%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWC106+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 : n018.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 08:56:51 AM UTC 2026
% Result : Theorem 118.38s 16.43s
% Output : CNFRefutation 118.38s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 6
% Syntax : Number of formulae : 55 ( 21 unt; 0 def)
% Number of atoms : 180 ( 49 equ)
% Maximal formula atoms : 18 ( 3 avg)
% Number of connectives : 200 ( 75 ~; 64 |; 41 &)
% ( 3 <=>; 17 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 7 con; 0-2 aty)
% Number of variables : 40 ( 0 sgn 17 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(ax4,axiom,
! [U] :
( ssList(U)
=> ( singletonP(U)
<=> ? [V] :
( cons(V,nil) = U
& ssItem(V) ) ) ),
file('theBenchmark.p',ax4) ).
fof(ax6,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ( rearsegP(U,V)
<=> ? [W] :
( app(W,V) = U
& ssList(W) ) ) ) ),
file('theBenchmark.p',ax6) ).
fof(ax15,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ( neq(U,V)
<=> U != V ) ) ),
file('theBenchmark.p',ax15) ).
fof(co1,conjecture,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ! [X] :
( ssList(X)
=> ( ( ( neq(X,nil)
| ~ neq(V,nil) )
& ( ( rearsegP(V,U)
& neq(U,nil) )
| ! [Y] :
( ssItem(Y)
=> ! [Z] :
( ssList(Z)
=> ( app(Z,cons(Y,nil)) != X
| cons(Y,nil) != W ) ) )
| ~ neq(V,nil) ) )
| 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)
=> ( ( ( neq(X,nil)
| ~ neq(V,nil) )
& ( ( rearsegP(V,U)
& neq(U,nil) )
| ! [Y] :
( ssItem(Y)
=> ! [Z] :
( ssList(Z)
=> ( app(Z,cons(Y,nil)) != X
| cons(Y,nil) != W ) ) )
| ~ neq(V,nil) ) )
| U != W
| V != X ) ) ) ) ),
inference(assume_negation,[status(cth)],[co1]) ).
fof(nnf_87,plain,
? [U] :
( ? [V] :
( ? [W] :
( ? [X] :
( ( ( ~ neq(X,nil)
& neq(V,nil) )
| ( ( ~ rearsegP(V,U)
| ~ neq(U,nil) )
& ? [Y] :
( ? [Z] :
( app(Z,cons(Y,nil)) = X
& cons(Y,nil) = W
& ssList(Z) )
& ssItem(Y) )
& neq(V,nil) ) )
& 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)
& neq(sK1,nil) )
| ( ( ~ rearsegP(sK1,sK0)
| ~ neq(sK0,nil) )
& app(sK3,cons(sK4,nil)) = sK2
& cons(sK4,nil) = sK5
& ssList(sK3)
& ssItem(sK4)
& neq(sK1,nil) ) )
& sK5 = sK0
& sK2 = sK1
& ssList(sK2)
& ssList(sK5)
& ssList(sK1)
& ssList(sK0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK5,sK2,sK4,sK3]),skolemize(U,sK0),skolemize(V,sK1),skolemize(W,sK5),skolemize(X,sK2),skolemize(Y,sK4),skolemize(Z,sK3)],[nnf_87]) ).
fof(sk_co1_neg,plain,
( ( ~ neq(sK2,nil)
| ~ rearsegP(sK1,sK0)
| ~ neq(sK0,nil) )
& ( ~ neq(sK2,nil)
| app(sK3,cons(sK4,nil)) = sK2 )
& ( ~ neq(sK2,nil)
| cons(sK4,nil) = sK5 )
& ( ~ neq(sK2,nil)
| ssList(sK3) )
& ( ~ neq(sK2,nil)
| ssItem(sK4) )
& neq(sK1,nil)
& sK5 = sK0
& sK2 = sK1
& ssList(sK2)
& ssList(sK5)
& ssList(sK1)
& ssList(sK0) ),
inference(cnf_transformation,[status(thm)],[sk_co1_neg_sk]) ).
cnf(c_190,negated_conjecture,
( ~ neq(sK2,nil)
| ~ rearsegP(sK1,sK0)
| ~ neq(sK0,nil) ),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_191,negated_conjecture,
( ~ neq(sK2,nil)
| app(sK3,cons(sK4,nil)) = sK2 ),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_192,negated_conjecture,
( ~ neq(sK2,nil)
| cons(sK4,nil) = sK5 ),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_193,negated_conjecture,
( ~ neq(sK2,nil)
| ssList(sK3) ),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_194,negated_conjecture,
( ~ neq(sK2,nil)
| ssItem(sK4) ),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_195,negated_conjecture,
neq(sK1,nil),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_196,negated_conjecture,
sK5 = sK0,
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_197,negated_conjecture,
sK2 = sK1,
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(sK1),
inference(paramod,[status(thm)],[c_197,c_198]) ).
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_196,c_200]) ).
fof(ax39,axiom,
~ singletonP(nil),
file('theBenchmark.p',ax39) ).
cnf(c_266,plain,
~ singletonP(nil),
inference(clausify,[status(thm)],[ax39]) ).
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_321,plain,
( app(C,B) != A
| ~ ssList(C)
| rearsegP(A,B)
| ~ ssList(B)
| ~ ssList(A) ),
inference(clausify,[status(thm)],[ax6]) ).
cnf(c_327,plain,
( cons(B,nil) != A
| ~ ssItem(B)
| singletonP(A)
| ~ ssList(A) ),
inference(clausify,[status(thm)],[ax4]) ).
cnf(c_23875,negated_conjecture,
( ~ neq(sK2,nil)
| cons(sK4,nil) = sK0 ),
inference(paramod,[status(thm)],[c_196,c_192]) ).
cnf(c_23876,negated_conjecture,
( ~ neq(sK1,nil)
| cons(sK4,nil) = sK0 ),
inference(paramod,[status(thm)],[c_197,c_23875]) ).
cnf(c_546,negated_conjecture,
cons(sK4,nil) = sK0,
inference(resolve,[status(thm)],[c_195,c_23876]) ).
cnf(c_23877,negated_conjecture,
( ~ neq(sK1,nil)
| ssItem(sK4) ),
inference(paramod,[status(thm)],[c_197,c_194]) ).
cnf(c_547,negated_conjecture,
ssItem(sK4),
inference(resolve,[status(thm)],[c_195,c_23877]) ).
cnf(c_23878,negated_conjecture,
( ~ neq(sK1,nil)
| ssList(sK3) ),
inference(paramod,[status(thm)],[c_197,c_193]) ).
cnf(c_548,negated_conjecture,
ssList(sK3),
inference(resolve,[status(thm)],[c_195,c_23878]) ).
cnf(c_23879,negated_conjecture,
( ~ neq(sK2,nil)
| app(sK3,sK0) = sK2 ),
inference(paramod,[status(thm)],[c_546,c_191]) ).
cnf(c_23880,negated_conjecture,
( ~ neq(sK2,nil)
| app(sK3,sK0) = sK1 ),
inference(paramod,[status(thm)],[c_197,c_23879]) ).
cnf(c_23881,negated_conjecture,
( ~ neq(sK1,nil)
| app(sK3,sK0) = sK1 ),
inference(paramod,[status(thm)],[c_197,c_23880]) ).
cnf(c_549,negated_conjecture,
app(sK3,sK0) = sK1,
inference(resolve,[status(thm)],[c_195,c_23881]) ).
cnf(c_23882,negated_conjecture,
( ~ neq(sK1,nil)
| ~ rearsegP(sK1,sK0)
| ~ neq(sK0,nil) ),
inference(paramod,[status(thm)],[c_197,c_190]) ).
cnf(c_550,negated_conjecture,
( ~ rearsegP(sK1,sK0)
| ~ neq(sK0,nil) ),
inference(resolve,[status(thm)],[c_195,c_23882]) ).
cnf(c_23883,negated_conjecture,
( A = sK0
| neq(sK0,A)
| ~ ssList(A) ),
inference(resolve,[status(thm)],[c_299,c_201]) ).
cnf(c_1764,negated_conjecture,
( sK0 = A
| neq(sK0,A)
| ~ ssList(A) ),
inference(copy,[status(thm)],[c_23883]) ).
cnf(c_1864,plain,
( app(B,A) != sK1
| ~ ssList(B)
| rearsegP(sK1,A)
| ~ ssList(A) ),
inference(resolve,[status(thm)],[c_321,c_199]) ).
cnf(c_23884,negated_conjecture,
( cons(sK4,nil) != A
| singletonP(A)
| ~ ssList(A) ),
inference(resolve,[status(thm)],[c_547,c_327]) ).
cnf(c_4350,negated_conjecture,
( sK0 != A
| singletonP(A)
| ~ ssList(A) ),
inference(paramod,[status(thm)],[c_546,c_23884]) ).
cnf(c_23885,plain,
( sK0 != nil
| singletonP(nil) ),
inference(resolve,[status(thm)],[c_4350,c_297]) ).
cnf(c_6720,plain,
sK0 != nil,
inference(resolve,[status(thm)],[c_266,c_23885]) ).
cnf(c_23886,plain,
( sK0 = nil
| neq(sK0,nil) ),
inference(resolve,[status(thm)],[c_1764,c_297]) ).
cnf(c_6799,plain,
neq(sK0,nil),
inference(resolve,[status(thm)],[c_6720,c_23886]) ).
cnf(c_6801,negated_conjecture,
~ rearsegP(sK1,sK0),
inference(resolve,[status(thm)],[c_6799,c_550]) ).
cnf(c_23887,negated_conjecture,
( app(A,sK0) != sK1
| ~ ssList(A)
| rearsegP(sK1,sK0) ),
inference(resolve,[status(thm)],[c_1864,c_201]) ).
cnf(c_23692,negated_conjecture,
( app(A,sK0) != sK1
| ~ ssList(A) ),
inference(resolve,[status(thm)],[c_6801,c_23887]) ).
cnf(c_23888,negated_conjecture,
app(sK3,sK0) != sK1,
inference(resolve,[status(thm)],[c_23692,c_548]) ).
cnf(c_23889,negated_conjecture,
sK1 != sK1,
inference(paramod,[status(thm)],[c_549,c_23888]) ).
cnf(c_23874,negated_conjecture,
$false,
inference(copy,[status(thm)],[c_23889]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWC106+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.07/0.35 % Computer : n018.cluster.edu
% 0.07/0.35 % Model : x86_64 x86_64
% 0.07/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.35 % Memory : 8046.5625MB
% 0.07/0.35 % OS : Linux 6.8.0-71-generic
% 0.07/0.35 % CPULimit : 300
% 0.07/0.35 % WCLimit : 300
% 0.07/0.35 % DateTime : Sat Sep 26 12:18:08 UTC 2026
% 0.07/0.35 % CPUTime :
% 0.07/0.35 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.07/0.35 % Process 419218 was started by sandbox on n018,
% 0.07/0.35 % Sat Sep 26 12:18:08 2026
% 0.07/0.35 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.11/0.38
% 0.11/0.38 % From the command line: assign(max_seconds, 300).
% 118.38/16.43
% 118.38/16.43 % given #500 (I,wt=47): 703 -ssList(A) | -ssItem(B) | -ssItem(C) | -ssList(D) | -ssList(E) | app(app(D,cons(B,E)),cons(C,D)) != A | C != B | ssList(f35(A)). [factor(363,d,f)].
% 118.38/16.43
% 118.38/16.43 % given #1000 (I,wt=60): 1228 -ssList(A) | -ssItem(B) | -ssList(C) | -ssList(D) | app(app(C,cons(B,C)),cons(B,D)) != A | app(app(f35(A),cons(f33(A),f36(A))),cons(f34(A),f37(A))) = A. [factor(722,c,d)].
% 118.38/16.43
% 118.38/16.43 % given #1500 (T,wt=10): 6817 neq(c3,c4) | singletonP(c4). [resolve(6800,b,6722,b)].
% 118.38/16.43
% 118.38/16.43 % SZS status Theorem for theBenchmark
% 118.38/16.43
% 118.38/16.43 % Proof 1 at 6.93 (+ 0.98) seconds.
% 118.38/16.43 % Length of proof is 34.
% 118.38/16.43 % Level of proof is 8.
% 118.38/16.43 % Maximum clause weight is 25.000.
% 118.38/16.43 % Given clauses 1974.
% 118.38/16.43
% 118.38/16.43 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------