%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWW469+1 : TPTP v9.3.1. Released v5.3.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n005.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 09:14:17 AM UTC 2026
% Result : Theorem 0.17s 0.45s
% Output : CNFRefutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 3
% Syntax : Number of formulae : 21 ( 8 unt; 0 def)
% Number of atoms : 60 ( 17 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 66 ( 27 ~; 21 |; 13 &)
% ( 1 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 2 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 3 con; 0-0 aty)
% Number of variables : 19 ( 0 sgn 12 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(fact_0_state__not__singleton__def,axiom,
( hoare_165779456gleton
<=> ? [S,T] :
( S != T
& is_state(T)
& is_state(S) ) ),
file('theBenchmark.p',fact_0_state__not__singleton__def) ).
fof(conj_1,conjecture,
! [T] :
( is_state(T)
=> ~ ! [S] :
( is_state(S)
=> S = T ) ),
file('theBenchmark.p',conj_1) ).
fof(conj_1_neg,negated_conjecture,
~ ! [T] :
( is_state(T)
=> ~ ! [S] :
( is_state(S)
=> S = T ) ),
inference(assume_negation,[status(cth)],[conj_1]) ).
fof(nnf_1,plain,
( ( ! [S,T] :
( T = S
| ~ is_state(T)
| ~ is_state(S) )
| hoare_165779456gleton )
& ( ? [X0,X1] :
( X1 != X0
& is_state(X1)
& is_state(X0) )
| ~ hoare_165779456gleton ) ),
inference(fof_nnf,[status(thm)],[fact_0_state__not__singleton__def]) ).
fof(sk_fact_0_state__not__singleton__def_sk,plain,
( ( ! [S,T] :
( T = S
| ~ is_state(T)
| ~ is_state(S) )
| hoare_165779456gleton )
& ( ( sK1 != sK0
& is_state(sK1)
& is_state(sK0) )
| ~ hoare_165779456gleton ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[nnf_1]) ).
fof(sk_fact_0_state__not__singleton__def,plain,
( ! [VAR_0,VAR_1] :
( VAR_1 = VAR_0
| ~ is_state(VAR_1)
| ~ is_state(VAR_0)
| hoare_165779456gleton )
& ( sK1 != sK0
| ~ hoare_165779456gleton )
& ( is_state(sK1)
| ~ hoare_165779456gleton )
& ( is_state(sK0)
| ~ hoare_165779456gleton ) ),
inference(cnf_transformation,[status(thm)],[sk_fact_0_state__not__singleton__def_sk]) ).
cnf(c_4,plain,
( is_state(sK0)
| ~ hoare_165779456gleton ),
inference(split_conjunct,[status(thm)],[sk_fact_0_state__not__singleton__def]) ).
cnf(c_5,plain,
( is_state(sK1)
| ~ hoare_165779456gleton ),
inference(split_conjunct,[status(thm)],[sk_fact_0_state__not__singleton__def]) ).
cnf(c_6,plain,
( sK1 != sK0
| ~ hoare_165779456gleton ),
inference(split_conjunct,[status(thm)],[sk_fact_0_state__not__singleton__def]) ).
fof(conj_0,axiom,
hoare_165779456gleton,
file('theBenchmark.p',conj_0) ).
cnf(c_10,plain,
hoare_165779456gleton,
inference(clausify,[status(thm)],[conj_0]) ).
fof(nnf_2,plain,
? [T] :
( ! [S] :
( T = S
| ~ is_state(S) )
& is_state(T) ),
inference(fof_nnf,[status(thm)],[conj_1_neg]) ).
fof(sk_conj_1_neg,plain,
( ! [S] :
( sK2 = S
| ~ is_state(S) )
& is_state(sK2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(T,sK2)],[nnf_2]) ).
cnf(c_12,negated_conjecture,
( sK2 = A
| ~ is_state(A) ),
inference(split_conjunct,[status(thm)],[sk_conj_1_neg]) ).
cnf(c_13,plain,
sK1 != sK0,
inference(resolve,[status(thm)],[c_10,c_6]) ).
cnf(c_14,plain,
is_state(sK1),
inference(resolve,[status(thm)],[c_10,c_5]) ).
cnf(c_15,plain,
is_state(sK0),
inference(resolve,[status(thm)],[c_10,c_4]) ).
cnf(c_17,plain,
sK2 = sK1,
inference(resolve,[status(thm)],[c_14,c_12]) ).
cnf(c_19,negated_conjecture,
( sK1 = A
| ~ is_state(A) ),
inference(paramod,[status(thm)],[c_17,c_12]) ).
cnf(c_21,negated_conjecture,
sK1 = sK0,
inference(resolve,[status(thm)],[c_19,c_15]) ).
cnf(c_20,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_13,c_21]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SWW469+1 : TPTP v9.3.1. Released v5.3.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.17/0.43 % Computer : n005.cluster.edu
% 0.17/0.43 % Model : x86_64 x86_64
% 0.17/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.43 % Memory : 8046.5625MB
% 0.17/0.43 % OS : Linux 6.8.0-71-generic
% 0.17/0.43 % CPULimit : 300
% 0.17/0.43 % WCLimit : 300
% 0.17/0.43 % DateTime : Sat Sep 26 15:56:33 UTC 2026
% 0.17/0.43 % CPUTime :
% 0.17/0.44 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.17/0.44 % Process 2498211 was started by sandbox on n005,
% 0.17/0.44 % Sat Sep 26 15:56:33 2026
% 0.17/0.44 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.17/0.44
% 0.17/0.44 % From the command line: assign(max_seconds, 300).
% 0.17/0.45
% 0.17/0.45 % SZS status Theorem for theBenchmark
% 0.17/0.45
% 0.17/0.45 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.17/0.45 % Length of proof is 13.
% 0.17/0.45 % Level of proof is 5.
% 0.17/0.45 % Maximum clause weight is 5.000.
% 0.17/0.45 % Given clauses 12.
% 0.17/0.45
% 0.17/0.45 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------