%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWC189+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 : n004.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 08:57:06 AM UTC 2026
% Result : Theorem 18.84s 7.84s
% Output : CNFRefutation 18.84s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 1
% Syntax : Number of formulae : 20 ( 9 unt; 0 def)
% Number of atoms : 125 ( 42 equ)
% Maximal formula atoms : 18 ( 6 avg)
% Number of connectives : 153 ( 48 ~; 43 |; 46 &)
% ( 0 <=>; 16 =>; 0 <=; 0 <~>)
% Maximal formula depth : 23 ( 7 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 9 con; 0-2 aty)
% Number of variables : 52 ( 0 sgn 28 !; 16 ?)
% Comments :
%------------------------------------------------------------------------------
fof(co1,conjecture,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ! [X] :
( ssList(X)
=> ( ! [X3] :
( ssItem(X3)
=> ! [X4] :
( ssItem(X4)
=> ! [X5] :
( ssList(X5)
=> ! [X6] :
( ssList(X6)
=> ( X3 = X4
| app(app(app(X5,cons(X3,nil)),cons(X4,nil)),X6) != U ) ) ) ) )
| ? [Y] :
( ? [Z] :
( ? [X1] :
( ? [X2] :
( app(app(app(X1,cons(Y,nil)),cons(Z,nil)),X2) = W
& Y != Z
& ssList(X2) )
& ssList(X1) )
& ssItem(Z) )
& ssItem(Y) )
| 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)
=> ( ! [X3] :
( ssItem(X3)
=> ! [X4] :
( ssItem(X4)
=> ! [X5] :
( ssList(X5)
=> ! [X6] :
( ssList(X6)
=> ( X3 = X4
| app(app(app(X5,cons(X3,nil)),cons(X4,nil)),X6) != U ) ) ) ) )
| ? [Y] :
( ? [Z] :
( ? [X1] :
( ? [X2] :
( app(app(app(X1,cons(Y,nil)),cons(Z,nil)),X2) = W
& Y != Z
& ssList(X2) )
& ssList(X1) )
& ssItem(Z) )
& ssItem(Y) )
| U != W
| V != X ) ) ) ) ),
inference(assume_negation,[status(cth)],[co1]) ).
fof(nnf_87,plain,
? [U] :
( ? [V] :
( ? [W] :
( ? [X] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( ? [X6] :
( X4 != X3
& app(app(app(X5,cons(X3,nil)),cons(X4,nil)),X6) = U
& ssList(X6) )
& ssList(X5) )
& ssItem(X4) )
& ssItem(X3) )
& ! [Y] :
( ! [Z] :
( ! [X1] :
( ! [X2] :
( app(app(app(X1,cons(Y,nil)),cons(Z,nil)),X2) != W
| Z = Y
| ~ ssList(X2) )
| ~ ssList(X1) )
| ~ ssItem(Z) )
| ~ ssItem(Y) )
& 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,
( sK3 != sK2
& app(app(app(sK4,cons(sK2,nil)),cons(sK3,nil)),sK5) = sK1
& ssList(sK5)
& ssList(sK4)
& ssItem(sK3)
& ssItem(sK2)
& ! [Y] :
( ! [Z] :
( ! [X1] :
( ! [X2] :
( app(app(app(X1,cons(Y,nil)),cons(Z,nil)),X2) != sK0
| Z = Y
| ~ ssList(X2) )
| ~ ssList(X1) )
| ~ ssItem(Z) )
| ~ ssItem(Y) )
& sK0 = sK1
& sK7 = sK6
& ssList(sK7)
& ssList(sK0)
& ssList(sK6)
& ssList(sK1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK6,sK0,sK7,sK2,sK3,sK4,sK5]),skolemize(U,sK1),skolemize(V,sK6),skolemize(W,sK0),skolemize(X,sK7),skolemize(X3,sK2),skolemize(X4,sK3),skolemize(X5,sK4),skolemize(X6,sK5)],[nnf_87]) ).
fof(sk_co1_neg,plain,
( sK3 != sK2
& app(app(app(sK4,cons(sK2,nil)),cons(sK3,nil)),sK5) = sK1
& ssList(sK5)
& ssList(sK4)
& ssItem(sK3)
& ssItem(sK2)
& ! [VAR_0,VAR_1,VAR_2,VAR_3] :
( app(app(app(VAR_2,cons(VAR_0,nil)),cons(VAR_1,nil)),VAR_3) != sK0
| VAR_1 = VAR_0
| ~ ssList(VAR_3)
| ~ ssList(VAR_2)
| ~ ssItem(VAR_1)
| ~ ssItem(VAR_0) )
& sK0 = sK1
& sK7 = sK6
& ssList(sK7)
& ssList(sK0)
& ssList(sK6)
& 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,
( app(app(app(C,cons(A,nil)),cons(B,nil)),D) != sK0
| B = A
| ~ ssList(D)
| ~ ssList(C)
| ~ ssItem(B)
| ~ ssItem(A) ),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_334,negated_conjecture,
( app(app(app(C,cons(A,nil)),cons(B,nil)),D) != sK1
| B = A
| ~ ssList(D)
| ~ ssList(C)
| ~ ssItem(B)
| ~ ssItem(A) ),
inference(paramod,[status(thm)],[c_332,c_333]) ).
cnf(c_335,negated_conjecture,
ssItem(sK2),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_336,negated_conjecture,
ssItem(sK3),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_337,negated_conjecture,
ssList(sK4),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_338,negated_conjecture,
ssList(sK5),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_339,negated_conjecture,
app(app(app(sK4,cons(sK2,nil)),cons(sK3,nil)),sK5) = sK1,
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_340,negated_conjecture,
sK3 != sK2,
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_2949,negated_conjecture,
( sK3 = sK2
| ~ ssList(sK5)
| ~ ssList(sK4)
| ~ ssItem(sK3)
| ~ ssItem(sK2) ),
inference(resolve,[status(thm)],[c_339,c_334]) ).
cnf(c_2950,negated_conjecture,
( sK3 = sK2
| ~ ssList(sK5)
| ~ ssList(sK4)
| ~ ssItem(sK3) ),
inference(resolve,[status(thm)],[c_335,c_2949]) ).
cnf(c_2951,negated_conjecture,
( sK3 = sK2
| ~ ssList(sK5)
| ~ ssList(sK4) ),
inference(resolve,[status(thm)],[c_336,c_2950]) ).
cnf(c_2952,negated_conjecture,
( sK3 = sK2
| ~ ssList(sK5) ),
inference(resolve,[status(thm)],[c_337,c_2951]) ).
cnf(c_2953,negated_conjecture,
sK3 = sK2,
inference(resolve,[status(thm)],[c_338,c_2952]) ).
cnf(c_2948,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_340,c_2953]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC189+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/5.39 % Computer : n004.cluster.edu
% 0.11/5.39 % Model : x86_64 x86_64
% 0.11/5.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/5.39 % Memory : 8046.5625MB
% 0.11/5.39 % OS : Linux 6.8.0-71-generic
% 0.11/5.39 % CPULimit : 300
% 0.11/5.39 % WCLimit : 300
% 0.11/5.39 % DateTime : Sat Sep 26 12:27:57 UTC 2026
% 0.11/5.40 % CPUTime :
% 0.17/5.40 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.17/5.40 % Process 1692081 was started by sandbox on n004,
% 0.17/5.40 % Sat Sep 26 12:27:57 2026
% 0.17/5.40 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.17/5.44
% 0.17/5.44 % From the command line: assign(max_seconds, 300).
% 18.84/7.84
% 18.84/7.84 % SZS status Theorem for theBenchmark
% 18.84/7.84
% 18.84/7.84 % Proof 1 at 2.02 (+ 0.17) seconds.
% 18.84/7.84 % Length of proof is 11.
% 18.84/7.84 % Level of proof is 3.
% 18.84/7.84 % Maximum clause weight is 38.000.
% 18.84/7.84 % Given clauses 166.
% 18.84/7.84
% 18.84/7.84 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------