%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWW469+5 : TPTP v9.3.1. Released v5.3.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n009.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 0.08s 0.42s
% Output : CNFRefutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 3
% Syntax : Number of formulae : 15 ( 10 unt; 0 def)
% Number of atoms : 26 ( 15 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 24 ( 13 ~; 7 |; 3 &)
% ( 1 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 5 con; 0-2 aty)
% Number of variables : 20 ( 3 sgn 12 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(fact_0_state__not__singleton__def,axiom,
( hBOOL(hoare_1883395792gleton)
<=> ? [S,T] : ti(state,S) != ti(state,T) ),
file('theBenchmark.p',fact_0_state__not__singleton__def) ).
fof(conj_1,conjecture,
! [T] :
~ ! [S] : ti(state,S) = ti(state,T),
file('theBenchmark.p',conj_1) ).
fof(conj_1_neg,negated_conjecture,
~ ! [T] :
~ ! [S] : ti(state,S) = ti(state,T),
inference(assume_negation,[status(cth)],[conj_1]) ).
fof(nnf_15,plain,
( ( ! [S,T] : ti(state,T) = ti(state,S)
| hBOOL(hoare_1883395792gleton) )
& ( ? [X0,X1] : ti(state,X1) != ti(state,X0)
| ~ hBOOL(hoare_1883395792gleton) ) ),
inference(fof_nnf,[status(thm)],[fact_0_state__not__singleton__def]) ).
fof(sk_fact_0_state__not__singleton__def_sk,plain,
( ( ! [S,T] : ti(state,T) = ti(state,S)
| hBOOL(hoare_1883395792gleton) )
& ( ti(state,sK0) != ti(state,sK1)
| ~ hBOOL(hoare_1883395792gleton) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK1),skolemize(X1,sK0)],[nnf_15]) ).
fof(sk_fact_0_state__not__singleton__def,plain,
( ! [VAR_0,VAR_1] :
( ti(state,VAR_0) = ti(state,VAR_1)
| hBOOL(hoare_1883395792gleton) )
& ( ti(state,sK0) != ti(state,sK1)
| ~ hBOOL(hoare_1883395792gleton) ) ),
inference(cnf_transformation,[status(thm)],[sk_fact_0_state__not__singleton__def_sk]) ).
cnf(c_81,plain,
( ti(state,sK0) != ti(state,sK1)
| ~ hBOOL(hoare_1883395792gleton) ),
inference(split_conjunct,[status(thm)],[sk_fact_0_state__not__singleton__def]) ).
fof(conj_0,axiom,
hBOOL(hoare_1883395792gleton),
file('theBenchmark.p',conj_0) ).
cnf(c_136,plain,
hBOOL(hoare_1883395792gleton),
inference(clausify,[status(thm)],[conj_0]) ).
fof(nnf_52,plain,
? [T] :
! [S] : ti(state,T) = ti(state,S),
inference(fof_nnf,[status(thm)],[conj_1_neg]) ).
fof(sk_conj_1_neg,plain,
! [S] : ti(state,sK2) = ti(state,S),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(T,sK2)],[nnf_52]) ).
cnf(c_137,negated_conjecture,
ti(state,sK2) = ti(state,A),
inference(split_conjunct,[status(thm)],[sk_conj_1_neg]) ).
cnf(c_149,plain,
ti(state,sK0) != ti(state,sK1),
inference(resolve,[status(thm)],[c_136,c_81]) ).
cnf(c_253,plain,
ti(state,A) = ti(state,B),
inference(paramod,[status(thm)],[c_137,c_137]) ).
cnf(c_254,plain,
$false,
inference(resolve,[status(thm)],[c_253,c_149]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWW469+5 : TPTP v9.3.1. Released v5.3.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.36 % Computer : n009.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Sat Sep 26 15:57:45 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.08/0.36 % Process 556546 was started by sandbox2 on n009,
% 0.08/0.36 % Sat Sep 26 15:57:45 2026
% 0.08/0.36 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.08/0.38
% 0.08/0.38 % From the command line: assign(max_seconds, 300).
% 0.08/0.42
% 0.08/0.42 % SZS status Theorem for theBenchmark
% 0.08/0.42
% 0.08/0.42 % Proof 1 at 0.03 (+ 0.00) seconds.
% 0.08/0.42 % Length of proof is 8.
% 0.08/0.42 % Level of proof is 3.
% 0.08/0.42 % Maximum clause weight is 19.000.
% 0.08/0.42 % Given clauses 64.
% 0.08/0.42
% 0.08/0.42 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------