%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWC207+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 : n001.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 08:57:09 AM UTC 2026
% Result : Theorem 37.72s 5.29s
% Output : CNFRefutation 37.72s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 6
% Syntax : Number of formulae : 62 ( 17 unt; 0 def)
% Number of atoms : 246 ( 94 equ)
% Maximal formula atoms : 30 ( 3 avg)
% Number of connectives : 309 ( 125 ~; 114 |; 47 &)
% ( 2 <=>; 21 =>; 0 <=; 0 <~>)
% Maximal formula depth : 23 ( 5 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 6 con; 0-2 aty)
% Number of variables : 67 ( 0 sgn 24 !; 7 ?)
% Comments :
%------------------------------------------------------------------------------
fof(ax13,axiom,
! [U] :
( ssList(U)
=> ( duplicatefreeP(U)
<=> ! [V] :
( ssItem(V)
=> ! [W] :
( ssItem(W)
=> ! [X] :
( ssList(X)
=> ! [Y] :
( ssList(Y)
=> ! [Z] :
( ssList(Z)
=> ( app(app(X,cons(V,Y)),cons(W,Z)) = U
=> V != W ) ) ) ) ) ) ) ),
file('theBenchmark.p',ax13) ).
fof(ax15,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ( neq(U,V)
<=> U != V ) ) ),
file('theBenchmark.p',ax15) ).
fof(ax28,axiom,
! [U] :
( ssList(U)
=> app(nil,U) = U ),
file('theBenchmark.p',ax28) ).
fof(ax71,axiom,
! [U] :
( ssItem(U)
=> duplicatefreeP(cons(U,nil)) ),
file('theBenchmark.p',ax71) ).
fof(co1,conjecture,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ! [X] :
( ssList(X)
=> ( ( ( nil != W
| nil != X )
& ! [Y] :
( ssItem(Y)
=> ( ? [Z] :
( leq(Y,Z)
& memberP(X,Z)
& Y != Z
& ssItem(Z) )
| ~ memberP(X,Y)
| cons(Y,nil) != W ) ) )
| neq(U,nil)
| ~ 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)
=> ( ( ( nil != W
| nil != X )
& ! [Y] :
( ssItem(Y)
=> ( ? [Z] :
( leq(Y,Z)
& memberP(X,Z)
& Y != Z
& ssItem(Z) )
| ~ memberP(X,Y)
| cons(Y,nil) != W ) ) )
| neq(U,nil)
| ~ neq(V,nil)
| U != W
| V != X ) ) ) ) ),
inference(assume_negation,[status(cth)],[co1]) ).
cnf(c_121,plain,
( C != B
| app(app(D,cons(B,E)),cons(C,F)) != A
| ~ ssList(F)
| ~ ssList(E)
| ~ ssList(D)
| ~ ssItem(C)
| ~ ssItem(B)
| ~ duplicatefreeP(A)
| ~ ssList(A) ),
inference(clausify,[status(thm)],[ax13]) ).
cnf(c_129,plain,
( duplicatefreeP(cons(A,nil))
| ~ ssItem(A) ),
inference(clausify,[status(thm)],[ax71]) ).
fof(nnf_87,plain,
? [U] :
( ? [V] :
( ? [W] :
( ? [X] :
( ( ( nil = W
& nil = X )
| ? [Y] :
( ! [Z] :
( ~ leq(Y,Z)
| ~ memberP(X,Z)
| Z = Y
| ~ ssItem(Z) )
& memberP(X,Y)
& cons(Y,nil) = W
& ssItem(Y) ) )
& ~ neq(U,nil)
& 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,
( ( ( nil = sK1
& nil = sK2 )
| ( ! [Z] :
( ~ leq(sK0,Z)
| ~ memberP(sK2,Z)
| Z = sK0
| ~ ssItem(Z) )
& memberP(sK2,sK0)
& cons(sK0,nil) = sK1
& ssItem(sK0) ) )
& ~ neq(sK3,nil)
& neq(sK4,nil)
& 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,
( ! [VAR_0] :
( nil = sK1
| ~ leq(sK0,VAR_0)
| ~ memberP(sK2,VAR_0)
| VAR_0 = sK0
| ~ ssItem(VAR_0) )
& ! [VAR_0] :
( nil = sK2
| ~ leq(sK0,VAR_0)
| ~ memberP(sK2,VAR_0)
| VAR_0 = sK0
| ~ ssItem(VAR_0) )
& ( nil = sK1
| memberP(sK2,sK0) )
& ( nil = sK2
| memberP(sK2,sK0) )
& ( nil = sK1
| cons(sK0,nil) = sK1 )
& ( nil = sK2
| cons(sK0,nil) = sK1 )
& ( nil = sK1
| ssItem(sK0) )
& ( nil = sK2
| ssItem(sK0) )
& ~ neq(sK3,nil)
& neq(sK4,nil)
& sK1 = sK3
& sK2 = sK4
& ssList(sK2)
& ssList(sK1)
& ssList(sK4)
& ssList(sK3) ),
inference(cnf_transformation,[status(thm)],[sk_co1_neg_sk]) ).
cnf(c_200,negated_conjecture,
( nil = sK2
| cons(sK0,nil) = sK1 ),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_201,negated_conjecture,
( sK2 = nil
| cons(sK0,nil) = sK1 ),
inference(copy,[status(thm)],[c_200]) ).
cnf(c_204,negated_conjecture,
( nil = sK2
| ssItem(sK0) ),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_205,negated_conjecture,
( sK2 = nil
| ssItem(sK0) ),
inference(copy,[status(thm)],[c_204]) ).
cnf(c_206,negated_conjecture,
~ neq(sK3,nil),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_207,negated_conjecture,
neq(sK4,nil),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_208,negated_conjecture,
sK1 = sK3,
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_209,negated_conjecture,
sK2 = sK4,
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_210,negated_conjecture,
ssList(sK2),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_211,negated_conjecture,
ssList(sK4),
inference(paramod,[status(thm)],[c_209,c_210]) ).
cnf(c_212,negated_conjecture,
ssList(sK1),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_213,negated_conjecture,
ssList(sK3),
inference(paramod,[status(thm)],[c_208,c_212]) ).
cnf(c_295,plain,
( app(nil,A) = A
| ~ ssList(A) ),
inference(clausify,[status(thm)],[ax28]) ).
fof(ax17,axiom,
ssList(nil),
file('theBenchmark.p',ax17) ).
cnf(c_309,plain,
ssList(nil),
inference(clausify,[status(thm)],[ax17]) ).
cnf(c_311,plain,
( B = A
| neq(A,B)
| ~ ssList(B)
| ~ ssList(A) ),
inference(clausify,[status(thm)],[ax15]) ).
cnf(c_312,plain,
( B != A
| ~ neq(A,B)
| ~ ssList(B)
| ~ ssList(A) ),
inference(clausify,[status(thm)],[ax15]) ).
cnf(c_384,plain,
( ~ ssItem(A)
| C != B
| app(app(D,cons(B,E)),cons(C,F)) != cons(A,nil)
| ~ ssList(F)
| ~ ssList(E)
| ~ ssList(D)
| ~ ssItem(C)
| ~ ssItem(B)
| ~ ssList(cons(A,nil)) ),
inference(resolve,[status(thm)],[c_121,c_129]) ).
cnf(c_4668,negated_conjecture,
( sK2 = nil
| cons(sK0,nil) = sK3 ),
inference(paramod,[status(thm)],[c_208,c_201]) ).
cnf(c_559,negated_conjecture,
( sK4 = nil
| cons(sK0,nil) = sK3 ),
inference(paramod,[status(thm)],[c_209,c_4668]) ).
cnf(c_563,negated_conjecture,
( sK4 = nil
| ssItem(sK0) ),
inference(paramod,[status(thm)],[c_209,c_205]) ).
cnf(c_748,plain,
( ~ ssItem(A)
| C != B
| app(app(cons(A,nil),cons(B,D)),cons(C,E)) != cons(A,nil)
| ~ ssList(E)
| ~ ssList(D)
| ~ ssItem(C)
| ~ ssItem(B)
| ~ ssList(cons(A,nil)) ),
inference(factor,[status(thm)],[c_384]) ).
cnf(c_1260,plain,
( ~ ssItem(A)
| C != B
| app(app(cons(A,nil),cons(B,cons(A,nil))),cons(C,D)) != cons(A,nil)
| ~ ssList(D)
| ~ ssItem(C)
| ~ ssItem(B)
| ~ ssList(cons(A,nil)) ),
inference(factor,[status(thm)],[c_748]) ).
cnf(c_1574,plain,
( ~ ssItem(A)
| C != B
| app(app(cons(A,nil),cons(B,cons(A,nil))),cons(C,cons(A,nil))) != cons(A,nil)
| ~ ssItem(C)
| ~ ssItem(B)
| ~ ssList(cons(A,nil)) ),
inference(factor,[status(thm)],[c_1260]) ).
cnf(c_4669,plain,
( ~ ssItem(A)
| B != B
| app(app(cons(A,nil),cons(B,cons(A,nil))),cons(B,cons(A,nil))) != cons(A,nil)
| ~ ssItem(B)
| ~ ssList(cons(A,nil)) ),
inference(factor,[status(thm)],[c_1574]) ).
cnf(c_1649,plain,
( ~ ssItem(A)
| app(app(cons(A,nil),cons(B,cons(A,nil))),cons(B,cons(A,nil))) != cons(A,nil)
| ~ ssItem(B)
| ~ ssList(cons(A,nil)) ),
inference(copy,[status(thm)],[c_4669]) ).
cnf(c_1661,plain,
( app(app(cons(A,nil),cons(A,cons(A,nil))),cons(A,cons(A,nil))) != cons(A,nil)
| ~ ssItem(A)
| ~ ssList(cons(A,nil)) ),
inference(factor,[status(thm)],[c_1649]) ).
cnf(c_1776,plain,
app(nil,nil) = nil,
inference(resolve,[status(thm)],[c_309,c_295]) ).
cnf(c_4670,negated_conjecture,
( A = sK3
| neq(sK3,A)
| ~ ssList(A) ),
inference(resolve,[status(thm)],[c_311,c_213]) ).
cnf(c_4671,negated_conjecture,
( nil = sK3
| neq(sK3,nil) ),
inference(resolve,[status(thm)],[c_4670,c_309]) ).
cnf(c_4672,negated_conjecture,
( sK3 = nil
| neq(sK3,nil) ),
inference(copy,[status(thm)],[c_4671]) ).
cnf(c_1816,negated_conjecture,
sK3 = nil,
inference(resolve,[status(thm)],[c_206,c_4672]) ).
cnf(c_1817,negated_conjecture,
( sK4 = nil
| cons(sK0,nil) = nil ),
inference(paramod,[status(thm)],[c_1816,c_559]) ).
cnf(c_4673,negated_conjecture,
( nil != sK4
| ~ ssList(nil)
| ~ ssList(sK4) ),
inference(resolve,[status(thm)],[c_312,c_207]) ).
cnf(c_4674,negated_conjecture,
( sK4 != nil
| ~ ssList(nil)
| ~ ssList(sK4) ),
inference(copy,[status(thm)],[c_4673]) ).
cnf(c_4675,negated_conjecture,
( sK4 != nil
| ~ ssList(nil) ),
inference(resolve,[status(thm)],[c_211,c_4674]) ).
cnf(c_1820,negated_conjecture,
sK4 != nil,
inference(resolve,[status(thm)],[c_309,c_4675]) ).
cnf(c_1821,negated_conjecture,
cons(sK0,nil) = nil,
inference(resolve,[status(thm)],[c_1820,c_1817]) ).
cnf(c_1843,negated_conjecture,
ssItem(sK0),
inference(resolve,[status(thm)],[c_1820,c_563]) ).
cnf(c_4676,negated_conjecture,
( app(app(cons(sK0,nil),cons(sK0,cons(sK0,nil))),cons(sK0,cons(sK0,nil))) != cons(sK0,nil)
| ~ ssList(cons(sK0,nil)) ),
inference(resolve,[status(thm)],[c_1843,c_1661]) ).
cnf(c_4677,negated_conjecture,
( app(app(cons(sK0,nil),cons(sK0,cons(sK0,nil))),cons(sK0,cons(sK0,nil))) != cons(sK0,nil)
| ~ ssList(nil) ),
inference(paramod,[status(thm)],[c_1821,c_4676]) ).
cnf(c_4678,negated_conjecture,
( app(app(nil,cons(sK0,cons(sK0,nil))),cons(sK0,cons(sK0,nil))) != cons(sK0,nil)
| ~ ssList(nil) ),
inference(paramod,[status(thm)],[c_1821,c_4677]) ).
cnf(c_4679,negated_conjecture,
( app(app(nil,cons(sK0,nil)),cons(sK0,cons(sK0,nil))) != cons(sK0,nil)
| ~ ssList(nil) ),
inference(paramod,[status(thm)],[c_1821,c_4678]) ).
cnf(c_4680,negated_conjecture,
( app(app(nil,nil),cons(sK0,cons(sK0,nil))) != cons(sK0,nil)
| ~ ssList(nil) ),
inference(paramod,[status(thm)],[c_1821,c_4679]) ).
cnf(c_4681,negated_conjecture,
( app(nil,cons(sK0,cons(sK0,nil))) != cons(sK0,nil)
| ~ ssList(nil) ),
inference(paramod,[status(thm)],[c_1776,c_4680]) ).
cnf(c_4682,negated_conjecture,
( app(nil,cons(sK0,nil)) != cons(sK0,nil)
| ~ ssList(nil) ),
inference(paramod,[status(thm)],[c_1821,c_4681]) ).
cnf(c_4683,negated_conjecture,
( app(nil,nil) != cons(sK0,nil)
| ~ ssList(nil) ),
inference(paramod,[status(thm)],[c_1821,c_4682]) ).
cnf(c_4684,negated_conjecture,
( nil != cons(sK0,nil)
| ~ ssList(nil) ),
inference(paramod,[status(thm)],[c_1776,c_4683]) ).
cnf(c_4685,negated_conjecture,
( nil != nil
| ~ ssList(nil) ),
inference(paramod,[status(thm)],[c_1821,c_4684]) ).
cnf(c_4686,negated_conjecture,
~ ssList(nil),
inference(copy,[status(thm)],[c_4685]) ).
cnf(c_4667,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_309,c_4686]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC207+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n001.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 12:37:12 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.37 % Process 1806425 was started by sandbox on n001,
% 0.09/0.37 % Sat Sep 26 12:37:12 2026
% 0.09/0.37 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.09/0.38
% 0.09/0.38 % From the command line: assign(max_seconds, 300).
% 37.72/5.29
% 37.72/5.29 % given #500 (I,wt=52): 722 -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(377,a,f)].
% 37.72/5.29
% 37.72/5.29 % given #1000 (I,wt=52): 1247 -ssList(A) | -ssItem(B) | -ssItem(C) | -ssList(D) | app(app(A,cons(B,A)),cons(C,D)) != A | C != B | f34(A) = f33(A). [factor(741,a,d)].
% 37.72/5.29
% 37.72/5.29 % SZS status Theorem for theBenchmark
% 37.72/5.29
% 37.72/5.29 % Proof 1 at 4.37 (+ 0.23) seconds.
% 37.72/5.29 % Length of proof is 38.
% 37.72/5.29 % Level of proof is 8.
% 37.72/5.29 % Maximum clause weight is 72.000.
% 37.72/5.29 % Given clauses 1374.
% 37.72/5.29
% 37.72/5.29 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------