( 2 <=>; 16 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 5 con; 0-2 aty)
% Number of variables : 43 ( 0 sgn 23 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(ax4,axiom,
! [U] :
( ssList(U)
=> ( singletonP(U)
<=> ? [V] :
( cons(V,nil) = U
& ssItem(V) ) ) ),
file('theBenchmark.p',ax4) ).
fof(ax15,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ( neq(U,V)
<=> U != V ) ) ),
file('theBenchmark.p',ax15) ).
fof(ax54,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ( ( segmentP(V,U)
& segmentP(U,V) )
=> U = V ) ) ),
file('theBenchmark.p',ax54) ).
fof(ax57,axiom,
! [U] :
( ssList(U)
=> segmentP(U,nil) ),
file('theBenchmark.p',ax57) ).
fof(ax68,axiom,
! [U] :
( ssItem(U)
=> strictorderedP(cons(U,nil)) ),
file('theBenchmark.p',ax68) ).
fof(co1,conjecture,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ! [X] :
( ssList(X)
=> ( ( strictorderedP(U)
& segmentP(V,U) )
| ( neq(X,nil)
& ~ singletonP(W) )
| ~ segmentP(X,W)
| 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)
=> ( ( strictorderedP(U)
& segmentP(V,U) )
| ( neq(X,nil)
& ~ singletonP(W) )
| ~ segmentP(X,W)
| U != W
| V != X ) ) ) ) ),
inference(assume_negation,[status(cth)],[co1]) ).
fof(nnf_87,plain,
? [U] :
( ? [V] :
( ? [W] :
( ? [X] :
( ( ~ strictorderedP(U)
| ~ segmentP(V,U) )
& ( ~ neq(X,nil)
| singletonP(W) )
& segmentP(X,W)
& W = U
& X = V
& ssList(X) )
& ssList(W) )
& ssList(V) )
& ssList(U) ),
inference(fof_nnf,[status(thm)],[co1_neg]) ).
fof(sk_co1_neg,plain,
( ( ~ strictorderedP(sK1)
| ~ segmentP(sK0,sK1) )
& ( ~ neq(sK3,nil)
| singletonP(sK2) )
& segmentP(sK3,sK2)
& sK2 = sK1
& sK3 = sK0
& ssList(sK3)
& ssList(sK2)
& ssList(sK0)
& ssList(sK1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK0,sK2,sK3]),skolemize(U,sK1),skolemize(V,sK0),skolemize(W,sK2),skolemize(X,sK3)],[nnf_87]) ).
cnf(c_190,negated_conjecture,
( ~ strictorderedP(sK1)
| ~ segmentP(sK0,sK1) ),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_191,negated_conjecture,
( ~ neq(sK3,nil)
| singletonP(sK2) ),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_192,negated_conjecture,
segmentP(sK3,sK2),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_193,negated_conjecture,
sK2 = sK1,
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_194,negated_conjecture,
sK3 = sK0,
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_195,negated_conjecture,
ssList(sK3),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_196,negated_conjecture,
ssList(sK0),
inference(paramod,[status(thm)],[c_194,c_195]) ).
cnf(c_197,negated_conjecture,
ssList(sK2),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_198,negated_conjecture,
ssList(sK1),
inference(paramod,[status(thm)],[c_193,c_197]) ).
fof(ax69,axiom,
strictorderedP(nil),
file('theBenchmark.p',ax69) ).
cnf(c_231,plain,
strictorderedP(nil),
inference(clausify,[status(thm)],[ax69]) ).
cnf(c_232,plain,
( strictorderedP(cons(A,nil))
| ~ ssItem(A) ),
inference(clausify,[status(thm)],[ax68]) ).
cnf(c_241,plain,
( segmentP(A,nil)
| ~ ssList(A) ),
inference(clausify,[status(thm)],[ax57]) ).
cnf(c_244,plain,
( B = A
| ~ segmentP(B,A)
| ~ segmentP(A,B)
| ~ ssList(B)
| ~ ssList(A) ),
inference(clausify,[status(thm)],[ax54]) ).
fof(ax17,axiom,
ssList(nil),
file('theBenchmark.p',ax17) ).
cnf(c_294,plain,
ssList(nil),
inference(clausify,[status(thm)],[ax17]) ).
cnf(c_296,plain,
( B = A
| neq(A,B)
| ~ ssList(B)
| ~ ssList(A) ),
inference(clausify,[status(thm)],[ax15]) ).
cnf(c_297,plain,
( B != A
| ~ neq(A,B)
| ~ ssList(B)
| ~ ssList(A) ),
inference(clausify,[status(thm)],[ax15]) ).
fof(nnf_4,plain,
! [U] :
( ( ( ! [V] :
( cons(V,nil) != U
| ~ ssItem(V) )
| singletonP(U) )
& ( ? [X0] :
( cons(X0,nil) = U
& ssItem(X0) )
| ~ singletonP(U) ) )
| ~ ssList(U) ),
inference(fof_nnf,[status(thm)],[ax4]) ).
fof(sk_ax4_sk,plain,
! [U] :
( ( ( ! [V] :
( cons(V,nil) != U
| ~ ssItem(V) )
| singletonP(U) )
& ( ( cons(sK4(U),nil) = U
& ssItem(sK4(U)) )
| ~ singletonP(U) ) )
| ~ ssList(U) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(X0,sK4(U))],[nnf_4]) ).
fof(sk_ax4,plain,
( ! [VAR_0,VAR_1] :
( cons(VAR_1,nil) != VAR_0
| ~ ssItem(VAR_1)
| singletonP(VAR_0)
| ~ ssList(VAR_0) )
& ! [VAR_0] :
( cons(sK4(VAR_0),nil) = VAR_0
| ~ singletonP(VAR_0)
| ~ ssList(VAR_0) )
& ! [VAR_0] :
( ssItem(sK4(VAR_0))
| ~ singletonP(VAR_0)
| ~ ssList(VAR_0) ) ),
inference(cnf_transformation,[status(thm)],[sk_ax4_sk]) ).
cnf(c_325,plain,
( cons(sK4(A),nil) = A
| ~ singletonP(A)
| ~ ssList(A) ),
inference(split_conjunct,[status(thm)],[sk_ax4]) ).
cnf(c_326,plain,
( ssItem(sK4(A))
| ~ singletonP(A)
| ~ ssList(A) ),
inference(split_conjunct,[status(thm)],[sk_ax4]) ).
cnf(c_13257,negated_conjecture,
segmentP(sK0,sK2),
inference(paramod,[status(thm)],[c_194,c_192]) ).
cnf(c_543,negated_conjecture,
segmentP(sK0,sK1),
inference(paramod,[status(thm)],[c_193,c_13257]) ).
cnf(c_13258,negated_conjecture,
( ~ neq(sK3,nil)
| singletonP(sK1) ),
inference(paramod,[status(thm)],[c_193,c_191]) ).
cnf(c_544,negated_conjecture,
( ~ neq(sK0,nil)
| singletonP(sK1) ),
inference(paramod,[status(thm)],[c_194,c_13258]) ).
cnf(c_1036,negated_conjecture,
~ strictorderedP(sK1),
inference(resolve,[status(thm)],[c_543,c_190]) ).
cnf(c_1702,plain,
segmentP(sK1,nil),
inference(resolve,[status(thm)],[c_241,c_198]) ).
cnf(c_13259,plain,
( A = nil
| neq(nil,A)
| ~ ssList(A) ),
inference(resolve,[status(thm)],[c_296,c_294]) ).
cnf(c_1758,plain,
( nil = A
| neq(nil,A)
| ~ ssList(A) ),
inference(copy,[status(thm)],[c_13259]) ).
cnf(c_13260,negated_conjecture,
( A = sK0
| neq(sK0,A)
| ~ ssList(A) ),
inference(resolve,[status(thm)],[c_296,c_196]) ).
cnf(c_1760,negated_conjecture,
( sK0 = A
| neq(sK0,A)
| ~ ssList(A) ),
inference(copy,[status(thm)],[c_13260]) ).
cnf(c_13261,plain,
( sK1 = nil
| ~ segmentP(nil,sK1)
| ~ ssList(sK1)
| ~ ssList(nil) ),
inference(resolve,[status(thm)],[c_1702,c_244]) ).
cnf(c_13262,plain,
( sK1 = nil
| ~ segmentP(nil,sK1)
| ~ ssList(sK1) ),
inference(resolve,[status(thm)],[c_294,c_13261]) ).
cnf(c_4657,negated_conjecture,
( sK1 = nil
| ~ segmentP(nil,sK1) ),
inference(resolve,[status(thm)],[c_198,c_13262]) ).
cnf(c_13263,negated_conjecture,
( nil = sK1
| neq(nil,sK1) ),
inference(resolve,[status(thm)],[c_1758,c_198]) ).
cnf(c_5021,negated_conjecture,
( sK1 = nil
| neq(nil,sK1) ),
inference(copy,[status(thm)],[c_13263]) ).
cnf(c_13264,negated_conjecture,
( nil = sK0
| neq(nil,sK0) ),
inference(resolve,[status(thm)],[c_1758,c_196]) ).
cnf(c_5022,negated_conjecture,
( sK0 = nil
| neq(nil,sK0) ),
inference(copy,[status(thm)],[c_13264]) ).
cnf(c_13265,plain,
( ~ strictorderedP(nil)
| neq(nil,sK1) ),
inference(paramod,[status(thm)],[c_5021,c_1036]) ).
cnf(c_5026,plain,
neq(nil,sK1),
inference(resolve,[status(thm)],[c_231,c_13265]) ).
cnf(c_13266,plain,
( sK1 != nil
| ~ ssList(sK1)
| ~ ssList(nil) ),
inference(resolve,[status(thm)],[c_5026,c_297]) ).
cnf(c_13267,plain,
( sK1 != nil
| ~ ssList(sK1) ),
inference(resolve,[status(thm)],[c_294,c_13266]) ).
cnf(c_5028,negated_conjecture,
sK1 != nil,
inference(resolve,[status(thm)],[c_198,c_13267]) ).
cnf(c_5031,negated_conjecture,
~ segmentP(nil,sK1),
inference(resolve,[status(thm)],[c_5028,c_4657]) ).
cnf(c_13268,plain,
( segmentP(nil,sK1)
| neq(nil,sK0) ),
inference(paramod,[status(thm)],[c_5022,c_543]) ).
cnf(c_5053,plain,
neq(nil,sK0),
inference(resolve,[status(thm)],[c_5031,c_13268]) ).
cnf(c_13269,plain,
( sK0 != nil
| ~ ssList(sK0)
| ~ ssList(nil) ),
inference(resolve,[status(thm)],[c_5053,c_297]) ).
cnf(c_13270,plain,
( sK0 != nil
| ~ ssList(sK0) ),
inference(resolve,[status(thm)],[c_294,c_13269]) ).
cnf(c_5055,negated_conjecture,
sK0 != nil,
inference(resolve,[status(thm)],[c_196,c_13270]) ).
cnf(c_13271,plain,
( sK0 = nil
| neq(sK0,nil) ),
inference(resolve,[status(thm)],[c_1760,c_294]) ).
cnf(c_5164,plain,
neq(sK0,nil),
inference(resolve,[status(thm)],[c_5055,c_13271]) ).
cnf(c_5166,negated_conjecture,
singletonP(sK1),
inference(resolve,[status(thm)],[c_5164,c_544]) ).
cnf(c_13272,negated_conjecture,
( ssItem(sK4(sK1))
| ~ ssList(sK1) ),
inference(resolve,[status(thm)],[c_5166,c_326]) ).
cnf(c_5167,negated_conjecture,
ssItem(sK4(sK1)),
inference(resolve,[status(thm)],[c_198,c_13272]) ).
cnf(c_13273,negated_conjecture,
( cons(sK4(sK1),nil) = sK1
| ~ ssList(sK1) ),
inference(resolve,[status(thm)],[c_5166,c_325]) ).
cnf(c_5168,negated_conjecture,
cons(sK4(sK1),nil) = sK1,
inference(resolve,[status(thm)],[c_198,c_13273]) ).
cnf(c_13274,plain,
strictorderedP(cons(sK4(sK1),nil)),
inference(resolve,[status(thm)],[c_5167,c_232]) ).
cnf(c_13275,plain,
strictorderedP(sK1),
inference(paramod,[status(thm)],[c_5168,c_13274]) ).
cnf(c_13256,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_1036,c_13275]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC348+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.37 % Computer : n016.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % 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 12:56:30 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.38 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.38 % Process 913616 was started by sandbox2 on n016,
% 0.10/0.38 % Sat Sep 26 12:56:30 2026
% 0.10/0.38 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.10/0.40
% 0.10/0.40 % From the command line: assign(max_seconds, 300).
% 176.04/24.10
% 176.04/24.10 % given #500 (I,wt=52): 701 -ssList(A) | -ssItem(B) | -ssItem(C) | -ssList(D) | -ssList(E) | app(app(D,cons(B,E)),cons(C,A)) != A | C != B | ssList(f36(A)). [factor(362,a,f)].
% 176.04/24.10
% 176.04/24.10 % given #1000 (I,wt=73): 1226 -ssList(A) | -ssItem(B) | -ssItem(C) | -ssList(D) | app(app(D,cons(B,D)),cons(C,D)) != A | C != B | app(app(f35(A),cons(f33(A),f36(A))),cons(f34(A),f37(A))) = A. [factor(717,d,e)].
% 176.04/24.10
% 176.04/24.10 % given #1500 (T,wt=13): 2869 -ssItem(A) | neq(c1,A) | c1 = A. [resolve(334,a,333,a),flip(c)].
% 176.04/24.10
% 176.04/24.10 % SZS status Theorem for theBenchmark
% 176.04/24.10
% 176.04/24.10 % Proof 1 at 6.23 (+ 0.65) seconds.
% 176.04/24.10 % Length of proof is 43.
% 176.04/24.10 % Level of proof is 12.
% 176.04/24.10 % Maximum clause weight is 25.000.
% 176.04/24.10 % Given clauses 1538.
% 176.04/24.10
% 176.04/24.10 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------