%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWC210+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 : n003.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 08:57:10 AM UTC 2026
% Result : Theorem 9.33s 2.00s
% Output : CNFRefutation 9.33s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 4
% Syntax : Number of formulae : 29 ( 14 unt; 0 def)
% Number of atoms : 94 ( 18 equ)
% Maximal formula atoms : 11 ( 3 avg)
% Number of connectives : 97 ( 32 ~; 26 |; 28 &)
% ( 1 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 5 con; 0-0 aty)
% Number of variables : 17 ( 0 sgn 10 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
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) )
& ( neq(U,nil)
| ~ singletonP(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) )
& ( neq(U,nil)
| ~ singletonP(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) )
| ( ~ neq(U,nil)
& singletonP(W)
& 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)
& singletonP(sK2)
& 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) )
& ( ~ neq(sK1,nil)
| singletonP(sK2) )
& 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)
| singletonP(sK2) ),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_192,negated_conjecture,
neq(sK3,nil),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_193,negated_conjecture,
sK2 = sK0,
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_194,negated_conjecture,
sK1 = sK3,
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_197,negated_conjecture,
ssList(sK2),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_198,negated_conjecture,
ssList(sK0),
inference(paramod,[status(thm)],[c_193,c_197]) ).
fof(ax39,axiom,
~ singletonP(nil),
file('theBenchmark.p',ax39) ).
cnf(c_263,plain,
~ singletonP(nil),
inference(clausify,[status(thm)],[ax39]) ).
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_1798,negated_conjecture,
( ~ neq(sK1,nil)
| singletonP(sK0) ),
inference(paramod,[status(thm)],[c_193,c_191]) ).
cnf(c_1799,negated_conjecture,
( ~ neq(sK3,nil)
| singletonP(sK0) ),
inference(paramod,[status(thm)],[c_194,c_1798]) ).
cnf(c_543,negated_conjecture,
singletonP(sK0),
inference(resolve,[status(thm)],[c_192,c_1799]) ).
cnf(c_1800,negated_conjecture,
( ~ neq(sK3,nil)
| ~ neq(sK0,nil) ),
inference(paramod,[status(thm)],[c_194,c_190]) ).
cnf(c_544,negated_conjecture,
~ neq(sK0,nil),
inference(resolve,[status(thm)],[c_192,c_1800]) ).
cnf(c_1801,negated_conjecture,
( A = sK0
| neq(sK0,A)
| ~ ssList(A) ),
inference(resolve,[status(thm)],[c_296,c_198]) ).
cnf(c_1802,negated_conjecture,
( nil = sK0
| neq(sK0,nil) ),
inference(resolve,[status(thm)],[c_1801,c_294]) ).
cnf(c_1803,negated_conjecture,
( sK0 = nil
| neq(sK0,nil) ),
inference(copy,[status(thm)],[c_1802]) ).
cnf(c_1795,negated_conjecture,
sK0 = nil,
inference(resolve,[status(thm)],[c_544,c_1803]) ).
cnf(c_1804,negated_conjecture,
singletonP(nil),
inference(paramod,[status(thm)],[c_1795,c_543]) ).
cnf(c_1797,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_263,c_1804]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SWC210+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.15/0.41 % Computer : n003.cluster.edu
% 0.15/0.41 % Model : x86_64 x86_64
% 0.15/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.41 % Memory : 8046.5625MB
% 0.15/0.41 % OS : Linux 6.8.0-71-generic
% 0.15/0.41 % CPULimit : 300
% 0.15/0.41 % WCLimit : 300
% 0.15/0.41 % DateTime : Sat Sep 26 12:33:23 UTC 2026
% 0.15/0.42 % CPUTime :
% 0.15/0.42 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.15/0.42 % Process 2877156 was started by sandbox on n003,
% 0.15/0.42 % Sat Sep 26 12:33:23 2026
% 0.15/0.42 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.15/0.44
% 0.15/0.44 % From the command line: assign(max_seconds, 300).
% 9.33/2.00
% 9.33/2.00 % SZS status Theorem for theBenchmark
% 9.33/2.00
% 9.33/2.00 % Proof 1 at 1.44 (+ 0.10) seconds.
% 9.33/2.00 % Length of proof is 16.
% 9.33/2.00 % Level of proof is 4.
% 9.33/2.00 % Maximum clause weight is 15.000.
% 9.33/2.00 % Given clauses 126.
% 9.33/2.00
% 9.33/2.00 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------