%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWC204+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 : n015.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 08:57:08 AM UTC 2026
% Result : Theorem 199.09s 27.00s
% Output : CNFRefutation 199.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 8
% Syntax : Number of formulae : 74 ( 22 unt; 0 def)
% Number of atoms : 258 ( 108 equ)
% Maximal formula atoms : 16 ( 3 avg)
% Number of connectives : 314 ( 130 ~; 126 |; 38 &)
% ( 1 <=>; 19 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 5 con; 0-2 aty)
% Number of variables : 56 ( 0 sgn 22 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(ax15,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ( neq(U,V)
<=> U != V ) ) ),
file('theBenchmark.p',ax15) ).
fof(ax18,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssItem(V)
=> cons(V,U) != U ) ),
file('theBenchmark.p',ax18) ).
fof(ax22,axiom,
! [U] :
( ssList(U)
=> ( nil != U
=> ssItem(hd(U)) ) ),
file('theBenchmark.p',ax22) ).
fof(ax24,axiom,
! [U] :
( ssList(U)
=> ( nil != U
=> ssList(tl(U)) ) ),
file('theBenchmark.p',ax24) ).
fof(ax28,axiom,
! [U] :
( ssList(U)
=> app(nil,U) = U ),
file('theBenchmark.p',ax28) ).
fof(ax78,axiom,
! [U] :
( ssList(U)
=> ( nil != U
=> cons(hd(U),tl(U)) = U ) ),
file('theBenchmark.p',ax78) ).
fof(co1,conjecture,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ! [X] :
( ssList(X)
=> ( ( ( neq(X,nil)
| ~ neq(V,nil) )
& ( neq(U,nil)
| ? [Y] :
( ? [Z] :
( neq(nil,X)
& app(W,Z) = Y
& tl(X) = Z
& ssList(Z) )
& X != Y
& ssList(Y) )
| ~ 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) )
& ( neq(U,nil)
| ? [Y] :
( ? [Z] :
( neq(nil,X)
& app(W,Z) = Y
& tl(X) = Z
& ssList(Z) )
& X != Y
& ssList(Y) )
| ~ 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) )
| ( ~ neq(U,nil)
& ! [Y] :
( ! [Z] :
( ~ neq(nil,X)
| app(W,Z) != Y
| tl(X) != Z
| ~ ssList(Z) )
| Y = X
| ~ ssList(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(sK1,nil)
& neq(sK3,nil) )
| ( ~ neq(sK0,nil)
& ! [Y] :
( ! [Z] :
( ~ neq(nil,sK1)
| app(sK2,Z) != Y
| tl(sK1) != Z
| ~ ssList(Z) )
| Y = sK1
| ~ ssList(Y) )
& neq(sK3,nil) ) )
& sK2 = sK0
& sK1 = sK3
& ssList(sK1)
& ssList(sK2)
& ssList(sK3)
& ssList(sK0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK3,sK2,sK1]),skolemize(U,sK0),skolemize(V,sK3),skolemize(W,sK2),skolemize(X,sK1)],[nnf_87]) ).
fof(sk_co1_neg,plain,
( ( ~ neq(sK1,nil)
| ~ neq(sK0,nil) )
& ! [VAR_0,VAR_1] :
( ~ neq(sK1,nil)
| ~ neq(nil,sK1)
| app(sK2,VAR_1) != VAR_0
| tl(sK1) != VAR_1
| ~ ssList(VAR_1)
| VAR_0 = sK1
| ~ ssList(VAR_0) )
& neq(sK3,nil)
& sK2 = sK0
& sK1 = sK3
& ssList(sK1)
& ssList(sK2)
& ssList(sK3)
& ssList(sK0) ),
inference(cnf_transformation,[status(thm)],[sk_co1_neg_sk]) ).
cnf(c_190,negated_conjecture,
( ~ neq(sK1,nil)
| ~ neq(sK0,nil) ),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_191,negated_conjecture,
( ~ neq(sK1,nil)
| ~ neq(nil,sK1)
| app(sK2,B) != A
| tl(sK1) != B
| ~ ssList(B)
| A = sK1
| ~ ssList(A) ),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_192,negated_conjecture,
( ~ neq(sK1,nil)
| ~ neq(nil,sK1)
| app(sK2,B) != A
| tl(sK1) != B
| ~ ssList(B)
| sK1 = A
| ~ ssList(A) ),
inference(copy,[status(thm)],[c_191]) ).
cnf(c_193,negated_conjecture,
neq(sK3,nil),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_194,negated_conjecture,
sK2 = sK0,
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_195,negated_conjecture,
sK1 = sK3,
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_196,negated_conjecture,
ssList(sK1),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_197,negated_conjecture,
ssList(sK3),
inference(paramod,[status(thm)],[c_195,c_196]) ).
cnf(c_198,negated_conjecture,
ssList(sK2),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_199,negated_conjecture,
ssList(sK0),
inference(paramod,[status(thm)],[c_194,c_198]) ).
cnf(c_220,plain,
( cons(hd(A),tl(A)) = A
| nil = A
| ~ ssList(A) ),
inference(clausify,[status(thm)],[ax78]) ).
cnf(c_281,plain,
( app(nil,A) = A
| ~ ssList(A) ),
inference(clausify,[status(thm)],[ax28]) ).
cnf(c_285,plain,
( ssList(tl(A))
| nil = A
| ~ ssList(A) ),
inference(clausify,[status(thm)],[ax24]) ).
cnf(c_287,plain,
( ssItem(hd(A))
| nil = A
| ~ ssList(A) ),
inference(clausify,[status(thm)],[ax22]) ).
cnf(c_294,plain,
( cons(B,A) != A
| ~ ssItem(B)
| ~ ssList(A) ),
inference(clausify,[status(thm)],[ax18]) ).
fof(ax17,axiom,
ssList(nil),
file('theBenchmark.p',ax17) ).
cnf(c_295,plain,
ssList(nil),
inference(clausify,[status(thm)],[ax17]) ).
cnf(c_297,plain,
( B = A
| neq(A,B)
| ~ ssList(B)
| ~ ssList(A) ),
inference(clausify,[status(thm)],[ax15]) ).
cnf(c_298,plain,
( B != A
| ~ neq(A,B)
| ~ ssList(B)
| ~ ssList(A) ),
inference(clausify,[status(thm)],[ax15]) ).
cnf(c_3079,plain,
( ~ neq(sK1,nil)
| ~ neq(nil,sK1)
| app(sK2,A) != A
| tl(sK1) != A
| sK1 = A
| ~ ssList(A) ),
inference(factor,[status(thm)],[c_192]) ).
cnf(c_3080,plain,
( ~ neq(sK1,nil)
| ~ neq(nil,sK1)
| app(sK2,A) != A
| tl(sK1) != A
| sK3 = A
| ~ ssList(A) ),
inference(paramod,[status(thm)],[c_195,c_3079]) ).
cnf(c_3081,plain,
( ~ neq(sK1,nil)
| ~ neq(nil,sK1)
| app(sK2,A) != A
| tl(sK3) != A
| sK3 = A
| ~ ssList(A) ),
inference(paramod,[status(thm)],[c_195,c_3080]) ).
cnf(c_3082,plain,
( ~ neq(sK1,nil)
| ~ neq(nil,sK1)
| app(sK0,A) != A
| tl(sK3) != A
| sK3 = A
| ~ ssList(A) ),
inference(paramod,[status(thm)],[c_194,c_3081]) ).
cnf(c_3083,plain,
( ~ neq(sK1,nil)
| ~ neq(nil,sK3)
| app(sK0,A) != A
| tl(sK3) != A
| sK3 = A
| ~ ssList(A) ),
inference(paramod,[status(thm)],[c_195,c_3082]) ).
cnf(c_3084,plain,
( ~ neq(sK3,nil)
| ~ neq(nil,sK3)
| app(sK0,A) != A
| tl(sK3) != A
| sK3 = A
| ~ ssList(A) ),
inference(paramod,[status(thm)],[c_195,c_3083]) ).
cnf(c_544,negated_conjecture,
( ~ neq(nil,sK3)
| app(sK0,A) != A
| tl(sK3) != A
| sK3 = A
| ~ ssList(A) ),
inference(resolve,[status(thm)],[c_193,c_3084]) ).
cnf(c_3085,negated_conjecture,
( ~ neq(sK3,nil)
| ~ neq(sK0,nil) ),
inference(paramod,[status(thm)],[c_195,c_190]) ).
cnf(c_546,negated_conjecture,
~ neq(sK0,nil),
inference(resolve,[status(thm)],[c_193,c_3085]) ).
cnf(c_3086,negated_conjecture,
( cons(hd(sK3),tl(sK3)) = sK3
| nil = sK3 ),
inference(resolve,[status(thm)],[c_220,c_197]) ).
cnf(c_1682,negated_conjecture,
( cons(hd(sK3),tl(sK3)) = sK3
| sK3 = nil ),
inference(copy,[status(thm)],[c_3086]) ).
cnf(c_3087,negated_conjecture,
( ssList(tl(sK3))
| nil = sK3 ),
inference(resolve,[status(thm)],[c_285,c_197]) ).
cnf(c_1839,negated_conjecture,
( ssList(tl(sK3))
| sK3 = nil ),
inference(copy,[status(thm)],[c_3087]) ).
cnf(c_3088,negated_conjecture,
( ssItem(hd(sK3))
| nil = sK3 ),
inference(resolve,[status(thm)],[c_287,c_197]) ).
cnf(c_1843,negated_conjecture,
( ssItem(hd(sK3))
| sK3 = nil ),
inference(copy,[status(thm)],[c_3088]) ).
cnf(c_1861,plain,
( cons(A,sK3) != sK3
| ~ ssItem(A) ),
inference(resolve,[status(thm)],[c_294,c_197]) ).
cnf(c_3089,plain,
( A = nil
| neq(nil,A)
| ~ ssList(A) ),
inference(resolve,[status(thm)],[c_297,c_295]) ).
cnf(c_1921,plain,
( nil = A
| neq(nil,A)
| ~ ssList(A) ),
inference(copy,[status(thm)],[c_3089]) ).
cnf(c_3090,negated_conjecture,
( A = sK0
| neq(sK0,A)
| ~ ssList(A) ),
inference(resolve,[status(thm)],[c_297,c_199]) ).
cnf(c_1922,negated_conjecture,
( sK0 = A
| neq(sK0,A)
| ~ ssList(A) ),
inference(copy,[status(thm)],[c_3090]) ).
cnf(c_3091,negated_conjecture,
( nil != sK3
| ~ ssList(nil)
| ~ ssList(sK3) ),
inference(resolve,[status(thm)],[c_298,c_193]) ).
cnf(c_3092,negated_conjecture,
( sK3 != nil
| ~ ssList(nil)
| ~ ssList(sK3) ),
inference(copy,[status(thm)],[c_3091]) ).
cnf(c_3093,negated_conjecture,
( sK3 != nil
| ~ ssList(nil) ),
inference(resolve,[status(thm)],[c_197,c_3092]) ).
cnf(c_1933,negated_conjecture,
sK3 != nil,
inference(resolve,[status(thm)],[c_295,c_3093]) ).
cnf(c_1939,negated_conjecture,
ssItem(hd(sK3)),
inference(resolve,[status(thm)],[c_1933,c_1843]) ).
cnf(c_1940,negated_conjecture,
ssList(tl(sK3)),
inference(resolve,[status(thm)],[c_1933,c_1839]) ).
cnf(c_1954,negated_conjecture,
cons(hd(sK3),tl(sK3)) = sK3,
inference(resolve,[status(thm)],[c_1933,c_1682]) ).
cnf(c_3094,plain,
( ~ neq(nil,sK3)
| app(sK0,tl(sK3)) != tl(sK3)
| sK3 = tl(sK3)
| ~ ssList(tl(sK3)) ),
inference(xxres,[status(thm)],[c_544]) ).
cnf(c_3095,plain,
( ~ neq(nil,sK3)
| app(sK0,tl(sK3)) != tl(sK3)
| tl(sK3) = sK3
| ~ ssList(tl(sK3)) ),
inference(copy,[status(thm)],[c_3094]) ).
cnf(c_2240,plain,
( ~ neq(nil,sK3)
| app(sK0,tl(sK3)) != tl(sK3)
| tl(sK3) = sK3 ),
inference(resolve,[status(thm)],[c_1940,c_3095]) ).
cnf(c_3096,negated_conjecture,
( nil = sK3
| neq(nil,sK3) ),
inference(resolve,[status(thm)],[c_1921,c_197]) ).
cnf(c_3097,negated_conjecture,
( sK3 = nil
| neq(nil,sK3) ),
inference(copy,[status(thm)],[c_3096]) ).
cnf(c_2497,negated_conjecture,
neq(nil,sK3),
inference(resolve,[status(thm)],[c_1933,c_3097]) ).
cnf(c_2505,plain,
( app(sK0,tl(sK3)) != tl(sK3)
| tl(sK3) = sK3 ),
inference(resolve,[status(thm)],[c_2497,c_2240]) ).
cnf(c_3098,plain,
( sK0 = nil
| neq(sK0,nil) ),
inference(resolve,[status(thm)],[c_1922,c_295]) ).
cnf(c_2510,negated_conjecture,
sK0 = nil,
inference(resolve,[status(thm)],[c_546,c_3098]) ).
cnf(c_2514,plain,
( app(nil,tl(sK3)) != tl(sK3)
| tl(sK3) = sK3 ),
inference(paramod,[status(thm)],[c_2510,c_2505]) ).
cnf(c_2919,plain,
app(nil,tl(sK3)) = tl(sK3),
inference(resolve,[status(thm)],[c_1940,c_281]) ).
cnf(c_3099,plain,
( tl(sK3) != tl(sK3)
| tl(sK3) = sK3 ),
inference(paramod,[status(thm)],[c_2919,c_2514]) ).
cnf(c_2968,plain,
tl(sK3) = sK3,
inference(copy,[status(thm)],[c_3099]) ).
cnf(c_2974,negated_conjecture,
cons(hd(sK3),sK3) = sK3,
inference(paramod,[status(thm)],[c_2968,c_1954]) ).
cnf(c_3100,plain,
cons(hd(sK3),sK3) != sK3,
inference(resolve,[status(thm)],[c_1861,c_1939]) ).
cnf(c_3101,plain,
sK3 != sK3,
inference(paramod,[status(thm)],[c_2974,c_3100]) ).
cnf(c_3078,plain,
$false,
inference(copy,[status(thm)],[c_3101]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWC204+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n015.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sat Sep 26 12:33:59 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.36 % Process 4053462 was started by sandbox2 on n015,
% 0.09/0.36 % Sat Sep 26 12:33:59 2026
% 0.09/0.36 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.13/0.39
% 0.13/0.39 % From the command line: assign(max_seconds, 300).
% 199.09/27.00
% 199.09/27.00 % given #500 (I,wt=49): 693 -ssList(A) | -ssItem(B) | -ssItem(C) | -ssList(D) | -ssList(E) | app(app(D,cons(B,E)),cons(C,E)) != A | C != B | ssItem(f34(A)). [factor(359,e,f)].
% 199.09/27.00
% 199.09/27.00 % given #1000 (I,wt=44): 1213 -ssList(A) | -ssItem(B) | -ssList(C) | -ssList(D) | app(app(C,cons(B,D)),cons(B,D)) != A | ssList(f37(A)). [factor(711,d,e)].
% 199.09/27.00
% 199.09/27.00 % given #1500 (T,wt=13): 2164 -ssItem(A) | geq(A,c1) | -leq(c1,A). [resolve(334,a,276,b)].
% 199.09/27.00
% 199.09/27.00 % SZS status Theorem for theBenchmark
% 199.09/27.00
% 199.09/27.00 % Proof 1 at 2.01 (+ 0.41) seconds.
% 199.09/27.00 % Length of proof is 46.
% 199.09/27.00 % Level of proof is 10.
% 199.09/27.00 % Maximum clause weight is 32.000.
% 199.09/27.00 % Given clauses 1529.
% 199.09/27.00
% 199.09/27.00 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------